A fuel-efficient cruise performance model for general aviation piston engine airplanes

Chapter 5 discusses tHe perfermance ef naturally aspiTated r 51 pisten engines, and develops the NEA subsystem input-eutput medel.

Chapter 6 integrates the APA ami. NEA subsystem input-output medels to. form the new cruise perfermance model ef the airplane- atmesphere sys tem. The implementatien, use, and engine centrel requirements ef this new medel aTe discussed. Thepercentage increases in R* offered by the implementatien ef this new model in any GA airplane, relative to. R* achieved when eperating that airplane in accerdance with current GA practice. are estimated.

Finally. this new medel is compared with the POll cruise perfermance medel develeped in Chapter 2.

Chapter 7 presents cenclusio.ns and recemmendatiens as a result ef this study.

Appendix A discusses the fundamentals ef the Peint Economy Functien R*. The reader is urged t.e read tliis appendix prier to commencing a detailed reading of Chapters 3 through €> .• Appendix B describes the standard and' non-standard atmosphere models used threughout this study.

Appendix C develeps the airframe perfo~ance model used in Chapters 3 and 4.

Appendix D develops the propeller perfoTmance mo'deI us'ed in Chapter 4.

Appendix E develops the naturally aspirated sr piston engine

performance model used in Chapter 5'.

1-16 ---------------------------------- --Kpp-end-i-:iC-F-pre-senn--a--ori-ef--d-t-s-c-us-s-i(Yn-o-f---alTt-oi-gn-id-o-n-;-- -------- ------------------------------ \ detonation and knock in spark-ignition piston engines.

Following Appendix F, there is a tabulation of the nomenclature -I used throughout the chapters of this study (other symbols used in the appendices are defined locally). For historical reasons, and in consideration of other peoples' work, a conventional notation has been maintained throughout; this has sometimes resulted in the same symbol being used for different quantities. For the same reasons, English rather than Metric units have been used throughout.

Finally, the list of References is presented. Reference numbers in this list are cited in parentheses throughout the text.

Interesting Results Without unduly anticipating the logical conclusions, presented in their separate place, it may be appropriate here to consider briefly some of the difficulties overcome in, and interesting results of, the research. Given that the problem of maximizing specific range, R*, is significant, one finds that it is not amenable to theoretical solution. On the other hand, one finds that costly experimental or test data which have been accumulated are inadequate for the purpose at hand. The thesis is the propo- sition, in detail, of a prescription for experiments to be made.

I first review classical airplane cruise performance. In

principle this is very well understood. A new iTterpretation, 1-17 however, ·of that performance is given inasmuch as 1. The effects of wind and auxiliary equipment power on R* are presented in terms of new Equivalent Quantities.

2. The effects of center of gravity (c. g.) position on R* are specifically formulated in terms of a) R* appropriate to a reference c.g. position, and b) A correction factor for variations in c .g. position.

Next, classical propeller performance is reconsidered. A compact representation of the combined performance of the airframe and the propeller in terms of novel Corrected Quantities is made.

In particular, 1. Propeller performance is presented in terms of a novel non-dimensional quantity, the Speed-Thrust Coefficient, CR' This, in conjunction with the well known propeller advance ratio, facilitates computations of the effects of equivalent airspeed, gross weight, c.g. position, propeller shaft speed and atmospheric density ratio on propulsive efficiency.

2. The effects of compressibility on propeller performance are represented by a correction factor, f . Such a comp correction factor is not new, but has passed out of use since the advent of modern computational fluid mechanics.

This study identifies the importance of f for compact comp computations of General Aviation eGA) airplane c.ruise per- "1 formance; and recommends further effort in quantifying f for GA propellers.

comp 1-18 ~ ,

I

:------ -------- _~'_:::::::::::t::i::~::::::::~:::~::;::~:::~--------

I subsystem cruise performance for all values of gross weight and altitude.

Further then, I synthesize a fuel-efficient steady state per- formance model of naturally aspirated Spark-Ignition (SI) piston aero engines from a widely scattered literature. Using this model, novel Corrected Quantities are identified. The cruise performance of the Naturally aspirated MBT ignition timing Engine-Atmosphere (NEA) subsystem is then represented in terms of these Corrected Quantities.

The subsystem integration is summarized in a single block diagram illustration (Figure 6.1). This figure is an original, logical abstraction of the developments and models which are presented in the body of the work. It shows the connection between the important inputs and "controls" and the overall system per- formance which is of interest.

All this appears to have significant implications for efficient and safe GA airplane operation. Finally, 1 present calculations of the fuel savings which might be obtained by improved computer- aided operating practices. Increased specific range, R*, is conservatively estimated to be 20% to 26%.

1-19 TABLE 1.1 PARAMETERS CONTRIBUTING TO R* Variable Contributing Parameters V Equivalent airspeed E P Atmospheric ambient air absolute pressure atmos T Atmospheric ambient air temperature atmos V Geocentric wind speed and direction w Airplane heading Airframe power-off drag coefficient where W gross wei gh t airplane = he longitudinal center of gravity = position - c mearr aerodynamic chord of the wing = V Airplane true airspeed T P atmos T atmos P Auxiliary equipment power AUX

-

Propulsive efficiency = np[V , W, h, N, 0, r'1yJ np E

where N = propeller shaft rotational speed

o = atmospheric air density ratio

Mr = propeller helical tip Mach number

c The following apply to naturally aspirated and turbo- charged SI piston engines: Fuel mass flow rate per engine 1-20 ~ i ~

I

1- ~ ---- -------- - -------------. -..(;~~~)-------------.----------

I

Engine geometry and grade of fuel

1 I

These define Fuel-dry air mass ratio the I gni tion timing Indicated Engine shaft rotational speed Horsepower (IHP) Inlet manifold absolute pressure Inlet manifold temperature Exhaust absolute back-pressure Cylinder head temperature Detonation .....

Engine geometry These define the Lost p Horsepower m (LHP) p e IHP Indicated horsepower The following apply to Turbocharged SI piston engines: Turbocharger characteristics Aftercooler characteristics Throttling absolute pressure losses 1-21

AIRPLANE - ATMOSPJ-IER£ SYSTEM BLOCk DfAG'RAM

1l!tJE IlItS7'E'E.:D "( ,.

~--------------------~ V T GROSS ~ ..

, - 1 WE.IGHt W ---'---------s AIRFRAME.

PROP£LLfR

h C.G. PostnON

L=W·

, .

E7j, = l)oFF

PROPELLER

N

GOVERNOR CLlHMANDEIJ PROPELLE'2.

N

c SHAFf SPE.£1) G£AR :Box

G

AiJX ILLJIIRY "D AuxlLLlIIRY f.&llJlr"ME.Nf IRvx PclN'£R E~/JIPMENr Ft:JW£R TAKEOff INLE.r MAIJfFOI.!J

Pm

'P2ESSU1C£ fOEL - ])R.Y fill(

F

MASS Rlmo .IGllmON 11M/NO, 1: ( ATMOSPHERE

Pl?ESSURE. tiLT/TUDE Cr ~oy

H~ WITH

-

~ = __ '_OH_S_~_N_r_: ___ A_~_P_LA_WE __ H._~_~_b"_WG_·· __ ~ ____ ~ WIND

r,/fUR£ II 1-22

rn.::l '.

-------------------------------- -------------- ------------------------------------------ ------------------------------------ - ------- ---------- ----------------- -------- CHAPTER 2 USES AND LIHITATIONS OF POH CRUISE PERFORMANCE DATA FOR MA~(IMIZINC; R* Table of Contents Page I NTRODUCTI ON. . . . . . . . . . . . . . . . . . . . • . . • . • • • • • • . • • . . . . . • . • . • . . .• 2 -1 PILOT OPERATING HANDBOOK DATA •••••••.•••••••••••••.•.•••••.• 2-1 CONSTRUCTION OF A CRUISE PERFORMANCE MODEL FROM POH DATA •.•• 2-3 Fuel F low Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2-4 Power Diagrams ......................................... 2-6 Tne POHCPM... . . . • . • • • • • . • . • • . • . . • • • • • • • • • . • • • • • • • • . • • •. 2-7 APPLICATIONS OF POH CRUISE PERFORMANCE HODELS •••••...••••••• 2..:9 The Computation of R* ......•.•.•..••••.•.....••.••••... 2-11 Flight at Maximum Groundspeed .......................... 2-12 Flight at ~1aximum Possible R* .............. , ........... 2-14 Flight at a Prescribed TAS ............................. 2-17 Flight at a Prescribed Groundspeed ..................... 2-18 LIMITATIONS OF POll DATA FOR MAXIMIZING R* ••••••••.•••••••.•• 2-20 SUMMARY AND CONCLUSIONS .••.•.••••••..••••••••••••••••.•••• " 2-21 Summary. . . . . . . . . . . . . . . • . . . . . . . . . • . . . . . . . . • . . . . . . . . . . . .. 2-21 Concl usions .....................•.................... " 2-21 TABLES 2.1 - 2.3 ................•........•......•.•.....•... 2-23 FI ClJRES 2. 1 - 2. 11 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 2 - 26

CHAPTER 2 USES AND LIMITATIONS OF POH CRUISE PERFORMANCE DATA FOR MAXIMIZING R*

I NTRODU cn ON

The manufacturers of GA airplanes provide detailed cruise per- formance data for each airplane sold. These data are available in the airplane Pilot Operating Handbook (POH) and in the Federal Aviation Administration approved Flight Manual for each airplane.

This chapter describes the construction of cruise performance models frOT;) POB data, and examines the usefulness and limitations of such models for maximizing R*.

The pilot operating handbooks of a number of typical GA air- planes are first examined. The construction of cruise performance models incorporating the common cruise performance variables in this POll sample is described, and this is illustrated for two GA airplanes.

The use of a POH cruise performance model for maximizing R* is dis- cussed, and illustrated for one GA airplane. Finally, the limitations of POH cruise performance models for maximizing R* are discussed.

PILOT OPERATING HANDBOOK DATA A sample of Pilot Operating Handbooks was examined in order to determine what variables are commonly included in the cruise performance data of such handbooks.

Ten airplane types and four manufacturers were represented in the sample. These are listed in Table 2.1, along with the operating 2-1 point variables included in the POlf cruise performance data: and the operating conditions pertaining to' those data. Single' and twin engined airplanes are included in' the' list" some with naturally aspirat'ed '(', engines and others with turb-acharged engines.

The five variables common to each airplane listed' in Table 2.1 are: 1. Pressure altitude 2. Engine rotational speed 3. Engine inlet Manifold Absolute Pressure (MAP) 4. Fuel flow rate 5. True airspeed (TAS) This constitutes the majority of the listed variables.

Some of the sampled POH's specify a leaning criterion to establish the given fuel flow rates, such as an Exhaust Gas Temperature (EGT) relative to peak EGT, or a Turbine Inlet Temperature (TIT) relative to peak TIT. However, it is not clear in every case what 1 eaning procedure results in the given POH fuel flow rates. In those cases.

where the leaning criterion appropriate to the cruise performance data is clearly established in the POH: the POB informs the pilot of the TAS and fuel flow rate which will result when the airplane is flown at various pressure al titudes, wi th various combinations of ,.

MAP and RPM, under certain operat.ing conditions Cone of- which is the leaning criterion). In those c'ases where the leaning criterion appropriate to the cruise performance' data: is not c1ea·rly established in the F')H: the PUR informs the" pi.rot of the' TAS which· win result 2-2 I I

I

,

I

I

~-~~----------~~~~-f~~~~ar~p~~~~~tu~~~-V~i~---~---------

~,

j

I combinations of MAP. RPM and fuel flow rate. under certain operating

conditions (excluding a leaning criterion).

' Sufficient information is given in each POH for the computation

of R* (Equation A.7) throughout the operating range documented.

given a knowledge track. However.

of the prevailing winds peed along I I in no case listed in Table 2.1 does the form of data presentation

I

facilitate maximizing R* in current operations.

CONSTRUCTION OF A CRUISE PERFORMANCE MODEL FROM POH DATA This section shows how the POH cruise data for an airplane may I I be used to construct a cruise performance model which facilitates the computation of operating points which maximize R* in the cruise operation of that airplane: a cruise performance model constructed i from POH cruise data is referred to as a POHCPM. The cruise data for the 1974 Cessna Centurion and the 1974 Cessna Turbo Centurion t are used for this purpose the former airplane employs a naturally aspirated engine, and the latter a turbocharged engine.

The cruise operating point variables. presented in the POH data for each of these two airplanes. are the first six variables listed in Table 2.1. The POB data format for these two airplanes is that shown in Table 2.2. The POHCPM of each of these airplanes. con- structed here from their POH data. is comprised of the following plots: t The data for these airplanes were taken from the airplane Owner's Manual in each case. The information contained in these manuals is issued for more modern airplanes in the POH. These two Owner's Manuals are here referred to as Pilot Operating Handbooks in keeping with this practice.

2-3

1. Fuel flow rate m (lbm/hr) versus true airspeed'V (statute

f T t mph), for constant values of pressure altitude eft). Such plots are referred to as Fuel Flow Dia'gt:arns.

2. MAP (inches Hg) veTS,US "V . (s:ta.tute mph) , for :constant T values of pres'surealtitude fft) ,and 'engine RPM. S:uch plots are referred to ,as Power Diagrams.

The source POH data for each of these models ,and hence th'emode1s themselves, ,apply only to the 'following operating conditions: 1. Extended range mixture (fuel~air mass ratio) : established by leaning to a specified EGT increment rich of peak EGT 2. Standard atmosphere 3. Specified gross weight 4. Fixed (but unspecified)longi'tudinal centero'f gravity (c.g.) position 5. Undercarriageretrac'ted 6. Flaps up 7. Cowl flaps: position 'not determined by author. How'ever, cowl flap position was commensurate Mithrequired Cylinder Head Temperature rCHT) in each case 8. Some specific configuration of avionics aerials and other external equipments.

;i: Fuel Flow Diagrams The POH fuel flow data for the 1974 Cessna Centurion 'and Turbo Centurion are plotted against TAS for fixed values of pressure 2-4 2 3 + + a (2.1)

V = a a a V

roof Vr + T 1 2 3 T 0 -t is fitted through the fuel altitude in flow data at each pressure these two figures. T'ne data points pressure altitude fall for .each very close to the fitted curve, the standard deviation being less than 0.5 lbm/hr in every case, except for the Turbo Centurion at 20,000 ft where the standard deviation is 0.73 Ibm/hr. Each data point corresponds to a reconunended combination of MAP and RPt>1. For this Cessna data, it is apparent that every combination of MAP and RPM, given in the POH and yielding a given TAS, corresponds to a fuel flow rate ro lying very close to the relevant altitude curve. The f t curves of Figures 2.1 and 2.2 are therefore taken to apply to all t combinations of MAP and RPM within the limits of the POH data.

The hatched boundaries of Figures 2.1 and 2.2 represent the reconunended upper cruise power limits for the respective airplanes (see also Reference 4, p. 414). Such boundaries correspond either to the maximum percentage of maximum continuous power (brake horse- power) which the manufacturer recommends for continuous normal cruise operation; or to the maximum available cruise brake horsepower when this is altitude limited; whichever is the smaller power level.

Occasionally, as in the case of the 1974 Centurion, some of the tabu- lated data points lie outside this boundary and are presented in the t This close proximity of ro to a single curve, for various combinations f of MAP and RPM at one altitSde, should not be taken as an indication that MAP and RPM have no effect on R* (see Chapter 5).

2-5 POH merely for interpolation purposes. The boundary should be drawn (as in Figure 2.1) on the basis Qf the manufacturer's recommendation and not as the upper power limit of the data tabulated for each pressure altitude. The recornrnend.ed power boundaries of Figures 2.1 and 2.2 both represent 75% maximum continuous brake hQrsepower, or less when altitude limited.

Power Diagrams The engine MAP and RPM corresponding to the (m ' VT) data points f t

of Figure 2.1, at sea level and ro,ooo ft, are plotted in Figure 2.3

for the Centurion. Similar plots corresponding to the (m ' VT) data f t points of Figure 2.2, at sea level and 20,000 ft, are shown in Figure 2.4 for the Turbo Centurion. It is apparent from Figures 2.3 and 2.4 that a great deal of redundant engine s.etting data are availabl e to the pilot for the cruise operation of these airplanes: at each TAS and pressure altitude, an infinite number of (MAP, RPM) combina- tions may be selected. At each TAS, one recorranended combination of MAP and RPM would suffice. In Figures 2.3 and 2.4, a straight line has been drawn through the set of data points appropriate to each pressure altitude. Each straight line represents an arbitrary tra- jectory of (MAP, RPM) over the TAS range at each pressure al ti tude: l l points (a, a ), (b, b ) etc. on these straight lines correspond to (2200), (2300) RPM etc. respectively. When all of the (MAP, RPM) data for one airplane are plotted against TAS, and a straight line inscribed for each pressure altitude, a unique combination of (MAP, RPM) 2-6 i I

I

I I

I

j-- :~----------may-bepres crIbe.ffor flight at any- T AS-aIid-pressuie-afiTtude-by1n~------------ I terpolating between the inscribed straight lines.

Figures 2.5 and 2.6 show the results of the above construction I ' .for the Centurion and Turbo Centurion respectively. The s traigh t lines of constant pressure altitude correspond to the inscribed

I

straight lines in that construction.

Points a, a etc. in Figure ' 2.5 (2.6) correspond to points a, a' etc. respectively in Figure

I

2.3 (2.4). Lines of constant RPM are shown dotted in Figures 2.5 and 2.6.

Plots such as Figures 2.5 and 2.6 are referred to as Power Diagrams. The fuel flow rate shown in the Fuel Flow Diagram drawn for a specific set of operating conditions, corresponds to the MAP and RPM in the Power Diagram drawn for the same set of operating conditions, at the same TAS and pressure altitude. Consequently, variations in m with MAP and RPM, at any TAS and pressure altitude, f t are accounted for in these Diagrams.

The POHCPM Figures 2.1 and 2.5 constitute a POHCPM of the 1974 Cessna Centurion, for the operating conditions stated in Figure 2.1. Figures 2.2 and 2.6 constitute a POHCPM of the 1974 Cessna Turbo Centurion, for the operating conditions stated in Figure 2.2.

The cruise performance of any GA airplane, flying in specified atmospheric conditions with a specified gross weight and c.g. position, may be completely described by one Fuel Flow Diagram and one corre- 2-7 sponding Power Diagram. (The units used in these Diagrams would be Nautical mph or Statute .mph,andlb/hror gallons/hr, .in accordance with the POH data.) Di.ffer.entFuelFlowand Power Diagrams are required to describe the airphan-e perfo.rmance for different values of: 1. Atmosl'herictempera'tureatfixed pressuT~ealti tude, 2. Gros's 'weight, 3. C.G. position.

Each pair of Diagrams would b.e;appropriate to: 1. A mixture (fuel-air 'm'3'5:sratio)esta'blished by.a specified . .. t l eanlng cTlterl0n, Undercarriage retraC'ted, 2.

3. Flaps up, 4. Cowl flaps ei therclos,ed,or .openedthe·amountnecessary to achieve a specified.CHT, ~., 5. A specified configurat:ion ;.of.avionics aerials ,and other external equipments.

The cruise performance of ,%any GA airplane in all operating con- di tions should be well repres'ented by linear interpolation between pairs of Fuel 'Flow and Power DIagrams for the ,c.onditions l-l2listed in Table 2.3. Such a set of Dia.grams, for a'given'airplane, would constitute a PGHCPM applicable to ,aU operating condi tionsof .that airplane. In the event that ·the Diagrams are found to be influenced little by c.g. position, pairs of Diagrams 'for conditions 1-6 only , i ':

i

tDiscussions with the GA manufa:cturers indicate that,&oodT~peatability of fuel flow rate, in given-atmospheric conditions and'ata given MAP and RPM, is achieved using a leaning criterion based 'onEGT or TIT, although no repeatability 'statisticswere made available to the author.

f :02-8

I

~ I

I

i

I i L--.-----------------------wLu--suf£ic.e-t.o--descrihe-_the __ p_er.formanc_e .• ____ Th_e_)la~-u-e_QL-R~-.i-nc-~~~-~~------------------l ' ~~

l . continuously as the c.g. is moved from the forward limit to the aft I

I 1

I limit (see Chapter 3) so that the choice of conditions 1-6 only would !

~ I

be a conservative one. If the range of gross weights were great, it may be desirable to include an intermediate gross weight in the POHCPM.

Three values of anyone parameter in Table 2.3 affords the use of parabolic rather than linear interpolation for that parameter.

While the use of Fuel Flow and Power Diagrams reduces POH cruise data to a simple form for fixed conditions, the prospect of manually interpolating between 6 or more pairs of such Diagrams is a daunting one. However, this task is a simple one for a computer, and may be performed enroute by a microprocessor installed in the airplane.

The POHCPM may be stored in a microprocessor as sets of coefficients of cubic polynomials (describing the Fuel Flow Diagrams: see Equation 2.1) and straight lines (describing the Power Diagrams).

The following section describes some of the uses of a POHCPM.

APPLICATIONS OF POH CRUISE PERFORMANCE MODELS One obvious function of a POHCPM of a given airplane is to inform the pilot of the engine power (MAP, RPM) settings required to fly that airplane in any given operating conditions. The model is entered with values for: 1. TAS 2. Pressure altitude 3. Atmospheric temperature relative to standard 4. Gross weight 2-9 5. Center of gr.avity position and values of MAP and RPM aroe returned. The corresponding fuel flow rate, also obtainable from the POHCPM, ·would h.e established by the pilot using the le.aning c:rit,eri.on appropriate to the POHCPM Cor established directly using £n'el flow instrumentation) ..

However, a PQHCPM has wme more important uses than the compu- tation of MAP and RPM (and fuel flow rate) for specified flight COR- di tions. In this section 'weexamine the use ofcruis·e performance models for various optimizations. Inpa.rticular ,we examine the ,compu- tation of the operating point., for a particular .airplane, which sa tisfies the following alternative requirements; 1. Achieve maximum ground'speed, with an R*constraint 2 . Achi eve max imum poss ibl e R* . Maximize 3. R* while flying at a prescribed TAS whil:e at groundspeed.

4. Maximize R* fly:Ln:g a pres.cribed The use of cruise performance ::models for the ,computation of R* is first described, with the aid of the 'POHCPM of the 1974 Cessna Centurion: Figures 2.1 and 2.5. The above .four optimizations are then discussed in turn, using -the POHCPMof th:e 1974 Cessna Turbo Centurion: Figures 2.2 and 2.6. Throughout t-hesediscuss:ions~ the operating conditions areassum.ed to ,conform to thec.ondl tionsper- taining to Figures 2.1 and 2.2. Zero and non-zero wind conditions are considered: computations involving the latter employ the wind -profile shown in Figure 2.7.

2-10 the Fuel Flow Diagram, which is a graphical representation of Equation A.7:

v + V

T w t ground miles/lb (2.2) ID f t where

VG = groundspeed, mph

TAS, mph V

=

T V true windspeed component along track (see Appendix A), mph

=

w Headwind: V < 0 w Tailwind: V > 0 w

ID = Total fuel mass flow rate to all engines, lbm/hr

f t (ga11ons/hr) .

Con?ider the Fuel Flow Diagram of the 1974 Cessna Centurion: Figure 2.1.

In zero wind conditions, operation at any TAS and pressure al- titude is represented by a point on Figure 2.1: the horizontal coord- inate of the point gives the TAS (=V ), the vertical coordinate gives G the fuel flow rate, while the inverse slope of the radial line from the origin to the point gives the value of R*. For example, flight at 2,500 ft pressure altitude and 169 mph TAS (Point A in Figure 2.1)

results in a fuel flow rate ID = 87 lb/hr from which R* = 169/87 =

f t 1.94 ground miles/lb.

t(Nauticalor Statute) miles/(lb or gallon) in accordance with POH data. The present examples use statute miles/lb.

2-11 In non-zero wind cond'itions, R* is again re'adily obtained from '.

Figure 2.1. The windspeed may be represented, by plotting V alorig w the abscissa; headwinds plotted t.o the right of the origin and tail- winds to the left. Then for any operating point (TAS, Pressure Altitude: Point A say) and wind condition (Point B say),- the ground- speed is the base BC of the triangle ABC, and the value of R* is given by the inverse slope of the hypotenus'e BA.

The MAP and RPM required for flight at any given TAS and pressure a1 ti tude are obtained from the corresponding Power Diagram (Figure 2.5), and are independent of w-indspeed. The MAP and RPM, corresponding to point A in Figure 2.1 are; MAP = 24 in. Hg, RPM:: 2425.

We now address the four optimization problems previously men- tioned, using the POHCPM of the 1974 Cessna Turbo Centurio.n shown in Figures 2.2 and 2.6.

Flight at Maximum Groundspeed We here demonstrate the usee, of the POHCPM for computation of the operating point yielding maximum groundspeed with an R* constraint.

i I n zero wind conditions, maximum groundspeed is achieved by flying at the altitude where the maximlDD TAS is achieved. This al- titude and the corresponding maximumTAS is represented for the Turbo Centurion by point A on the power boundary of Figure 2.2.

I t may be impossible to fly at point A because of insufficient fuel capacity; that is, R* at point A may be unacceptably small. Let us assume that a fuel constraint exists which requires R* to be greater than or equal to some' minimum value R*. Plotting a 1 ina with c 2-12 ; I

I

i

j~~ ~--- ~~- ~-~~---~~-~---l>1ope-l,lRt*lb-per--hr-JmphJ-onJig~re-2.2-m"l'-resuLLin-line-1lR.-~i" -------- -- -- ---~- ---

I , ::::d:::: t::i::t::~:i:::t:: :::U::: ::::::: ::l~:::Ven by

the point on the power boundary furthest to the right and on or below

I

the line OS: point B in the case drawn. Clearly if line OB intersects the power boundary above A, then maximum groundspeed may be achieved

l

without violating the fuel constraint by flying at A.

I~

However, only a few specific altitudes are available to the pilot, many being precluded by topography, weather, cabin environment requirements, air traffic control or perhapsNOT~1S.t As a result, it may not be possible to fly at A or B in Figure 2.2. The operating point for maximum groundspeed is then determined as the point at an

I

available altitude on or within the power boundary, on or below line OS and furthest to the right. For example, if all altitudes above 20,000 ft were unavailable, the operating point for maximum groundspeed would be point C.

In nono-zero wind conditions with no fuel constraint, maximum groundspeed is obtained in all cases by flying at point A on the power boundary of Figure 2.2. When the fuel consumption constraint R* > R* is imposed, the procedure for determining the altitude and - c TAS for maximum groundspeed is similar to that used in the zero wind case. In fact the analysis varies from the zero wind case only inas- much as the line OB with slope l/R* is drawn for each altitude separately, c the origin 0 being shifted along the abscissa to the wind component prevailing at each altitude.

I t NOTAM : Notice to airmen.

2-13 For each cruising altitude the procedure is as follows. Consider cruise at 10,000 ft pressure altitude when the minimum tolerable value of R* is R* = 2.35 miles/lb, and the winds aloft V are given by c w Figure 2.7:

1. V = 15 mph tailwind

w 2. Plot point D on Figure 2.2 corresponding to this windspeed V w

3. Plot line DE 'with slope l/R~ = 1/2.35 (lb perhr./mph). It

is possible to fly at any operating point on the 10~OOO ft line, on or below line DE.

4. To achieve the maximum allowable TAS and hence maximum groundspeed, assume flight .at point E. The groundspeed is given by VG = 177 + 15 = 192 mph.

Flight at other pressure altitudes i.s tre:at.ed in .similar fashion. The resul ts of these computations for all pr.essureal titudes from sea level to 25,000 ft are shown in Figure 2.8. There the computations are tabulated and the maximum groundspeed achievable at each pressure altitude is plotted against pressure altitude. The maximum possible groundspeed is achieved at 25,000 ft even though the largest headwind exists there. The value of R* is the same at each pressure altitude.

The engine fuel flow rate, MAP and RPM required fOT a chosen pressure altitude and TAS are obtained from Figures 2.2 and 2.6.

Fli'ght at Maximum Possible R* We here demonstrate the use of the POHCPMfor computation of the S' operating point yielding the maximum possible value of R* .

2-14 j I

I

I

" -----------------------------------------hr --zero-willd--colldi-ti-ons-;--t-he-max-imum-va-lue--o-f--R-*--aeh-ievab-l-e----at -~ .

t

I a particular altitude is obtained by flying at the point of tangency

of a radial line from the origin to the appropriate altitude curve of Figure 2.2. At sea level this flight condition is at point F in

I'

Figure 2.2; at 25,000 ft it is at point G. The pressure altitude and TAS offering the maximum possible R* correspond to the point in Figure 2.2 at which the slope of the tangent line from the origin is least (Equation 2.2).

In non-zero wind conditions the tangent line is drawn from the appropriate wind reference rather than from the origin. For example, when flying at 25,000 ft with a 40 mph headwind, maximum R* is achieved at H in Figure 2.2 rather than at G. The pressure altitude and TAS offering the maximum possible R* correspond to the point at which the slope of the tangent line drawn from the appropriate wind reference is least.

It is of interest to determine the altitude variation of the maximum value of R* achievable at each altitude (R* ) for the Turbo max Centurion. For zero wind conditions, inspection of Figure 2.2 reveals that the value of R* increases continuously from sea level to max 25,000 ft as follows:

Sea level (point F): R* = 130/57 = 2.28 miles/lb

max 25,000 ft (point G): R* = 175/70 = 2.50 miles/lb.

max This represents a variation of 9.65% of the lower value. For non-zero wind conditions, the variation depends upon the wind profile. Using the wind profile of Figure 2.7 the value of R* from sea level to max 2-15 25,000 ft has been computed and plotted inFig~re 2.9. The compu- tations, tabulated in Figure 2.9, were performed as follows at each pressure altitude: 1. V was taken from Figure 2.7 and inscribed on the abscissa w of Figure 2.2 as the wind reference 2. VT and the fuel flow rate ID were determined from Figure f t 2.2, at the point of tangency of the straight. line drawn the wind from reference to the appropriate alt:itude curve 3. V = V + Vw G T 4. R* = V G/IDf max t The computed values of R* plotted in Figure 2.9 show a maximum vari- max ation of (2.67 - 2.39)/2.39 or 11.7% of the lower value. In-this example the wind profile has increased the percentage variation of R* with altitude from that obtained in the zero wind case.

max At any pressure a1 ti tud e on the curve 0·£ Figure 2.9, the T AS may be oltained from a linear interpolation of' the TAS values tabu- 1ated in that figure. For these values of pressure aTtitude and TAS, the engine fuel flow rate, MAP and RPM are determined from Figures 2.2 and 2.6.

When a fuel constraint dictates a minimum value of R*, some al ti tudes in Figure 2.9 may be excluded from candidacy for a particular operation. Other constraints JIlay also preclude operation at· certain altitudes in Figure 2.9. In such cas:es, Figure 2.9 clearly shows the available pressure a1titude'yielding the maximum possible value of R*.

2-16 Flight ~.:t a Y;rescribed TAS To achieve an approximate trip duration, a pilot may choose to fly at a particular TAS. We here demonstrate the use of the POHCPM to compute the operating point which maximizes R* at a specified TAS.

The method of computation is independent of the choice of TAS: it is here illustrated for a TAS of 185 mph, for which all operating points lie along the line JK in Figure 2.2.

In zero wind conditions, the value of R* is determined at each

altitude as R* = VT/m at the intersection of line JK and the appro-

f t priate al ti tude curve. In this case the value of R* increases con- tinuQusly from 5,000 ft to 25,000 ft as follows:

5,000 ft: R* = 185/98 = 1.89 miles/lb

25,000 ft: R* = 185/74 = 2.50 miles/lb.

This represents a variation of 32.3% of the lower value. Note that flight below 5,000 ft is not possible at this TAS due to the presence of the power boundary.

In non-zero wind conditions, the altitude variation of R* is determined as follows. At each pressure altitude: 1. The fuel flow rate ro is obtained from the intersection of f t the line JK and the appropriate altitude curve 2. The wind component V is obtained from Figure 2.7 w V + V 3.

=

VG T w 4. R* VG/ro

=

f t

Figure 2.10 tabulates these computations for V = 185 mph and shows

T R* plotted against pressure altitude. For the wind profile used, the 2-17 value of R* varies little above 15,000 ft, reaching a maximum at x' 25,000 ft even though the maximum headwind exists there. The maximum variation of R* in Figure 2.10 is (2.42 - 2.02)/2.02 or 19.8% of the lower value. In this example the wind profile har> Significantly de-, creased the percentage variation ofR* wi thaI titu&e, from that ob- tained in the zero wind case.

At any pressure altitude the engine fuel flow rate, MAP and RPN required for flight at a TAS of 185 mph are obtained from Figures 2.2 and 2.6.

A fuel constraint which dictates a minimum value of R*, or some other constraint, may preclu&e operation at certain altitudes. In this event, Figure 2.10 clearly shows the available pressure altitude yielding the maximum value of R* at the prescribed TAS.

Flight at a Prescribed Groundspeed This mode of operation may be selected to satisfy a particular trip duration. We here demons'trate the use of the POHCPM to compute the operating point which maximizes R* at a specified groundspeed. 'The method of computation is independent of the choice of groundspeed: it is here illustrated for a groundspeed of 200 mph.

In zero wind conditions, the method is identical to that shown above for a prescribed TAS. In this case the value of R* increases I .. I continuously from 13,500 ft on the power boundary to 25,000 ft as follows:

13,500 ft: R* = 200/98 = 2.04 miles/1b

2-18 ---- ------------------ ----- ------ --2-5,000-f-t+-R-*---=----200/-81-.5--=---2-.-4-5--mi-l-es-/-l-b-.----------------------------------------- This represents a variation of 20.1% of the lower value.

In non-zero wind conditions, the altitude variation of R* is determined as follows. At each pressure altitude: 1. The wind component V is obtained from Figure 2.7 w I 2. The TAS is computed as V~ = V - V I- 1 G w 3. The fuel flow rate ro is obtained at the intersection of f t this V line and the appropriate pressure altitude curve in T Figure 2.2 4. R* = VG/inf t Figure 2.11 tabulates these computations for VG = 200 mph and shows R* plotted against pressure altitude. For the wind profile used, the value of R* reaches a maximum at 25,000 ft where the maximum headwind occurs. The maximum variation of R* in Figure 2.11 is (2.38 - 2.22)/ 2.22 or 7.21% of the lower value. The wind profile employed in this example has significantly reduced the percentage variation of R* with altitude, from that obtained in the zero wind case.

At any pressure altitude on the curve of Figure 2.11, the T AS may be obtained from a linear interpolation of the TAS values tabu- lated in that figure. For these values of pressure altitude and TAS, the engine fuel flow rate, MAP and RPM are determined from Figures 2.2 and 2.6.

As for the previous analyses, a fuel constraint which dictates a minimum value of R*, or some other constraint, may preclude operation at certain altitudes. In this event, Figure 2.11 shows the available 2-19 pressure altitude yielding the maximum value of R* at the prescribed groundspeed.

LIMITATIONS OF POH DATA FOR MAXIMIZING R* A POHCPM can only maximize R* subject to the constraints imposed by the source POH data. Two sets of such constraints are listed be- low: these constraints constitute typical significant limitations of POB data for maximizing R*.

1. POH cruise data pertain to specific values of (see Figure 1.1) : a) Gross weight W: data for more than one value of gross weight are often unavailable b) e.G. position h: data taken for more than one c.g. position has not been observed by the author for any GA airplane c) Pressure altitude and atmospheric conditions: data for specific pressure altitudes and standard atmospheric conditions are usually provided, and in many cases data for certain non-standard atmospheric conditions at these pressure altitudes are also provided.

Interpolation for performance in all cruise flight conditions is only possible when multiple data sets are provided.

2. POH data give the performance which can be expected when the airplane is operated in accordance with the manufacturer's recommendations. Those recomm'endatiorrs constrain the fol- lowing engine variables (see Figure 1.1) : P a) Inlet MAP m 2--20

I--~: ------ --- --~- ~-- -- ~ ~-1»--£ngine-=t~Hona±-.peed----~-~---- -~-NE- ------

I

c) Fuel-air mass ratio F d) Engine ignition timing The effect of each of these variables on R* is discussed in detail in Chapters 4 and 5. Current GA airplane manufac- turers' recommendations for setting these variables are not appropriate to maximum R*.

As a result of the foregoing limitations, it is concluded that a POHCPM, constructed from currently available POH cruise data, is an inadequate tool for maximizing R*.

SUMMARY AND CONCLUSIONS Sununary The POH cruise performance data for ten airplanes have been considered. The construction of cruise performance models based on POll data, the use of such models for the solution of various opti- mization problems, and the limitations of such models for maximizing R* have been discussed.

Conclusions 1. On the basis of computations performed herein, it is con- eluded that variations in R* over the cruise envelopes of GA airplanes are sufficiently large to warrant the development of airborne micro- processor cruise performance models capable of performing fuel-use optimization computations.

2-21 2. It is concluded that a POHCPM, constructed from currently available POH cruise data, is an inadequate tool for maximizing R*.

2~2 TABLE 2.1 SAMPLE PILOT OPERATING HANDBOOKS EXAMINED CRUISE OPERATING POINT VARIABLES PRESENTED AIRPLANE TYPE MANUFACTURER t 1974 Centurion t Cessna Pres~ure altitude 1974 Turbo Centurion RPM 1980 Centurion 2l0N MAP 1980 Turbo Centurion T2l0N Fuel lb/hr and/or gal/hr TAS and CAS (1) % BHP (2) Baron B55 Beech Miles/gallon (3) Baron S8P . C d·· tt peratlng on Itlons O Arrow IV PA-28RT-201 Piper Mixture - see Chapter 2.

Seneca II PA-34-200T ISA Temperature ±~ OAT (4) 1 or 2 gross weights (5) No wind M20J-201 Mooney Fixed c.g. position M20K-231 Undercarriag~ retracted Flaps up Cowl Flaps closed (6,7) CAS given for Beechcraft only.

(1) Except Beechcraft.

(2) (3) Mooney M20K-231 only. I Non-standard OAT for some airplanes only. I (4) 2 gross weights Hooney only. I (5) All airplanes listed have cowl flaps except Piper (6) Arrow IV. I Ascertained for all but the two 1974 Cessn+ airplanes.

(7) !

i tOwner's Manual tt cruise data for each airplane apply to some The specific airframe geometry, including avionics aerials and other optional external equipments.

These details were not examined.

TI1BLE Z.!

EXTENDED RANGE MIXTURE EXTENOED RANGE MIXTURE Standard Condition. ~ Z.ro Wind ~ Grou' Weigh •• 3800 Pound~ S.andard Conditions~. Zero Wind ~ Gross Weight- 3800 Pounds 7500 FEET 10,000 FEET 384 liS. (NO IUnRVE) 534 lllS. (NO RESERVE) 384 lllS. (NO RUEItVE) 534 LIlS. (NO RUERVE) IANGI ENDIt. lANGE " TAS llS.1 ENDII. RANGE ENDR. IANOE ~ TAS llS.1 ENDI.

MILES MP IH' MPH HaUl HOURS MillS HOURS HOURS MILES .PM MILES MP IHP MPH ~OUR HOURS ItPM 5.7 1065 94 4.1 '165 825 8.1 U4S 2550 23 '5 10' 81 4.4 69 187 2550 21 '190 41.0 1095 22 'J1 183 89 4.3 845 6.5 1175 82 4.'1 20 65 1111 84 810 8.4 1130 4.8 810 8.11 lU~ :1 8' 1'JI 114 77 5.0 19 61 135 8.11 1160 7,4 1235 20 83 1'12 4.9 890 166 12 5.3

'9 18 56

1080 8.3 1180 91 4.2 780 5.8 1135 2! 13 185 21 411 184 115 4.5 Ill5 855 8.1 1190 21 89 1&0 86 4.4 800 8 •. 2 171 80 4.8 20 63 820 6.5 1145 860 7.2 l220 21 65 115 82 4.1 171 5 .•• 19 59 1115 1245

5.0 845 1.0 "" 895 7.7

20 61 168 '11 55 163 10 5.5 , 41.3 1120 11\15 85 4.5 805 4.9 860 2400 23 ea 1'J9 21 63 177 19 8.'

825 8.8 7.2 1220 22 &4 114 81 5.1 890 4.' 20 59 171 74 U15 141 5.0 845 7.0 PIS 7.11 1245 21 80 168 Ui3 70 5.5 19 55 1200 1250 5.3 865 7.4 5.8 900 8.1 20 57 182 111 51 66 15"

'2

J3 84 .,:1 830 8.8 880 1225

80 4.8 59 170 74 5.2 '.2 2300 2300 21 1115 1245 5.0 845 1.0 5.5 895 22 80 188 '18 20 55 163 10 '.8 7.4 1200 900 8.1 1250 21 51 182 12 5.3 865 155 68 5.8 19 51 5.7 815 1.9 8.2 895 1245 20 53155 88 48 144 62 '.8 ,., 1185 .895 1245 5.1 855 54 162 10 5.5

2200 23 51' 188 '.2 2200 21

'4

810 1205 5.8 900 5.4 51 154 86

22 ' 58 180 '.5 20 '.1

'I 7.11 1220 895 8.6 880 144 112 41.2 21 52 154 6'J 19 48

5.'

•• 4 1225- 885 9.2 6.1 880 134 58 6.8 20 4' 148 84 18 44 9.0 1220 6.4 815 111 46 138 59 I

MANLJI1L EXTRACT

OWNERS

(974 C.fMTURION

CEssNA

TABLE 2.3 FLIGHT CONDITIONS REQUIRED FOR PO:-I CRUISE PERFORMANCE MODEL Standard Atmosphere Standard Atmosphere Standard Atmosphere II o o _30 C +30 C [

/ I I I

I Minimum Maximum r·linimum rlaxim~m r'faximu~

I Minimum

Gross Gross Gross Gross Gross Gross i Weight Weight Weight Weight Weight Weight I I N I N V1 i Position C.G. Position C.G. Position C.G. Position C.G. tion C.G. Position C.G.

posf " linlit Fwd limit 4. Fwd limit S. Fwd limit 6. Fwd limit 1. Fwd limit 2. Fwd 3.

i Aft limit Aft limit 10. Aft limit 11. Aft limit 12. Aft mit 7. Aft limit B. 9.

lt I 10 X 10 TO THE CENTI METER 46 1513 KU ,n f:L t\: F.c;o;:,l: R CO _HI:! I~ U', A N N 0\ 1)1" ••.. , '1 In l( 10 Tn 1I1[ (I-NTI"FTrn f( I ~ I, , I I H I ,,' I P f f' ..... "/" ,. 46 1513 N I N .......

to x til TO Tiff r:rN II Mr I rr, 1>" J1r, 1"13 1-11111 1'1 n' '-.' I r~ (/ ...... I ,', I, l'~~· ·'7 'l'-·',"1'rn-'T "'1';]· , .. ., .. ", .... , 'j" ., .. '1"'" '1 '-1 '''l'-'T'-~' -.,---',. \' .,' - . "f'-I] n- -,- '-'T~ .. !:::' !i : 'I>' i: i! :' ~ i ! < :: ., I . '! :.': ' ! ' ,i I:: !: .. ! , ' I : ' t. :

l

.,. I,.·. .. ,.,.,. """"."')e' .. ,. '~~'" I "\' £ ",', , ;.; ~ I 'I'

;"r+ \1+ ~1.~ H\l~ ~S ',., c~ I , fa, ::. I .: ,i :/NL i M~NJF~LD ~RESSUR£ .~.vs ... TAS;.- .. j . .:: '::: :::: ::' '\"" .. \:::: ,Ii: ' .... :.. .., I":" ,: ,: , " ; , I J; 1'1': J ill" :..' L . I ! I ' I"~ ;,,: I:: : i; :;"1 Ii; i,i! i: , ':'1 : . ,:;:\. I' : , i ': , I I " 'I ; I' 'I" . i : . ! I' j' '" i '" ," ""fH-4fH" i+:~ ' .... !. .. i. ~"'. ,,"' .. ' .... ::- ':'u ... : , .. i .. , .. 1; ..... I: , ...... ,." "i"-' ... ! ..... ; ...... 1. ., ....... , .•. : ........ r': .. · ._.., .... _ .. '-' '-' -.'

l

:;!i i,i: ;, ' !',i: iii, i.il ,I!' ! :,;: . ; J : .lli .. ' ::ii :,i : i '''I,: :i, . I, :to : .. I ,1 'I' 'J! ,·i ! : i' , . ,: •••• 1,1. I " I' '1'1 "'1' " I' "I" 'I', I ·;1 "I I "j,I, I I I, 'I' I I ., n::lfn: C,i!1; ill: iill; ij~Jn ::~:':.:::'::-:r o· : II : .i 'i;~.a' I ,: :~' ~s' : Li~ru. It~t . iA? ~tk ,,!' '. [:. ::::.:: iW1TI; CT;1i!ffi iii! Iiil'jt1,' r~~ T : r'; n ;:t:'N~ LJ:Nb;'~N5 ::": . i'~" I'~o, ~i'i!-"I;~:!rAND~IQ~' 'A~P#E ±';:~ .:::·\F ~~:il~~' :':' ::;~ ;i:'i 7 iii:: ii,!; l::i ,il;'i : 1!li II!! 1:1 '1:1::,' :" .. i !.: I' " f=IG.:: .. ,'. , ~:. i " : .. , I' , ,; , . ," :,:: .i: :i:' :':, .' 'i ::'i t II:, ;~ I, , 1.,11; Ij' ill I ~ J I 'I I. " '" I , ;.1 I I., ", "", " ., . " , 01 I .. , , '1 ,. I • d illl I l' ~_,:' I . :t' !,II 'I ':1; I. '11 :n -:-::~ ;"';: .... _·"t.. .~, .- J.' ~.: :~.~ ':7' ~l :':; '~l";;: ,1.:-; 'tl' '" j ,.:~::: ~.: .~"-:-~. : :-::, ;' :': iIi I ! I I I. 'I ,I !:;: : .. :., . t I .', I I ~. " ' • J I I • • ~: I, I, I! J :, !, ' . . . I ;' .:' I " : ; :. :;, 1 • 1, ,;,; i :: :: ': ,,:! ,I:: ,:. " : ; : : :,': I ': :,: I,," '" : , ' " ~ I : ! ' Jj Ii JWP' :4 ~ J. I : i a : :: 1; 1 Ii!! t! ~; .;;: ~Jl! ; : ,I : j ~ i ; I! : l! I :: II , : II:: ! ; ; , \' ! i; .;:: '::: " ' : 1, I: ' ,'; 1 :.:: ': > I!: :: : l ,: I, : i I: :!;: ,I:: ,~:: ':.: :::, :: : ::!: . I :: :':: ," ! :. :,:i :;; i I!;I i "nil"''' ' '+ ,i I i i ,,, ,. .. "," t" ; i I' i I;' ~ , IT ,. , .. , 'I"" ,.. .., I .. , .. .. , , .. " 'll""" I" " .,," " "I. ,. ..",. " .. ,,,,,,,, .. ,, Itt1t '1" >, I I ,"IUi .. I" I~·~ "77ttj.·l:I"1 ~~ .... -;-: 1;~" ~~;. "h! '''1~ ":-+1 ,~" ,_ .. , "-' T.:"": l' !'n' ...... -:- ~ ....... : ~ ...... ,I" +it: ..... ~" "i "':1 ~ ., .:--:- .t. " "I" ' ~H." • I ll ,til II ~.~111" 11:"' II"~ I, • ',I ,!, 1,1, 'I 'I ., ." ," "., "'. '.' I I{, , ~" ' ., ,,' ,', " "j "I, II" I. .,1. ,\ ", I •• ' .... ,' ". '" , •• 1" ,01 ;1:' Ii. m:~ '\ ',1'1;'" '; j' :::~ 1 1 • 1 I~: ,II!!: I ,~:. ,,;, :t,~ :'1: i:i:: " . 'A :, ,::: t 'I ;, ' !: 'Il::. :;t: :;11 .;;; :::: "., II': :1::: ! I:;: ::'.: j' "i :1.; .. ~1 iiI! 'ii t rfil \ .• 1 ,,' ." ... ·1 '''I "1 II" '1" "" .... ' .... 'II, ... , ... " ".~. I·.. . "I, "" " .. ,I., " ,,,,.I, ,.Ij .,., ." ..... ""1'''' ,.1, "., "I' " " ...... "" '.,.

f:II'I' t.: .: ~":Ul,' I'! :II,!:,: .:. 'i Ii, '··tlili: 1'1\ ~i 'I" I,:, :", ,!, ::11.' "., , 1 tt' . 'j!: ':1 '.:: l'i'II' I,:; :::1 :'i\' I:': :;1: I::' .. i: :i,: :iI' ii', .:" i:l: :: ii: ,ttl' .:1: ;~ 1;1 I! I t': "t. _~ .. :+! t~:~~ill4iw 'l.u : ...:.J.l!:~ !:++ 1+.11 :~ii .. ~l' G:. iH.' t-·:~t , ~ . .:.1 Lli ~:~ ~~~, i~~l~, !l!~~t i~' nIl JlI 'i: ~:::I.ll.4 :;,: ' !I :'[: .. :: .' . ,,; .:; ::: " 'I~' i~~11I '11"1 . '" I "'If I;;; 1'/ t'll I' 'I ,,,, I, 'II "tLt' ., " '1" ":,, \." ", '''' " •. j •• ' •• ",, I' 'I' I , .. , ", ." I, .,11 "I' ' ~IU" ~"j ':!' I ,"', I . '. II,,' , ," 'II " " ,.",," .",." ". . ~' I .". , " '''' I' ""." "I"" "'," 'I" I' ,. I ." ." " """,,,, 11 ':.1, 't " 1'1 :1 ::: ,':: il' :::111:1,' 'II! IJ 11: I' '. :.:, i::: 1:1) ,,:, I,': ;' . ~;; :l:: ,: :,:, :11: III, l!tt ;,; oil' 1111 ::1; ::.1 ::,' I~: ,":' J' ::'j ::,' :::. :11 :,:' ;:t!

l G' , I. • 'I .. ~ I'" .\. , "'11' , .. " " ." ,." '1" "., ... , ...... , ..... ii' ., .,,' ,'" "" ,,', "'11'1' "'I "~ .' j "I'" ~,.' .•. 1 ,i .. rtt' II .. 1, ,. , ''I .,+ . • ,Ll ,t" H!J :j II :; j; ,Ii PIP! Iii " i:! i ~.! d ,.i,;.. iI!: I" 1 ;! i ! iii !' i I Iii! . ': i '; :; i 1,; 1 i! ::!! : -: l' I ': . , ': I !;:; ':: i !:! i ! Ij' ,j!; :: ,: ;: I : i !! 'Ii : I I : i ,; ;;!; : i!: : I I: i I : ; iii t: i: i::: ! Ii; iii: :;: I q:li ;tl' ;;,',1I1'l!I' ,;\: 11 II:j' >11 i~~:' ilH~lr~itHI'rH h'i ~~Til ;:h tl':: !!h ·n; ':1; .. +:~ .. ,,"! ::t :·~tt'::~::. I~I: t~ t~:I' :t:~ ,:;, I::! :i,1 ::"1 ::tt :::: Tii, ill: :::1 ::,; : • ...; :::: i: i :;:: t, 11. U'll!ti 1" I'I! l:iJ ;', ::, :1 :,:1 I:;' I:: :1/ '1 ::1 ' ,: :" :1'; :1:" ,',' '1:' ~ .. , :::~;! fI':I-' ~4~': "I' 1: ';; :11, '1:1 ,iii :::: :d i:;' ! ,j 1! :!'I: IiI, .::: ;!:: .1 I ::lJ 1.,1 't 1 tIll' I. ,. "'I:'" .• 'J' 1,,1, I" " .. " I'" "I, • , ... " , , .... ".."..... tl' ."~I'~. ", "" "" .... " ••... , ' .. " .l •. , .,. "" .. " ,", ,I ..

':I: !n!' I!: ·'1' ,lid l i il :UIl:;!UI: ';1 I,' ;,Iilll !i I> . '~'''.' :"i .:: l?" I .. ,: flJ ,~ ;. " ~ "i,: ' Iii:' ;:ii:::" .:: .::, I::' Ul'I;' , ,'!: I"~: ,,:; 11'1 :i, iii: "'I ft'" I I lli~1 t" "1 ':jUl"" I I:' "'Ill tl iI" :;i " '" "" . I r'~"~";1 I: t:' ,',., ",, .,11 I'~' Ii

7 1

~ ;;;: ~'11 11':; lUI' Utt,II~lj i j, :;" :j'ilii ; :':HI't::: ;;:1: 1'::1 :,' I ii' ~::: 1: ;b -:-:-i' . .:.~: i , 1 :" ;-- .... yt: .. : .1::C1!t ... :,':' . J~ ~I--I':~;' $:~dI ' tdu':' A .... ," :; ,< ", ,::. ;:. ~ :::: :;; :::; N : Hit t.t 1 • nl'! : I, i:::, .'; I :::: I I i ,I I 'I ::: I:. ~:::, i ;',:,: :' " .:, : :: II' ,:/I,! '.... :,; :'! i ' 1: :;:: :! j: ,,' I' i!:: :.; I Ill+l t r,t' I I '1 +;,. I." .. , ... ,1 "" '" ". i • .." i .. ,," " ... .,. ", .. 'j' " I"" .", , . ...,.. v' .,. ,I" 01 ..... , ." .. ,., "" ., ..

l ~ I::i! 1.'11 i:.: II,! II: i I: idl :1: ::i' I:: Ii I::' ! :; I!!! ji 1 I: !i I;, ::::1':,', !' ,I ,:' '~. , 'J': ;'::: ',:,! 'i Ii ' :tlliG·' " ':'1: IiI! iii: I;:; ::, ,::: Ii!: :::i "It "I", iiI. ,I I tlll:l 1. .. 11' ...... q .... ,,,' lill H ' l........:.H~:.~',.i.'~I" ,~ •••.• :... ;".~' ... ~, .. .J' ... ~ ...... i ,l-!1 ,J .. ~ ... ~:! "~1!.. ,. ',';. ............ " , " " . ,'1' '." /,1 . '1 ...... 'I;j .,., i ::;1 HI' 'Ij' Ii:: ,n: P:I :'I! ::!: jl , 'f .!:' '",: ',iii '11f! iii . :~;,:; i:' t ':1 ,';, V ,,\ ,I' !;;:I':I: II ;": i:j; "~,,' :: ,;" ::!. :I : :;:1 ,:.::, " ' : ,.:.

:;.:.L ':,; I.:: '!': ,'I' !~Il : ~: ,:.~: !l :::! ,:1 ,II til 'II : ' " !;, I '! . \. I. I :1 :'1: :: ,',: ',1 :':, :';1 ,:i ,':! .1:: ::,: .':~ :',' j'l: :.;; .: : ! :! '" I~ :11 .::: •• " .," .. " 11 .. !,1. 'f 'W'U .... , ......... ,,,' ,.1 ''':1 I ... ,. " .. '" ". ~' I . .., .• , ,." II' • '''1 .. ,1 ... , .I ........... ,,' ., ........ " .•.• ,." ... , II, 'i' .".

: ~ .: ': i. ..:. I: i' 1':: : I: : i t l!:, ' :, : :' :, ; : :: : :' ,i I I: :,: .. : : ,' ,,: I', ,;, 1. : :' ; 'i! : , ' ! :: 1:': ::;; : : I I : : , . ; !. ;::. . ! ; : ji ,:.: . I ~: ':: I : i ! : '1' I." IIi' ""lil"lil' 'I .. ", . :!,!:'II'" "I'II:d ,',', ',' II " . .,,",', 'I '"I''' "'''' '," .,. ," ... " "" ., I': , .. 'I" " '" ~.': f~" I:" J;': ,I,: :+, '" ~~H-Hf' .~~ .. ~0~+ti;~ Itt; ~tt :~h . ...:-. ; ..... :,~" "::i" _.... . ~ .. :::-: ~::-:. ~+!-: >~ ,+,~, ~:;~ :..+: ~:,~ ~':' ,:',::" .'" :, .. ~: :::. ,', .:~ :" :: ' .. ::' .!. ". '.' III. ;!" 11'1 'II" I ,I' I ., ,III ", II, I I, 1.1 " '" ,',' , " j' III 'I'! ,"" ." ", ,., I •• " .". ", "" 01, • ,I"~ 'I' HII · ; ,: : ~ ,:: :. : i: : 'I I :, ! Ii' .: :: , : I ::::' : :, !:!: : I I : : I , : , : ' , ,l, ::: I , ' . I I. ' ., . , . : ': l::; : I :, ,; J I 1 1 ' I : . : ' 1 " :'.: ": : , .: i j : i: :': ,::: " ,. ;: ~: ,: I I .!:' : { ': : i.: :::: P! 1 !l i ~ Ii! i : ~ Ii :. ~ I 1:,' I : j , ,': i ,:: i U l; i I Pi! :;:! I 'I! . t: ::: ; i~V":I':. ': : i i!; ',:; !:'! : ;': : ' ,i i i : i ;;;, -: :: i': : .!;: : ~! ~ :,!::! ~ ~ ~. :! ~ ~ t; 1 i ; :: ... ~ _ ....... ·I¥.m.: 1t ;' .... ,~ ... ~+'-!+ ,." "It .. , ,."... .. .. ,'" (ill· . . " .. _!¥.: , .... I~.I .......... " .. , , .. , ...... - ·'m-· _.,,, ..... :.1-. - -- ~ F .: ::'. :.: ;Hi ;!i: ;11. iii; j'i' ;:- I, !: i :! !i!! !: . Ii ' I, ',;,':;:' . i ' ,,' : ,i,Y:: ,,' "I:' , > ': ': .. :;' ,: :. I ,:'\,;::: :\:~: " ;I~: !;; '~: ... '''' .. ,." II/, "II .. t. "I~ , ... \ . .., , ... ,'" 'I' "I, .. ' ", \"" . I .. I ..\, , .. , "" .", .. "j' ., "." , 1 ,." .. " .......... I... ,'.... .. ,... ........ .. ... " · :: :!!' . ~ :, : i: ~ ~:!: : l : 1 . ; 1 :.;: '~. , ~ I ::, ' ; .; ~ ,! : :H' I ".: i' : ~:! : i :; . ;: II .: ' i . : ~ :'; !;: ,i!l ; 1 : ~ '::: -: : " :: : ~" . ' : I' I : .1: :. .' I !. . : .:: : i :' :'; :;: ~._ ...... ~~ ...... ~+~ .. ~~ ~b •. "\'''' .- ... f-::-:-- ........ ~ ;:..i.ff. •• ""\L'I' ., ..... , ' ....... -+~ ... , ..... ~.~ r.--.~' .... , ... " ...... ·,-t·· .. ,-,.-. '.-, .• - .. ;...j.;.;.; •• _,-- .~ ._.jc.;.;.<.+ .... '-!

l " ... "" ,:, !I!i I::. ,:,. ,:::: I .. " :1 :! i Iii "I ., :: " 1:1 I.,', . I ", i '" ii, I' :1; ,,:: "'I" I :1 ' , '"., I. '.:,. ':' ., ",.

· : ;. ,::, ' :. '::: :! I ': j; .' I: : " I:': :!,: I.:: ,::' ' ! I: \ ' ~ " : : ; " I : I , .; :' I, . , I, ':: :" ,::; ,:,! ,'.'. , : , I , ,. : .'.: t .' • > "",'" I ~" ; , ;, , .: ,,:: .... '."'" 1~'lt I'iiil "l .... !',... .. ,. , , ... I'" "\' "', ''', ,II' ""I" ,. I .. ·,. ..,', " .. "., I", . ,I .. " '"'' I" . '1' " ""I" ..... ,,, ..... "" .. " .. ". "" .. " ''1' :::: ::;. -::: IltI! jill" ii' It::: !!,:': ii:':; i;1 Iii::; Ii:",' I!: :;:I'li:I'; :::11::: ': "f' , '1 ':: ,'I: :;:;,l1i',' :11:: ::!, :" :' \.': : ',,' ,; :: 1:" ,'I.., ,:i.; : I :, '. W"; :.; :,!: .. ",,', " 1\ • 'II I' .. ~' 'J' "", .. '''' " ' , ,.. " , , , u' "" ", " , ",. ,I'" ""," , " , .. t' , . ",.." .. , .. . " , .. " ~~................. . t .~ .... ~ ...... ~ I ......... -t ........... -' .. 4- t-~"" + ...... Ittt l.r.t .... ·t "f~' l_ ............ , .......... ~ -+ ..... t- ................... 1 ..... · , ....... '- ...................... ....... o-+-+- ...... -~.. .......... .. ........ 6--1 : .. : . ,., '\: I 'I 1\ \I , I: , : " : : !:;" : : . , I I " : ~ I: \ : I ~ , :: , ' • ,'!. " .'. : j :! I':,; iI',: d II' , ':. : ; I, \'" ;: : :. : , : ' • : ' , I , '. : \ I: i: t ! . "I. ' : . :: ,':: : . : .' , II " II" 'Hill /11 ,I ,. I' ,.,. '" ,it ., !, .. " ,11, II ,. , • t 'i " I, 1\' I I I, I, ". '''' I ,. I,' ,I " ,.> •• II •• ,. ".1, • 'I '1 ", .11, :::: :.:: :::: 1 Ii : t I I:;: I: i: :, " : Ii ,i :!. ,::: I, ,:t: :::;: i: !: \. ,::\ ;:: i ,.. ,: ' ::. ,:: .:: 1'1:: i'l'! III: .. :: ':. :" " , "'.:,::::.:!: , .. i ::: ;1:::: :,' I: i!:: :: ':1':' .. , :,: .. :;: : .:: ::. :::, ':::~11 ,I :llilii: 1::: i!::~' ,: .. :1: 'i," il'i':: ;;:1 ':" illi': :', I ' "I"::' . ;'" ~",I,.;: ·.i ,:til©':' i !!d :':i ',:: i:,'. "I':'! ,,:: 'il; 'ill .::: ;:1: i!::: : i:i; :::i': . ,ii' ii: ::: , . '" .. I: fli II 1.11 ,.. '1!~ I,'. ::1 t' 01,11:, 'I 'J ' i "'" ,,' "" • ~1;1.1 I I." ;~ "" "iI.' ""'" '. 't· , ••• I t'I'. I, .". ".' "" ., "" ot ~~~ .. ~ ,~. ,I, I ,,,. .~. ·~t ···f··~~ !" G1 "I ;':1~~ I' ~tt, '"!1 ''''t .~-~ 6-HI ~ .......... ~ '., t+H! "ttit- .. ..I, ;-~~ ':":;!" ........... , ":~', ':'I"i!1 .. ' .. , ... 'I' ,I ~,"''''':-- . ,................. ,.

".. .. I'" ffi' '~l iI i!," " "I" "I, I "I, I .. I" 'I' :1\'"'' i .. , ,,' I, "I I'" '"II''''' "1" ""I'" , ""I'''' .". ,,01 " .• , ". ,,' ,.. ," "" ,," .": ,. !: 'tl' : I ' 1,1: I::." .1:: 'I;'; :.:: ,: ;';, :. III I: : ':, \"":' t', '" :1 ~, ::1 !:!I !'~! I ~: : ,: ;:' I" : ,I ,!,~ 'oll !:,: I':: :.;1 :jt! !::: ill: :::: ',':, ,;: .. :1 ~:: · :,." ," Ill' ,+ t' ".! ," ,,, , , , ," . . , ,. "" I' II , .. , I" I I' , I' , , .",.. .. . " , ,," .,. I" '\" , 'I .. , I" . ,... . , " " , " ".. ,1', ,"",,",," I' "" . "I'" .... ", .. " .,,' ::: 'Ii: i: .,': : Ii I : I : I':',;::.. :!:.,': Ii,:,:" I ;,: II:: "i'; i: ; 'i "':" , ii', '! i ' 'I i I ; : :: I!, ," ": i : ,I"::: '::! .::,,;:'::: Ii.:, :: : : iI: ':":: : ! i:: : ,: :" i :WHtt: +t1!~lt: :P'I :fit%1 tr 8" it:":' ':~ ~:: I',' ~ :: i:J. ~~: 'I: ,~:, d: : ~~.l .\:. :~"I" ;A~~': i:f:~';I::'~b..:; :";,~:; .2~.d:j :+ +: <~ ;h ::H H~: T· ~+ ':'l-;' :~+~: .::~ .+ '., ::!:':. 1:/ ::: ;11. '~'l j,;, 1: . ':,' .. ,P, :1 : "'''" ~," ,!' .. ,: ,ru· .: "'~ .~I~'; ,:.'~ll!:!~:""":' ~- t r-:l ',,'I ::': 'I:: . 1i ':,':: ,; .. , :.' ''', "; ,','. ': :'~: " .. ":: ,,', '1' ", ..... '" .. "." ." ."'" 1. . . .. I" "I'PI" ." .., .. ..,. ""WM'" "~' '." "" ,,," , , .. " " , ,I" ... , '"~ """" '''''' I" .. '" "" "" .,', ," ':::;.' : I I 1 I:: : 1':1 : '1\ :.;' : i. I ;: I " . ,!,: j I, U'" ': I"~:': I '.' I ;.. " , ~ '\t.t"': 1 1'1 'l:: ;::) ! ~ I " ~.' , :: : .: '::: ... ; ,,\, . i:: I .. '.': ',: tI· '" , •. , , I. I" I,., \' ,I , •• 1 'I" ,. ,j ,I , '" "t "1 I' I, , I,' I, 'I I"'" '" II' »joj~f= '...c' t.:,L ,., ." 1.1 . " "I ." ., .. \.1' .. , '!'j :'::. ~:;; ' .. : 1.;.;.; : ..... :8++ :.l+ill:~" W~· .: .... ;~ ... : ".: .:. :,,;:: .. ~; Ii I:,: ·1 : ,,;1\ .... , ... 1 : ;:,.\ 'f .. - ~,'. """1"., iU ., ,-".. .: •.• ~: .. ~, .:.:: ... ! .... : ••• ii .• ...:.:. -~:,.: .... , .. ::,: .. .:..i.' ':':':.

':; iii: ::: Ill:! 1:\:t\!~l :;j! ;::; i~:'I':' :;i ~: 1 ::: 'T ::'1 1 .:: I,::: 1:;:!!1,!1 ':::1:: .:: II: . ':1' ;: i:!:: !ij::::; '.:':.! '~r ' I· : ::1'.:: :::1 ;.; .. ' !'::: .!if: ;:':1:'.:' ::.)i i:: :::'1 ':i , ',,, .' I! 1.1::;, ,t l: :: U : " t :, ;: : I I! t. ' : . : !; I: ~: ' , I '1 : ~ ., ,,' t ,l " : " . I.: '; I' ': ..' :'.: •••• , ••• , 4++~- "1'" !- •• , ... 1... • .... , ... , , . " "p .......... , 'I" ...... , I' .. ", ........... H ,-~. ,,,..... ' ., ................. , ............... , ............. ' .~ ;:': ,:,~ !~i1 !i: :;1; :,11::: i !. . ::1 t ' ,::~, ! ;; 1 ,:,!::: ,i ! ,: :: ':.! :;;: iii .:r::. ;~;! .. ' i ' ;. I. ';,:. ·1' I :' .. , ,. , ...... I"" , .. I ., ,,, t, • "I' .\, ~' ""I~~ .. , $. ", ,,, , ,,'" I ,,, .. , ' , ' .. I·" ... ,.. . .. ,. ,., I '

... , '"~ ", ..... ' . I' .. . .. "/j.,,'··' ~ .. , I ". ,'" ... , ' , ,., '

• \:: : I; I'!:: ::; '. ., " , I' (I -,;iJ), l. 1:"0. ' ::, !, : i::: L :: . . :' I :. i

'-~-...----...-...-~-..~,~. ~---- .. '-- ....... ~. -.'---.,.., -..,-r-...,......- , . ,",,"

,-

10 X 111 to "Ir f'f f\!1It,1r lrr,'

.-

I\flllill Jl I'

-

N I N "i: 't;:: ... " '1 !

111 • ':1 Tn H'f ,:., 'il"-' ,rl~ it r, l' \ 1 .~ I I ' 'I .", I ~ '." , .

. . ~ . r; _ \ : 'I

!'" '1

" ;,.

, . EN(;IN E.

I i " :

.... ; ,.MA.d . . ANi>

!: DpERJt(ING Co,.,D,IIO"5 AS IN FIGU~E.. 2.1 N I ~ o I i " \. , I.

, i I !

~iRfJE: i'

. ':1 " , ',i.

'------------- --- , .- ..... i !

" r; 1',1"\

;---';---1

.------ .}J/;~Jr:tll~U .... ltL~dlJtL+bk,b~ ·:r.::J.·P--~NJ'N£

I .. _.:.~_. ;-:-L)~q~I""~ ",EDJAGRAJ\:1 ' Iii,.

::.!. \F: ;:~!ji! ,:il :) ':j:: .. ',i· OF~llnNG CoNbrriONS I

: 1 .

. .• 4 ••.• ,:1

:-:~ "' '!) l: ,ili!+ "I'I'! AS 'N F,G<11!£ 2021" 'II

;:1,.

j

' •• i " I ~ 'i~'li; .. 'i~~......,....,.~.-.,..-~~ff1't!tt~' 1 1 '

":1

:>i

..... , ... ,1 .: .:: : .::1 , , i:1 :::!

.1 "j' .

l.'t ... ", .J,'.~ l!l '>( HI TO TItF crNTlMFTf f1 46 1513 h ,\~: t\f I" I II. I'. 'f' .'.11.1 f"1l , .• 1\1', 1"4 i, ~ IJ!.I ill: !!lIll!!IIIl!llllllll! ITT]11: inl~;!ilN.· :j~:!ib: ::&1:: !! : !! i ::;: . 'I!ldliiiTTmmTl!; ::<p1~ ::::tI :::! II! l:E:;' Pi :i:: ::: :;;!r:T nl! ·ilt :lIlli, 1 ' !'" . '1111, I! It 11111 lui!!' ,

111111

1H qI. '.f. !~:: H!l 'I 'n;", ;;~ H!: Hf ..: . '::: \M1NrJJ' :':' :' . "'::!: ':': :: . :::' I::' :Ut! . r'WI" ':ij, ,!!' t, t ; .. iI' ·iI:!t~ 4- I q·.t ':! ·11:' .. , .... ;; .. I .. .. ... ··Ii·.. . . '... , .. . ...... " ', ... ". 'I .... ,II I II .... "1' '1" I I i!il' I Iii Iii' .... , .. , II'" I " I ·'1 "" ,,, oj . . .., . . . .. .. ·'·'1::1." ..... ,. ,.1 "i "i' I'il . 'I 'II IlL 11l1! iii: ';, i:: :i;~ i ii ii!j' iii'! i;i: iii; ... :; r4 ... ; .... ;;i I) ::;~ .. ;;.'~':~::j~':; .. : t: ~ . ·'i,:;/t t:~~-ih~t ti1itll<il'l iil:jl,'!! Ii! iiiil::iili;ji I, IllU 1 1'1111 I: I lin": ; ;';r r';;' 4t: : Ii .:1 U f' .I.! I::' I:;: !: •. iii: ;i:: of': T .. :: ;.:; :::1 ::·i .;:. : '." , "~l': .. ;: ::.: : ;: : .. ; .;;: ' .. ;: :::". ;:: :;: :;;; I;:: .: : :1 ; ".! I! I; Ill· !:l'~!!~+'li~'! !I, , .1: 1... , :ii: I: ::J :i! iiii ;Ii: ii,,:: :!I: i!i!,;ii: iii: ;;:1 :H! i:; ::,: 'i:: i::~!i.J r~ :::1': lid: iii: ii::.!:: ~ '1'1 :1, ::i !i:;: :~: :::: I::: :11 :1 :'1 1 'I' il !It I \', Ii 111 1:'1';' I. • i I I., i 1\, ,II, .: II !. t, .. , I II II' I ,., ., I~';-';+ I ,." •.•• AI ~ 1:1 1 ' , "'''51'' .,... ~..;. .... . .. 6 ... .:.t I', .• ,. I. , • I I 'f,'. 'u+-" H++ttH+t1+ttl+tt+i' :-:-:. ...... ....,._-+'~.....,.......,.-..,~~ !Ili' i ::[ .. 'i~:t' 'j'I'1 i!lli :1"1' 1 iii: lilt:j! iii! Pi: '1IIlil' If:::j i rrr: :::i~;J.L_:~ 1 .. 10\ ;:i' . il· ~ L 11:! T: ~}Iiii! i'i!TT :1;: iii: FIT;:; :'11i !il::; Ii!i Iii rll!:iii a;'i;.i.J..o.. .. ; iiILII;."jIUi..Jl,;,EI£~:·Di~I·!;1 ~JI .. ~1. .-... • r· t .. t •• l~ ,I,. I .I.~' ,I,ll .. " r-H(iJ~i"u 'I '\ rr; , ... t!" ... , .... '''''1 "Ii .1 .. q.1 '01' .I.~ I,,· • \. II I •• -11t1 ~t-t 1 -'"I" ... ,'.UAi .tt~~"1D~ .

;i ::1;; ::1 j ,II Ii :;1; lid :::j iHUll !!:: i :ii! i.: .; ;;;:~ .. ·:j:ll: .:i F iiii Ii:: ::l !iii :::1 ::: :iii iji ij:! iii: : Ii 1\ ::\ i !: Iii: I I P Fr !,MGl DOMJmAC~ MPH , : ,;; ;:, ,.; .. I jl: I' '1i: '1'1'1 ::;1: I;:: ~;,: ::i:lt r7+1 ±-::;:fP-I:;;~ ·;t'O"" : :~~I~f:ittf§ ~::I: :U;: ;::,;;:- :1;: :1;'; ::!I :;;; ·t 1 ::1'1 ;I':~ Ill: \'\'\'i 41: \;:.;; l;lli;i' ~t' ;,' u·; .~ .. ;; l;' I• li ; ,: I I:: ;; II . ,: I J' I': I I' I: I' I'::· I': I' ,:': I I'::::;::;:: I' I Ii;: . : I'!! :.:: 1':: .,: I :: i! ::: II :: 1'1 : I' : ': I: : I' : i'111' i'I' I ': : I I : I' Ii III: 1 '.;;: I:' . \' \ l I 1 j: '" .. ,... ... 1· ,. , . .. . 'i i '''1 ". .... ... , II . . I • '. '" i' I r·· 1 "I' .... .... .• .. ,... •• • , 1, ' 'i i I ..,., i i . r; , .......

l ii :1:' Ii; I I ! I :11: :!:l ::'11': ; 1'1' iii, IT :.: I:,: iii .; . ,Ill ;'1· III i .: I;:: ;;;i 1'1,1 ;:ii :i· :Ii: :1 : ii' ': ," ;!i I I:! Ilii: :11: ,::~ j: : • I' If I ,. It: !.: ! : ':,! ':;; :~, ;.: I .:.. I,: ::ij It:l~iJl.iL; :+t: .: ::. ,I:: ::1: ,:: 1 :::1 I.:: :111::::, :! I: ~I I I! 11;1 II,: :'!IIIII' , . 11#' '+1+++++11 J.H++jf+++>', iiil! ~i; I ~ J.i~ 1 iii! !if~ U:I!:i H~I iUlll illlii! H ~!!II! ~~. :1 1 i ~ il\! ~(lt l~\~ ~U~ !iU Ii jiitliii il'l Wi [Wi III il .~ Ii t"i tIT,. wH 41: -j~~;r j fi q l 1 .. , 1::: .. .1 f • I if" iii .... in .. I'll :! .. h I.:; II 1.1 , . .. ,1 I" I" .1 ..... , .f! .. 11 I .. I .! L '1 . ! i JI .. , I II 'I' i . .. j":;' ""}i I I I 1oIJ. I ::1 ~:: ::: : I t I !' I:::,: ql! 0 !,1 i:. !:1111 II ill .. ; I:!: ;; .:i: "1:1 ::: I !i: III~ :11' :d: :I!I ::: I:: I.: ·~C'UM~~~~iJr:.~""rt<f+H+H+fI ':: ! ...... :·III·I··:·· I' :1:' Iii I 1'1 : ::1' ;:;:T ··, I' ,.'1 '1., I!: :I" ::;1' '11:~:':1 I:: .,:\. :11 1::1 1:1" :!I 1'\ I;: H'ii : .~ I';: I:,' 'II I I' !I'I : . II' 111'1' I::: :: .. ~. :1 ' : ,Ii, II ., " ,I .... ,..... 'III' IG H" '" ·!l·"",.·· '1 .. , .. , .'.~ ", .. ~I ,.. f~' I· "II I" I' I . "1 'II· .~~ n (~I JH+H.H+ffiriLI :: P,. II l-'T' iii ' nit U:~ tl~: t 1111 Ii :.; :dl tlii pt.111 Ii: :'1:; i:' iii !ij 0: n'I'~ !1! '1,1' tr rh I tiJIi'li ,111 : I~i it Ii. lit I' ttr .~. ~: . i iii r' ; I ' , II I I:!: !: • il" II i 1 : ! II' i i;: ! 1111 Ii::: ',' II ~ i I ::: III 1 ,Ill·,: II i : 1\ . I II: I; 'II: n H ::: ~ j ill JtUtl+tI-il l li n Iii j I ii, 1 1!If ill i: f Ii!l fl~ H\! llii ill I I il, :\ illi .. , liii liill it ~Ul rn Ul 11 i .i l~'IJ' i:~ I! II i Ii ~ !~i :~;j~:LE Ij : I~' H+H+fHH'I·rl ri..!~ I ,lllll I., ,~ I I' .r.: 'It!~' II't,· . i,:.I .• ::: ,':. t· :!:t Itt, . to 'Il~'!· H· ·t t ~ d.JIt~ '.

I,: Iii ill . " ! I" !:! !!Ii jI !!!I!li i!!l! !I~.:! IJ .. , !:~ :!:~ ! :1 :;!i III II~I :: !:: i~I!: p ii:! : II ;: !Il; ;!!~~~ Ii' .

1i1 WttHtHI II ili I ill ~tiH ~ [I' Iq~I'l!l~ ~1111 hll]1 :i . !d J.l! lnf f;;:I 1 ~!.! i d~ I: lj 'l·lIl 'fiii' iii' !!II~ H~~~JI t' I~:tt \' ttttttitl I :~lllii hi jI I' \lit Ii:' Iii :.1 lilii II III ! . iii Ii! idI!;1 i:i , Iii! ,I i III! 11l1: Ii i II I'll .Ii: !ililli:' illl

lI

~ 1 ;~!! .!! I~~!' ii' II 'i" lUi U i !! \1 j ij' IU: II lill ?!,:I JH l:l I~~ 111 : ~li DT I Ii I: It'll! I !' llh: 1 iii:' dil ~FlUJl· , ~.·iidiH . Ii . II ~ I :TI1ii l iii III I. ! 1 HIt Pi 1 Iii i:1 tillili .=:[1 tt iii !i: iii! Ii;: iii Itt· Ii 1ft ~il!; rr it i;1 Ill! ~Ii t~ :tnillltlll!i HIiIII; ,I' IT l 1 it W H Ul ~llill:! \+!l Hli Irll! ~ !li! I rl~, ~ i,III:!. ::.'.1; !"!I HI jij till UU !HI I:,:! IH ill ~4f if II:; It I [IIi W['if); I: iii: '1I";i lll ·"lll1·.illllIl·IIIIIIII:lllllflll"1 i ·1; :1 ii: I!;: I!! :i:;' Iti' Iliil! I Ii i. l!il !;I "r :!ii :;:! .:t: :; il :11' qi !iii i!!i :lll I: n illl il I i I .,. !IP !iL .::IIIIIIIiIHlllililllliilIIIIHIII 'ill i ::.:;1.' l :L1!! i:;i ILJ:: i Ii !l1!1: P '11:: ilil: !I.fl:l· \\'ll:11; ::ii"fii!.ili ::i.: ;;:!ilW 'ii I'! II! Iii:: il'lil' :i!l i!:[ mil il! i i : i·lll if!i: il liP Iii I i i I'i 1 I !llil [1: 111 : 1;iIT:ITTPlmm11Inlll!lllllltl\lllil!'

1 l 1 • .L • ":~+!"1-" "t .. ••·· • .. I~ ...... , ............. ,,, .. !!.1" t .. , "1'" ... ~ .. t f.! ii .. 'jl . I .~.. II II, ... I' Ii. :':, I:: :: :1.: :ili i::: 1\1 :! I H iii Iill ;.1; :ii:::: [!i:' .. :: iii! .... lit! ;, .... I Ii ill 111;: ::: 1 i;: Ii Ii I:!' , ItI:, \, 'Id :1:1 ';jiill 11'lilll II' '.' I . ·~I :::: ::::.: :: ~ :::' :::: .::: :~I: :::~ ~J I ~.:: ~~~: 3. ;;·~Iill.+~· ·~~*tf ~ ~~ r!i :::: ',': !I ::: ,~, ::, ':::, .:~rl !~ 'It~:: :"1 :;!: ~ I, .. ~~ :::~ :: . . .: III I ! II ., ....... .1.. '" .:r ......... " .... ,: 1[1' '," "I! .. ,. ... . .... ~ ... , II I ... , ... Iii' .... I·' I ." 1101 .. ' I!' .01 I" I\ll I'" I ... ..I· .. ·, I' '1" .. I. .' ~I'''' I . iI I' I : : ; ':~ ~ .. : .::: : [I! :::: '.:' I:'· :;:; : u: ;::! :: J :,:: :; : :::: : : ; ,:: ! .: •. :: :: II :: I: ::.' : I .: : I' ! I . II ; . 1 Ii II . 11 :. ;!, 11: . I':; I I : j I I' .; I !: :, I : :; :: I: :. . : Ii : iI , I l ,.. •.• • ... 1 ............. 1 ......... , ........... , ............... I. .... , .......... , ...... ·t ·f· ·Jt .. !lll·'· .. · .. .. I. ':ili' t I·· .... 1 ........ I .... ·it 1 I:: I·.:. ::.: :;:. 'I:: .:;; .. ;. I:;: ::;; ::.: :i;· :11' I::: ::·1' I.:' I!: I:; :;::. :;: :1 1 ::;;::: ".: .::! .;'. 1 1.:1 '11" "' 1:· .:;' :'11, I' :'1::: I· .; '1:: ;:', :::1 ill: : I; :::; II ' I ii' ,,, ,...... 1 II·· .. · . " Iii' Ii'" . .1. 11" ';il '" '1 I ... ...... "1' ~ ... ,I "'I I"· 'I ...... " ... .. ii' .. ·,:llii' Iii I . I' I .... I, .... ·iil ' . "q ,.. . I 1 ,: II i; ::: : ; :; i;:; : i ;: ::;; ::; I':: :;;: : Ii: ::;: ;; I : :;: '.1; :;; . : : ~t :~tt '. ~~: ; I: :;': ;:. I;: ~:.:-; ; II i ; : ;:, i; I: ; 'I i ,::. i:: I I':: I 1"1 I j I i l' I I: l' Ii I: i 'I; :: i i :;: : ; fT:; 'I';; ; : 'I ; i : i :,,: lf / i!: ! H ·fJ ~~:~! :iU ~!~j ~qt ~i~ on; ~ig ~;!f U~~ ~~:i f;~: ~q!l i;~: .:;: ::;~ :!~;,. :~ lPI :ili !i·: 1:1: ~~;~ :'~I: IH !!L L~~ q~f P!· :;U ![l rtf I tit 1t ·tt~ ~!\t :f~ii' l~q ~ t Ii ~!L i:r~~ l H .

l 1 i\.. '1" ., ...... , ... , . II.:! I" .... "I' .... ........ 1141; .... "'1 . ... .. .. 1, .... I. . ·1" ... , .. 1:1. ' I'" I" I" .. 1. ·'''Iil,· il I I' i I' ::1\' '1 .... ':!;' 11 .... '.1 ., .

f i ,. . I 0,. • • I • I '11' ., o. ,! ! i : ' . t; .. . . 0 I •••• t I . • ., I· 'I" . , ... .. :! I: >.:; I'" . .. I"' . '1 ., I I • I., . II I" .•.. ll~' I I -, I I • 1/1' . I' • ttl I: . . " I I , I I I • I *1':: f¥ -:: ;:: :::: ;::; ::lli ::.~:'I ;,: I:;I::Y ~~;: ~~~ :::: N;:~ I:; :::: :::1:' ::: f'l: :fir ;:~' ;;;. I::: -;:: ,:il :::j I:; ;;;; :;:; ::;: ,t jll: ;:1 : p I :1:: iii: I';; :;.; ;;:: ;;:: : il ; :::::; illl't :1: .• : u;',; : ::. ; I!' . i ::.: .::: : II: :: II: ',: t::· , :; ..... : : :: I: .!: ::'.;: 1 !::: : ; I· -/, I' :::: ::: 'I!::::: :: 1: j:; I I.', j]'11: :::: .: I' I:. II: 1 :: ,I; I::: I: '1. :;:::::::::: I I :! :;: I j':: J: ":1": ..... .. ....... , .. t··· ........................... 1 ........ s· .... j .... I'" , .... , ...... jjtt "1 tll+ I l' .... , .. , ... I .. ··llllJ· ..... d •• 1. ........ , ..•.• 1 ..... 1 •. , • • 11. ~;. : ..... ::: III: 1.1 ::1 :: ::1: ;';::: ,,' '" '1': ~ .• ::: .::1 :::: ~: I II :i ,: .. ;:. ;;;; ., II ;::. ,,:: : I: ::.: :::1 'I:; :11: :il. :;: I:: :1:: ;:.: :~:: :.;: ::1;: II:: :;:1 i!: I : I I'; :;;. :,.. . .:.' '" ."... .. • ...... 1.. . ...... . ill· . .., '!I .... • 1'1 1 1 .... ,. , .... ,.. . I' ii" II" 1 i.'.. .... .. I" ..... , III '11' I'" .,'. Ii .. 'ji:' 1'1 .. 1,,, I .!/ ' ~." I .... ~ .~': I'.' .~: .:. :::: ::: .. ~~:~. ~:.: ~ ... :: ':. :.:::-. ·~~8! .:~ ~~ .. ~~:~:. ~ :: , .: ",. :~ ~:-~f.~: ~~ ~~~: -::.: ... : .. : I':' : .: .... : .. :: ,:, >< :.: I~: ..

I:. Ii: .:: :.: ... : :,;. : . .! .'1 1 I' ............. ··1······ .. .... . .11 ........ I,· III! .1 .. il," '1" ....... I'· .. · ....... I"~ .... .t .•. J,- .... II'" I 011' '''1'''/ I . II" i::: :,:: .::.::: .::::::: I; ::'j :. ::.: ~::. : .:: :. .: I 1 :: I ::; .. :::!:; . ::'. :' 'I: :: ~. : 'I:: ! ~ 1'1:: I : I I 'II ::.: ::.: ,: II' '1'::';; I· :! :!!: .: i: : I: :t:t "I: :. : II' 1:;1 L:;I 1·1 .

I ................................... 1 ..................... ,. ... .... ...... . ... II .. I ...... I'·" ..... .1 • " ..... , ... ,.I I. ..... ., ......... 1 ...... ,., .. I. I .• I.. n' f' , ... '1' .... . ., ',. , .. , ... .. . . .. . . . . ..... .... ..... '" . . .. I II .. '. I'" .... ... .. . . II . .. .. . .... . . . ... ,........... I' I : I "lI' .. : i ....

.

:: [. 0;: 0: : ':: .::: ::.: :::: ::: I ::: . : : : : ' :: .:: :':' . . : ,'" . ' ! . : ::. . : !: : .. ' .: ';.:':::::!:: :: .: ; : ~ . :: i. '::' I:: . ;: t :;:; q: i :!::: i! Ii I I q ~:: t :! : . · . Ii: .. ;. It) "I· .. · Hi2~:; ii:; iii: :.3P I';: ;!:JI •.. ~~ ... !:; ·:·1::~~·:: . :i 1:\: !J! :m ill! !::~ :!j: [![; ;11

. :·:i: I: . .. U 1- :Mo. .. :::. :: ! .. :; .: ;:, 1.· .:.: .: ,'.: '11: :11 iii

: '.' .. ;···lAl .~'j -.; rt ..... ;-. .. .': I .; .:~; '.·L :~~ :~~"i •. :~ ·!t: T~ :~-: :;-: iii: iii: ;pr

i

C . FON£WT/. f"LONG ~ K i: .,MPH. ·1·· L .. :: .. : .: :!~ :!;~::: .: Ii:; :ii::q~ qfl

•. t .•••.••• I .

.. ;

.. ..1 I 11'1: ····"1 . il . I 1·:··/·/":I;::J:J:iil::jl¥ T~/\. It :f~

, ..... ,.. ...... . ..... . .l. ,J,:.Ji~ c.; :LJL :1 : Ll : .. illi. ,Gi! :~j . .

-------~--'~, ---~---'-----...,......,..... ._-----' ...... ---.,.. .... ,----.,., ......... ------

---'---

In • ,". ( f..'t In ~ ,n TO THE (' r NT1 MrTrR kIIH',l. (\ r<',<,IR III -.u·, l'IIt' It, 46 1513 Ildl~; ':; :::: I:!! Iii :j! :1!l4li!~J:-lilil:i r~;:, :-1': :,: ~.;: i:. :,~ ! ,: '; t '1:: :;;: :!i ::' ~~S$' AL:r. ,il\.J~l,,::I;" ,:W:!,JI~jL" li:lWi;;~, "~ ' .. I'i ':'!I m ;j ." \~~rUifa t ~H+I ~j IxrM: .. Iof ':::'. 'IEr~~' L ,:; ,:. p, ..... :lrl 'I, I, Jll., 'Iii. '" "W ... :.:: .. i. "I""""··: I.. ;. ~ll. :·i'ill.~' uf. 14h';IL,.,. li.·;"i I , I:, . I ,.. ." . J... " 1-" ...., , .. I"~ .. ,,".. , u ~.:. ii.!:!.1_ I ...

I Htf!. JJ •• .JJ" .:; :.:.: .. '4-. "': . .:l.:.' F ..... MPH MPH MPH· "IN la' illt!)! Ih )l ~~i ~Jlllil~r~'til Ii 'l~jl1fl~id H~) .. :~·14'1 ~ ''': 'I";~' .' :!1i 1i .. ': ::. Ii: iii IJl-Hl~i~:'I:lii fiji. ·ii: ;b~Ji ::;; ':i:rilL :liJ 11'fll~ iPll~\Jl iW.~f: !}I~ 1 iii! illi :1'1" lJ ,i' i\ ~rl1l" ""lIr :1 :",~(;JfV~ J~ . 1:1[; l' ,I. ',I::' ""1 :LI.,1i .1 !1(,I/'I" "" "11'1'\ 1I1::,Iill!r 1:/ "." IHi ~u.

,i !,< ::1 : . ":1' -I::: I:j:t -:.. , ::':jr;-:I'~~I:' :11' :.'.:: . '" "~IH:: if ' :·}tt'itri- ;i~ ;: ~~i?: ';~b.' Ii: :;: :Ii~: I:;: :;11. .:! ~'if~"fjl'7ii ',!il Itt;"~ $: I: lU;1 : i' ; lilll'I.'. 1-::.:' l: ' I' '!;. ... ' I. ,.. I'" I" "" "'[ I •• , , 'I' I" ." I' ••• ,. .. •• I' . '1'" .:l . "I' . rio.: ". '" ~ "I, 1:1: I ' I tid ':1 :"1 :~:: 01' :.':: :.: ,'1: :.:: ::"Hm: " ':" ::': I::: ,: . :':1 ':: .... :,1: I:! ;"1 :.::: 'i' ':': .. ',:' .::.:- :1:: I::: :;ii ... ';1 ::1: :~:. i~" ':1 ".' :1 .

H illiI: 1 ;'1 .: .. :;.::1: :IP': I:!: III: :;~i :1:: i I! . ::1: ::1':" '::i:I . ::::li:l: 'I:: ::.1 II, ':JIA.::.i~:.i. !::, .. :: U 'i'j I::. :1· 'li~i"'!il;I:: I:d . ttl Ilil!1 :i'i il:,! ,d :~:. : ': :~.: ': :,: ': :::: I : "', :':", ',~~ ~: ':' ':. :': •• : • "', '~, ':' :.': :.:. " .~~~U~II.~ ~.: ;J~:: ., .. ~Li(:'J'," ': ~.. H-t.f.·lf.'Hm:~f8+!-t++++8f'r~-WH4I IIII'" """Iil'n:" 1"'111"1" 11 "1' j·"I·' .. " ... , .. :I'+'I!'''I "" 'I' . !J.~ 0>£"1' 1"·~ •• wl'I .. ,,.:, ,t.~SII:··I':I~~ II~:'II' ~. ! U,'i':I,I' I ':! :.1 t':.: . 'I i :! I l' : 1 'II' 1'1' "....... 'I 'I' , . i!' , ", I" I ,. ,I , I.~. '1'" I ·r.!".~! ,. j •• ') •• 'I; . II ,I I I I

P

'1'" ';'1 '" 4. ; • ,. I,: • ,.. •.• .:. ;:: I. :: :., ,:.: ... ':\1 .: 1::'11:': :,:::t. ,'.;1.' :;: .::: : rli. :111 .:~ •• :t. ...... : I", IIP' " •• I :I~ ~ r: I .' I,. it :::,1:: I: : iii!:: I'::: Ii IIi':! it: i .. iiiili: .:: ::i! ;! :;! ::11 I:!I iil'l i: ,:11 ii, ::I~:,: ..... ~ii ;:. I::' iii: ili· ::1: :J;~' "'d iP' "'i~i.i+ '111: I: I 11 Ii ' &: 1l4;:~11 ;1 : :; :;;:;.; iI,: ; :1,: :;;. :1::: :I';~~; . ;:1:1: .;:. :::I!I:: :. ::! :.;; <: :::: :::: ;1::: :;.; +P ' : . i:~~~~':::;~,O·~~~v~.;:r.-j :~. ii~D.~J!!:1 :::: .1;: !/~~" ~6.:·1++,ft*,:~: l!+l1jl': '19.:-t)~:! :11',[: ':li · I: :,: rJ..

i l , 'I ' I ... I' , I I I I J I • • , ., I' I 'I , , • I , , • 11 L • ,. "! I" II . 01. ,I I L lit I ." j oj I" ,. ,. I;'" ~! Ii ,::,; I ,: :; ,I 11 ' I It: . 1 ,'. i :: 'H,l.c,.

;' .. ~ :~ ; .. : 1+: :i I.; It;; I L hi: :1:: :;~: .:.: Ir I,; ":i ::i: ::4' .. : ,; II •. :Ii :: ill" I: .1 'i;j,!l ... :. ;,1:1 :HI1.:~ :.::: II I"; P·i.I.··: I •. iW l:i;l , I' ~:l:t+HH+HI

IU

iii L~'~ I i /111 ;:ii : i!ii :li; il:: i! i Ii:, ;ii: iii; iii: .iil i'd iii; ,';::::: ill! iiil 1:: ';j ii! j' tI:~;'b.c~!:: :iiH-j:.i~Ii! iij. I::: ~'a:! '!iiillilJ~li:! i: ;11 I/!ji iii: I'tl~ l ;ni Ii "It; .: "'[' ill:i:i :;i: il:; :i:: ii:: iiij' :ij: Ifll: il::i1·:i ':;:.:: ;:q 1::i: i:lll I':: iii :;1: .:'. ;;;1 I;;; :::i .:;'i:i ;ii ' ,I:. i::; ·:i: .. : iii: jii~I":: iij'ilml"ti 11,;1: .: i"iiiiii ;Ii; Ii:: lill":' j ttl" ,.:. ;:: .. :: I.:;. ::It I::: , :1 :1I: !:.: :'t !!.! ':1': :I:! ,::; I::: .:;: ::1. .. : II ::" :'11; :il ~.':":ll'lq Hltl ;:il I,,: !tl ,:~: 1;'1: ::~ :;~II.t: \-i: :: :1\ If: I I+!H+I+IH+H-+H+il-i-HW! I 41+m Iii,' :::1 I::, :::'::.1 :i II:: I!: :11: i;: :1 ' :::i : I: ::i; ::1 :.:: ::i; ::11 ill;I!!:' ,:' Ii': ii ,'IT I:,:: : :I'I::!!;: Iii,' ;:ii i: ::,'1 :il'! 1'10: 01: I:: I'li: Ii I II \TIi II i, II:: l : / Ilf ,I: ::;: ~:i ,:. ~: II!I I. ::1: :!:L :::. ti· I ~ ':!l . :! !l!: : .. j ::1 h [,:' : . II :, ::1 ::~ I.' ':"1,1; HI :::1 q : ': :. II: ttl I l: 1/ II, II In: II 11 !J; l iii 1 '~I!i Ii H'II :i;, .::: i r:r ,q :i:i i llili ~ ::H: ii!: \1 : Iili .ill .::i. :iii ;::; iii: I~::I' i! \I:i pi 1111 :1/ j::j !:: III' n::1j ii:j il!!' ii:; Illi ;::I il :l lii I!q l' !.i Iiiltti '1 II rn I Iii • H,' dir ::1 : t 111 ::!! I. .. !: :! III I::: .1: '1: ::.. ::;: ~:1' I::: :·11 11 ,:: i11! 'ill :!1 n!l. l!~ H ; .! !tl. 11 ~;!~ .l-~ ::J!!: tt+~ ~i U it-; r ~ltH!+HI!+i+H+I++!+II+HH-!+I , i: ~JJ ~ '.: ,:: I i i :: i 1 iii j:! i : Iii i jI ::;, i i :: I 01 :: ii :: i : ~ i: :::: Ii: iii ! i :: I rrIT I : II I{ i I: I I: i' : I! i111 I :: ii I:: : :' : III III: i II :: I jI I Ii I II! I l l 1; 11 I: !rr:t;l' !i~:::i ]; :~: j' it .ili liit'i iii] i,ii !ii: il 1i ; 1: 1 ;; iii! j ~u) ;[U 1i:l U~! lint/'ill iiil ! .iil 1;1111111'ill; j; ; ili! 1111 :ill ;,'JJi'l: ;i ; ~l: :~f'I' 'i;i : I' , 1 t IJlhl :4j;il )HH+l++I+fH ++++tj fH

l H 1

, :: Ii:: : : : :: ;.:' ::. . I : : : " lit :::: '1;: '::. !: Ii, ! : ' :: :::: ::: I :: I' ::,: : I:i ill' ,1:, . :: : :: : I: :: I : ~ II: : j 1: !t ' I: i: :::1 :::! Ii : r. : 'I t I ! i !:. I Ii I IIi I' ',. I l j Ii : :,; ::::1-1::: I: i'11111 ;:t! I :::1::' !:I! :Iil I::! 01:, .!:: .::' :: ! .::' ::!lliI:I I!:I ,I:: ' ':' , I:, ,::1 :ii Ii ': :11 I::: IIU :il: II ::! !i I 01: Ii 11:: 01 !

z: ,4t rHr~~j < I: 11!!IHI,~jll n! <,ijl,l fijI f!if if!: Ill! jlill: !~!~ ~li! ll'liJ@%::lll,:!!,!:::j11Iill 'I ~lli' :14 Di,! m JU; j !~~'I! 1m ~\ll: 'II~~~I)I: :~l' U1j;f Ifi ' 1!:I1I" II i : il 1;11 {lll\+ttt1tHtl+tttltt1 l l t".1 '! II: iiK: ~ :::: I i:: : ::;: il ::: .,': ,::: I. j: I I:!::: i i :: ; 'r I .:: j .:: I I :: I: I! i: I ~: I I ; j J ': Ii II I : ~: I d' 1.1 ,:' I : I I' I J I ii, 11 lit: , l i~ I I: ::t·\: I::: .:: III: i! II :i :P! [Ii :I'ii lT~ HII Pi: ! Iii I:;: j:i,:i jil:'II'l I iii: i.,q,: I'I!I: ::!! II!! II :, ill' PI l'~'" i !II :1'1' ii'~' iill !, 1~!IH':ii Ii Ill! 11:!!I'I'1 Ii ji III . !

". 'H'" ...... , .\.. ,.1.1 it I d ... U Iii" I I. .. I I.l 1 "" .. , I' ... , n" ···Il ••• ,l n +.1. 'I .. 11 iii' I ~ 4H~-H+f-H·HHf.lI+'Hf.I f nil !1Ii HI i::::::: II ~j :1, :~q iii liiii ;u Iii llii~ I iF ili: iii!:1 ilillliilililii l!!idlil Ii i Ill' i! I: I iii lili' Iii! ill I ~! Iii II i Ii ! II ii III ! 1 i !';5, illl: :ij11 :. : iii: :1 I iii! lin ilil ii:i j! i Ii/I pi: !J II i::; !i:: ::i: :l: I 1,111 I'!!! ll'I'III!III!I'lll'!; II : ::,1 !::, : ill I I iii iii: Ijl! I l!P ill 'II ~ Iii II! II ill :: I liU ijlii I i : ~ ~ ~ ~:~. :: ..... :~n :: I :~H ;It! :;:t !~:i !::: ,H'I :H::· t::: :::: :;:: :. t: II i~:! ,.' iP ! II :::;: :::! ::q t IIH!! t :;:.1 p ~Jd t., ! I :"' ~~ ~t+ j: ~~ r! I ~t' fH 1 : "'-.J : Il: ~:.'-_ : 1'1',:: .:'1 :!1I' 1:11:::::1:: I::: illl'll II':: :111 1::: :::: ::!: :;:1 !': :.:! ::111 Id'Il8" II I':: :,1: :;:: . I:: • I 1'1':: Iii ::!!:1. !I:: ;111 I' ::, Ii'l !: I'::: Ii!: I , :" :,1".:, .::' I' tL-:- 'II'~IIIJII' !I' ,. II "I ~;..!.~~:. I··· , .••••••••.••• :..:....!.:~."~; ~. ", ':..1'" .,. ,.0, , , II "1' •• 1 ii". ..1 ,. !:''':.I1++':';';' 'q;'~i+!+I-l.fH+~.;..;.aI+w.l1l!#8ItI I: ; ~ :'li:': ' ji:: ':1' ;:'j I'::: ;:: I:: :::- :::i .-;" :::1 :-.- 7: ;1; ~'::-; :':; ,:ti L:; :1:1 ::i,· i11j ;'11 'Iii :IPIl'i; :IH ;::i :11t I::: :',:11 :Ij~l ~';I :j :1:: \It :'1 ,::: ti' . 't ", .. ,,' t' : r-:.I ::. : .::: :: : :i: :!: :i:: ::1': ::.: ::'.:: ~lll!: :::; :.:. :::: :;: :.:: : :: 1::: !III ';, I'! ::, I.:) I 'I!:II i' ::;, :Ilt I::: ;I! ::, ::: i I!:: II··: ':1 I II:!" :!!i .I:l:ui i '~ . i:; .. :::: ... ::~: ·:1: ::1' t'~: '1': ::.: :::: I:!: ':" :11 :" I::: .::: :::: :::! .::. :: : ::::. :::: !:!' ~!,! '::1 !t-:,'11J !:':: ::t-: :1" I::; 10! :::, :.:, IN'! :::: ,,. '!j' I !.,~ : !, I ;-t1t ... , i I ; :::: :1:. ' Ii:: ::: ·:Ii I:;: ::.! .: , ::::Ii::: :;:'Ii; I: ::: '::1::;: :::'1 :::: .. : :::: :::: :::! ':'1 ;:;1 '1::'1 1.1: 1:'1: : I! :1:: ::1 ' I:': :I:! :iii ::11: :' I::: Ii: ,: ! ::1: :! :, I:.:,:' ':.1' :, I f , .. " .,., ' ~ ... 011 ,," '~;.l.~':'~; ~" f~ft·, ....... ~ .. "'t ... ~. ;.!..;l"~'-" , ". ".,' , . ,.". '" .... "I' ,ii' .!, , ". !I, ." .. " ., " T:: :iiij: .~ <:i: :Pl !::: :L:: (, ;::: iT.;: 'IC;-' ~ .. !!:; ?'} Lil< ;:;: ;:;! ::r 7; I :i:: ii!i :!!; ::~; ·::,T ':.: :q! i:~: :::: i: ti l[! i!ll~! !:I! lill II: :~il q;: i: 11,'.

~ ..... , ,." ...... l ..... , ... j ", ................ II " ... J , .............. " ,'" .... ,," , ... , ... , ...... , ,H •• ,,\ " .................... " ........ l:7J , ... ,." t "!1 !1." I • I ... , Hi!

: .:: ..:.i.:~':"'" . j::1 :::1 ::1 I,:: :;:: ' .. , :. :T I:: :i I i' , I:;, ::: '::: :::' ::.: ':':, ::; I,: ::.: iii: :;:1 :::: I:· ::: ... : .. ;. :::i~\Ir:I: :: I :: I ::1 Ij: I I ::1111l1 ;' : ..... :~ ml,'" .: :~~: .:::~ ~~, ::~: :.::. H~:~~~ ~~i~ ;t:~.~ ~~ .... ~,:~~~:g@~ ;~~~ ... ~.~; .:;~)< §~0~::: :::: ::'-E~ :::: ',:: ~~:~~~~..: 1',:1 ~ :::~ ,,': :::1 !!~ . I R:I.:: :::1 : iii::;: iii1 :;i:.:: i: ·;;1' ::: .:1::. :: . ::il'O:: :i i:;'i .. ':i !. ;': ii:: i.:i ::i ·::i:: .1:: Ii:; ::"~':" .: '\::; :::: II :!I! ::ii!U II'!" I! . :1' I::: I~II;: ~I!I • ....... 1 .. .• " ..... 1 "'I .................. ". ..... ... . " .... " ... " ... , .... , ... ,,,' .,,' ". "'1 .... " ..... , , ....... " .I..... I· .. · ,... I"'" .... .• l' : '~"I .... . .. " .. " ··1· .. · ... JI" ... ,., " "1 '"." "II .' " ...... " '1 , ... T' .. " ....... , "" II"~ i' ""1' ". , .. ,.:.:, .. '1 · : .' .; I:' ~:' : : ~ ~ :! ::,: .. : . : . : .: .: : , ~ : : : :. . .: .' ; .. ' 1 ;: : :: : i . l ::: :::: :.:: .:, I :::: : :: ::, I .!:: ::. : . i i' i: I:!:' :: : :: I',' , I , .u.~2~ ,. ,,, .. " ........ , . .,.. '1' ... .. I"" ... " , ' :i·· ... " " '''' " ... 1 ...... I. ..... I. "11,,1 .. ", " \IT"'" 1: · ·;1· .::: .' ' ... ;" ;;.:: ~~ .. ~ ~-- :' .. ~ ... :: :: .... ~~!: .~-~ ......... - :::~·I·:~ :": ::~: ~": .. ~ .... , ....... : ; fl :;1: I::' ::i; :,-: .. ::: . I .'J .... :: .. ;. I,:' ·tt, I'!: I': :'11 II ' 1\1' : \1 ':'11 111'1 \1 Iftl H ' .... " ' " ..... "'1 ..... 'I .. ,.1. ' ....," ,. ".. .. " , , '1 "', ", I I' . ,,, .. ' . i':, .... :; I'" \1' I' "II .,' I "I \1 I .. '" I' 1 I' .D..j.::. Ii:: .,. .. ~:: :::: .::! ..... ::. . ':, ::: :ii: ;: ... : ; : Ii;: .::::: :;;; .. : '.:; :.: ; j 1\ ~Hi I'ft I!:: :':. ·::V·;· I::. ·:i ':i' I::: ::, I; :!II ::!I :f! :·1 t ::f( iii: I: t . ' ''':r-:' Im.o.~ 10... •• ;:; ... _1 ::: •.••• :.~ •• , ...... ~ ::. :iL :.; ... :: : . '~":I .:: ; :. :: ..: L: ... ill~ .~L IJ~L ~:l/;:: .. : .... ~l~;i Li i.~~U 81.J: Ii': .!; I::: :::i dl:: i:' .. ,,",'" ,..... . ~ I . : Ii:' I,. i.; .... :,. . ':::: :::: : . ;: il;. i",. ':: I::: ii' :11' 1 \ . :: I I ', I :.:: ". ~ • '" : • ~ I ~ .: :: I : : :,: : :: I I ,: I : : .. , 1.:: ~ 11.' :. , I ..... .. .. .. . . ".. .. .... lI'" I::'" '1:' ... , . .. '::: I'j' ... , '1:: :j!' :'1' ., :

' I ". ,.: : ,: .. ' ,II: I': ':,'i :,1. ,jf 'if

.. , .... ":'. .\.. :.: ..... : 'I' .. ~; .... , ·V· .... '.' ; .... :: ; ....... :-:+ ...... : .- ~:: i'~ -' : ... < ;I:i i!i

I

' .. I, I .... , ........... I. ..... ,1.

,: I lii.:J i I:: I: :: :I~W

iv=JGMREI2.: l'r r! ~ i ~ I t tl ~ I If i tt~ ~lttl,s~~ L~ I ~~'~~.I$Jctj~~~l~~ f

I I.

IH 'I( .", f M 111 X HI T0.TH'" r.£NTIM[TFR 46 1513 HIIIIIIl. 1\ ".'., r .. (II '>AI·"'" II' A iii: H::I:;:;I: :iJi;:J!i!!li:liIH!II!!11I!ii!PItW:T:i! l~~:iIT :r::Y,: ~ .. ::~; :::~ :'~LT';:~ :---;::. ~. ~ESI Afr.:,I, \(j:: I : 1\4 ','i:, ,;JI~~':: Ji;, i m" ~';:: ,Rft:, jl1 I1 lin: i f'MAX'IMUM' R* ::ji' : ':')1' .' 't' .:: ':i: iii: :;':. ::: / F' i :-: .:: fliP;; "~=.l.~ :1" ':::\1.": :,)h,' i:: ,',' t' ':1 I ~·I~"'.l.iilA. iii; ~ H-:- . . ", . ;"'!+ :1'1. It :~~ :H+~H+.~~~ : ...... ~: ... ;. .. '... N ,.,~ r. n I.US, Iff:;:, :.~ItY.lll: ll "I ~,i ;1 ::: ,:.: i:il . ,: :I;i !II: ii" I..:: :: I': ' :: :::: ':p :t ! :::: ::, ,: ,I., '~":' :::\::' : ,': I'~"I, i: I'iil 1,11' i' j'il" 'I,' II 'i'l II: :i . ·iii I '\'.1 ::;11 ;[;'I'll'ijo1 i::: :[:'1 ji'I': :ni '11i H,: ; :i, :'1::': ': . '; ii ' Pi; iiiililil 'iii ;;; ,I: :;, : J ~:~ :L: ';: ::li,"/idt i:: :t.:.;\,~ 1,!: ~I'r !)ijliiil < .j': 11 i !' 'I,Jt:i~t; : titl l : : .. ::1 :: ::.' I:~~:! ' :.:' ';1: 'i~';"~ :.~ ."i;I~:"- -~~:. t~t 1l+ihtt I;::~:.. +. ~; ... Jyt~. ,:...l- 4L!~~ ,:;. ·;f~~· ~ fW.I!.S4;~I~1 ::,': , : ~ I~. I:' I ! ~Iil i ::11 !iTI iii iii: 'U':i ;il: i!:! i!!i II;: :::I! 'il: :':, .'::. i 1: II!; :lll!ii::! ',:1 I::! i!·· ,ii' '-~W~io i!i, :1;: J~ :Ii II: ;ilfJ:' 'OA-i!i i!i: ~i.?j~ ]'I! :1:' Ii ;10 i' 'ii I '1' I; :;:!I 'I,~HI !HI ;:;: Illi :117 :i;: 11/1: III: '::!:, I: i ; !'I: ':':; !; !i:::: i If~:W:'I: :::: Wi'::' :;,: :;: :''::>AO'(.!I!j~ij iii: ;:. :1:~~~ .;.!H ::.: !:;:i i: 3W.!~~' ~I;'I' I::: fP~g' a~I." :r i! W" :' Ii': : ~ ~. ·:t I I '" dl .. 'I" !lll;:,' I " 'II' '1' , •• 1 •.•• • II I .,., I I .,,, I ,1 ,II 1" ,. :-jl' ". .1. I. 'I, .,;, fl. "I :1 I i~ I I:" : if, :1 'iii 1'1 :11' jill:!' ;;;1 :!ii iij!1 iii! i,ii ':1:1:: il'i- tl'I'~::: 1 '1; i ;;1: :'~; :::; t: tit :'1; !Iii',' :t;~ iii; ~jf: -t ·~'J'rsJ.j.,1ii: i;: I;,.~)"I: it :Ttt1~Gr~~li!;:i;i ~f ci*1 til! ;! ; jj~:i II 1 : Lf~;' liti I ~ it :~tfi1rIFrt Iii! % lFlI:ld!1j(llijil:i:' III i!i: ;:;; :::l/i q:i;! i"l lili iIi: !;i: u: 'i:~lJ1~iil !r!]~ !lJ ii: :i:: !!J~~ iii! :litlj~: ~ rr 1\ ,~ ~ d I ;~ i l q;: i;; f<:I' iii: ii' i::: ~:: :1:i'l: iiill ri: Iii :!Ii iii; 1'1 ! I!;; ;:i; i::i ::;: iil~i i ; ; I :il 1: 'I 1~~I'I::i :ii.' ~t '~:I ;.;.:.oJrP1'i I:; ll!,t:; i:I':, :;;; ;iii. : !Il:: ':1"11: i!t :~ 'I;' ':: jllllj i'i: . lot. il l ~ 'l:+ ':';'" !:.:~ . litH I H-H' tit'" U:.; I.: :~;t I!!; I I: i: ! !::t l:~lli~l ~l I 1 1 fll :!: :; :1;: .:; .. ~l~~~.~ .:!1. !.~t~~;l~ W!., ::1 ~:l . t;'1 L~' :~L ; f;t I ~lf~ • it l l 11 :i ;i~ ~::" ::i l , liP I, .::; 'Iii :d: I':: ::ii ':: ji!I': 1 1' :::: I:;; 1,::lii,' ji' II: jI':: II:: :1:, !: .... :~i ",;.;,Iilill:: llHt+-!1 ;i:: :::'1;:;' iif/I :l!IIIII,:7:7II:: :r !I Irt:,: : II I~ .rvvJ :'.! II11111 iii: 11111\1: ': :1' : i: II: :1 .;1:11:1 "::II!I III !Ii~ 1\:: ill ;';:.i:~~!"'CI.I~:i' 'ii' , ,"'i' ':, '''/11:'; . II i :111111('rfi II i ' , I, III • .

/ l I i :iIi: :1; :~:f' 1,!lI!l iii: it'ji I'Pi i ': l' l' i: llii :1I! ',i: iii: Ii:: iii: Ii! \ fill 'IT Iii: i i '" Y rl' "I' I ',":1 1 ,:" ,,,. '1·'1' '1'1' "'llil I':. :1 1 ' "ii' 11' i'l; "'; ""m:' 'ii :' ,"'.':" jll It 11 .:~ p.::l nq:'~1+! I:q. t+ 1 : II I" :~. i :.Ii !:~i ~::! ,I:; ::!1 ii" I .: lli'l i I i:I"1 ,J 'i' 1:' t It '1'jl~ I::. 'ii I Illi 1\+1 " 1~ I ,; + t i .1.1' , l

l l

.p .: .:: :: !~I " I iii! :ii1 !illl'li: I ill :I!i! ,ii I II: I:!! :;:i :;;: !Iii::: 1 ij,l 1::1' Ii iii! Iq . Ii!: .: i I;\! I:i: iii Iii :1 IIPi Iii :i : illl I Ill:, : '.I I".... '11 I" Iii II 11111 Ii" I I. "I' ,,,, iI:, " II I "-Hi Hffi'l I 1\ ,II I. I Iii ". !II' ," III III ' III, II:, Illil II II! . Ii II: ,':1 i:'I': I 'lJj',' II' .1;: 'j ill II];: :1'1 [I iii' \ IP: .:1: :::: :1 1' I::: I~'I ii,' l' 'l'r'I' i TTj\ :I II' III 1:11 :ffi' i:: :1 '1 1;1',:1 Iii tJII'I'1 iiI' ! III I: . I 1 ~~:.:' '1'1'" II' I: 11 I ; I! 1 Ii 11 I "U 'I': 'I ':: I ' : I ' , , ~;! 11 I t WI:'" II ll! I " I 1 . 'II,-t' IttHIttH i h ir~' :j 11lij h Inil '111111,11 iii! ! [ill Hii iiii 11;1 jiP r II il. Ii I !! i I Ii ilp tlil H!I iii 1 I Jill] Iitti Illi li!l! HI 1111' r I I :r HI : :' ' 1 l il' u" ::.: ::1 lllll:i iI'[i I I Iii! I!li Iii i!ii :1 ;; iii, i :::1 :iil :::"11'1' Ii i\t1' i: 111!i' ! III till IllI )1'1 im' ilil'l ili I'll HI' Illl! : '\1' 1:[ ',' • It! i! I I '!Ulii liU': I: ~. . .~:.: .:t :.:;..t~11 W... i!!!. I • .- U:! !!~ :~. ;::! :::. !:;:H " .• .: ,~:.l .. + !l1~~ .. t ~ :\; ;! .. , :1 ~ tl 1. I t~ I II » :: :i I::: ':' 11 ::IIII( II!i: . :i 'II: I': :.: :::i . I;:: ::.: :::: ::·II;:i:.l iii:: ::,::" I,d li I II :: 1:. :ill II: 1:1 II:: I: iii I: III I '1: : :: :1 1i::I:! • /:" i'! llill :1 !I~: \/1: lit! :.11: . I:: ::!: I:' :il. :::1 :: ,I '1:1 :: I :: ! :iil :1', ': •• Hld !iIi Ii:' Ii 1.1::1 I: IIi I I Ii ,!i , II iii ' :

m

::: ;: I : . -: :: I' 1 : i::: ::,! Ii:: II Ii ~ill: 1'11': I':: t' :::: I I ll:: ; I:: ::: i : iii I'::' :: I' I : 01 : ql' :: I I' : II': q 11 'II t": / j': I' i ::: I : I: I I::: i:: I,;: :: iI : ;'ll' : : I: ! I" 1:1' : I I 'j' I 11 1/ 'I i: :1 I! :: ,!' : ,:i,lilli ·!U Ii[ ·Ii II1I r: : II :ll: I '1: ::It I::; :'Ii :1::1 I I I ::, I: I I: ::1' ill t:l :M ::1. :w:,1 II:: I,:: ::.: ::t! I; II: IL I I I II I I U :' ... lra:i r-;:': ·:~~tttl~! ~tl t~, : .. ·!lI'; t I;~" :,1:: .:: ~ttt ~::: :"111' :t:'lll ~ • !',1 , "': :I'~ :[1" tlj+' I r!'j : ::~i: .. u:: I~i; "::. :~·t~ 1~'llr . 'lii!- ~~ i f" \I 10;; I ;1 :1.Ll:"~,::' I: 'I,j i: lill!! II III:!: :I!; 1:1: III,: ;plt !::::!' :::1 I: I 1:1, !; I: ::, I:' II 'I: : 1:::1 :,': Ih :/1: 1:,:li iI: 11'1 II, d :' I: j I..... . I'll '!JO'I .... II., I", ':: II., , II , , : I \I. ..II ,,,. . ''I' .,," ! II : II . I I " I ' : I, I . I., J I! .. , ,,I. I,,,,,, ; ~ .,,' H / I J ' • ,d • l :~'m::i: :t:t:: .' ;i 11!l! iii!! !iL~1 Iii: illl' 1:1'1: I:I!:! iii: i:il ,ll'I'lljiii :!il Lil il Ii !! i!i! ;111i I lli'(I,li IIi: jill'!I! ::1,1 1 i! I I:ll iii! :'Iii iii! ii!i L. N:QH' l:' Ill!' 'i ill II 11 ., 1,'111j! :: t I:

l

.................. ~ tit. iii 1 ....... 'P \i" H ,.· .. 1 I." f! t· .'\, ..... ' .. li'li . t· If 1 'Ill'" "'li""!1 t 1'1 '·11'" '" .. , IH' .J... . 'H 1i L I U .. t l ':::: : :1:.: .::: III: ' II ::1 I::: Ii: Ii I: ili'l: :li '1:: I P! ::.: :::! ::" ::: ii, I:: I: : I ': II ' 'i I P :.1,:: 'I:' ;:1: 1i':II:I:;1 Ii I I:' ',I I III .t 1/ iti,; : :: :' ::.:,::: Ii Iii I ! I ::! .::: I Ii d I I: I I I ::. Ii' : Ii ' I II I: :: I: :: I: ::,: II::: II IIi j. " : I I:! I I I, 'I,': I:' :::! I : I ::, I :, II ;: :.11 • I: Ii .:: : l ·~· ;::: ::.:: .. '::: i,'i: I·lt :::1 :: , :i:I' Ill': iii: :ill' :::i II I I:: :::: ,,: I'll i::: ::,: 'Iilliji i: i I: 11'1: ,1/: III' Iii/ ill :::i :::: :Ii: I::; [':1 ::1: II IIN~' 1: ' [II' [1:\ ;:1 I' ;, : I : :~I: ':'l ::. :':. ,: ': :11 : : I': , : ,.:::" I::. I! I::!: ::;; .:: ::.1 .,::: :: '·1,1, :l.' ,: I : I ,: ::!II:I lIlli, I: .:': ;::: ':.~ II;'~ ::: :11:: 1: I': I: I \1 ." Iii : I II

l

:.' '1,: .:, :~ ...... ::~. :!!::: :": I!:: ~': ::::::: I::::!' I:!: :::: :::: ::1' :::. ::I! ,I 1 :~:! l~" ,: !.I: :1. ::: •• t ::!" I::: :::~ I:: n:l :1': :: 1f.1; , , !:' I:: t' , II! Hi t: ~ :'::::...;:L.L:;.' . i!i!! 'II I::ii: .: :/':: : I: ::1: I::! :/:::I! .::' .::: .:: ::'1 :':1 :::1 1:1, ::.:, :.\1' :1'1: :ill'l :;:1 II I 'ii ::d !';i ::i: I:' I: ::1::: I:f:': I':! I ::i! I I. :1 :11 I' ': " ,t'W .. I!t'~IDD~"~~.I~J.:.-~""''':.w.:I+4+:.!.:.;,*:.:.:~.~:::. .. :;~~::!..::::J.:ll:':':.:.!:: il;~.::' ", ,,1.1 " ,UI·"·;,.::·' "f", :1" ·,,1'1 ,,' 1, , l.t 1.1 1:. ·'1 :':: ::; 1:: 1 ' ::: :1.: :::. :::':: ,I:: ,:::. : ,':: :: .. ,: i:il I:: :::: 'I' :m": ';'1 :11: :"1'1 :'\ :'1"1 :::: :.:: ; .. 'II: :111 :'11 ll'l :: .. 1::1' I::' ,; : IITfT:1 , ::" II': I: :: .. .,-, . il" .... "tl ..... , - "I' .. j ••• ,1 ,. ."... . .... \. I" ,.1 .,- ""~. 'I' ,I "j' ,I ,I ,t "" ·,,1 '. , I, . "I, ", 'I' 'III .fti.; ~I I ,.,1 1. . 'l!j'l' ,.Ii 11'1 " ! ..

; .!~: 1:: : :.~: Ii;: ::.! ::.: I::. ;:,: I::: iii! :;::: ::: .. :: I:: :!!i ::11 'i:: :1'1' I::: iii: i::! I :::·:U :lr tt ,: :;u :::: ::~~ I:,: I!i: :~:: ::,1 "Iii Hi t!~~U : I:~I ':1: : t ! 1 ~~!! ,~, .;.; ~m · " . .,. ,/1. ,.. .. I. ... ,., I " ",. ,,, I. , ", ,,, .. ...::" 'I I"" I , ., I", I ' I, "1 "., ,I 'li . "II "', "" " . II" ,II' ., 1:1 I I ," I : I' • d I. I' I" ,III : I . It- I 'I" ! i' ' I I

~ l II

, 11.·1. 'I.··· II ., .. , .. i" I'" "". _"I.. ' .. ':, .. , Ii! "II .," ::j: .,' "1 'I" 'I I "1' , ... 1,'1, I I I,.' . "il I' ':I! :lli' ~II' 1 '11';1 111 "'i ,.1 I!' • ~'. : :;: .;; ~ :;:~ ~.;; :.:; ::; :;:: .:;; ;;;. I~;: :: ~ f:~~ ~~ -: <;1: !: .j:; Hii 71 t·1t 1 > :1:; ':;; ;;;; ;:Ii:; ;;;; ;:;. :;:; ;. , ;:~: ~f. :1: ::;: f:-f p:1 :;;I~'; ;;:; fl'; 11'l i ;;;1 ;;;; 1:1(:;: t ;.'1 ~"~i:: _:: .:: ::~: :1 ;.: :1:: .::' :;:: I::: ' ... II! ;:; ; .. :; ~;' - ::: :: ::11 .. : :;" I: ,:1. ::~! .::::: ::: :::: .:: ,:::: : :i ... :: ,," :':1 :.: I::: ::': .: ::': :!, :\: :::: :~.;: ::: ,I :-: · "1""'" .. , .. " .......... "" ".1 ." .. ", ,., ,,,. ,,, " .... , .,.1 .. " .1" " I .... "II ; " ." ...... ". "II " . " .. "" " .. "" " .. "', .. II II. ." "" ,,/. '" ·iil. 'i .• ".! •••• t '" 1.1 •• · I,: .'.: '.. . j: i: :::: .: I: :. ::::::::: :::,:. : i:: !:; .. :' :::: :.:;:::: I, .: 'I I :: .\: ·j'I::; It :;:: ; I : I : :::: ,.:: : :: .;.: ::! ;:.': I: ,'11 .:;' I!:::; ~ : :: I II ; :: I I ~ i:' I ;:: i d 1: i II : I ~ 11' ii'" . ! i' "" .. " , /" .. "" , '" ". . 'I' ." ,. ,. I ' ... ". .., , ." I, ""',,,.., 'I '.,,, , .. , """" " . ,. .. , ,I ~i '" . ", : loi( I'" '. . : I ' ; i . .. , "" Ii'" . II . , : :91 ~i': . .• iii! ::rt ~ii: . ~> if: ir t!~i ::'. ::1~ :~ -:-; ~:; .~~: .-~; '~t· ~i0 .;:: H: !:;!~Ht> :i;: iill :il:;; ;:1: ~-:; ::~ t: ~;~: ~T ::i: :~ :rt: I:~ i:ii i~!i ii! iii! 'ii i;i: ii:: i Ii ii' l ·VJ···· 4'" ".1. ... " .," """ .. 1" " .. ,,, ... "I ". . ... '''''''' " .. ".I ... 1"" .1,. "" ",' .. " .p. ·ii , ... " .... " .. "" "" ". ,," .1 •• "" ... I,lr "+. '1" ", ... , ....... ··1· ·~i··-t 'ill ::; :. :::: :::: ::::: ' ; ':: ::. ::: I ,;: .. ::. .; t .:;:" .: I : I:,: i I:: : :,;: :::: ::: i :, i: : i : : i': :::: :.:; :: .. ,: I: :::: : T : i!.1 i::' : T : i I I: Ii :. : Ii: 111\ i .:::: IJ I:' : I iI i ;~ :: ... -~+~~f%~ ~: .. ~i'I+~ ++ -- .. Hi; ~:. "'~I''': '~;i .;.: ::~. +1 ":[1 iW ~:i~~+'~~it: *H~~ }I: :'1';: \::;: :::: ::7: :W8i: +t :1\: :II:I'~ :,::1: ;;:: :::: S'I :~I;.l.:; ~: :::: 'l'li: ~ ![II i:u:rll ' .. :. J; : ::.' .: · .::;; .. ;: : ... :::: I:. :: :;: : .. " :.: ':1;." : ': ~II': .. :; 11\ 1':1 :1" :1,: t ',' I:: I::: ':: :-,; '~:: ::11 :1:: ' It : :\: : .. : ll:j 'I: : 'I :,:: :'11 ' ': : I it · .... ..... . ........ "....... " .. ".. ... . "I' '" " .. . ", ... , . " " , '" I "I" ." .. i 4', .... I I. , ...... "" ".. .,,, "I' ... I'i ' .. jj' "" . ,. ~I'.' ,I, "" .1" . I·· .

~

. " . . .... " 'I' I.... ,,' ., ." II' '''' I' ' 'I I" '1' I 'I" "II I' ,", "'" I " 'I Ij , , Ii' """, I '... . .. ". ., I ..

::', ~. :::' .:. ::::: :: .. I::' ::::;. i :: . :I::!::! :! I:!: ! 1-4+'1 :iil::::rm" '~":' t; ::: ;:;.: ::1. II:' ::,11( ',:11 ;.': ::i:! . ., ", ---4--: •. L .. - ...... "H~" ....... ~' ............ I ............... ,,+ ••• "II' '''M.1.; "1 -,,+>J.l.. • ~.,,~ ._ ••• - .~ ~ X ... !f 'I

' .... ,. . " , 'I" , 'I ", 'I' , .. ", , . '., ." [I ' , "'I" "'11"/ """ ,d, 'I 'I'

! I ' -:. :.' ::: . ~. 'I ' :! i,'~ '::: : II!: i::: :; i !: , : I: ::: :: ~il .. ~.' .': '.' ~':: :: ':q ;':: ::1, :111 I::: :, : ::~: ::!: ; :! :'\ .. I . "",,.... . '. "",,, .. , I' ... , ,," ,I. " .. ,I. . ,I. ... . .. ", '" , .. ', ... 1. .... "" ... 1 .t ........... 1 ••• , •• . .L .. 1. ... .:: .; .. 1.,. i. I ,: :: '" .L :.:: :::!~:: :L. ~~ .. :.: it; ... ~ ,: .. ,, __ .i~~:' .~.:4~.~ :;~:.L ~::. ::.: :::: :: :!i" .jil I I, I" I' . . .,. :!t

'!'.: I ~ ,~ r ,~, .,' I' . "J)J "r... ,. i' "l· ""1·"1' t'::: W

'. ~/~;i,rn:E'·. "'~":' 1 • i 1 ,L4I.! L~ i t~ I" t." . L~. I.,~" ~O:lJ .~ . 2:3 1 2J41 2~ J2~:: .2 'J' :!~,,,,::,.2f7 . :;3.:, .. :: _ luun 2. ') .. :.1 ... :~:.I.: .~J .1..:. _ I _J. I. . , .. "R_. ,GRelll .. MILES /IU1:..FUELI :".:-. : .. Ji_:. -" .. : .. _ , .... _ .. 1 •• ..: , .... It '--1---,-------,.----~

,-----

,------------,----------------

IA X ;t'·,I"M 10 X 10 TO THE CENTlMrTER 46 1513 KtUFTf L 1\ r~~;£.R co M",.I ''01 ""'''

~rrr.T!TTTT1TT'TTTTTT1TTITt'T1'~~'- I

11 Ii , :Ip! ,/:i! :11 lid! "I!I! .!lllIW !li:bl~:: : ... : ::11 fW~:~:::Vt)! 11il.:J::: (!!Il~j~'i l~ ~i& Ii Ji 1~11!!I !!L~!J!IUll. ill!!llll1: ~L.ijj ,;il~t ;jjjl'.ll:I:L:lilll :'Ijll~,~. :/1111'1 II rh I' i IW: !Jt:IW; :.::1 'ii '-:Jr.1[r:C'!li""j[l:Jtl II\" ';;~" .," . . ., "I' 1M, j ,,~p~ I~~! ,::~ ·P.tH II tit:' !tHw· Ilu..;~' 'II Ii' tf:1 if::JI I" ',....~.ci~fw.'r1',U ~.II(_~ :i;. ''''~'!;....' :1;1 ~ . . . ... :! iil .• :;; : I Ilii: Ui ::F"i:!UJ!: . " '~PH' ~ I' 'M H ., i ,~WJ II I j 'tijJ'IUi:

A

iii iii ';'m"': "+::0 ;':iI""I':"i':" :i:I;~:I .. I i!j ,il: :,;i ... :10 ",.':: i " .. :' 'I,. ;ill :)iL ;::: ::;; iiii 'ii .'!i j:", ;;;i i:' .::: .i: ,:; i"/If' '1':: i'i ;i·: ;' ; f"':' I' "'1 :' . , ... ; ....

rl mm:~" ..... ,,, I. ... II .. ,. II, I, ... ,. " '. 1IIIItiti f:ii 1:\: :,:. :;:, II!: Li! 11/::IUti',;li: ;!:: :i:i p:: iliH: fi:· :1:; :!L :;l! ;!:; ::!':. it:; ::\i :! !. t f rHii!~: ifl I :~i i IoU!!1 ' I:~: :::::;:.: .. ; .... : liil i .: ····1 :.:. :: ; .; .... : i:' ;1 '1'11\:1:: Wit: :1: 8Hk,',:: i:~ilt :;,t1h '!I'~l~ :;:1 i,i ';: iii! !ji: :W~~ .::~ ;',':: 1(;: ;!!i~~ lit: Iii " ::!:::: ' Itt i ,:1' .~ II I l .:: II:: :1, .::: I:;; .::1 Hl':H j.: lil: ::11 ::11 .::' :.: i ., II III ::i;' : I/RUjf.;i:wf"llFi~~~LI·illl::: 'tIl : :!':K!" W:l~;: .:" II. '1'1 I fi ,~W I ~ i11 nn ijP:H p: :!jj tlij i:jl iffl Ii: liil Idl jj!i ill : !iiiLij: Ii ,I Hdl:: :., .",bH,., :11 ,It:: !d' 1 ;i1~i~LJ:lili1q :iji 1 i,lll iii,' 11: qC liD. 'I , : , ... I • .•. • I" • .,' I j II ",' II 1111' , Illt I If III " : I' ,. III ' . ...u..:. .. ~~ ~ ~ I t I'" I ,. 111 rJil ~~t)! .. ~..oJ.II4+H""-M-i: '.lffi 11J.j' fHlI+ 'if!J~rJl'llo!!!+l++: I , H+H.J+IIW1~I-+mH+l1.J.+.4.HJ'K!l#I~1-tI lf ~i ij~i i!!I'j ;ilt II~tl ii!! i j rilll 114,111: iii! II' ilill iii iii :p'!li il!J Ifll :;11 JIr! :i\~! I~ll~~ ~j!: :il! Wi ti~! I!: :!!i?l~~i~!i! ;)f!iv. 'j Ii! !!l jr;~~' Hi I!! iU;: 'jj~ I 1 .:: :::: ::,~ :': .'!i :!I::, ,:! Ii!!!'!,:: !:~. !. ~!, :I! t! liP !:!~ Ii:! ::!! !1:: iil:;i !III Iii: ,ill:; "J+.l ih ~ ;W5!i~b~~:: :':414: : ! !I!: :I!! !~f~, !':! !:. Ijl i ~ ~ ,'l: I i ::i J!: :::! :;:l ::li i:l': jl:[ !il :j: 1I 1f!: !~; itil :I:::lil it: ill'l I 'iI' ::i! :,:: ii! j·t .. iii j;'I: :Pi I:,: :: .. j: I;i:: HI"'~ i: :~i!~ J1;~'~":';';. :;;:I:+!-: ; !:+'iIHl:ii il~. ~Ll lij: ;r:I'~ :llll~i t ~! !

l ..... ~i .......... ~ ..... '.u .... I.... .1 •..•. I., •• 11 "II II, J ..... , •• 1.LtJ- ...• I". I' "ii" . ii1r .• "'''' .1 ...... ,..... '0' w.., I' ~ .•• I.I'l·· .. , ~. II' t~ I lI.l!~ . I I~j .U.!. .

fB • t til ...•.••••...• ,I,. 'lii]I" 'I" ,. ,.j ii" "" ". '" II "" "I" .• ", I . "1 ii I' ",., " ' , 'I I,,· , •. '1' Gt'bO'" . '" .i" I' I " ~rr:" i~ 1'''1' ., ~ I:' .... ,,-:1.' c.:.:J ....... , I' , .. ",. " "..., ... , ".: I ' ,., , 'II " . " I' : i • II . I"" I:" :: I , .. , I. "'" :, ''';+I' i Iii I' i'/' I: '1" ;.. '!' ., ij, I ~ II: :t::~: .... :,:: I::: ,I :1 'l~~ 11:1 ::1' ::1 :;:~ ;:u II': Ul ,~:: :~11 .:: i::: : :1 III' I . ;:;: il:1 :j,' II:: :':':' II,. ~,: :"1;. : :1 ii:' II':: I.. III i1iil~ I ."" I i i Jj ii~: :.:: I:: '~I: !:::!iI H i'I ~:~ iii: ',Iiii :!!:'I;II'l 11'1 : I:::! !;:; :~ii ;1 ::i: i 'j: :;;. i'lill iili ,i:;,1 Ilt:'!r!I.11 iii: j' l'j; . iiI I !i; ii.: ::i: illi'I:li;"L iY 'Ii!ji 'i:i ;'ii :,'m": [1"ljl' ;: : L"I :1;'~':;11; :f1:iit' il': 'ii; 1'" I 1 n:"I""-'~"" .... i~ ~, .. " ...... ··"1· II , ..... , .......... t .,,' II! '''''' 11· .... p,.··· ft····f ";'[1'''''''1' ·'t· ... "i"" ., I.: m" '1 :: : :: :::. ::: :,::.' i '1::'; '1'1 Ii::' I; II:, .,:, :, 'I I:::::::: I .:: i:: 'I,': II'::':·:: 'I';' .:: I: :'::: i: :: I I:';:' : : I' it: : I .. ':, I:: I Ii I: I I; ii' 'II : .. "Ii '" ,.. ......., .. ,' ,. ""'" .. , I ; i , :' . "I: i: i ." '. II' I, , i II " , .. , II" I ."., ,I" ! I' '; i "'''' I 'I"" I, i i '" III 'i' III I·: ,I l lr llin:;t iiU[~llU. iii: ~j :;;~~l iiitiin:if ~ ,i';! t:,'11 n;l,!l :\1, ili:,'lll i;I:[: i;t:rl;i!~.il; (l'l;i iii!; 1;:,1, iiI! iii! ;:i: 'lili !m!ii iii; 11' [I: II ln ] ii~1 !i~:i U litlij!!;i: [1 ir ~I;ijl f'ji I: ,P,:.. IWllli iW.,~·\l ' , I' .. 'L,;.;.':" ... "::" ..,. , I' , .;: Ii i .. "., .. I .. , "., '" .. ",'"'' " 'I " .... ,:' . Ii 'II ,., " .. ' i i" I: i ' I 'I I I ..

: i: . UIIU : : I j': I ~: :'.. I : I I ~ ! I II ; :: :;;: 'j! i :::, I ~ : 1 I : . : I : ~ ., 'i.:.l !:; , II : ' , ;; : I !II:: I I::: 11 iLl IIl.;!;.I I '" : : I • Ii : k Iii im' ':H; ;.; ·:1 ::: ;'1 iI' :ii'l ,: I 1 III! I: ;:" " 'j':: :Ii: ill! :::1 :::: :' ! :::: ::T1'l :i!1 Ii iii: :::: i: l~'::: I ::il I::; I !! ',!I: ii, III \'Iit !: . :!. i ': I:.' 1'1 iii' piP l j fH~' ."" ., j'" t 1'1 ., 1" I, "II H" '11' ,,,, .. " , ... 'I' ,,,i ........ i I, I'"~ '''I 'L "t· ,." I' . II' "., 1"1/1 ' ,. i • 'I I ' .L! lIiI H

t

!ill :-:L ~:: ":TI! ,:~ ::.1 , .~.! I" ; 'I iq:, lr.~ 4jf :~I~ 1;:1 ~:': ;;:: :I:i riii ~::: !::: ::1, :: :!!i !::: 1.1 I ! ::1 ~:!t !~': I I: ;:~~ ,i!~ 11 i:. :: "IIi" :'j ,. i q :: Il lI;:'tHt+HttH H jj,:::':!:: :: L:'" • 1 I Ii :! I' ,I : i : I I I i ::!: I I:' :.:! :.:; : II i :: Ii: d :::' I::' :: ii i' :::, :.: I j\ : :::. !:: I .!: I I :: :::: :: I . :!!':: ' : \I ,I I . I i I :!!

l tv 'I H!: :::1 ::: :;:: i' d!1 I!: 1:11:' 1'.,: i;i:' :!!: 'I : I: I' iI:: I'!:: :::: j";: :~,I ill,li!l 1,'1: !:;: I':: iil'H!1 :i :,: ;:i]' ','IP :j';'I' ::,: II::: !i:: !:' ::!J :t:l: i,',: 1"1 ,ilillj' 1\ 'I' 1:1 I:j!t Iii l I ~ ...... , .... .~! .. , II. . 1.: ' ~~" ,. I If' 1.:" :J I .... ,,' ., .. , ,... .. ,., iii'" f+~-' '. ..,.. . .. "" .. t. . j I H Ij~ I' "I t' e".J : :~I':: i::11,:l ·:I, I( I' Iii 111'1 :: ,I, 'I I ::1: 1 'I II iii: i:jj' :::: ::i:j'j' :Jl i'I'1 ]iii I;:; 1:: :il it: r:-t i :; :::: :::: :I!:: !1r: !:::i: :-:11 I: :~, I ,j In'' I : U1 1 : :, : :. 1tIIIII_ :: I .:: ".. ': .1 ,: ::,: ,,,: .: :::, 'I:: : i, 't1 ~ili.: ~~:: .:: :: I ! I Ii ,I::!:::::: :: ::,! I i': i~ ~ .': ; i ," " • ,:

~

i J.m Hl~ :~n ~; .. .d lll!d tjlilljlll i iii! tl! i:i\: ji: Ii lit! ~:Il' j~lt H Ii ill'I' ijl! :i:i H iii: I: :1l1 J! II ill jii: iiii fll'i 1i!!~iIl ;'i ;!:n i1l11l !! ' i! 1 :~' ;~!: :1.:,', ',.1::, :,:.:. i.!. i.,:,:, :.1 Ii! i,1 'Ii! i I::q :!i! :I':!, 1'1 ';!I :1111 !;ij :!iili:illp: I :: ; I I!!:i 'ji,il'l' ;i~ ,: r I;i; :1; i f1l:j 'li' Ii" :1 i ~ II n I:: : I 'I :: L : ill I: 'I' I d It';:. II: II ~ I!. ;: , II: i I ! I : I :::. ! I !, I. 'II: :: III : ' !:;: II:: 111 :. l' , , , , ~I l ;C ::: i'I:::: .:! ::i: ; :1,1 :!!i t'li: i::! il'. ::tI '1:: Ilj :i: i::: ::'11 ::.: ,1'1! i,l! iii :i: liii ::: 11': I[ !:!i!i ['j'!::i :i,'j' j'li.ltih ,:1; ':1' ::11 fil 'I::! I' " i' :i!: I i1'11'm' ,I : ' t: I ::E:0II:: .. :: '.;.! ;; ... ' I::: .11 !' • !!!1 l:: :;:1 :d. ::,' ::: I: : .::: ... : I:H I;:: .1.: 1.11 I! !'I' ::1 I::: ':. :;:1 'r . "~ ,::: .. ;1:1 ':1: III; I : 1 ,.:1. II :: II; I. I I ...... .. .... , ,'m .... ,., I'" , .... .\ ,,,I ... " ...... , "I "f " , I .. , ... I· 'Ii , .. , ",.1; 'I .. " II '"1''' II'" . .. I ., I ' " 'I ", 1I ~I I I ".:':';" I"" ,.", ,. I" .... ,.. ... . 1'1' "· .. · .. 1 ... , ... 'P' .. II" ,", I' '" ", 'I' '11 "'I ... ,'" IlL' Ii:: .. , 'I:' I: III I 1 ! .:.ft~.., ~i1: :,! ':11 :':1 .:::~ ;1.:: :_:; .H:l!..W .~~l~;": ::,1 j:.:: Ii!!! .: II ::11 :~;.. :1.': ':, 11'1 ! :11: ':1 ;p .. ~.g.i.~: ....... ~+~~H- ~~ ':1 , :: II; '!I .. ·IIi.

·~ :.'., ::1: ::: '::::':1' .. : ':. '. ;;1: .: .. ,'::;: :1:' ':,!lII:: il ,:, 711 :: :'I'I',1i i::]I: .. ';'·:::·: 7':: ",: It"I 'I: : I::'" I: ':'llii;::·!I: ., 1 Ii : : .,:.4, . I:: .: I 4 : :1 .:: I I:' " . ': J' ::::.; ... ' J :: : 'I: ,::: I' 11·, ':, : 11:," :. J : I I:: : :::: ::: .. :: I.'. :' I:: J , : i :.; i:l i: :: 'I lit I '::!,! I':' : .. ........ . .. ':11' ' ..... 1 ............. , ~I '" ...... ,... . .. ' ." I " .• " •• I .. 'J .... 1, .• 1. .... .... "...... "!" "11' . 1. ., t .... 1" ~~. U. t" '/ : :' I :;; ,:;,",.: I: ..:, I:' : :' , :,':1 '::. I": ,i!;:: :11' :': !I.: : I!:: ::,1 ::: :" .. : , I '1.1 ,: :1:: ,: ::1 ",I ' , 1:;:1:,: '1:1:: :

i

· ., "., , .. ,I , .. , , .. I ..... ..... .. ' I' . "', , .. , , "" .. Ii: '1" .... " ... ... ., '." Ii" ;; .. , "I '!I . I '''ii... '. I' _ ~~! II' "'!I""~, " .'...;J' ,I,· '4,,1 , ",~" "~,I' ~~~!~~ '. " " 41~11 1111" " ,. II!I,"" , -I :;- : Ii: 'ji ;:i:' ':;" .'- .~ ... ~ :: ~r- ::-" .... :r .... '7~ t· ':: \ ::i .i:: ;1,·' I: ':: ;:; ::. :::. V' . ~ - :: ; II:I:! 'Iii :1:: ·'1 ji!1 -il :.\ i ::l! !I::' 'Iii: il'~ i .. , 'II' -I' ,.11 ", " I" ",., .,. . .. , ... , .,' ." " I 1 II " .", , .. , . ,,' 'I 1,1" I'\! 'l " , 1 :'1'" !I" · ........ .." .. ,' ... ...... ... ..... .... .... , .... ....., .,. ". , .. ., ... , .. " ,. 'i I' .... ... ....... .. ..., I" "'" .•. " .. I.' t'I". I .

· I';' . : I!' 'i:; :;:. . i!.· :: . ::11 :!:. ::. . ::i !':: :!: iW.ii. :I! :i!! I:: :: :': : :~: ::. '. ::! Ii:: i!! :!:':I ::11 'i I':: 11 I:.:: !i,':' til il,!!

~ __ : '~ " .. ,.. .~. .., .. . I .--c' .. ~; • '1 ... , 11" . , .... "'" ., .. ';7 0':":'.; .• ~: "" '''' .'.' "I :J.. I:" " • .... ..II '

~

.11 -. : I -~ I: :.:: ::1 .:~ ::" .~ ..... ~ ;-'1'" '!f; ~.:: "; :, .. ' .7'. :C 'T "': 7: i:: :/1, .. :: ;::\' :I:i :Ii: :. -::. C~·'· C I:! .: I':: :lli .: Iii ~: .. ,nT ';" '1' i' : ii: .;/i iii I: .,1 11 l .v. '1 ,~', " ... , I' - • , ' I,. Ij , ,,' ,I, "I 'It II:, II .. ", '.-, , j." I .,,' I. 'I '.'1,. , ,ill,' II, "i' ·VJ·" .... . .... Iii '''1 .... ........ . ". .I. ....... .• ....... ....... . ...... "" ..... '~1 tt" .... :.j! .... ....... 1 ... " ... '"'''' "ii .......... '1" .............. ,.

l.&i':: I I. .:: :: •. '::: . : ' .' ·oi; ,oj . :.: .. ::: .:: :;':;: .. 1 :1: II:' I::: .':: r.: :.:. :jj .. : : II:. j:Ij'i I Ii":' ,. . ....... " :]i· ~.II- .. ~ :~+ :['ft :::: :·~·f- ·····1···· :.':, .: ::11 + .. :.: ,~.:.: ~L. ·~H ::;i '·7 ,:.; ~;:.::: ;:, :::; :i,'; ~:;: tit-·~ ::~~ ~- ~< : ::~ :'1 :·.i·F ::i: ::1'1 :::; 'j:IIII\: 11\" :.j Ii III! ,,/t " I I I: : "ll, ,:. : :;;: : .. : . , : 'j :: '.:. ': ,:: ;!:; i, I Xi; 'I; : .. : ::' :1 : : 'I:~: :II'!' ;::1 1 " I II ::1 l: 1'1' I ii 'l · ,: . . : 111. :11 II!:' : .. ':... . ," .. ::: .. : ... ' .. ..: .: .. :," I':!' :::: : •. : 'II" . , .. ::. , ...... :: .... , .: .. .tt: ::,' ~H!': I::, 'I': '1: :1, . ":: .:. :1l~ :'" :.

~

'-......... . I' . , .. , .. .. .. ., .., I' ... , .. 'I'ill ... :1,' ...... ':'1' 'II'" I'"~ .... t", Ii .'" I' ',: 1',:1 r,-. '~, I:' ::. :::: : ..... ~4_ ..... , ._ ... i .. , ... _~~ .. _: . ...:. , .. : ....... ".: ... ; ~ .. - ~:.: ~~. ~~~~:Iiii~ .. H: :Lu .. - .~. ~ .... ~~ ;.+t >_:"1: :::: "" :~~~~ .. 'Il : :~:: -:~: :: ~ ::, ::: I" P .. , ....: : 1"1' : . . I .. . ::.... ::: :1. :. .: : .. II: ::: :I::.:,: h· l::: .::::' iii: :i' '!i

t

:' ':' "j ....' .... : .. :: "I.. 4 .. )~: ~'I~' ~1~' ::. :~: ::': ::;: ~~l' "11 :: . :~: llilf~':~ 1~~: ~~: ~~: ;;:~ ::: :;'1

I ,.., I.. J.,. '.. .. ., . jI..... II I ... "I" .... ,' ." " .,!

_...... .' .... \ ...... : .... ;.,. . I , : ..... ::. ~i;; .:.:..: .... .:.:' . ...:: .. - ,I.:' :,;.;. -~~;.: :~; .. ,. Wl!~"':';';~· ..;!: :;..;8.

, '. . i i:' ,. . ! i: ., : j: .:::,:!: i!: . :: I 'I'! : i: :;i: ' .. I,' .:,. . ..... , ........ ,,,.,. , ...... ,', . "I I I " . ." :... . .... Wll ': I i 1 ! . i····:' :. :1.:' . :: :. .::;'.:

\

.• C FIGU~E ll>.~ .'1' L~ t, Iri It If .I'r ... 'f· 1 i~I~.2 °G~~~Jn t ~:s~~ 1.1uiL'~·· .. L" JZ~12r t3r,'1 !

i I I~' )0 .' ". t 10 X 10 TO THE'CrNTI M[TrR 46 1513 Kr-Uf J fL l\ p;.~, R ( ~ I "-4111>' 1" II A I 111 ill!l!!tlld' '11"!!'II "11I ,!i) il!tlJI lUll!! :;!! II:~M::! ':'~WTT :::;r·;~:i ;:~ ;:rJjl:!:::: :I:;~;i'l VI:! i:!: ,I:: ;!!I :!: II:: !!jl i!,I...Jt.l., ;.::LT. '1 \'MJ' 'l~~' ·H:I· ~'" ii:i'J l · q:: :; 'm" Ht ~Hl ffdl ,Inllt· .I~.l " •• t It :a:~.' .!!, .~~' , ... '; :~L:: I:~ '; ::.: ;:~~ :I~ L:: ;UI .1·I~j 5i l;~. ; ... ,- .:; 1:.~! ; .1: . H~I+tJ;' I: 11\' '!; ~r .. c;JC il J ~J riJi: ::;1 ". ,j.. .. :1;: . : :i: :::: :!: ::: ;Ii':: , FlJ.i:I·." ~Ap'U'" I . M" p,iJ 1, ,. ?11'1'w!r_ I+llli+l-l+>+JII ..• i" . ., .: ~ ~ r ... . '. ~+ . .!.1 ' I ,I ,I' I· , I, , I ' "", , , " ;, • IV' " "I .....: r "" . I I' . i m': ':id· .. · <lii::M" 'ill:' ::,. iill ::::\., : :,ij ,., ··Ii·: .. I: .. ,,, .' :;i l ·;· , .. :::: q;:1 :iii i;:; !i!1 ii'I'· .' .. :: &;:j i: ;;. ii, :'1': i· :1111-'tt;~ii:: iU:j' m;i . li'i' : I f.l . " " .. "" •. ;: 1;';"'R~"": ~IJ· :::: j: 'II:': iiii :::: ::l: .::: :: •. :.:: .,1: I:;: :,:. 'll "n" i':: :::1 'r: .::: .~Il :; j i:.: iii: 'IP: ';iiri'::' .Ii 111 j .t 11i i ! : ~~JrIMI: ::I'~' .. ~ I ,:1 i!:ilill:.! !I ! !!~~ i:ii :!:: <ii ::;; .ii I:!i '!:II il q!. !i;: !:!! !,~.i!:~i(: !::: w~ :!/lb!I:I!!:~I!I'" ~ I! I,!:! !+~ 1 , '; ';I~:": ,00ill'I··I· .,:jll'jI :;:11';::1·:; ':'II':~' :::1 I; j 1:. :I!!:;'I' :::.:: .ft"'U'HIi.~:JL..~' :11' I::; "iii I'; .:I;l51ij(·l.Orl~~'''':.·: ::: I;",I. :!III::; 1,1t ~;d • 1~I:J' I: .1 ,,', "'! ' I., i ,t., ,II ,," ,', I "'III "J I" I' •... 1, ' n\.j N,~L'7 ~LI: " ,.,' "1 ' ' ,.' , I P'!~ tI" 1" 1,,;'1l I" I,., ~ 1 ' ,rt ' :;1: :!: li,::: I,: ::: Iii: ;:: :;:: ::;' '. . ... ..: :;::Tr~ ::1 : t :1: :::~:i)J;'I~I:::: 1:: 'il~h~~::i: lii1 ::1: I~': I ,:"+ItlIHH'H+!+H++I+H+1I+H11-1+++1-tJ.m II. I ," II ": 1"1 ., '1'1, ,j, . .I. "1' I'" .,,:, fill -H . , .. 'II "I I' I " ,1.1 ..... '01, ..,' • II III II .; " I ~ Ii ' 1+I+H.LH *',T'++1,· :::; ;:iitlil: ,';: ii"llli ;; 'i :t1t;,: 1::i jii :::: Ii iiii ;;i; iii! ;:1: iii flf:!'$ t~; a;~ii: 'Id til;! iii; i'll ~::I,,~:.i ::lJ1.:: iii: I;l·~r. j; iii: ;i;;I~I'~\ 11.1; l u.

t . fl tlt~ldittHlrrll' 'l'jjJ: ' l' , r ' : ~I' 1i:)I' :~'I' :iij II' rliild :! iql iLlil :!:. :~I.i! !1 ::11 ~: fiN,t!jiHi Ih1 n.:: :1 :'L~~IJ~ u,;: iii; IIi,jr!~I· jl!+h !!~; ·li.ilni 1+; ... .w. , ....... ·.-...l.JUL , l t. "11'1' I I I, , .. I' "il Ii 111'11"'" 'il "" ., ;1 ';1 ' .. , 11'1111" "III" .. 1 I ," ;t'~ e." III !I:: '. I :Ii' "I' ~'J)I 'II r l

1 i

III; i;i w.;iii il~1 illi W' ;!W,~,; :iM iii: :;: if;: \'1' Li fW':: .:;: TII'I ~::; "n" ;t:l . il .::; ii .. :1'1 :;;t p:j ;i + : !-l..j'; 1-rt1~·~i ~H~i iii: ;li"l'~W:; l'I!li :;'1': fJ.1L.JJ.l 1: ill i H+tIIHH+ .. II,+++++u.!I~ 'I' +1' !I :... ! •.• ;;1 1::: I!; ; :::, :;.! ,I!j'!' t i ~:. :~:+ t\:: ~Ii !!t L!.!,;l :~: .~ ,li .l V,iqrv.:! i-1 :!!1 H- ":1 q : ~.l.!;t.i tl' HttlH1+lfl'!' !

'11: W; ii: I' II Inji' I :!,j ;.:: ::; ':::Ii; II': :: :.:: Ii': .:i.:1 iii, '::1 "II/I :: ' 'I ;:' 1'1:1 :':1 :: ,:~ :.ttJ~:.II .... , 1'1: ::':rlir It:. "1: ::wJ,;'!l+ : I !HiIi Wj Ill' !! II I III: I' :1" :1:' ::1 I::: I :: !Ii ::ii ilL :iit !l;llilil ::i, Ii: :;! I :i! Iii' :Iii :.' ~:IC!{~~:: 11':litfirill iiii lJii t.rl(I1..t)1 Ii l i :.:: .;; ::~' ';; I i It'l'i j!i :::1 iii: iil ::i;' j';il ilii :::,:. iii: '::j ;![': liP; iilt iilll:;j: i TTI'I: 'lIl H'I:t~1 :.:: ';ii :::1: \i;.iliii 1:\'i: :oji i::i :\:j: :':j ;:i'\' :i; . i ii; '," i 'i" "'j, ' ji :w. ~;: ,.~. ~H .111 H ! 1i i:H t!:'t-;~ :::4 !~I tl-+':~ l:.: :t~-4 ! I,' ~l Li- Ii!:: ! I ;~tl !++I tt ~'Ih" .! ~TI' T' It;, I. 4. . L Illi Ii rPi::l' ill i: 1111 Iii Iliilili iii liiii iii : I: 1::1 :::: :!i% liii liP i Ii' : II' Ii riiil: ! iiilillL Jii !lil/li!: 1111 iili tiilljl I II' I I • I!II t hli :~!: j:~'lllH: !; Ill; U i :liH: Ii.!! :;:111 . i~:! ~:ii iiii Ii ,11' PI ! II II! I ~: liU ilili :tlll!l!! ~'lj Iii II ! llii ilild;!.1 '; I' I Iii: ~I : I::;: i~ 'I' :it 'i: tilt I: 1 'HI ,: +il'~; t::l~ ::ii I:;; iPi fi.1 i: iii I It II! 'I T: di '1 i:1! lr;i . 1: H rili [inn-ll:i Iii I Ii tt t HH+HmHHI·J.I.Ifjj~!.I.J.I+I mJ..I.uw~.:",IWJ~, :il :: 111:1 iii I I': II:: I ::'1 ::Ii I.:: ill II III I II ' Ii: II ,i ' :lil ': 1!1i~ II I I: iii' i i J'i ::!!.] l ;!i.! '[ii liP l !~: im!! [::! t'Lt:Ii II' Lii iii! ii:; iii; III ill I i I ii ~Ii!i :Ii tll iiij Ilrij til l' i: tiL(i':.jj;1 II' I lli I: '; tIll" , I++l-ij~I.: t fit; ::1 ,itt I : ::;flil:' 1, t : 11~:1 rr': ;:tt \::: ;l!: I:!: :111 it: iii:'! . :: r:- 11+1 :Ii; ;:f: 'Hitj !HI ;: v'1 .: t ttl l' I: H !+HtltHtl+H+lfHtlfHHi L 1'1. ., III" I , "I II, I II I.. 1'1 I"" . I "I";t,, .". 'II!' .I.! ," I I' "I,!.. I! ' I: ill i' I' Ii, ,. I ' : j II!'I !, 1:1 II " I." I I H' ••. I, .. , ",II Ii til! Ill, +Itt 1111 I II ,,1,1 1/ • I if HI I' I ',., 'r ,,:, f!

~I.l~l,:; i:.i: ~:il 11 tlU4l!lll\1: liUIJ.;lIWI' lll~Pl illl iJ11 i~lj iUi jl~ ~m ;l!1 ili~ j Jl iiw j~U I'll' Hl~ !It!ll) II li~ UU ! ~l't)t iii! 11'1';' ~i 1. ' tHtt!+HilllHH.H+tH .fHt1-HHtI H i,~'1! I.:'~i rs, ::,"1 :.' I' Ir 1"1 t · .. , .. I,,:! 'I' Ii "~ "II ,.1 'I" 'lil ill I ,!!, .]il I:! ,', I" Iii' Id· IT, . '~i! IIIi II' 1,1'1 . " II 1 : JLL 1m ~ II. I t I j ;: ! II: II: I ~. II :: I ;;: I:' II::: : I ,11 q I : II :: I ; 'I • '; • III: !" I' I q I: ~ I ':; I: : I' I l :~. !il .::' ,:1' ·:i i i III ['i ;! ~II' ::illiiil' iJ iill I Itti: :i!:t· :i!i iiii liii !!!II ill!1 :d iii! Iii II:!! \i:ii i 11 l'jlll :: ! \'1'1: :I! illl! :U: ! !lli iii lln" 'I i I iii 'i 1i M 1:::' .:, ,~~! 'il ,:: I: Ii it n fh ,:~, ::[1 :1;1 K . ~~ !::I 1~:: 11'1 :·t, flU' :ij.t) :i': I I, ::t nfl' r "tl H't n:' .: I!: :, 1 ':! ~i' lilil ','1 ',' 1i"1 III .. f,.. •. , Ii'1 I I .. I. ..... , ,,,. I" "" I'" li!i '!'ii: "I 'il:lp·d' . I II . 'I" I ' III, "lh'l HI :.1 :.1,' !II'I,

l 1

lI,i, I I:j ::~',: ,: I H : II If:!!::: !:: li:1 I:: ::1: t!l: Hll :!t it ;' "il 1111 I I I I 1111 I III I II :,1,: I II I ;:1 I : i!'!'i ii :::i :1 IT: 1IIIil' ii i iii! iii :::: i. • :i!j::i ji! ::/1 iii! I::: :!['. :11'1 !,liJ 1:1 i,';: !jli 1 . i :I li'il:n I il' I IIUI' l!ji~PII';;: qli :111 iii! il'\1! l.l1ill lilli' \' l' tl'n ' l,ij!dttl!!jU

l

l ; :1 :Ij :Jli: '::1 ;i "il ~~ ltf: I~H j~:~ L: Hi! :::~ Ii dl ::il }\ Pi: !!::~. Ltl :it i::i \(; t I Hfi iiil i i 'til! 111!;lfqj ;il iilt~l!i IL! ilil pl I::n ~II! :111 n : oj .• :11!'1 .. _ .:~ ,:: I:+-l- ::: :::: :;:: I::: :: ~H+ I ~;:i tJf :::: ::1: I:,; ;::: :::: ::!, :4, :::: "::: : ,:iI ,,:' ::, II.: : ,,:dl!. ': !I!'!::: I'll :" II: ::1 :1:: :H' " l i · fr ,." "I,· "1' "'1 ." ....... , ". '1 "" "I I'"~ ... , ...... " '" ... "" .. , , .' II'" I .,1 1 I'" I", \., "I" I.I,I~ 1;11 'I" 'Il jill I' I': '; II! ,. U' '11 '4\ UiI" :.1 ; -::rn": .. ;': .: I::: :1' 11;1 :.': I:: :.::.: : .. ::::t, 'I: :.;: :::: :::: :::.:: ::11: :: ::!: ',I: I': ::;, '1':' ::1 : I ':.;: :1::II:~~i 1.:1;,1,;11: : ,::1 11!li I 11 'I .·Ii, i!

~

j ~ . "ii' .. .. ... til ..... " , ...... 1. ..... " ',111. .. '''' "" ....... "" ... , . ., .. " I. .. ,), ....... \1... . n" ; ..... " "" "1' .. '...... • ....... • l' :. : iii .1: : I::;: ,:,; :::: . :: :: : .. :: i:·· II : .; IJ ;,::.::; '.::::: : j: ,.: :; \I .. : Ii::: : i:: : i;: : II I I:: :::: Ii I: Ii:;:; i:: iT, ! li:;t : II: Ii i Ii:: ::! 1'1: I !!! ,:; : iI Iii Ii:: i ::" : .: ::~I : :l!::: ~~,:: ,::' ,,~: I::: :':::: ::~I ':;~ ~ I::: :::: ::: ::~: ::1 :~.i_ :~.~ ':: :::: !!:~ ~:: :1:: ::: :::: 1I~ : .. : :::: :,~II!>: ::.! ,::1 :: : .!:: ~ t:' ,::~;~' I:: ~!: I!I::,. " ... 1.". "'1 ' t'" ", .... 1 .. · I,., .... ". ,,,,\1" .. " ... , ".,... . .. "I·' 'I' '" .• " ".1 "I' IW' "" .'" '11 ,. ~ .. It, I "II "., II. .. ·1 ."." ~ III 'Hi 'I"I~ 'jl ' ',,",:: ':j:' ,::, :::: :::1 :::, :::: ': : '" ::11 ,::: ': I!:; ::" :::1 ::;: :;; .. ~: :' ,;:: I,:, ::1: :~L :::1 :;,;, : :'1' :::1 ;,,1 I:,' .' ,~':I 1:1. I: ~ I: ;: 1 ::1::1, (I '. ":1 : I .~.,..... ... .. ,,, ....... , ..... 'I" ... , I .......... I" ." .. II .... "I' .. , .......... 1 .... " ...... " .. '1' 'I .... ' 'Id ..... ", I'''' .. ,1 .. "'I "" Ii' ... 1 .. I " I t J n I.. • j · ::: ... ~l- I:;; .::: :i;ij: ::: ;:: .::: ::. :::; .::: ::I'i I:;: ;::: .:1; :,i l :U:: :: :i :::: l .1:: '::11.:1 :.:: Ill: I;): :::: ::IIIY .::. ij:: :::. I;: II: jI:: :::,:: .111: 11'1:1 Ii:: i :, 'i: · *,..,~,~ :::: ::1: ~!!_, :::' ,::: :::: :>~ ::~: ~ ~, :::: :::: :::: :~!! ::: h~ ~l~ :.~@~~ ~~~ ~:: :::: :::: :1!: ~!I: :~:H~~~ ~::: :::: ::1: ::': ':~. , :: ~~ , :::: :: :[1, : :':: ::', ,I:: :'~: :.

". ,,, .. ". "" ....... " .......... "'11" " •. " ... " ", ... , ...... , ". l\" ., .. , .. ",' " .. 'I" ·'1' ........... II" .. , .. ,1 .... 1"'li I' .,' 'I"" 'II' I 'I" .. I, ', .. , . 111"1 :1, ,:, :i~:; :::: I'!l I:: I;: :::: ::, ::1';: :'1. ,: , :;1: :;:: ::1; :';'~; :~ii ,.:: I::: I: :1:: ::;; 'I:~ :1:: 1 ';:': ;:;:, ,;;; ;';, I:; ;:;, .:!: ~'" I::: ,:1: :1:: ;;,; II: I:' I'll': 'II : 1,1:.

J l · . .t. ....... . ....... ,u .................. " .. " ... , .... ,,, ......... 1. .... '1" .. " " ........ ·• .. Ii ....... ,II. ''1' "" .... '"'\''' .". "" "" '1" t····· .. ttl' "'I't '1 .;.(, + .1 t· ~t l · :!: i:;' ':!! :~'! i::: ~:: ::' '::: ;:,: ::1 ;:,; :;:! I!': :j!: '::: ::!! ::: <il ::!I ;;1; I!:: i,i: :IJI :::1 ::: ii:' I!I~ :::: ::: ;;:: :::: :i :i:: :II: :::!d,I:III:::: i ;:11' . I I ",,, I '~:,' "':l u;1:J.i~' II' .. I. ".' " ...... ;~ . .:.:. .. 'd' .j.l.;H4':.4 .~;.!. "·':.1;d.;.:.t.: u:.' 1",1 I.. """I.i.H It.;. .. :lif!:~'++i' !.c' ;1,· II, 1111'1111' " I ".i ':;:.; : II:::: : .: r: :~ ~. :':i •.. ~ :',1 I;:~ ::1': ~.:: ~:: ... ~:.: :::: .;:: I:'~ :i:: :::1 .i;\I\:: r:r": liT :::1 '::: '::; (: I':: il;; :','1 :j .. II: II': ::1': ::'1 :il' 1 11 : illl ::111'11 Ill: I"tl! ii' , : : : ' ': , ::' ,':: :::: I': : : : : : , ',:::, . '; : 'I I: : i: ' : : : : :: I,!, ::' I I :, 'I:, : I : I : ~ : ,::': ! I' I! I ! ' :: ;;:: ,: : ,:;: :' ~:: i I .: I: ::'!: i I', II: ' , :: I 'I ; : : It: I · .:: .... :.. "I!:! . :. :::1:1: :!: .. : ........ : ... :.1. t·::: .: .. ::1 .: ":: !::: ::!! I.:: II:' I: it:. I .! : :: .[! :!':.:: I::: ; .. I:;' :1:: :1.: if:: :;:r:.: :ti' ::,' Iii: II: ':.: :tt ~.~ . L :!

~

l l I~:: ~ : I:i: ::~::1~ .: . ::.. :!: j: ::1: .:1 :i :: ::::::1 I:: hi Ji; :ii ,I:: : :: I ! iiii .i::::: i . Ii: i!:! ·!L i[i kll I: :il iii' :11: W: ::11 ::;III:i 1.1: II ! !i · ::'" i:"'~ :::: --- .................... ~. ::" ~:-:-I"" .... , ": ~.:: :::~ .... :::: iI:~ ::f: ::.111:·: :::: :11: :'Ii :.: ~:~~ ;' ....... T~ ";;:: : iii: ii' ::1: .:Ii::: III: ':;, ;:Ii :::: ilj' IIj. II :,.: :: ..... , : :::; .:. .... "I' " .:: ;:: ;::: :::: Y! !!H Ii:: Ii:: :;: ' .. :: :::::: .:\ ;H: lit: iii: ;;H H :t !ii: ;::1 HH hi I!!' !+ H .. _. ~~ .,. .. ::.... '" .... ..:.: ....... 1 .::: ~:. ~:~; ~:L ::~. ....... :~J;L .::~t!.L i:';~ ~:l:I.....i~itljl. ::!: :i; i::: !II: i::I~': , "I • !. . i;: ii: :: ::. i:;: i: .:: ;:i: :Ii :1/: iii I ..1 . ......""" I . .... " ......... 01, '11' .1 · . "j , : ! . ! :: : jl :!: .:'. :1'::: it: :: i.!.

" 'j • " ""'~" YJ C~~L~£. Z:rl !" ! 'rl. Irll~j .'~!~L'·~ I. t i't"tGk;tNbth:~S/ t I ~~L'ti;U~W!tJ:itJiliC~ J~ t,------- ---- ---- ---- ----OiArT-ER- -3--- - ---- ---------- ------ ------------- - ---- --------------------------------

I THE AIRFRAME AND THE ATMOSPHERE

i Table of Contents INTRODUCTION .•••••••••••••••••••••••• - •••••••••••••••••••••• 3-1 TIlE AIRF~ MATHE~~TICAL MODEL .••.•••••••••••••••••••••••• 3-2 DEPENDENCE OF R* ON AIRFRAME OPERATION AND A H10S PHERI C COND I TI ONS . • . • • • • • • • • . • • • • • • • • • • • • • • • • • • • • . • • • • 3 - 5 Airspeed, Altitude and Gross Weight................... 3-5 \~ind.................................................. 3-8 Auxiliary Equipment Power............................. 3-10 Center of Gravity Position ............................ 3-12 Conclusions ......................... , . . . . . . . . .. . . . . . . . 3-18 A CONVENIENT R* MODEL ......•...•..•.••••..•.••••.•..•..•.• · 3-19 SU~RY •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • •• • • • • 3-19 TABLES 3.1 - 3.2 ••••••••••••••••••••••••••• - •••••••••••••.•• 3-21 - FIGURES 3.1 - 3.13 •.•••••••••••••••••••••••••••••••••••• ••• 3-23 ~ I

I

I

--------------------------- ------------------ ~--------- -- ---- --- ----- -------------------- ------- -------------------------- ------------------------------------------------------- -- -- -------------------------- ---------------------- '(

I CHAPTER 3

I THE AIRFRAME AND THE ATMOSPHERE INTRODUCTION In this chapter we commence the development of an airplane- atmosphere system performance model suitable for maximizing R*. De- tailed consideration is given to the airframe and the atmosphere only, while the propeller and engine contributions to R* are repre- sented by the variables n (the propulsive efficiency) and c (the p engine brake specific fuel consumption).

The model developed incorporates the following airframe and atmosphere variables: 1. Equivalent airspeed (EAS) V , knots E 2. Altitude, represented by the atmospheric air density ratio 0 3. Airplane gross weight W, lbf 4. Windspe~d along track V , knots w 5. Auxiliary equipment power P ' horsepower' AUX 6. Airplane longitudinal center of gravity (e.g.) position hc-.

The airframe model of Appendix C is first discussed. The effect of each of the above variables on R* is then examined, and each of those effects is illustrated for the LASA 60 airplane under the assump- tion that np and c are constants. An expression for R* (different from equivalent expressions for R* in Appendix A) is derived which, after expansion in later chapters, will prove most useful to the task of airborne computations.

3-1 THE AIRFRAME MATHEMATICAL MODEL The general airframe mathematical model presented in Appendix C constitutes expressions for: 1. The airframe drag and power required, power-off and power-on (Equations C.l - C.8) 2. The airframe drag coefficient, power-off and power-on (Equations C.9, C.lO, C.29 - C.3l).

The approximate geometric and aerodynamic characteristics of the Lockheed LASA 60 airplane are presented in Table 3.1. For this air- plane, the longitudinal range of movement of the c.g. is assumed to be limited to 0.15 < h < 0.30 by considerations of stability and control power.

Experimental power-off drag data for the LASA 60 with an unspecified c.g. position is presented in Reference 19, and reproduced here in Figure 3.1. The power-off drag polar for the LASA 60 was computed, using Equation C.29 and Table 3.1, for h = 0.15 and h = 0.30. Plots of these computations are superimposed on Figure 3.1. The computed curves fit the experimental data over the range 0.09 ~ C ~ 1.2. Deviation from L 2 2 the dat; when C > 1.2 is considered unimportant: such C values L L correspond to flight at speeds well below the minimum drag speed for which c : 0.8.

L The power-off drag coefficient of the LASA 60, with the c.g. at the aft limit (h = 0.3), is represented in this work by:

CD = 0.0402 + 0.052 C (3.1)

L 3-2

i

I ' ____ . _________________ . _______ Eg tl.E.-.1i 0..D-_ ~_~_L rep_~_e s e!!!_~ __ ~!l ___ ~Epr_~~_~!Il.Cl_!~ __ ~!E.Cl_~~h £_!~~~ ___ ~~~ __ !~r~~~ __ ~~_: _________________________ __ 'j

j

experimental data of Figure 3.1, plus an increment to the lift-independent

I

term to account for modifications made to the LASA 60 owned by Princeton University since those experimental data were collected.

I

The relationship between the drag coefficient power-off Co and the drag coefficient power-on CD is discussed in Appendix C. The difference

I

_ ON between CD and CD arises because, in powered flight, the following ON parameters have values different from those pertaining to power-off flight: 2. C m o 3. a with corresponding values of oW' LW and e o t w 5. i w -In Appendix D it is shown that variations in lift-independent drag with power result in (3.2) where the slipstream interference factor fD is a constant. Equation 3.2 reflects changes in CD and n (the term ~t2 KtStnt/S in KQ only) t pm 3-3 in Equation C.29, due to power. Substitution of Equations C.I and C.S in Equation 3.2 yields: >!'

(3.3) Changes in i te.ms 2,3 and S aho:ve. and additional effec,ts of changing nt' alter thiS' rela'tioTIshiV between C and CD for fixed values DON of C and h. The effects af such changes on CD were s,tudied for the' L LASA 60 using Equation C. 29. The data set of Table 3. I was used as a base, and items 2-5 above were separately varied. CD and the term pm t.:t 2KtStn/s in KO were constants in these computations. The: range of variation of items 2-5, and the corresponding maximum percentage variations in ICL/cDI from the value pertaining to the basic data set at the same C and h, are shown in Table. 3".2. The actual percentage L variations in CL/C , which varied with C and h, are the ~egative per- D L centage contributions to fD resulting from the variations in items 2-5. Table 3.2 applies to the range of lift· coefficient 0.3 ~ C ~ 1.2 L and to the range of c .g. position' 0.15 2. h 2. 0.3.

For most GA airplanes it is considered that the incremental changes in items 2- 5 above, due to power, will lie well w.ithin the incremental changes shown in Table 3.2. The corresponding maximum percentage variations in ICL/cDI shown in Table 3.2 are taken to indicate that the effects of power on drag, in addition to those considered in the formulation of Equation 3.3, are' small for GA airplanes., fO is taken to be a constant in this work, except in the discussion of center of gravity position. in this chapter.

3-4 ~ I

I

f ! .

DEPENDENCE OF R* ON AIRFRAME OPERATION AND ATMOSPHERIC CONDITIONS --- -- - -- ----- - -- - --- - --- -~ - -- -- - - - ---- - ---- -- ------------ - ------- - -------- --- - --- -- -------- --------------- ----- -- ----- -- -- - - -_. __ ._-_._--- ------- -; In this section, an expression for R* is derived which is equivalent

f

I ::et::r:::::u:n:X::::::::::O:o::r::u:::::d:: :~ i:h:e:::l:X:::::i::p::::::g

the propeller and engine contributions to R* in terms of the variables np and c.

The airframe and atmosphere contributions to R* are illustrated

I

for the LASA 60 under the assumption that n

and c are constants.

p

I

It is assumed initially that all of the variables contributing to the value of R* are constrained to have specific constant values, with the exception of equivalent airspeed, altitude and gross weight. A simple expression for R*, which accounts for these three variables is presented. That expression is then expanded as V ' P and hare w AUX consecutively introduced into it as explicit variables.

Airspeed, Altitude and Gross Weight In this discussion, the following assumptions are made:

np = constant = 0.75 in all Figures

c = constant = 0.45 lb/BHP.hr in all Figures

h = constant = 0.3 in all Figures.

With these assumptions, the most convenient form for R* is (3.4)

R* =

3-5 which is obtained from Equation A.12. Consideration of Appendix C (Equations C.4, C.9, C.l1 and C .. 29) reveals that PRIO is a function only of V , Wand h for a given airplane. Therefore with the above E

assumptions, P ra and R* in Equation 3.4 are functions of V and W

R E only. Figure 3.2 shows R* computed for the LASA 60, plotted against V for a range of gross weights . The family of curves in Figure 3.2 E applies to all altitudes.

Line A in Figure 3.2 represents the variation of R* with gross max weight (R* is the maximum achievable value of R* for a given gross max weight). Since R~ax corresponds to flight at maximum L/DOFF under the stated assumptions, line A also depicts the variation of minimum drag EAS with gross weight. The variation of R* and the minimum max drag EAS along line A are shown in Figure 3.3, the former being presented as a proportion of its value at W = 3,000 lb.

Equations C.Il and A.IS show that for flight at minimum drag (md) EAS with zero wind,

EAS is proportional to IW

md R* is proportional to l/W max These are the forms of the curves of Figure 3.3.

Consider the following two flight conditions: 1. Flight at constant EAS as the gross weight varies 2. Flight at constant power as the gross weight varies.

Lines Band C in Figure 3.2 represent flight at constant EAS with varying gross weight, the EAS corresponding to minimum drag for 3-6

W = 3,000 lb and W = 3,400 lb respectively. R* varies from R* along

max - ------- -- ----------------- ------ ----- ~ - - ---------- -------------------------------- ----------- -- --------- --- - -- -- -- --- -- -- - - ----

line B (C) at every gross weight except W = 3,000 (3,400) lb. This

variation is expressed as an R* penalty, defined by

R

* - R;ax]

R* PENALTY

r 100 %

= R~ x

L max

Lines Band C in Figure 3.4 correspond with lines Band C in Figure 3.2 and depict this R* penalty.

Similarly lines D and E in Figure 3.2 represent flight at constant power with varying gross weight, the power level corresponding to that required at minimum drag EAS for a gross weight of 3,000 lb and 3,400 lb respectively. These lines D and E are straight with a slope given by differentiating Equation 3.4 with P constant: R (3.5)

=

The slopes of lines D, E in Figure 3.2 are therefore different and invariant with flight density altitude. Curves D, E in Figure 3.4 correspond with lines D, E in Figure 3.2 and depict the R* penalty (also independent of density altitude) for flight at constant power as the gross weight varies.

It is clear from Figure 3.2. that both V and W have a significant E effect on R*. The curves of Figures 3.2 and 3.4 indicate that as airplane gross weight decreases during a trip due to fuel burn, it is more fuel-efficient to fly at constant EAS than to fly at constant 3-7 power, whenever the EAS exceeds the minimum drag speed. At constant V and W, R* is independent of altitude.

E Wind this discussion the following are made: In assumptions = constant = 0.75 in all Figures np c = constant = 0.45 lb/BHP.hr in all Figures = 0 PAUX constant = 0.3 in all h = Figures.

The effect of wind on R* is clearly seen from Equation A.12. With the above assumptions this is written (3.6) R* = The effect of wind is to multiply the right hand side of Equation 3.4

by the factor (1 + Vw lO/v ). For any given gross weight, P ra is

E R a function of V only. Therefore, for a given gross weight and EAS, E the effect of a given equivalent windspeed on R* is identical at all altitudes. The altitude yielding the maximum value of R*, at any gross weight and EAS, is that at which. the equivalent windspeed

V ra is a maximum. If a constant tailwind (headwind) V exists at

w w all altitudes, maximum R* is achieved by flying at sea level (the highest altitude possible).

A plot of P 10 versus V facilitates the computations in Equation E R 3.6. In particular, the EAS yielding maximum R* in any equivalent wind 3-8 I

I

I

condition is readily obtained from such a plot, as illustrated for - - -------- - ---- - -- ---- - ---- ------ -------- -- --------- ------------- ---------------_._._ ... _ .. _------------------ - ~.

the LASA 60 in Figure 3.5. The equivalent windspeed is ~nscribed on the abscissa, tailwinds to the left and headwinds to the right

t

of the origin. The straight line drawn from this V IcJpoint yields w

I

the EAS for maximum R* at the point of tangency to the appropriate gross weight curve. This construction is shown in Figure 3.5: points

t

"

t

A, Band C represent the operating points yielding maximum R* corre- sponding to equivalent windspeeds V /<J = -20, 0, + 20 knots respectively, . w for W = 2,600 lb and any altitude.

Computed performance for the LASA 60 is shown' in Figures 3.6- 3.8.

Figure 3.6 shows the EAS required to achieve maximum R*, plotted against V , for three values of the gross weight Wand two density al- w titudes. When the abscissa of Figure 3.6 is relabelled Equivalent Windspeed V IcJ without a scale change, the sea level curve for each gross weight ' w .'

f will apply to all altitudes and the 10,000 ft density altitude curves will cease to be meaningful.

Figure 3.7 shows the ratio of the maximum value of R* obtainable with wind to the maximum value of R* obtainable with zero wind, plotted against V 1cJ, for three values of gross weight. These curves apply w to all altitudes.

If an airplane is flown at the minimum drag speed in non-zero wind conditions, the maximum possible R* is not achieved. The 3-9 variation from the maximum is expressed as anR* 1>enalty, defined by

R* PENALTY- [ R*mdR~:;ax . ] x 100%

where R~d = R* atminimum.,dragllAS

R* = :maximum ·achievable'R*

max both computed for the appropriate gross . weight and ,the prevailing V w and o. Figure 3.8 shows thisR*penalty plotted against'V,;o,for three values of gross weight. These cUJ::vesapply .toallaltitudes. T·he R* penalty is in general more severe for headwinds·than'for.tailwinds.

The effect of equivalent ,windspeedonR*and upon theEASfor maximum R* is clearly significant.

Auxiliary Equipment Power In this discussion,the f61l0wingassumptionsare made: np = constant - 0 .75in:all -Figures c = constant -O.4:51b/BHP.hrin:all -'PiguT,es h = constant = 0.3 in.all Figures.

The auxiliary equipment.power deliv'eredper engine is 'defined by Equations A.4 and A.Sa. Whenc isdefine.d equalto.c' ,then P AUX is defined to be zero.

Equation A.l2 shows the,depend-ence ofR*on PAUX:

~ I

-~

(3.7) c ... i I 3-10 ,

~:------- - --~~:~~~~~:~::-=i~~~~::::::!~~:S;~~~L1°::-:-;::;::;O:~;i;;; - - -- ---

I

I to the curves of Figure 3.5. The effect of P is to shift the plot AUX

1-' of P R Iii versus VE verti call y by the cons tantamount E '1> P AUX ro-

Consequently, as P increases (decreases) from zero: AUX 1. The value of R* decreases (increases) in every flight condition, 2. The EAS yielding maximum R* increases (decreases) for any given equivalent windspeed.

Figure 3.9 shows the effects of P > 0 on R;ax (the maximum AUX achievable value of R* at a given gross weight) and on the EAS required for R* ,computed for the LASA 60. The curves are drawn for three max values of the gross weight, two density altitudes and zero wind conditions.

When the abscissas of Figure 3.9 are read as P 10, the sea level curves AUX for each gross weight apply to all altitudes, and 10,000 ft density the altitude curves cease to be meaningful.

When the Equivalent Quantities V ' vwlO and P lcr, and the gross E AUX weight are constants in Equation 3.7, R* is independent of altitude.

Equation 3.7 is now rewritten as: (3.8) 1 + The form of Equation 3.8 is convenient for the following discussion of the effects of center of gravity position on R*.

3-11 Center of Gravity Position The airframe model of Appendix C assumes that the airplane is laterally symmetric about its lengitudinal center line, with respect to' geemetry and mass distribut.ion. The airplane center of gravity (c. g.) is assumed to' lie on the longitudinal cent.er line, at a

distance he aft ef the leading edge of the mean aerodynamic chord

of the wing.

We now consider the effect on R*ef varying h. Considering the right hand side of Equation 3.8, the quantities which are functiens of hare 1. PRIcJ - see Equations C.4 and C.29 2. - Equation IL48 shews that np depends upon f , D which has been shown abeve to' demonstrate small variations with h.

P IcJ and np always appear tegether in Equation 3.8 as the ratio R n/PRIcJ. Instead ef introducing h as an independent variable into PR ra and n ' it is mere co.nvenient to: p 1. Compute np/PRIO fOT a reference c.g~ pestien hrefc, a-nd 2. Adjust that cemputed value fOT variations in h from h f' re by means of a correction factor which is somefunctien

ef dh = h - h f·'

re

This precedure is equivalent to' expanding n /P ra into a Tayler

R p .

'" I Series in dh.

3-12 I I I

I

i

j _. _.___ . _______ ~CCOrd~ng~ ,:~fi~e_ __ ______ _ __ . _____________ .

I [p n:O = p n:o at h = h C

ref I R R ref > h

J

= R* at h = h

R* ref h ref pquation 3.8 is now written: 1 + E Now from Equation A.13, Therefore

325.65 n

p and invoking Equations D.47 and 3.2,

~ = 325.65 na

L (3.10) C" V f W J P E VO R

325.65 n

L (3.11) = -=_=---~a V f W DON E J 3-13 where na = propeller efficiency in the presence of the body, f = constant.

J Equation 3.10 shows that, if fD were truly a constant, variations

in np/P ra with h could be evaluated in terms of the variation in

R L/DOFF with h, assuming na is independent of h. However, fO varies slightly with power. condition, h and C , as previously discuss:ed.

t

The variation of Tlp/PRIO with h is. therefore more accurately computed from the variation of L/DON with h, as shown by Equation 3.11.

We here evaluate the variation of L/DOFF with h for· the LASA 60 airplane, and propose a general model for such variations for GA air- planes. A general model for the variation of.L/DON with h is then proposed, and used to describe variations of R* with.h for GA airplanes (n is assumed to be independent of h.in this discussion - the validity a .

of this assumption is addressed. in Chapter 4).

Using Equation C.29 and Table 3.1, the percentage variation in L/DOFF from that pertaining to the nominal forward c.g. limit was computed for the LASA 60, as hand C were varied. The full line's L A, Band C of Figures 3.10 and 3.11 show the results of these compu-

tations for C = 0.4, C ;.. 0.8 and h = 0.3 respectively. These per-

L L centage variations in L/O with hand C may be visualized as the OFF L height of a surface, as shown schematically ih Figure 3.12. Lines A, Band C in Figure 3.12 correspond to lines A, Band C respectively in Figures 3.10 and 3.11.

The form of Figure 3.12 is considered to be typical of GA airplanes.

The height of that surface for any particular airplane is a function. of 3-14

The height of the surface behind the aft c.g. limit (nominally h = 0.3

for the LASA 60) is not of interest for current GA airplanes, since the aft c.g. limits of such airplanes are prescribed by stability -+- considerations I • From this discussion of L/DOFF for the LASA 60, the following model is proposed for variations in L/DOFF with h for GA airplanes: (3.12) where position he ~. J = L/D OFF corresponding to the c. g.

OFFJh

[

= L/DOFF corresponding to the c.g. position

;OFJ h

h e

[

ref

J ref

dh = h - h > 0 for he aft of h f e ref re

~ = positive constant

t that the maximum increases inL/D along lines A and B Note however, OFF in Figure 3.10 occur for h > 0.3, and correspond to positive tail loads.

Laitone (20) has shown that induced drag is minimized with a positive tail load (upload) for all values of C > O.

L 3-15 and both he and h e 1 ie anywher;e within the allowable c .. g. range.

ref This linearization app.ears· j:ustified on the basis of Figures 3.10 and 3.11. For t'he LASA 60 airplane.' defined by· Table 3.1, lines A, Band C of Figures 3.10 and. 3.11" (corresponding t'o' h:ref=' 0.15) give z::; '" 0.375.

The sensi ti vi ty of z::; to all the geometric and aerodYnamic characteristics appearing in Eq\1ation- C.29 for CD was'- not studied.

However, as an indication of this sensitivity, the foll.ow.ing studie:s were performed: 1. The dotted curves of Figures 3.10 and. 3 .. 11 give: the effects on z::; of a single variation in CD . , while alI pm other variables retain their values in Table 3. L For those dotted curves" h = 0.15' and z::; ",0:.467.

ref A low lift-independ.ent d,rag coefficient· therefore contributes t,o a high drag'-sensitivity to c.g.

position at any G • L 2. Figure 3.13 gives the effe.cts on z::; of varying C m o at C = 0.8, while alL other variables retain their L values in Table 3.1. Eor those' curves, h f = 0;15 re and: z::; '" 0.217 (a) for C =, 0, m o

(b) for C = -0.25, z::; '" 0.479

mo 3. Indi vidual variations in the parameters. g.iVen in Table 3.2 (with the exception of C ), within the m o limits given therein, were performed while an other variables retained their values in Table 3. L 3:...16 j I

I

I

---~ ____ --------------------- ___ ]'h_~_!:_~~~!_!..~!!K __ ~_~~~a t!.~_!l~_~_~ ___ ~~~ __ ~'!!f_~~ e _ ~~ __ ~_~_~1:'e ~~~------- -- -- --_______ _ __ __ __ _ from the surface corresponding to the basic data set of

I

I

Table 3.1 were not large in the region (0.3 < C < 1.2, - L 0.15 < h < 0.30). The corresponding variations in ~

I

(with h f = 0.15) from the basic value of 0.375 were

_ re not computed, but are expected to be small.

The effect of c.g. position on L/DON may be determined from the foregoing discussion. Running propellers effect changes in CD and pm in the parameters listed in Table 3.2, as previously discussed. It has just been shown that variations of these quantities do not change the form of Equation 3. 12, but merely the value of~. For powered flight we therefore replace ~ in Equation 3.12 by ~ and write (3.13) where ~ is a positive constant. The values of CD and the parameters pm in Table 3.2, used to compute ~ for a given airplane, should be average values pertaining to the powered flight of that airplane. The above sensitivity study of the effects on ~ of variations in CD and in pm the parameters in Table 3.2 indicates that ~ will probably differ little from ~ for most GA airplanes.

From Equation 3.11 we see that the percentage variation of np/PR I<J is identical to the percentage variation of L/DON with h.

3-17 Therefore, (3.14) h ref Using Equations 3.9 and 3~14, we now write R* for the c.g.

posi tion hc: V w (J 1

~J'

[ R* = 1 + -v;- . 1 + EP ;at~].

(1 + ~CL dh) AUX ;; p . R . , . n f re

where both hc :0 (h f + dh) c and h f e lie anywhere within the

re re allowable c.g. range. When he is aft of h .£ e, dh > O. Equation.

re.L 3.15 is applicable to standard and non-standard atmospheric conditions.

This analysis has conveniently accounted for variations of fn with h. Henceforth fn is considered to be a constant when h = h f.

re Conclusions The following conclusions may be drawn from Equation 3.15, when n (at h = h f) and c are assumed to be constants: p re 1. When all Equivalent Quantities, gross weight and c.g.

position he are constants, R* is independent of altitude and when, in addition, PAUX = 0: 2. R* increases as the c.g. is moved aft within the allowable c. g. range. The maximum value of R* is achieved, in all flight conditions, with the c.g. at the aft limit.

... I 3-18 I

I 3. The percentage increase in R*. for a given aft shift

j- -;----------------- ------- -i~posi1:±on,-±nereases-wrth-increas-i"g_~d-henGe- - - ---- ---- -- ---

I (a) Increases with increasing \II

I (b) Increases with decreasing EAS 4. The percentage increase in L/D ' shown by the full OFF lines of Figures 3.10 and 3.11. are taken to be indicative of the effect of c.g. position on R* for the LASA 60.

The influence of c.g. position on the second term of Equation 3.15 is negligible when P is small. for all values of np' AUX It is apparent that c.g. position can have a significant effect on R*. The magnitude of this effect for any particular GA airplane.

characterized by ~. depends upon the geometric and aerodynamic characteristics of that airplane.

A CONVENIENT R* MODEL Equation 3.15 is equivalent to the numerous expressions for R* in Appendix A.

In Equation 3.15. PR/O at h = h is a function of V and W

ref E only. and all other airframe and atmosphere variables are explicitly represented. The reason for expressing R* in this form will become apparent in the following chapter. where the variable nature of n p is discussed.

SUMMARY Airframe and atmosphere contributions to R* have been examined.

Equation 3.15 has been derived and will be further developed. in the 3-19 next chapter, into a model for R* which is convenient for airborne computations.

Assuming that the propulsive efficiency and the engine brake specific fuel consumption are cons.ta.nts, it has beE;ln shown that; equivalent airspeed, gross weight a.nd equivalent windspeed have significant effects on R*; longitudinal c .. g .. llosition ca.fl have a significant effect on R*, depending upon the airplane design and operation; auxiliary equipment power in general has a small effect on R*; and when all Equivalent Quantities, gross weight and c.g.

position are constants, R* is independent of altitude.

3-20 TABLE 3.1 ________________________________________________ LO_GKHEED LASA <?9 CJ-LA.RACTERI ST I CS in Appendix C.

are defined The symbols used ft S = 55.43 ft = St

-

5.46 ft c

=

ft i 16.2

=

l...

:: 0.2 "0 3.98

=

A 7.13 At

=

w = 14.854 ft b ft b 38.687 = t \\ K = 0.011 K 0.011

=

t w = 0 0.4

= ~t

~w 0.028 = 2.0 ft

=

°t go power-off flight: In degrees i 5.80

=

-0.15

C =

w m -1 = 1.575 e 5.73 radian a

=

t w = 1.0

n

0.063

=

t ° w 0.0393 = 0.2 1" CD

=

w pm Values for ow' 1"w' Kw' E:: ' a ' e , 0t' Kt' E:: and iw were determined with t t w ow the assumptions that: 1. The wing is untwisted, has a rectangular p1anfo~ and has a uniform NACA 4412 section.

2. The tai1p1ane is untwisted, has a rectangular p1anform, and has a uniform NACA 0012 section.

3-21 TABLE 3.2 LOCKHEED USA 60 EFFECTS OF PARAMETER VARIATION ON AIRFRAME LIFT TO DRNG RATIO PARAMETER PARANETER ABSOLUTE % VARIATION CL/C AT D RANGE OF VARIATION FIXED C AND. h.

L 0.3 < C < 1.2 L - - 0.15 < h. < 0.30

- -

0.1 to 0.2 < C - 2 .. 5%

-

m 5.73 + 25% per radian < a 1.5% - w [wi th corresponding changes in <5 T and w' w C]t e see Appendix - t 0.8 to 1.6 < 0.5% n t ~ <.

i 2.80 to 8.80 degrees 0.5% w , tThese variations together yield· variations of +19% and -21% in the three dimensional lift curve slope of the wing.

3"-22 i i

I

I I

"

,

I

I

I

[2

. LASA 60:

CJ) VEI(SUS

FIGURE 3.1 LocKW££.D

L fT<OM TE.STS.

DATA FEATHE.R£D PROPELLER

3-23 ;'\ (" .'" 3-24 -- ---- .. ---- .. ·---_. __ ._._a __ !..f -, 46 1513 ··1 It I ' I, i III 1I 11t;11t1, ft' ill'I!1 'I 1 r 1'[1 m.i.1~ i: !~ i !:Ii ~~i! :iiJ lii.~I' !Ill :I"~;;~l'i ii.U:i ~ni;il~~ :'l;~' ',;,: iiii :l'i ' ::;; ill': ip: Iii! "'1: I i!'lij'tt' ;;1: i:;: \':: lilll :ijj l Ir fl .\ "!t th 1 It Ii ~r~· . I~ '~JI : !~tI~,~, ,if'. !~dlH;~ ~~ 1~~ I oj I!~: t:~i j. ::.;': :'-IJ'~nl :1 I II. ~l I H~~ t.: il '1-1 j : it "I l.! t II,:: II III ' I: bllUjj,: 'Jill Ui I 1 li ,ul,; iii; 'Ii !IW i !Ul:ll.i.L 'I,ll iii: 1'1' i :::! Ilil ::1; Iii, jlH iii ;II! !I Ii ;II! i' Iii' i": Iii: : d !P!

I 1 " , lilt, 1\, I , I II r, Ojl' ~~ ~(:~. Jlll (1.<" '-:".~ : III "J..H+Hl: I "l~ 1:' !I""" ,,',' I , 01 , II I I i' I .11 ' " ", 01 1 : i. I ! H ill 'I ifll w.: 11.! Ii :I)~ I111 II~#:'I~':' i:u.IDI :u :1!Uj~': ! .. ~; :·I'lLlnlj';:I ·l· ii,;.i~;': ':i[~' I'!lLlli!!!:~ ':~"'Idl Ir: IFI~J~'~ .~fjl:'j; :J'l: !il! i: i I, IIITI!!II !!i: ITl"!!: !::: Jill , ' 'I !I :1\, I til! It :II!, Ii! :1."" ._ l If : 1M' ..:. .... :lS~ .HI ~lfti'-i 8 HP.NFt. dt il ;::! I::J..:;!, I 11 !ill ~l:; 'I h ::!,' , " j:' ,I II'" I' I 11,1, 1,01 If I .' • ,,'0' ,.". ,!:~i . " .. ~' l~'''' I ":-'m'· "m., "'I'" "," " .. ,." ,"""" t In', II"~ .tt ... " I j' , '"'' 1'1 II: 1:'1 11' 1,1,;:: ii".' 'Il.i~"" Iltl ,," ,,,. ;'''''. l'i:j,'I~,I, ":~ '!.I,i "I I: ' I' , , ... '''' .. " , .. ,I, .. ," .. I, .1 'I I 'ill I,,,,, l:iJi·" , I l' II! 1+!I:'ill'11Ii 1 I l~rl!1~ifilf~ III .11 ""'" ,; ~tt~.::1 'l~IU'!I"I~:i IP+W+!~UI:I:llit::i:;d:::iiii1 1(11 :ILi::.!."f}' ' i !! I : ,:! I' i II 'I:; Ili' III! II i I lI1Li.L~ :I:~ I i :,trr.i.i~'" 'I.L~0'i ~T[~lr":':"T!: ;;i i:tt ~j~. ~uill :,' Ji.ll11'iM'!:: iTffttit Iii· :1;: !1'i'::lli!j! f !Ilil !I:; 'i: .: .. '!i I [ii ,f:~· H ~ 1,1 Ii ~ I!I! ,1 1~J:'rnLjm uiLtt~!l : ,:r~ i, ~~: i~U H~'1~1 w ~h,rrni.d:; 1~:I~tli! '11 j'i Hi tlli iUi r~~lihl itt! I 1tl, f,~I! HI· itj'~:~ I I tlI tIl II 'l II lill' 1~1+~~H+IW'1\W";}II:,!-' '1:ld),J..~IIIrt.,f~i~I'Ii!l~R !11.1PP,:r:t!:l1r:J II I dili,,:iiit:I';I:, l iljiii il fill ~ "j;l, W'! 'ill tI 1I I f i:I'l / ~Il'j\iii! j'l t 111 .... lliii !lli iji:jPI : :iJl III 16, iil KIll 'il~rj,~~ i Ill! "lit: "Ii jill illli'~'i i J [1111 :Ii: ll:'f~:' l!

iU 1 t ~ iI :JI !it I', t hh It tltttt f 1 I lit 1111 "p ,1 'j, H+ttt'l '<Hi1 ;i,lti::: 'i"~'~ ;,:iI' Ii! i'l II: !Hj!: ~ ~ I IJ, Iii' /,1", , ~ , , ~, I SrANDIITlb A b NON- rfTIlN])II1?1J Ilrl'1os.. I 1i1"IIJ.i+ mill 41 tlillil:, I '1d::1i.Si ii., 'I: t' I ' , ii:: 1 ; 1, ~ , ,! 11 it ';., Ii II ' I 1 ~!Itrr I ~ Ilj 111l1I!1 Illllllll~llllll III I': '1'\1' I Ijl II!!i!' :WlJillll!lllii IIll '~~I"~"II: 1'1 1 ' 111'j'l i'I' 1'1::: ~'~ iii' 11 till' ~ I:t I !' It" , "'I ' H' Hil 'Ij ·1 Jill'lI I ,I '~I+r.!~' ." 'It!" Dr lJ 1 ' "1 , , I 'j: "II ;, I ' ,qlU I 111 iili1 !ill~:1: ;I'I! !:fi l ::! il, II i\lt uti J ::w.u ,i. ,:11' ijii)!iii IF il'l ll Illi i~!1 ,j; 111 : ..

t , ",. lll! j ~ rt!tt l;l' I, ~' : 111111 , lli ' I" u... ,.. .~ .. nit": .' ' II II" I d' 1 , i I , .j.;" ," 'r I' I: Ip: I I' 'I,' I, II'j' II . :: I, ill! I ., I i'll' 1:11 i'!; I :: ill! ;lllITTlil!:l ~ :-:-!'+ ::i 1'1'1':1' I'j'i; 1\ ! i[!'!l111 II'ti 'II. !PI iijll!l'" Ij 1 f I'! l'Ul'j'! i.'.

II j II I I: H- I I I I d II 1l., L II 'Idal~~~t"!"':.: 0/ "It "I ,.1 "111 I :t I I it t )1 'H I I 1 I ~g L ".l. ,It' N '" HtHiH+ll 'HiIfT+tI!:1 1 lilt I' FI I'!', :liil!1 :1!TI' :ili Fi' ::I:'ili1:/lI!t~~7:: :::: I::i i:I'j \:1 ij'llli 1ii I ii ,:Ii ltil'lli ·;tl ' ': ~ Ii I, ·Ii:· liln 111 i Ittb:": a:·-~· l U1 II! III II , ,t " I,!, 1::No/'t 11I1 il' ': II lJ.;.; ~, ... ~ '1 , .. , Ii' ,I Ii:", I I Iii i I"'"'' ". l' 'i' d' 1 ,1'1 , ' II'''' , Ii:" t' I' f! , I 'II'!; 1'I1 +W1l'III;1! ' :,'; '''':jjii- 'i ' (T'" I' ;1'1;r ,p" l:ll:"~~It: :t:~ ~iiIHI'::-: ': :1': :·11 ill: if: I' 1/1 ,;; , . ;I~

ll

~d i :1' t'tl ii' ,I ,,\fa 111 ~ !~~H-:~~:;'B:~iIHlhid! :!I'tlr !!:II H ]!lllI1 • :it!I'lli ::! :: ill'ji ll~' lill lill hli H, :~ \1 i 1\ I llj'! I~i. ;fjl! j~ l l I1 ,= I l~ II~ ,,'1' I i l: 1: I~l Ill.:, ~1'· ~1[~I:!fI'j~+: +Il~ Ii ' 'il ~.~ tji:~ill~;~I' ~~i!; '·i ~ijll11~ll; !}iU ~:! ji~I@"I: H: lilii!!"i' :~II: 'I[{I; !j' I ~hl'llJ"lil:! I' ;'\4+I':!!~ i:i~'I,:I~: , , " Hi I 'til i;J. ,r'i: I ' : : I' 1 II I Jl I I ! I! I II' I i' P Iii· "I , Jill 't'!o!o TIt' , ~~H ~I' i :: ::, i j: I I[ 1: I II q ~ I J ' 'i ," I I; ~ lilL 1 : Ii':: iii Ill. il; lif: .~. ,I:: Ii:! illi li;il!' lijl1 , " ii1lrr'ml' d! !t r II i:L Iii: lilin ::1 i! 'ii' : I;i 'H-f+ ii' iii Ii! LJi lilllll! ill II i! 111 1 Ii i !lii 1: : oi,:~ l ;11/11: I,:,ll :"!:illrtm~i*" ':;:::_[:'1111:: iU , 14111 IIjl+ml l!111 ;'1 ~+trt:+:I",;~II~:i1 Tlfl'ill l:lij';il;·",·~It'U,w:;t+H:n, .'1"1':: l,h'IIIT I: ,f++'l-II;' tr ~~ tPlt H illl!:Jl illiwi j~ lil 1\ Ii li q Il'tfll' IIi II 'II' !llii 1I~1 i lit j !IP ::[1 :11111 iiL i!! ;I!\ [I I' 'I fi!! .!! !:!! !;:; iiT'?'~Hl! Jd~'iUlil!ll:l.1 :!!i ld, .: d Jill tii: i! f;;i l " : 1::'1 iii, 1l!!'IUI:!\" iii Ii :1: I r, 1\ j,l1I' , i I 1·,:1: d :',: ::'1: I II:' I II Iii I', \ /i" i li!\ ::1':1'" 11':: :1'; ':i:i::" ~ 'i:' i ,:iI 'ii' l:j': II ' ;1·11::' 1" ,;.~~t: 1'1 : .'1 III ill:[J a 'Ill I 'ti' ili I' I ·\ttl :1;1 ::L La: W~ III ;,: ,I I.J.L Eli 4.1;; ! 11 1.,1.1.1: ~ Iii·.. i::t '\ : 1 i: Lil~ :1.111;;': 1. ill~-: II I:: :j:' q, ::1 :11i! :Ii, ;,:: ',Ii :'1: "1'; I';; :1;: ::i i' . ;".: ""I, ,I:, ,;1: 'i" ;If :1·,:' 'I:' ,Ii :!:, I:: ii, ",I j:n :;::-1 .. 'I"~ iJi :111j!!i! III: iii. ,iii .~* lin 'III i1;r::- ,I' .!F·.

I ,'I: II::, i!t II'i!: "I: :t;' fi':ll lli;li:~' :1;' :I! :!L ':J~f : : ::1'1'" ::,: :1'11' ~I; ',I ',i: ;.; ill '::. -1i/'lll,:I' '1:: ,i, .:: I:' :,1' I I 1!'11: I i'l id, ::1: ::1: :::. ~ :'1' ,1"1 ,;;' I,: :1:: '.1' l 'j'!+J.t I l.hill :nJlrr~.):ut1'II,,,'I!. "'1'1,,11.11""11 1' ,,, ...... ,,',. "",,,,1,, "11 I, """I .. ", ... ", ",,1"1'" 'I."~'@"'.t'"'''' 'iii'll ,," , .. ~,.:NIi it J : ill 'I ! ,~, Ii !"'~rr.;~r.~l1:~:!ii ii: iJ1~~.1I:IIi Ii! i:ji 111111 : :!1: ;':11 ::: q., ';!i iii: illl Jili I: lii!,li!i :i::!;' Ii!' iii. ql! i!:\,ii!i iil:;i I !lil Iii! Ii' i!ii :ii! :;:. kif . : I:,:

[j

rrri ;. ,',.' ':: ;: 111:': '1 U ','ii' "',' :A; ,:" •. ~ ;fl:! j\ : '} . .;,:*" .. ;::: : :'\: ~,'. ~'.!!I! I : .':, ::~ :;,. r~;:::~f 'ft :;; ,;;i 11;:1 ;t~r;:h- ~it r::' :::~ r!:: :ttt~tt~I:;: :ft. P'I' fl'i ::1: II: i ;: Il ~:~ jiT< . :~i I:. ,':' "1:.: 'l't· :"., .: 1:: L • :II~ ./1" I"'~'::: III'~~ I I! I III~.: j' :,:1 ,:' 1;;'1::1' ,II ;;1 III" 'I' 1,1 :;1' ,:.1:, ::,. ;, ,;', :::i ':,1:1, I I L. f:: II Plti'j.1 1::: :::' ,!, :. ,:'t ' 1

I

'" . " ' ....... t· 11 ii 1.. ', ... , 'I" '''' 1. "~'. ", =,11. "'r.~'+ .. ,1,., ," .", ".I '" m" 't t 1 , fil,1 "" , .. ,," ," "'1'''' 01" 1"'liJ11~H' 'II It, 1 "1' "" '" '" ", iii: .'11' .:;:, I'," I 1111' ill' :;;:I:I!! :'i:'" " ,I: I: Ii '.:, I,:. ji: "Ul' :11'1 I 1,1\ ii 'II'! II!: I,,: I. !' 'i:· il: I':: 1111 Iii: 1 t :: \ ' 11 i] ;,,:: it! .',' :Ii i ~~H~ri :!!:: ill,: I .! t IJ,: 1.4 ~~~~t-H ~:~t p.~ i~4t ;r~~ "l ·WI t~ ·!i ~~p ;1!~ ~~,Pi:, ·H+ ~F~ lrtillP.+f~~~j :1:: ~~;~ l!l: ~~i~ r~~~ {rH-itH: fl~: ~~ if 1. 4 ~4~1;~;+t~. ·~~;trr t :': : 'II ' .:::: 1 !:~ I' ii,: It:!: Ii:: 'I I:: : I I. ,.: 1 I: : i:! iii, I I, . : i . ,1,. , ,j i : " .':" :: 1:: ii' :,: .! Ii ! 'Il '[ I: I' II 1111 Ii '/ 1 :: 1\, Ii': 1'1: :! ' ., I ,;. ' 'I!!: 1'1" I' 'II : t!, ! I I ! I 1111! '1> I "I I:: ::.': i: " " "."," , II i I II I I II" '''". . . , . '; \\ ; 1 i ,: I, 1\ ' " ". ,. . ·\1 ", I ' , I' II "I " .. , , ' "I' I" "1' ,. ,'" I" , I ,. , I' .. 'I' : I' ", \ ~::::jI ':.::; :t-4- , II "I '" .. , ,oj" """"j,! I!::":"" '1"11:'1.1 i:'I' U":: I" : .t.!.::1 ~·.:'I·I ~~fi~ ',; tl j::i.:':',' ,,':', t ,., "I :iii 'I "Ii tid'" i;i 11"li" '" ,'" " Iii' ,. :1 "I' "lid' d!I'1. .. , II .. ," '1liii 'iii 1,01 "" "Ii' . . , ,,, I.,,, "litHI' \\1 "i','··'·· ': ':,1 t\j ~~1 :lii :~~I:::l :ii;:< ::;',,:'::. :il~~L': .,,: >,::1> >1~~I;;i :::::' I', j'!;; I;': 5~~! ji!: :;;; ;;:; ';::1;' :.: ~'f:" ;1;;1;:': ;;::i:;:::: "a~~~ :'::: :"1;::' T';n :.:: ·1\: ::i! ·:i :::\iilli:! ;:i: ::::1 ;': .. \:: i :, ,I': ~:. '::\:: ::;'I'i: .... :.1" :: ,:: ;:: :.: :.:t ,!!: :;'~iHi) I~:J· ,·J'E').H',:: :/!Ii:; ':;:1: .. :. i'.' .' '" I:;! :LI::!: .- ....... , .. ,.~. e·.· ... t,..11-1 .;u .~, ._- '" •. , ... ' ... 1 .... 1 .. ,.,.1 .. · ..... 1 .... ,," ... ,I.. .... '. ',' '.": .". " .. ,,,~ ...... \:In\' ~~ ... WI '(1 ... &..jA:I. -"':':'''' ".:': .'; .... ,." .. ' .. : ,'" l.;J::l; jll1'~~ .iLll~;~l ~:jltU; :L, ;:"i111 •• ·.1i .. ,.;I!:" :[i1.1 . . .•.... :1:1 •..• i ..••• 1 > .:{ ; I'!! : .. i.._I[';:: lUi : .. liiJ 'lLl:;:: :: 'I ::. ::::;:;::: ':: :::! ::~jlr:' • ';":'1: . : :T", ,:11:,: : • ·:1 ::. ·1:::'· :;,! I: I:: 'il::: •... i: :! ':.: :::: I·; .... , ,I t ••• : , ':' .' :,' • :! :':: :: '1:' . :.. 'i' .: :: . :: . :! .. :: .l,i..., ru'· ,r,£ 3'" . ijt' I': . :, : I ! . I: . . : r' :'; : .. '::.:. ! ' .

::-: . ' : i . : ~: ; . ; . I I ! . 1 ! ~ ;.: .:' f.-I t.:7 , ~ ~" '. I' i !.~ 1 ' ::' \ ~ '_, I : ~ I ; • 111 '<: 111 Tn 1 fir ("rr-n IMI rfn .... II"fll " ,"'.111 (I ""/ ",1" f .' -~

t-- .. -------_,_ .. __ ";"._..'"""--· __ ..... _ .. -=-.I

U .. 'l: 10 X 10 TO THE CENTI METER 46 1513 n ~ t<EUF'rE:L & F.C;C;r:R co. MAl" Iii " .. "

i

II I ~Il [IT 1 fill ~~ITI1Jr ~i~:lJliJlill~· lI,llll I ~illiillU!IIUllllil:~;:1 OJJIU!n~~Ii; t::~·: ilHi lIr~ lj~~~J ~:lj!l\lt n !l!jll ~.i 11.!:.;iIUl;~!Llj j!lli~'IHl!11[ IUlII!llllllll Hll 1111 ., Ill! It:: l\\\ iUi f l: 1 I., 'IiPJ:' . ~'ji' ~r.: "lIpi~n, I:~l! ,I , : : .. : 'f : liii ",i::' fl'"1"t- iI'; ~ i iI:.~~ ;::! I I IfIILui"li: ::p

II

i

i1

Ill, I" I !IJ)[ ~if:i'i·:· tl:;liij:",li < rri; ;:1,·1::1:, .'iii;ri :ill!i i:ii liil' lrll[~~I:::-I:'11l!11!;~1i71il:: i·~·I' ':i;~ .;! :ijJG:' i :':. :i:W£!I:~:: :~;::r~!i!! ;:i:~!if'j~; :11·:~~·";~II: .. ,~~I~J'~.i;i~_i l~l:! ii~"II!ttl:i ij!i! ! j I' iit J!:Ji;; :i : ; 'I f+[!I' f1;"~ ~ ....... , II'· "" ,." 'I ' II" 'I' I' 'I' 1" .... ,., '1.,·· .. , .,,, T·Lt" ' ....... , .. I . "j"" -1 'I~. ' ' .. w" r • Ir"" '1,'" " j l I ' i!i! ,II 1:1 IP: !Iii !Iii iiI! :8 :i:iJ~ il I u1i iii Iliii:illil~f4! 1; E "~j i ;i: 'foli / 'IJ :, i~ ,·ji: " Hi I: '~IN ,Ui II \ I II!! Iji; !I!i i!!

J ' ij , 1 I' I '!I ~ili Piil!l!i Pl'i Ii/tit I lill ill' III! I; I~I 11'11 '~ITI.irrrl: 'I i ~;: . :;I~.. 'I W:·,:f :;mi::';I:· ·:;i.:I;I: :·il·': ;i~Hii T", ,:;;:TIf!, :·:i ::iij.;li iiI' , ... ,~~ ;'1': 111'i It II !!i j!~: llil ii ' , . ' I : r rl!!'-Il-tHil.tj·I'::I"I'j!JIIIIUlii 11Uj:i'! I: IijlliU:U>i:ft::::@jJj~~i:,!!r!! Iltl:: i:::!IHi;':lilj!j;:ili!:I:j,1iP:!!H~:fr:H Ilr H:'ll·!t!~+:1

j

I' t'. ,i. 'II' iii! I;i iiil~l:II[\ rn.t 1iJ:: I I' fill ~utJ~ ::~ ::' !!mra:", :1 i !:II:i IJ I.: iii:,!j:! :::i I:! 1,111' ! !I: 'iii ii! !dllil Iii it!: iii!:1 i !: . I:ii i m:I' i':. :::: ml Pli l1i: nIT i:D Jtlll~l.i.i ,~lli UU] I:jj '~I ~~JJ ~~t if·· ~:-:l::i; Ii,: i;"I~l;i l.H ;.l,j! iiU li oJ,!, I ~:~ dJltrm: r~ ~1!jll·ml , ['I ~Plli liJ'1 lhTji I 1111 II! I liTI\DTmtt ';i Iii', ., \;~I, :i!! I!lt lit! hi~ ;j'lll~i:!;: lI'li~~·jl.~lrJ i~ . : ln n·1. i~.itf.~:~ ~Li~~:~f1d~~i i~ll~il~ri'i ~ :~~',:~ rAI~:I: il!l iill!!!! !lliIUii: Ii tlLilllHll ~~I1 ... \\l:~tr!:~il!!l#n ·11 tI M:! .;;: ItI,:I; 1'1::: ' 'H ,!i , >Illllb TI r..~,'R. 1:'<:, !:APPLIES 1 ." i:i.~' ,. !.II :::' 'Li:.~~ 1:"" ' \ii~!.!. I:\!

~ ;;Hli; ':::~. ~I, .::1 :::1 :\:1 I:;: if:' ::ti ' : .·'1 I:j~ ;11 ~" ::A·~$i;l· '~"A"" 1!W,t'···~: 1"1'::lill:I;'III'IIIII'lllllljlllrll:;~··I;~'~ :::: lTlrth ~I:: . 7-': ~i'~k:Iftl.l1l:I:: ~II ,1ft: I' , r: : limtt . ~~~"n;! II!.! I ! ~Lt'1U':11; ~!!~ t.u :;:! ~L: .ii! ;::i :1 ill!! 1'1 , ,I:' 'I I TI CI :il,' :::i i:J I!d I'I!.! d~ Iii! I:~ ;!': !:l! till ~:;ll'iii :1!. U!~,~~, iI' !:j'~ I ,11!: J .~ !lh 'I ~11iAU~~~li.:--;·:· ·'i :1: I::: 1::: :.:' I;:' ::li I~:: 1" ,h ".,11. .. I .. ITII'"' ... ,. I" .... , 1 .. 11 .. I,. ,., ''', II: II. I:! . T;4,q~, [:: ,I!:III;: q: ,: .. 1.;....::.. :t,:, I::: ., .. :.

I . :DI :':i .::~ I .::. ::;1 ii~~ i~Ji!j llill1 SiANDI1'D tJ AND NON- SrANDR~:O A7'fVlOSPHE.RE5 "111 ii .. :. : :0l: +·l.lli;JL llil !:l . .2fi.r:r.J i':·: 1IIv;' I :j~ :1: I . I.

l !~ "'.i..': ..•. : .... l.i..,!,. :Ii :,.: '~: i::: : .. :if;:IT- ;:i; iTI 1"1 11'lllllj'rI!lttjlllln 1'111'1'111' 1"1"1' 1lllllf\llil Jll[ :11 [1 m:t:·: ·i:: .:. II!: 'I:: :::;::;:' ,.: .. , :,.·'I\i:'':i' I:. r:; I,:: :::1' 1 11 nt'i'. ';1: ';11 I:~i ::1~ :~: !j' ':1; !II:I' ;: t lj,j ::"[' ,I ,1.1 ::'. 'Ii'~ :\:: 1 II I I ::q 1II1 II I iii; !:.; I " I.!: '::: p:, : Ii ~1:: ~'\. ::;1 ,t\. 'I:: ':";~:!lIW! :!I :11: :11 1 ,,,.,, . t' it -, ~l .. t:~ ::t! l~~! ::r: :.j' :~It t!r: il 4 It! i~ ::~ :1. ih: !fl~f II!' ':1;.:': ':'; :!:! lii' ;:: :t Ill: ':, I:: ~:;: : ::I:':t i'!I'::: :!I! ;~:: ~J!! ::it :!t'I~'+ : t t ,1+,! "·h! :t f ·t ." ;::!, T '1I·:ij I: 'I ",. Iii' .... 'I" .. I , .. , I WI' "JI,W' ., 'I" I ~lll ",f I"· ... "', '"114·''' ·,'1 1\1 '.[' III .1" " .. , .. .1, 'I """ I .1" ·!i' ",. ~'ll' I' . Ui' 1'1' fJ"[' 1: , t Iud Ii, ,'ill II. :!:' I t l:j: :j!' iI' ':11 tt' it HLl4 '! i:iJ 1.: I lU: .. ll; lU: j:l ;ll! ,'i il!i ll~ Ud H~' 1':1 ILl ~l;! HI' lillllll: !I!i :I!I :11: SI :1 I ... ~ :: ~itl ~ Jll! : ,I 11 ' I Til fl 'q , .. , ,,1·I·il·I·!I'· " .. "1 II f ,." 1111 I'" I'" I·t: II 'II "II I· 'I' "~'I ,,1, '1 1 ,~tt 1:11 'I' ,. 'Itt I", I' "t ,:;11;,· II I , " ;!~' t.rr~, ' W:fj .. ~l I ·rr·' ., ']!It',f'l 'ill II :'1 iii: ,::: I l,ij Ii:, ':1' lJi I j' 1111 im ,!I: .ii' :': i I 1:li I::, ":: :"1 :1:: :.:, :illil!\]' ill I : 1['; :1· ~'I'I ·1/' '·:1' '11 I :: 111·:W,f·"1 I '\i '1 1: 1 !:l!j i l I I+H+HH~m" r tIt 1 .:U:4: r·t!1I :t: :: t' I'\.t ", 'ill ,I,: Im'l! j I':j i::' II:: :1': :·11 :::t :!il I;: II" j'I' ,i .. : ,::: l " .:;: ::, ;:i :. ,,: Ill: ,; III 'j I: : t.l tt I II I Ii ~ I "iI"Ii": :. IU' r~114:: : mIl .', I Ii I It I tlJl: 1: 1"1 m· Ittl '.111 I::: :1· ::" ::t; :1:1 :[: 11'1 illl' I':fi I I II:: 'II·: II,: :1'1 ;:11 \'1 II 'lili,Till I' "iii: 1,:1 Ii I! I P '1 I "I " ~.Iil 'I' !'Il:!: ~ "I I". Il""'L"'I;Hi'll'l 1 Lit I' "I "ll! 'U II I '''1 j'll ,. ,

I

. II I' II .' :1\1111 li:\, I': ;" t11: t I HI 41 rrPIt-'TtI::,; I' :1' irii H!; tl:.! it;: ;'+'rth T:T, j TI it l:l~ ,H+ I iff, i+:. :r'~ Httl'llt ~" ~1::lij.I': .::' W#:i' If[~' I" Ii'" :.

I ! Iii ~'I l II 11 i H' :1 I I'li liP ill j'l 'l' 'II 'I ,:!i '! I lit iii! ::;. 1.:: ill: jill iii' :il'l 11 I ij l!lIIlII'II': I!:,jl !! iii· 1:11 'i1 :"i}lil'! Plll! ,Ii I I!I iii 1ill'! iiI H f f :t i' jli; lil '1'11'1 ilr nd Id I I I~lilll:l I Ii!: I:d 'iii 1'1 iili !i::W"lj; iii'; nil !:i! ii!,lliUI P illl' i ,i:1l111:1!)!1 :i'l:iUiHi:j ; i:i; ;t 1 rIll :\ lrll: I l (1 1:, j~i I I Ij, III 'I .[ II II ,II' .Ii· til' Ill' U'! • .:lJ ;.t; !. 141 :!., .,!I ·OJ I!I ill I I ILLl~: '11; ,i:,8H +Lll.!~ .II ' , .ill ' . lill , .I!~ U-- L!l [ I Iff' : IJlil' I j' ~~:;t: ;!: :1 i'li : :, iii! ~,; 1'1 i 1 '[ 1.1'111111 I.,. :/1: [II: ::fi "i'l" ' II . ii; :I. I::: :IIT ilP :: III l!Ji'j;:: 11'; :I,'~ ;;;lII:!: I j'II:W~" I::: ~III' i 'Ii' '1l\I'ij

1 l

Hi

H i ~ m I I iii WI ~tH !I If!~ f If HH rill It!~! iirJ dp HI! qH~ 11'\ fill !Hi :;:. Jr: ::l dH lHiJill i\i H Ii! dl'lliJi :.:: ;, ' .) III l'II hJ8:Ij:l: Hif!ili il! I t \: I hil h!hi 1j I, I I Ii 1I11 'Ii'!l I:;l' !Iii willi I II m.t I L:,I ::;:llii: :111:;~:1 :1;:,;,:' :L! ::lIWl' c.:..u L' "".'-'.'''' .:,' 111:~.::'!!.:! :1: Ii iiJ.l1l :1/ :::: :ii: ", I ilill iii: I !I!

u

l l '1 : II II II " ;:1'1· IITI III :1i1111'~: :illllr'l \1' tlj \ .... [1: ::::ttm I' !1'I+j'"I·:;t ;r~II::-:I:1ti ':jiI:11 iil'i ' 'i~I'I' nil' 1+++\[: ql' I'~I'I: r~:·I'I'~·" ~'I·:: I~: 1· .... 1·!1 r:tt -~~'!l . I: ,II: d '11'1: ! I I J' I I I: :1· 11 1/'1'1' I, Iii I I It I: /1: 1 . 'I'll I: :.: :.:, I:· .Ij: ::1,1: ' :11 I II I I' . II I,,: :, :'.:~.: ' li':i I: I : II '1. III Iii [Il\'l' ,~l: I . III \ II I'" 'f!iil· t 1 I 'f '1 11 'I 1 I '1'1' I ~!" . "",. ., ,j .... , .. Ii 'I ' 'I' \, .. "I' ,... , I I !' it'l 'I' ". l' II\' 1 It~· r , I Ii ! d Iii' I ,! ~ :u: Ii Ii lid: ilii .1!lli lllil!i illllill idill j iill jill Li!J.lLHII :itl PI il! rijdL ~i ~lj lUiijj!:J.; .. : iii Ii: .Ill iil!:li iii! II ! Iii!! !il~ 'iii !!

' : I j P:I :1' +1 ~ III I i:p .:ffll; n:!: iii: iln pi/mil! I TflT Iii! illi: 11ttlll I [PI'I !!!j !!'. IH'@1I!i1':lillll.l';' IIi J1~~i pi i! 1I11'1'111 ! i ill! iill ill! I il ' ! iii: 1111.'\i: iP P l: j I ~ li!l t' , • I'WJI.I I:! :111l1 II:! till III" I 11 [' 1]1' I.: ,I, . '1 I::. :.:, I::. ']11 :I ' 111'1, It"·,I" ;!t. ~ ... ., :·:1"", .11 ~11~ ill" \ [' 11Jl'j'j",' I .J [ [,I: Iii· t: :,1 t

t l 111

I' , , , I I" I ,,,, .. [ III'" I I" "II 'I' , II " .. I' \I . I' ,1 , ' ,. .' " . lill : i '1 i i I: i I !I 'II .... !!:3"'~ : ' .,' .. " ' 't ' II" [i I 'I' ' "I ' ,'I' rj t. II IIIi! t: Iii Ii::! 'i .:: 'i ::1 : iJ· IL: I: 111 j i:If~lj :li: "11 1m I :ilj' I,.: :::, II!, it! Iii I • ~I I: 1 lll':,·:;ij :" 1 I \, I ! 1.\1 IIIi II iiii .t:j [ . I'i' iii ,il: , Ii ti!! :111 ;'1: 1 fIll I;:] .; I;;; t·;; ::li'~, i; :furj+~t. jt i :tt+! it\1 i;;t iilrt I iti :rTr :::~ ~:: 1111 ~~~ ~ -rt:I:.fr~ ~~;jf, 11:11 ri·'l ttli:l~tft:~ ,I '1: l'l~t\: 'I: ; ;:Ii i,:; II' [1' ,i'll :If: 111' It!; :;1 1 Ill I '111':11 t ~I Jilt ',:1 :~:f 1:\ ;:,J I:' JI'I ;1/111 'I :11 i ;::: "\'r: 111 I ::1; I:i'~;·# .r.;:' ,I\'! "'I'll, ! '.: I:'! Ililill .. 11 ; :1:1 1111 i: I' :!! 'I:' I [' :~'I ;'\ l ' j "I'll ·I·a . 't fi .I j., ..... [' t'" +.1 'II .1, ~'" ~"I .", I Ilr j' ""illi·" .,,,' I:~ .. ':1 '11 I, .1. ,,1,1,1···, '., 't 11-1 t tli' ",. '1" I" .. " I." t·,· ..... :.

t 1 1 1 ",; . ,I :'11 Illi Ii Ij,II:II: .::1 I i: "'I' iP::, Ill:' :':1 ", I::: 'I '11: 'iii I': ',LI:,o, 'ill.r. I!t! iU" 1 1 1:: ·'11 ::,1 1,1: :,·'1 ·1'1 I" : I I' II :1:: ·lll·l: II I' I I::: I::: ii 'i:: :t!jj' i ~~;Ii ::I!:" ::.'i!!:: :, . i:',~~ :::: :";i~ ~!: !I' LL Itml Iii! if-i. , Illg~. '1111/1 I:!~ .:~~4i . : .• m i: 1'111 ~iI I!i I' 1~lt ~p 1+1. IF: :;;~ :' I:, . , I ;::i :..i I:' ]1 ~d ~I: :1:: ::i '" I~' It' ,,' 1'1' II I,,, .. ,. "., II., "'1 .I, .. /, 'I" 1m I I III 1,1i I". ,II! '~"":;J.IT:"1irT'. 111:~ iJ'!"" 1.11 I[ 1: 1 Ii ,I", 1"[1"" '41' '1111' I~I ,ijl. ,,·1 '" III , I! ,,', I . "I II,: 'liI I llll "I' ,. ::\ "1 /:1111 i!'IL .I" .. " IJ.~· "I 'j" '1"1 ,,, III] J" lH~" ~~! ~II ~~ I' ., 1'- ,r:il' IJ!! III i!' "1' • '1'1 '1\ ( I '-!I' 'II 'II' I!i I 1'·\' "I" " i i!

1: 'I·I· IJ r'i t'n" Il!l II h JjJI'!'I' Ul: [j':; ;;;I! \': 1 1 , Jill:' I . !dl. .,' :. ,Ii· , :·';'H .,:: ltrl"'1 ,1'1': II~:!' 1; :,,: ;1:, :: , II. til': n' ,,) i,. j: I' ::.: >!. ;Ii: 1:,1 1j ,. I I I II Ii ,.,. 'I"" ·[1' 1'[11 " ··~'''rll.'· '. I" ':M..!'" 'i' ill'· "'111 ... ~e'I·· '.'''.' 'II .", 1""[" 1'·'11'11 ,,, 'I .1,' I II::' , I i' II I: :l:! 111:::illj' 'm' ~i'jll ' ~":*'i:::' 'I'!". 'ii ::q d::,I ..... ·I:! ·;,1; /:1, 'Iii 11m:' jlj' 't':· I,;, Ii:: Cll iii i I !lli ! I:: IIi! ii i~ ,.,1 ':;.,;. :1;;!LlI, +i+1'~:14j + ::, II" !:; I ,.11.::' ,., :'1+. H l:1l. +, ""!', i:rtt' ' ., ,,·r:4 ~ :'I'jr ;:+IJ.i~'fi:: 'it'- H. 1':1 il'l ., . ,~.+ .:~ i· q': !-i:! ·:·t ;'·1 "II illl' I : ,,:: I I' "'I'~' P. ;....:·T~I'!· ~~c:7trl' l;jj~:1 i Hi !~l I~r Q II ·iHl :YIIW.JjJ.i I} ~ !!:: M:i Ii!l ~ ~"I._i Ii!: lUi \' li~8Tii !Ii: ill;flllH ill1' Ilill jill! iii: 1:: ;(}j H 11I1 I'll! in, ! iill I d lLi l~IH pll i:;! \·1· nd iPI l I:;: I ! III II Iff! I i it!! w.+fW:· .~ :i: ~'II'. :1:'· +H\ i'ml 'I I I:!' wtl 'Ii f"li , i. 1:1' iili: ;11 1 li!II!11 'i Iitl ilU i: : tI, I:i. 1:1: ::11 i: I ill ililli III III I,! :1:: :;:: di ill: :11 L 'tf+il';· :1'1; II' 1,@III1""::;;··;;l ;; ;:r k.~r: ;: .. !tf¥ 1 '1 t tn' :11 tfl ~I:r i-'I :f •• ~ I ::1 1 :~I! it, :r! ~III~~ :)' ;:1: !!ljt"I'Ht I T r~ ; T':'1'11r~ !:: 1i;: ttlH ~~II 11'1 II :11 I 'I "I!!! 1 '1: 1\1 i I TrILt: ~~:; ti:- :1 ;:m::nl l I' " I' I 1::11 ,. t' .,., ., I I::.. ." , " L I 1 'I I, I ~~ 'III 1 ' .,'" ,.. ,I I "I II III 1" I I '\'" I, iii' I 'I I'I! I Ii: I, , j t: ~' , I l 'I", II i:!: :':' H';';' .;>'If 1 i, H! !::::dil'lj';" I:· ;':1 i[:1 i. il:.1 ~!:. \. i; ! :i!' 1::1 Ii!; ::, ~~I' t, .1, l'iI lH, 1'1 :~' :1'::: I, ::t! ill ' " I ttt! ,Pi \ i! ii : ::,: :.:. !:, I;.: iiI' lci~ m .II! ':11 !ll ,.!! '~~'T'.. T "I. ,I I' [ I" df " .... iii' I , .. iI ". I. •• '1liil ii'l ,!II·', ii;' ., ·'·1 "Ii II ill iI ' 'lJi [ii' lit. II:' lid "I: :. :1: q:, ·,Ii ~tl:~::W\:;~!~l~i!il;iii ;;;!f'·:,b·.· ; ... : .... ~~::: > ,/:fciJ~i :;.,' ':~~!:';":'!~D,'i!! ;:: i;g~ii):: 'H~P , " !~~', :,: iii! ;i~~ii:ii :"I;;~~l :;:. : ·,·\.'1(~::\11 .': I·: "Ilr~; ,,~. I::: .::: . i. ., '.\1.: r,l" ,::: .. ,:,: : 1 ,: I ii, .. :::: .::: : ... :. ,'. . ... I:' ,I:. E.l45 KNUj:S I··: :l >t-; . -~ +t\T'} .;~ ............. ·~i;"~' I:j : ... ::~ :: .. , .. :: :,. '·i··:: i'::~''1' :::; .. :. :1 ... : ... ,... . , .... :: ;": iT T: i. :~::I' .i ... (. ~ .... : .. tAlt 'III/J .. .... .... . .. H"",,", INu ", .. . ,. . I ." . .. I.:,.. ... ." .... ... ,.... ... ,···,·1· . , . . " : " S I': ,'.;. :\: "7:1! i .. : i . .• . :., .: i . . •• i ; L ,!. ,'!',\: ""','" '1'1, ~;~L~lt; 3id J ",'!," , "'H ::: ·'F ,'. !,i, ,.', I u.~ '0 X '0 TO THE CENTIMETER 'R x l" eM 46 1513 n «;; K£lIF"Ffl 8r rSc;FR cO. Mo\lU Iii It <;" Ii!!,"! If Ilf II I! 1l!1~II' ii!! It:! ill! 1l!:II~I!1 ~~'II~I: !~m. III ill!~!'I: i ;j:~! ~Iii d!! iI!!~l'l!ft:il 1~::I~'I::i till iii: !;:.~;I::: rW~:i! ~~i!,I]I1 III WH~lrrln~t, ffi: IIllII!!l! I IlJI!

'~I! 1 :n H+ IT ~,.l ' ., ~'; ~l,t·l,.ll~~i ~rJ' 'I "I·.. !j.j LJ~"" ... 1 I ", ••• , '~". ' .'" .11 iJ., ~11l II· rt.ll! '''''I!!, . 1" •. !

:11'1' !' I . ,: . f~;': ' " I: ":' '\,,' i ' .: '::', :i" I': li'l 'I: ;. ilili' I:: j',:' I::: 'I I:;; i, I ' " """,., ~" , '1' .." ,p. M ' . 'Ill' il II' "I 'Iii ' ~I' il ':I1il' . I';~I',[~~: :i':;:']' i.il .~·I :\ :'1' [Ill-L, , .. ".;, 'I' ~I'i: I::' : ,,;,~ililL. ;.:: ~7-"":i:. . ... >~ :: I ,. ; ''';llii: :, ;i· I~tt t l t II f';:} ::1:1 l·,i I:: ,:!I 111111 I II : l' I jl'll ill! I'll :111 l"t . d I;:: ;':: : ,; : .. ' '~oS T~l";&; I., , " IlL' 'I!l I'il t

l

m 1 I' , I rrttj llilir., ~:I ,t 1' :llm' "':: li'li: ; I 1: '1 ::t! i~' I :m'! 'i!t :::1' It:: ::.; ;:ll~TArJIJA1tnlJ:)}~AfNn~!tIO~lN~~srll~Ni.DII(r>~II)7(r.~~ri. ~[-~~;:l t'l' ,t-!, :1" t I 1 1 1 I .t II I I i! Il i' I P ,I :, I: I it' , I i ' , 'I,; I' I "1- I ': : 1'1' Ii: : : I: ',:, ' , . U 11 : I "I" II I 11111.1.K : to. .:. ::. I ' ,; I I i I I ~ 'I " , .IIi, ." ;' Ii II ~'.;iI.'" 'lW-t-:-~,~,:!:!. ":. I... ~(i ::., ,u. l>;\ ,~'. I.;.;.;!". . " '. ,I" I , 1 11 i i I:: II 1:: I'ij' II !II~III Tl rf!IIPI' "I'I' 'I:' i:' l{, II II ill II I II 1 : )1 I ::1: il'il i,li'iiTT"'7: ::i i "I'; j'WI':l ... ~· ..... ,~; (':Ii ~H·'1;i "Ii' "~~I' , .... 1: ;~: :11: U,'II :i/, ': i '1! I il. ' J I '~jll iI I : Ii: I: : \·11 t! 'i1 ,I, Ii It, 1 I '~' I' I :: I I I II .:; I I, Ii I ,:,' ,I 1lWJ.; i : i':· , I' : II I" I 'f Ii 1'1 Ii::': I I'" ,.. ... ,;: f.11 t D I : II! ,'I i" I; J!

l 11 ' I t, ri II;; I 'l'f'i.t! t,:lliiliiii,' tl :hif1i 1 1 1'1' IT I i 1:"" ~I ~ii!ii$'I'irl1i1idlll1liiPill: liiiiJ !1:::!Ulfijil IWJJfl'1\,j'ijiiiJ;1liiiliilmJ:Wiili :il1il II I !; il iJ ' J' t t Illt~ I ,!lJi. I III HH ~,t+t I 1!~!-I,i+++H'~ ~,fjI " • ~~' I it t til Sl·~! ill ilH U 'Ii · i II If'! ll" ~l ~'I;: ,~hl 11 ii ii!j' I Ii, : II/! '! i I'I! 'I!I 'I: I Ii II I q 11 i I I Hi! !i I !) Ill! lin lij I u.;;:'~~;Ui1J.l.w.L I i lLUi! 'I~U ili~ll.uLI iH; ~1i ~i ii ':; :H\i~ '~, 1 ~~ j~ ,,::loitif! "I Hi It 'II' I tt I III' t,J 'II "" If'" ... 1 ,., .... .t,I~!"V' .:.')fec.Ir.rc.llr.~kl'i""pW$'~.. ,·'t~;,t: "'~l' I~. II:! :tl!~ :~.! i!1 I', '~ ;,. iUi!'~ :!:1 :!I! " I l~ I ! ,Ill II 4~ 1~~111 '~4'n~ !it~+U l#'~w' :;U 1Ut Jf~! it;; ~itl~~: :~!: Ii!: i~+~:'%I~;i!li!~! i:!. ~ii! ~:~~~: ili~ I~!: ! 'I 'f "\ 'itt I:l #1t4" ~~.: ::)lH-s: ::11 IIIII! I!! Ij~1 I I 11111' 1III II' :11 :j'l iii: '::1 ";: I:;, I::: Iii'" I LI'1.. l.iJk' '1~:;i :~'" 111~~WJ' "iFij~~'" lilt' '~' ~fT:;~1 ~ I:' lt1,' :1: !:1 . II 1\ ~ , " lL~ , , .,,,.. ~II I 1 I , , JI I I I ' I I ,.,'", ... , II . .." .... (j It ~" It': ' ., ,A' ,.1 , . ,r1- ,ill,' .

lll; I: it. It 11 ,,:," nl:~;.o.Itl;':: Iiti.i.:~;;;, 111i :II! 1'1' II!!I: I 111 ,t~' ill 'I'i ill! ;i:i lin :::; j::: 1;:: ti:i .. /'! .. ft~ '~II~ ",i.i.,,~} ..... : ~L.'J~IOi~::j. J.:! ,u:: ~~~~l.Ij.t ~111

ill

I if'I!' 1 1'1 " 1,:1 . 111:11;~.'h:.:::'}~~'.".FH.:Jc.+t- Mil II :/il- ttHill.~~;:I'::::I'::ll;i::I'1 "r"rr;:~' ;rl,· ... I'I~I. ':fi:,-v~V:(l',~·:: ,:·:O~ :, .. , ::, iii Wi ti ;J+:H il'll itt' I: ill '1' ~I'" ~I: ~II .1IIi.I;~>: "".~.L!; ~~:' ~:Ii' 1;1 :l\IIIIII'! I: 1 : I'; 1!l, !i:',iii : I::: 1% ,iii iii; ,:1\ I' I!' .il ::.i :',j i\",'i ::··I:i: 11:;1): i'I': iii: liq·.:ii .. :: q;. iilq ::'11: ••• .. & t • I :J' II: !t' ;ii!- . ~';~ .. :~~~ , . I .;:,: Iii! 1'1 :~ t: ~; III: ill! ~:t t:;~ ill :.,1 I!!: ::1: \1., ~lli": !l'. :!:: l':1 iLI, .. t !tJ ~i ... t'll 11!~ ;;-:-: :~~; I'f~ I ' .. ~j r m : :: i I: ,,, It.. ; , , t: '. ' : if'.. :. I: I r ... ',. ' , ~ ; i , U l:l' I,' I, t' ::! I~I i : ., :;. I : I: I!': ::: I I: II w': I I:: 'I : I'. : I : i : 11 ,;, :' .. : I I : 1 t, I;': ';:. : I jI , :: :: I' ,'.. !, 1: 111 \ Hi :'1 'I it' i~ !Ii: II I II.' l' ",. J.lll ,I" ~ ~J.:' .. ~fi.Li~i •.• , oIoI.:i'~ I nil ~l I m: Jj~~ iW 1,1, :::1 ,1: tl:: II I : 1::: ': lid! 11" !!P Itl: ~Llil ' :m ,iii ;n llii dll I;;' H': ,I" :11 ttt7 't'l . " .. '~il' I '1""''-' "\'''' "ffirll'''~IJ.''1 '"'!'1IiI:±~~~H ., t, ,', I 'I' I' "'II!:' '·,1" " trt~ I"TITI:' ,+h rrtt I' IfW1M., I I "I III' 'I'" , ... " III!' I1'1 r p: P Itt I" \IIi I ': i 1: i'~~i~! .. 'Sl:, dlL.!l -:':-4 .:" 'i~:~ ~ '~"It 11 i II: til III :.1: ::" ,Iii tq ,iii q' ,i: It I I; ~q! 11,1 III "I:!il til P; f1! I!lj ;ljl ::,' ,: I ,1 ">! :!i U; .11 H-l,' J IT' It l'IIH~I;~ I;~'''' "~~;~~i; i.lJiHI:I: ,I:, . ~ .,,: 'I . ;;1: ;1':1 .1:. JI" IL, ;.1. 1:1 II!: 101: i!ji 11'I 'iLi I II ill .:l: nit' l!j :ttl :::::i : t' 1: ·:.r' r,!, iTT If) 'if" II . 'I.... ,to • "I~III 'iL tH' I,'" . 'fS" 'I' .,., "'I "~ ... If .. "\' '11' I'" , " "" 1'1 1"1 "I I ., 1'" I ",. 'I, 'I' I II'

'

Hi 'n li I I', I I:' !i~W.I'I·;, "~I' II',,~WJIJ ~~I 1';/ ,." ' . ..:.J! .!:~,I::, I;U" I "!! t"~ mit'II' II:' I,:i U'I:: ,I, .I.! I ,ii' !i' iPI'I\: illl'l Hi: :I;: Ii,: Ill' , I l I I r:~1.' I.·. t#' ::~r":w. 1m 't! ,I ~~I '1'" .," 1 I otl I' •• III I I I" I I " •• III i ,,,. 1'1 ,.

m'" ilII; II' ' 1'1 fT'" rr nil ";1r.T: ,,·; ~, ,:, I::: :!"!': .. ':;: "1i :1"', .. :.~! !~"I"I': .. I·' ,~rr it;· ",t '111 " If: ::~ 'II " .~ .. 11" 'jf' "I' "" I!' ", 'In l 1 '11, !r..; I!i I I!'l II tIl I I ':'i :;11:'1 : ... ' lli l-iliitllli'L" ,.' rl~4 '., I :.j "I " 10;.;,;.;/1:': "::!, ,:1 ',:.: ,II, :11' l. "Ii I, : iii,: Ill'jll;1 i:' ,I I:,: ill. ; ~" :')1 1 l \' It l' H "'11'1::: I.; Ii; ;;" "1 r."i li.n: If: 1', · ... Iii:l.;U::IY "lliD': :.,:I.~~ :1: I:: I:,: I ,. 1:1: 11:. II : ; ::;4 : ,I,: •• : :il1 .l!J. .. ;'I~ Itl: ' H q t :\: 1 il~.: Ii I: i iii ill i 1 Pit \Pi 1[\1 ilil i : " I~ ,~~ II iilq~I' ~~~I..·.i H :"E': . iL [j .~~:~ ,::: 'i;! ,I!I ii!',iill iiI' :li: iii: iiii ;::j :::: ,:: Ii 11 I l c..I ;11 I ; I~:;; Ii Ii!" I" , II 111[1'·:: iii'!':; Ii '1 Ii' ~u' i' f' ill: !Il'i; I r;f. iii": ~ h ~il i': m: ij: i!"(. :=~f.i;i:~~ ":~~i:Tri-t:t :iiilll~i.. " i' " ..: !i:i !.;~:,-.-H+ ~ ~~ I;': ::;: ::;: ; ::: ;7,: ;1;: ;: l 11 l ', :!\ iU' :, "' I : J ,Ii I!' 1 '1 Ii I I I 'I 11'1111';' ~ 'i~ 1,11. : ·:tt ::'lI~i' .:' '.' II '::' I: ".... . '" .:': .::: .. : ill :.:: ': 1 t t ..., r,H ~ 1.. + t-". t 4U ti t·\ In d t t .. ,:~ "~11 • .. t· lo.- ........ '., &.1....1-" •• , •• 11 ,!., ... ~ I'~' .', ." I .... ~.'"' -J......~, .. I •• ;t 00 liP :IT .. · :! lIT III II , Iii; Ii dq Pil iq Iii II : II li I I II i l'il '" ' "iWli i!i ::i! Ii;! it:: l"i ---. '~~_ ... .:..,~ /',1 !!ij I!:; ij!i~;il j,i.':,.. ... - a~ru' ; .. ;: ":; 'I H' I ' ! I':: I:' '1'1": j t Itt· III!II : It, +t-Fl :Hl I~' i,~, .. ~~,iiilrhT :Y :::. ':::r,'r;; ;r':lr:;;-'"c~,,!!!" ~i i~~; '"~~:~t~IlH-'~:;:' ':'±4'~ ~':U':--;' ~:~till1'I' ,::: li'~ ift I I III It I i Itjl I'PI 'I!: qlfll,lj I'i III 111"@I'i,'1'lilii ll :I:::i'i' :i:: i:i;I:~.i.i.L' I::! :i!~ iiilil!' ;;1: :iii 1::1' 'ilit:: ~. , F'.:! "i6i' .::::: ,:; . .,;,1:1:1 ttl' , ,:; "t It • I 1 lil 1 .1\' '1\' I II. 'tt ,I ,,, d, 11" ,1.1 ,I, ....... 01.... "II'" q" .,,' '" d·'!i·'·' .1'1'''' "... ._- II!!I, Iii:: i'~ ;!I !j I II I 'il I Ii! W, i liUi 'iii /' I I I Ii litl'r I 11ft I I II' i!'i liii:ii!l :::i iii! ·;·'tii:: :.... ." i::'II,;:IIIIIII1:;' iI: ;i;j :!j:lilii iii' .:. '--ttt:':-~r"t~' ,i fI; ,.':: ~".:., .:., ,'" I :, I~ I •• :t _I I I Hf+:1+ t-, !~~ .. 1 :: I " .::' +~~t++!:Jttt+t !~~ h" :': ".' , . I, d t ~.": • ''i: :::: ~! :. ~ ::.

"t, 'I' iJ! ,1/ , .. , 'j I" III Ill' lif "" "III!"'I~" 'II' "I!' ,[fill 111.1 "I ,., Il" ·1 I ill I .," "" "I' I " "1 .111 I'·' ,,, '1·' I'" " " , " . Iii ,,,, ll: It ! =1 ::t t':11 ,:" 1 I : til !II! :111 I,;: ,III,:.! 11 I Ii Ifi' I I::~ 1111 I::. :;1 i!~;! ;:tt 1\.: .: : tllt :;:1 II: :!I ::, j:: Ilt:1 1":1:' " , .. , !I, I t~: :·,t~l4l ::', lit. ',,: '!11 I' I !il ' ',,: I!~!:~!':' t!-': wit'IIIt'lil t l' 'Iiil' I :~11 l~:o\ 1:.1' 'I!IU'" :w.:':r t.;-;:, 11W'!: i':'I',I'11 ::'1'1["1:' :1:' 11:, .11', :.: '1:11 ,.:: ':1"1 ::", ::'t: I::: .::' . ~I"'~ I i"·· 1,1""" , ... I I . 111'1 ."" Iii· :1': I~~W."· " '~i;J,j 'I!~ !I·' " ~ .. I 'il' ", " .. 'U' '!!i ,,' 1'1"'" d... ", .. " ...... 10':;' "I .::~ :: : :.:' ::! :tli: ::. IHI iW, , It:: I: ill:: .1 I I ,r ~ rIIIl iJ;~ ii, Ii, .t:: T 1;:1 :. tHt l~:~ll: ill 4-4 Jil_H4~d: lliJl Ll'l :: ; II;: :!:: :;:i . ;.!. ILl. ~ ~+ i!:: ';'11 '~'" ::1; :iil ilii i;I': illl,,:. I I!:: !:~,';i 1.;.iotil::ii·i:!lLi;J"i,lili' 1'::1 H'II~_I.I: ··i!~i-+WJ:I" ui1.I',,~UIT ::illEWFi',:JllIlHt ii,i! II:'· 'Iii' Ii:: :::1 1:1 Il\'i !":I;!II' ,il! ~~5~Lil :~~~J!lllii: iii .. ,. :,. , "'f ,101 'HI" l FB U" t· III. ':~~:'Ji,Cl:~~ ';~~'~~ II~ 0,,,,,.., U~i'CI' p:~~ 'I..,~~ '~~,msS!" ~U~h~ ,. I' II "I' ,,' "~It I I': ," '!IJ ,II ." , ~2 ~1 '. ~![! l~~l!i :lll till iii! ~i! f!i! !!lJ&I¢.:A :'::~~i:l~ i!~'~!! i~'~iUi~~~/ :'j~~: !i~Uri:'j*~:+W.f ~;j; !~;. :L ~1;: ~Dl~~j~j4J.~~ :!!! !!!l ~:.':: . -:::'~~ ~~:n':j'; 8i! ~~ , . " ~ .. , I:!!'" I 1. , j" I'" ".;. ... ;1:':' . il. ·lfb'll;i:.u"i.J~'";"I~'" l.li: ," ··1;' "'.L:" L~L.l.;:.i.I. ·~j.,a:"I"'" ii' ,," "I I· , itt' '" :11: , .. I .... Il' iili ',,' tt" '''\ ;;:: .ii; .. ~; .;P ;1:' I!Ii :: d I q .i:i :!" .uuo.i i!,t!1 ~~~~ ~:i: ~;~~ ::!;t:t~ VE:id: S-M,wfll!,.i ~~:! ,.I, " ,. .., " ,I, '11' , I , ,'Ii II, ., I .".,' I , .. :~i: :;;: ::'~l: iii! qj!,li I i( ;:: !iiiji:.,mi:':I~.i,;~'lll:. :~ :illij:iL!.ll i I,L~~';lli . .' :!i ... 1::' ,:;; Iii ,I:: '.:,' .i,: :. i " .,.:. : I':' ,:" 'iii,·.:! :: . ii. I:: : .. : " :' :: ::1 ;:~:I·;iil:' ::I,!!I :tl!l: '1Itl'l\ ' I'i ,!i; ll~t lj~'~::~~~t~i'U:":i it I ~nl::~ :ij'I'.~~f~ ;j:: :1';1;: if iti ;:;! ::;: 1;1; r:: :s ~:~~.~ :;..+~ .~ ~~]ID r!ill~~~~! t.Wj;ij·'ij~:;.a) :ti j ~:::!:\im~, ::i\ :a ~f I :Iii 1 U!ll: j::: :;:: .. -:!: i:l! iii! iiJlu H I iili Iitli : Ii ::l'! I:~::ti iii: II:: di: :I:,t JmllP WI +filj !iii iiU ;'''' :. i; .! ~:: 1;;; Hi' : ttl':' ;::1:[ ::i: :li:: iii: :: .. j~W ~:;'. :1[ ,i::, :t.I~' ,:11 111",\: ': ' 'l'Ii:,: :;::: ,: jll! iWJl I 1':L l Iii: ::i 1 ii :," 111 I'll :1.1, Ii::: 11. ;,1: ::::":,,' ., ):' I", .. Ii 1111:" :ililll:i ::,; . 0: I:: :: ,:..:1 i l· 7-''1-:: ';;;',·f1 I:'; ~I'''i I ': :li:'Tj::I:~~ '>q ;: .. ;:~ :ifi'I!I' ['1 ft I ::i tmlll i Ii t:'11 :'1 i;r' I,t ::ll Wi :'I,~;rl Ii; i::: :-:-:-: ... ;00 .. --- ........ -.1' :, ,",:~~ ilii' ';'1 !tU!til! 7Y. A,i; . 'Ii ", :: ::: :;1; I:: ! ':; I 1,':: I,: :::. :'1 :' i::, ",',~ 1 I '~i: II' I:: 'Ilill Ill: ~ I,: :':I~I ;11 1:1 ,! 1:.: !,'! . I 'I'~:~~~ .!fi':!: ~~Q '.~' " ;1 I : ...... : ..... , " I 1 .. 1 .~. III II" .... II" .", , , .. , " .. ,'" , "I' "II' . '" I"" ,,\. I " .1" ", ... , "I 1'1 ,," "" d' . ., ,,,' I" '1" "" .. I;'" .... ,. '" .. ."

l

1 : 'i ". ':if" <Iii .dl :i, t\ it!,:·::, ::!: . i i:;: I':: ::'1' II :i.I!I:: ":i'I:::: :L: il: 1:::1 :I!. Ii:! Ii:, d:::": ::': ',:,:. :.;. : :: i :::: liP :i!i :il: 'I: Iii:: :.:' i·,. iii' ;,: :i :: .. :-" I ,:1, ,,,I,Ll.: '11 :; l.U ,,;., .... 'I" "" i" l:+i.·tn 1.1' "" '" ·1'1:" .. II I'''' 'li ;.4[1." 1,'1 ", " ", "." . , .. '" " ."". ".". ... :L·,·, :~, ~. ::li ::11 :tr: n!: . if": :t~ i'r:;T:~~ ~:.: .:~ ... ~~ _H': :'!~ ;~: 1;!: ill r~,: ~ri 'p-; "td "t :::' I·:~' ~rrl':t :;: :-::-r;T: :!'r ::;; " I ' '. I" ,,' I:', ..... : :' : :i' ". ", . . .... " "" I'" "1 .1 ", ." . '1 .. "I ", .. " 11'1 '!I' .1, 1 '1,\1 I" ' , ,,'" ,.1 II" ,.1, "" " ' .,' . I . ,. " " .. :1. '''' . ,.. I· 1,,··1 ". ::: :,,: :,i: I::: .:1: :::, .:1, 1:1: I:: ::, .:. " : ... I, ::,: ;il ; I ::" I,:, ".:, ' I':; I': ':i: ::: ,,:: ,::: :::: .:t : .. : :,. I ... :. i':: ;1:. 'i:; ,::: .. :. I:. ""'" I:: .. :: :::: : . I' . :! , :' ',;: :::: :;, ',::: ~';, :: ' I:, , " . ,It :: ' : I: I: i I' : II' , 1 . i' I;, ' i : ' : . :: .::, !, ii, " I ' ' " : .' !;, : , , ; : : I !, , ':' " I ,. "I'" .. , ,." .. , "..,." . . Ii" " "I! ," ,.. .. I' ' , , . ,,, I . . ", .. " "'. .".,: i ' ., .. " ". ...... . .. . .. , i :'-r:' s:pt "::':r "J'; ';~~~-J~A~:" ! ~t" ,. ·.:~~:i;;,.;.lJ~~,i'~I.i~ 'or·;: ::j,~~/j:" ~JAC·i~~A1KN:·'O·c?~sk . ::::j:::3b:. .::, ·~l..,~·J'''~'''I~m :.:-:.:~ ":T.;1 :lli'!·:i~:ii! 4'r WIWl!.. \ ... ~:II~'''''T' 't~!~~<'=j; ~ ~.~E~ AsoJ.;fT .....•..... uITA~i'I'!

.. r, C:J Uf'\., . . ,:) 4 , , • ··I! I: i ·1. ' I . i . i: - .: : '

-.---_b~ .. --._, ___ ._.c

~--,---- 111'" .". ,'" 116 1511 .r"\ 46 1513 .-.

[!.Ill! tfl' ;Ii

I!f

,

n : ' Ii

, .,.

" , l) ~

II

':' , I! ,Iillllllllill 11111111tlllllllllllllllllllllnu: 11111111!111111.IIULlII.l.J.J 't+liffilittHtH~imtl~~ffi~~~~m~ "

11 II i.. HHIHH!H+HHj-fj~fH#Htff+tttHftj·ttttttffttttItItttttttttlttttl

,.

~.

i i

I

I

!

i I,

I

I

I

I

I

I

I

I M

I

L!')

-

J

-

~ ~

c

.. :. '.:V1 . I:) 2.IrOO _t:r : 9 I ~ ---- --:~=~-:::- ~-==~= -:. -:-:.:::i ... ::-.::.;.· :::: '"=_- ~C; fI!"!~. :: .. ;:='~~~ -- .. ___ -fo_ -_ .• _.,.. •.. __ ..• . ::::: ( ~:::.r-.= ~= _, _. ___ _ :::t:=

---=

:---- "::: -.~=== :~::;::::r:::::::~:::::·

- - ~ ::::::::.::t;~::::=-: =:~::=: rc:~_, __ §5B- ----i!~- .• - '=;;'JD":~:~::Y:~:::~+":: - .~~~~~ ... :;:-::-=~==- -.:j::::::::,f::::":::1: :::---' .

. -- .. .. .. --_.-... .- .. - .. --.

:~~ :~- ___ =:~~~:;;::F::~:::~F-: ,- _ --=r- ___ -~-~ ;-:::~~ --:::~:::T~::i:::~r=f-- ~- ---- ~~ ~:~~-~:::~~::::;:~:+:;:;::::.

f-'--'--- - -+- ===-= -_-=~::~j:=~~ :=~.:~i:~: ~::~:::~ ;~i~~i~~1:·_·~.~.~~~j_~::~-- 3-31 :; - z .

... - 1."- " 'v- +- .. :~ =~-:::--: E~~~7-=;~:·~:_::r '~:'~3:c ~_ ---t- •.

. _--------- .. - .-.-.- P=:~'::~~'~~~~~J~.~::-~~~:~~: .. -::-- :t-~ -- -- +._- - • ..-."_.- ...

t::.;:: :0: ~:::~-c=:"f :~~~:~:=r~ ::: _:=i:.-==t:-- ...... ::::~9:: ::: :::~i. ::::::: .t.:~~~:. :": ~~ ~: ~ ~~.~ ;~;.;~~~:;~::~==~==~ .. -- --::-T:-;::~I~:-:::~::"::: :: \=:-::::::::'::~:':~~--:::=:.~:"" ------ -~ - ---- -- --. -_.

h· .:. ::.: :<:::~iii:;:;~~~~ ----- -----

:= ==;== ~~ ~::~;:'::!~;;~?~i::::::;:L: 3-32 I i

I

I i

I

I

( J C1

I

I

, ('f";

i

.-< Lt'l . .-< ~ ~

(

: =' It I- '" "' ~ ;: Zo t!u w~ :t<: ;-.r 0", 1-..; - ...

)(~ c· _:t.

rJ' ...

<; X -.

/ I 3-33

~j~.~-- -~+: .. -

~~::cX··::i1jlij:Ji~: ~: t=~~; ~:~ ::::~:==i:-~~-:~4:- ~~;~_=~ -::~:~~:.: :;~: ~~::~L~~~~~:.:=- t=.:~~L~L;: ~ ~~= ~:~_: ::~£~:~: .- - - ... - .--- .... - .. -.~-----.- ~;;~~~L::::~<l~~~::- :rr::::: :=- :.:.~::::::L:~: -::F:::::~'::: ~~i -~1~::;:~=~'~;~~:~~~~~ ~ ;:=-::~: _::.i: -: ::..=:::b:: t::~:~:~::~~-1:'~-- ~~:J .. =_. --- ~f -:::~~--+ ~::::::i::~: ::=.:=;:::::::=-$-- _=- . _ . . ~ ... "'- .-. "'-- .. - ..... - .. -. -- ,: .. :::.:--:. _.:.:.:,:.;.

f:-::. :::::;.

,.

-- -<==j ~--." "- C~= ::::::3 ~:-::::::=:~~:3: ._- __ ~;: _ ~_~~ ___ .~~§~i;~:_j -~: F=C =1==:-::' :=;:- ,....

~:~~~~r~.:;:~~:..:- -"-70 3-34

CHAPTER 4 THE AIRFRAME-PROPELLER-ATMOSPHERE SUBSYSTEM Table of Contents INTRODUCTION. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • . • • • .• 4-1 THE PROPELLER PERFORMANCE MODEL.................... • • • • • • • • • • • 4-2 AIRFRAME-PROPELLER-ATMOSPHERE SUBSYSTEM PERFORMANCE ••••••••••• 4-3 The Kernel Functions S*, Q* andf3* ••••••••••••••••••••••• 4-4 S*, Q* and f3* at Sea Level with Specified Gross Weight and C.G. Position •••••••••••••• : •••••••••••••• 4-9 Corrected Qtlanti ties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4-10 IJefini tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4-10 si gni fi cance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 -10 Corrected Performance Plots.............................. 4-14 Contour Plots of S*, Z 4-14 and 6 *' ••••••••••••••••••••••• c X,Y,Z Plots and X,Y,f3* 4-16 Pi ots ....................... .

Propulsive Efficiency n* .•.••••••.•.••••.•••..•••••• 4-16 p Corrected Performance Model of R*c, ~ and f3............. 4-17 FormulationooooOootttt"' •••••••••.•••••••••••••••• o •••• 4-17 Center of Gravity Effects .•••••••••••••••••••••••••• 4-19 Compressibility Effects •••••••••••••••• ~ •••••••••••• 4-20 Wind Effects........................................ 4 - 21 Engine Rotational Speed and Brake Torque •••••••••••.••••• 4-22 Input-Output Model....................................... 4- 23 Implementation. • . • • • • • • • • • • • • • . • • • • • • • • • • • • . •• • • . . • • 4- 23 S~Y •••••••••••••••••••••••••••••••• • '...................... 4-24 TABLE 4.1 •••..••••••.•••.••••••.•••...•••••.••••••• ·••.••••.••• 4-25 FI GURES 4. 1 - 4. 8. • • • . • • • • • • • • • • • • . • • • • • • • • . • • • • • • • • • • • • • • • • • • 4 - 26

CHAPTER 4 THE AIRFRAME-PROPELLER-ATMOSPHERE SUBSYSTEM INTRODUCTION

I

This chapter develops an input-output model for the cruise

I -\

performance of the airframe-propeller-atmosphere subsystem. The inputs to this model are airplane operational variables; the

I

I

outputs are the quantities R*c (knots/brake horsepower) and the

I

engine brake torque Q (lb ft).

E This subsystem model is developed by considering the perform- ance of the McCauley C33/90M-4 constant speed propeller, in con- junction with the airframe-atmosphere model of the Lockheed LASA 60 airplane discussed in Chapter 3. The McCauley C33/90M-4 con- stant speed propeller is installed on the LASA 60 airplane owned by Princeton University.

It is shown that, by presenting the performance of the air- frame-propeller-atmosphere subsystem in terms of Corrected Quantities; a compact input-output model of this subsystem, suitable for microprocessor applications, is obtained. The input-output model of this subsystem developed here for the LASA 60 airplane is assumed to typify such models for propeller-driven GA airplanes.

The propeller performance model is discussed first. The remainder of the chapter is a discussion of the airframe-prope11er- -, atmosphere subsystem performance, in which the input-output model of that subsystem is developed.

4-1 THE PROPELLER PERFORMANCE MODEL Thepropel~er:peT;f.ormanc.e model used .'inthis .workis :p.re- sented in AppendixD. The performance items .of interest here are: 1. The propulsiive e£ficiencY11 : required £or 'the compu- p tationofR":.c 2. Th:ep.r:o.p.eTler .shaft speed N (RPH) and ·torqueqa JIb ~ft) 3. The p.rope.llerbJade angle S degre.es (measured betw.eenthe plane of propeller rotation and ·the £latfaceofthe blade at a radius of O.75R,where Risthe ·p.T.o.pel1er tip radius) : requiredt:ocompute 'the contribution of compressibility ton :and'Q :pa' For straight and level s.t.eadyflight it is shown (Equations D.5-6, D.S8 and D.S9) that: (4.1) (4.2) (4.3)

s = S [VE,W, h, N, oJ

Appendix D describes the:eom p utationof ' Q and sin .t.e.rms p a of: 1. Theperformanc.e ofth.efreepropeller in the .abs.ence.of compressibilityeffec.:ts.1'heabsence· of compressibi'lity effects is denoted by the .superscript i (incompressible) 2. The propeller-body interference factors fn and f J 3. The compressibility correction factor f .comp 4..;2 i j I

I

I

!

It is shown (Equations 0.49, 0.48 and 0.40) that i (4.4)

. np = np fcomp

I (4.5) '1 (4.6)

= Qi/f

Q a a comp 0.55 and 0.57) where (Equations i i (4.7)

W, h, N, oJ

= n

EVE' na a Qi (4.8) = Qi h, N,

W, oJ

EVE' a a fD and f are constants whose magnitudes are dependent upon J the airplane geometry.

The method used to compute n , Q and 8 for the McCauley p a C33/9m1-4 constant speed propeller operating on the Lockheed LASA 60 airplane is summarized on page 0-29.

AIRFRAME-PROPELLER-ATMOSPHERE SUBSYSTEM PERFORMANCE We here develop the Airframe-Propeller-Atmosphere (APA) subsystem input-output model. This model consists of: 1. A model of the collective contribution of the airframe, propeller and atmosphere to R*: this contribution is the quantity R*c knots/brake horsepower 2. A model of the engine brake torqueQE lb ft in all straight and level steady flight conditions. The airplane operational variables are the inputs to this model; R*c and Q E are its outputs.

4-3 The model of R*-c is developed by int.roducing a model for the propulsi veefficiency np into Equation 3 . .15. nl'emod:el~f Q E is developed from a mo'delof the propeller shaft torque .~ (lb it) which is developed below.

A model of the-propeller blade angle 8 is also developed below, this being required for the computation of f which comp °nfluences both R*c and Q a· The development of the airframe-propeller-atmosphere s-ub- system input-output model proceeds in the following manner: 1. R*c, Q and 8 are expressed in terms of a a) The kernel functions S*, Q* and 8* respectively b) A number of simple correctionfact.ors, and an incremental correction in the case of8.

2. Utilizing Corrected Quantities, the kernel functions S*, Q* and 8* are represented in compact form.

A corrected p:erfbrrnancelllodeloi R*c ,Qand 8 is 3.

a defined and discussed.

4. Q is defined in terms of ~.

E 5. The input-output model is defined from -the results of $teps 3 and 4. The suitability of this input-output model to microprocessor applications, and the allocation of numerical values .to this model for GA airplanes, are then briefly discussed.

The Kernel Functions S*, Q* and 8* Consider Equation 3.15 fOr R*;and specifically the quantity 4-4 VE [np/PRIa] h therein. Invoking Equation 4.4, this quantity ref is written (4.9) E

VE [p:~lh = V [p:~lh fcomp

ref . ref We now define S* to be: (4.10) knots/BHP

(BHP = brake horsepower). It was shown in Chapter 3 that PRIO is a

function of {VE' W, h} only. This fact, together with Equations 4.5 and 4.7, gives the functional relation (4.11)

S* = S* [VE' W, h, N, oJ h

ref Substituting Equations 4.9 and 4.10 into Equation 3.15 yields:

V 10] (1 + ~CLdh)f S*

(4.12)

R*c = 1 + _w__ comp knots/BHP

V A [ E where the auxiliary equipment power loading factor A is A 1 + E ~CL dh)

=

pAux.o[ ~] (1 +

PRIO h ref ~CL dh) f ., 1 + E

=

PAU/O[~] (1+ comp

PRIO h ref (4.13)

= 1 + E PAUX.o [~:] (1 + I;;CLdh)fcomp

4-5 S* constitutes t:he' kenleJ of R*c; this kemel heing cor- rected for the effects of wind, auxiliary equipment powe.r, center of gravity position 'and compressibility by means of Equa,tion 4.12.

Consider now., the propelter' shaft torque Q. From Equation a D.29,

where E' = number of engines, e.ach driving, one propeller

p(i) = propeller shaft power, ft 1b/sec

a

= 2'TTIQ (i)

a n = N/6Q = propeller shaft speed, reVOlutions/second.

Thus (i) 5252.1 (4.14)

Q = -~=..::....~=

a ENIO ['n~i)].

p 10 " R IJ , , ,

Wi th the center of gravity toca,ted at h = h'ref"

5252.1 (4·.15) = ---=--,---=-.

Qil

a h ref

EN¥'; [n~", ].,'

IO PR , h ref Wi th the center of gravity lQcacted at h = h f' + dh., re' 5252.1 ); I I ~ I 4-6 Invoking Equations 3.14. 4.4 and 4.15.

Qil

a h ref (4.16 )

Q = -;'(-:;-l-+--::-~C-=-L:"'::;d;;:'h-::-) f-::----

a comp We now define Q* to be (4.17) lb ft

Q* =

From this and Equation 4.8 we have the functional relation (4.18)

Q* = Q* EVE' W. h. N. 0] h

ref Invoking Equation 4.17. Equation 4.16 becomes

= Q* (4.19)

lb ft Q (1 + ~CLdh)f a comp Q* constitutes the kernel of the propeller shaft torque Q ; a this kernel being corrected for the effects of center of gravity position and compressibility by means of Equation 4.19.

S* and Q* are related (Equations 4.10, 4.15 and 4.17) by 5252.1 V E (4.20)

S* =

ENIO Q* Finally, consider the propeller blade angle B, expressed functionally by Equation 4.3: B is required only for the compu- When the center of gravity is located at tation of f comp Hence (Equation h = h , B is denoted by the kernel functipn B*.

ref 4.3) , (4.21)

B* = BI = B* [V • W, h, N, 0] h degrees

h E ref ref

With the center of gravity located at h = h f + dh, this kernel

re function is corrected by the increment 6B: 4-7 S = S* + t..(3.

degrees (4.22) The Speed-Thrust Coefficient. plO:t (C~:J2) facilita,tes' the: compu- tation of t.S. Figure 4.1 shows that, when the 1±:ne:-s Q.f. constant 8 in the c~ :J2 plo.t- for the McCauley C3.3/90H-4 fr·ee· propeller are approximated by. straight lines. radiating frQIII the, origin at an equal spacing of e degrees, (4.23) where Ij; - angle from the: abscissa to the straight radial line which approximates. the 8* line on the C~:J2 pl;ot, degrees K = increment. oI 13-* bet~en lines of constant· (3* on the c~ :J2 plot, d:egre:es.

Equation 4.23 is assumed. to ty,pify the t.B. performance of propeller- 4- driven GA airplanes. FO.r t'heMcC.auley C33/9.0M-4 free propeller, , t.8 = -32. 74cos(L 758*-2) sin{l .. 7:5£*-2- 3i~~~) [Cl + ~CL dh}~-l] degreeS ..

Figure 4.1 shows that th,e straight radial line:. approximation of the constant S* lines, in the C~:J! plot for the McCauley C33/90H-4 a .

propeller, is a good approximation in the region; [1.8 ~c~ ~J.~, a 10 ~ 8* degrees 2. 23}. This is: the n01'lItal reg'ion of op,eration for the LASA 60 airplane. tt The ke.rnel functions S*,. Q-'!r' and (3* are func.tions of the: s·.arne set of variables {VE' W, h, N~o} with h = h ..

ref t Note that t.s is a functiono:f t8*,_ C and. db} only.

L tt Departures of' 8* from this range during fuel-.economical ope,ratil')ns-

may necessitate modificatloR of the expression 1/1 = 1.758*-2 d.egrees

(Figure 4.1) to accommodat:e all operational values o.f /3* in the linear approximation of Figure 4.1.

4-8 S*, Q* and S* at Sea Level with Specified Gross weight and C.G.

position: We now examine the functional dependence of 5*, Q* and S* on {V , N}; when the variables W, hand 0 are constrained to be E

[W = W , h = h ,0 = 1], this flight condition being denoted by

o ref

the subscript O. Note that VEo = V .

T

Consider SO' QQ and So for the LASA 60 airplane when

f

1. W = Wo = 3400 lb

I

2. h = h f = 0.3.

re

Figure 4.2 shows contours of SO' Q and So plotted for'variations

O

The So contours define a three-dimensional surface

in V and NO· E o with a single peak: for any given V ' the NO yielding maximum E , 0

So falls on the inscribed line passing through the peak. The QQ

contours define a second three-dimensional surface: the height

of the So surface at any point (V ' NO) may be computed from the

E

o

height of the QQ surface at the same point (V • NO) using E o Equation 4.20. Two lines of constant propeller blade angle S*

o

are also shown in Figure 4.2, constituting contours of a third

three-dimensional surface. Radial lines from the origin (V ' NO) =

E o (0, 0) in Figure 4.2 represent lines of constant propeller advance ratio J a O

Figure 4.2 is assumed to typify the SO' QQ and So performance

of propeller-driven GA airplanes.

We now examine how the functions 5*, Q* and S* vary from the

functions SO' Q and SO' as Wand 0 vary from the fixed values

O

[W = W ' 0 = 1]. This is done most efficiently by introducing a

O number of Corrected Quantities.

4-9 Corrected Quantities Definitions: The following Correcte,d QUanti't'ies are. defined::

D - D [.' woJ' Corrected airframe drag:, lb:· (4.24)

OFFc - OFFW' Corrected auxiliary equipment· (4.25) P AUX = P AUX 1 w~: ..

c power, horsepower' Correct:e.d airframe power req~ired (4.26)

= P

I w~: R (po.w er -off), horsep.o:wer: Cbrree.ted S*', knots/BHP (4.27) (4.28)

v V CorTee.te:d g~oc,entr:ic windspeed along

=

w w

JY

c trac.k, knots.

/:0 .

X V (4.29) .Gorrec:ted airspeed" knots

=

E y (4.30) N C:orrec .. ted propeller sha.ft~ speed~, RPM

=

/Y

[Wo]

z CO.-rrect:e,d' Q*, Ih ft (4.31)

= Q* w

These co-rrected quantities apply' to standard and non-standa-rd' atmosphe-ric conditions.

Significance: Consider an airplane in' straight and ley,el steady flight, in the following flight conditi'on. (denoted by subscripct 0') : 1.

Sea level, standard a,tmosphere: Density· PO' slugs/ft3 2.

Gross weight W , 1b O' 3.

Center of gravity position h = h ref 4.

True airspeed V 0" ft/sec 4,-10 (4.32)

True airspeed V = 0.5921 V , knots

T o 0 5. Prope1.1er shaft speed NO' RPH In this flight condition, the following equations apply: (4.33) 1b

La = Wo = [CLJoYzPoV6S

(4.34 ) lb

DOFFO = [CDJc:POV~S

(4.35) horsepower (4.36) (4.37) lb ft

Q* =

o 5252.1 V T (4.38) o knots/BHP

So = EN Q*

o 0

Now consider the same airplane in straight and level steady flight, in the following flight condition (no subscript): 1. Above sea level, standar~ or non-standard atmosphere: density p, slugs/ft 2. Gross weight W, 1b

3. Center of gravity position h = h f

re 4. True airspeed V, ft/sec

True airspeed V = 0.5921 V., knots

T

Equivalent airspeed Ve = Vip/PO = V~, ft/sec

(4.39) 0.5921 V , knots

Equivalent airspeed V =

e E 5. Propeller shaft speed N, RPM.

4-11 In this flight cond:±tioll the fo11iowing eql:la:tcions apply:: Ib (4.40)

L = W = C !zPO.' V ' S>

L e' 2' 11) (4.41)

DOFF = CD ~PO,Ve S

horsepower' (4.42.)

S,52,l (4.44) Q* =

ENIO[ ~ 1

. p ICY ..

R ; . .

5252.1 V: E S* kno:ts/BHP (4.45)

=

EW;- Q*" We now prescribe that,. for tires-eo two flight conditions: ( 4.46)

J = J (4.4 7)

aU' a Consequently: (4~ .48) (4.49) Hence constant; C1: corresponds. to. constant· X.

2. Since [CLJo = C'L' [CD]~ = Co (AppendIx C).

Therefore, from Equation:s 4;.34:,4.4'1, 4·.48 and 4.24, (4.50) 4-12 3. From Equations 4.35, 4.42, 4.48, 4.50 and 4.26, (4.51) 4. From Equations 4.36, 4.43, 4.47, 4.48, and 4.30, (4.52)

NO = N r~cr = y

5. Since [cDJo = CD: the Speed-Thrust Coefficient C~a

(Equation D.53) is the same in both flight conditions.

This in conjunction with Equation 4.47 yields (Figure D.6) (4.53)

S* = S*

o

(4.54 ) and thus from Equation 4.5, (4.55)

[n~ ] 0 = n~

Then from Equations 4.37, 4.44, 4.51, 4.52, 4.55 and 4.31,

rwo 1

(4.56)

Q = Q* Lw-J = Z

o

6. From Equations 4.38, 4.45, 4.49, 4.52, 4.56 and 4.27, (4.57)

S* = S* [~J = S*

o Wo c These results may be summarized as follows: Straight and level steady flight of a propeller-driven airplane under the conditions , ••• -<

h f = constant

1. = h

re 2. C constant

=

L 3. J constant

=

a 4-13 t with variations in Wand 0, results in invariance of the quantities The significance of these results in th.e present work is apparent from the converse statement: Straight and level steady flight of a propeller-driven airplane under the conditions

1. h = h = constant

ref 2. X = constant

3. Y = constant

t with variations in Wand 0, results in invariance of the quantities These results are an extension of the ideas presented by Pye(12) pp. 37, 38.

The Corrected Quantities P and Vware addressed in the AUX c c discussion of the Corrected Performance Model below.

Corrected Performance Plots Contour Plots of S*, Z andf3*: c The flight condition of Figure 4.2 corresponds to the flight condition denoted by the subscript 0 in the foregoing discussion of Corrected Quantities. Invoking the results of the latter discussion, Figure 4.2 does not change when the various quanti ties in Figure 4.2 are relabelled as follows: t In standard or non-standard atmospheric conditions.

4-14

x V (Equation 4.49)

=

T :~- ~-~--~-'-~/~.

, .. .--- y I (Equation 4.52)

=

NO />--:'.

I I Z Q* (Equation 4.56)

=

./ I

I

S* S* (Equation 4.57)

=

c 0 ..

I /f ; ..

13* 6* (Equation 4.53)

= ~~

I 0

-----~-- ).-//

. - -;--------- ../

I

t Figure 4.2 is duplicated as Figure 4 .3 in which this re1abe1lin( has been performed: Figure 4.3 shows contours of S*, Z and 6* c plotted for variations in X and Y for the LASA 60 airplane operating with h = h f = 0.3.

re From Equations 4.20, 4.27 and 4.29-4.31 we have 5252.1 X S* = knots/BHP (4.58) YZ c E Wo 5252.1 X S* = knots/BHP (4.59) YZ W- E Also, from the definition of Z (Equation 4.31), (4.60) '.'

lb ft ---.-~- ~~~:-.'-.-' The contour plots of Figure 4.3 constitute a comp1e.te-def'i~n.ttion of the functions S*, Q* and 6* (Equations 4.11, 4.18 and 4.21) for

the LASA 60 airplane operating with h f = 0.3. Note that in

re Chapter 3 where both nand c were assumed to be constants, the p maximum value of R* (=R* ) occurred at the airframe minimum .... ~-~ max . .' _.~ .. _." ---_. /./' /' drag EAS: Figure 3.3 shows this EAS to be 73.7 kts for the LAS' .. \ 60 when W = 3400 lb. Introduction of the ni model in this chapt~~ I p " has increased the EAS for maximum S* to 77.5 kts for that airc-ra.ft· with the same gross weight.

__ ---. -~-'7-

Note t that Figure 4.3 applies to standard and non-standard at~ospheric conditions.

4-15 Figure 4.3 is assumed to' typify the variatiens of {S*, Z, S*} c with {X, Y}, and hence the variations of {S*, Q*, S*} w,ith {V , W, N, cd, for propeller-driven GA airplanes. Note that each E such plet is constructed fer a specific value of Wo and a specific value ef h ; and that for the representation ef {S*, Q*, S*} ref variations with {V , W, N, o}, the values of Wo and h used in the E ref construction of such a plot may be selected arbitrarily.

X,Y,Z Plots and X,y,S* Plot;s: Figure 4.4 shows vertical sectiens through the X,Y,Z surface of Figure 4.3, for several censtant values ef Y. Plots such as Figure 4.4 will henceferthbe referred to as X,Y,Z plets. Fer a given airplane: an X,Y,Z plot and Equatiens 4.59 and 4.60 together yield S* and Q* for any set {W, X, Y}.

Figure 4.5 shows vertical sections through the X,Y,S* sur- face of Figure 4.3 for several censtant values of Y. Plots such as Figure 4 . .5 will henceforth be referred to asX~Y,S* plots.

Propulsive Efficiency n*: p It is of interest to' observe the functional nature of the

propulsive efficiency [n~Jh ' denoted n;. From Equations 4.5

ref and 4.7, (4.61 )

n* = [niJ = n* EVE' W, h, N, a J

h p p h p ref ref A plet shewing n* centeurs for variatiens in X and Y would completely p 4-16 i j !

I

I

I

I I define the function in Equation 4.61 as a three-dimensional sur-

I

face, for a given airplane and a chosen h f.

re

I

Vertical sections through the X,Y,n* surface, for several

I

p constant values of X, are shown in Figure 4.6 for the LASA 60 air-

plane with h = 0.3. As X increases, the maximum value of n*

ref p achievable also increases. Variations of n* with Y at constant p

I

X are solely responsible for variations of S* with Y at constant c

I

X in Figure 4.3.

Figure 4.6 is assumed to typify the n* performance of pro- p peller-driven GA airplanes. It is clear from this figure that n* varies greatly with the airplane operating condition.

p Corrected Performance Model of R*c, Q and S a Formulation: We now formulate a model for R*c, Q and S based on the cor- a rected quantities and corrected performance piots of the foregoing dis cus si on.

The following definitions (Equations 4.25, 4.28-4.30) are collected here for convenience: horsepower (4.62) V knots (4.63) w ,c knots (4.64 ) 4-17

{W;f

(4.65) RPM Y=N~W--W- these definitions we have: With l. From Equation 4.12, (l +~CLdh)f $* . comE (4.66)

R*c = [1 + V:cJ knots/BHP

II 2. From Equation 4.59, Wo 5252.1 X (4.67)

S* = knots/BHP

E YZ W From Equations 4.13 and 4.67, 3.

C

rAUX J

(4.68)

II = 1 + 5252.1 (1 +

~CLdh)fcomp YZ 4.19 and 4.31, 4. From Equations WZ (4.69) lb ft

Q = W

(1 + ~CLdh)f a 0 comp 5. From Equations 4.22 and 4.23, (4.70) 8 = 8* + lI8 degrees (4.71)

lI8 = -K COS1j; sin(1j;- i:@-r [(1 + ~CL dh) ~-lJ degrees

61T /180 The computation of f is performed using f plots comp comp (see page D-11) .

For given values of X and Y: Z is obtained from an X,Y,Z plot appropriate to {W ' h }; and 8* is obtained from an O ref X,Y,8* plot appropriate to {W ' h }.

ref O An X,Y,Z plot, an X,Y,8*plot, a set of f plots, .and comp Equations 4.62-4.71 together constitute the Corrected Performance 4-18 i i I

I

I

!

Model for R*c, Q and S for a given airplane.

a

I

Note that: • R*cW/W is constant for constant {V ' X, Y, dh, f , PAUX } O w c . comp c • QaW/W is constant for constant {X, Y, dh, f } 0' comp • S is constant for constant {X, Y, dh}.

Following are some remarks on this modelling method. First: the influence of center of gravity movement on propulsive efficiency is examined. Second: some typical values of f for GA air- comp planes are ,given. Third: the effect of corrected windspeed on peak R*W /W 0 and on the operating condition f~r peak R*W/W is examined.

O Center of Gravity Effects: Throughout this chapter computations of R*c and Q , for c.g.

a positions displaced a distance dhc from the reference c.g. position h f C, have been performed by multiplying S* and dividing Q* by re the factor (1 + ~CLdh).

The factor (1 + ~CL dh) was derived in Chapter 3 under the assumption that n was independent of h. This is not precisely correct. Con- a sider movement of the c.g. while maintaining constant X and con- stant Y. This results in: 1. Constant C , but varying Co (Equation C.29) L 2. Varying C~ (Equation 0.53) a 3. Constant J a . i 4. V ary~ng n and S (Figure D.6).

a 4-19 On th~ basis of Figure 3.10, it is assumed that a typical maximum variation in C with c.g. movement is 4:%. This results DON i in a 2% variation in C (Equation D.53). From Figure D.6, a 2% R a i variation in C at constant J results in a maximum variation in' R a i a n of approximately 1.5%.

a Therefore the factor (1 + E;C dh) is expected to introduce a L maximum error of 1.5% in R*c and Q ; and a maximum errol' of 1.5% a in the increment of A due to PAUX (Equation 4.68). The latter c error is expected to give a negligibly small error in A.

Compressibility Effects: Computations of f were performed for the LASA 60 airplane, comp using the Hamil ton Standard Method (21): the results of these computations are given in Table 4.1.

A detailed study of propeller compressibility effects, using the approach involving f , has not b~en performed by this comp author; such a study is desira.ble (see Appendix D). The following should be considered in an investigation of this matter (22):.

1. Computation of propeller performance in inc'ompressib1e flow may be performed using- Goldstein-Lock analysis (8) which employs 2-Dimensional (2-D) airfoil data. This is accepted practice in the propeller i.ndustry.

2. It is accepted practice in the propeller' industry to compute propeller p~rformance. in compressible flow.

using Goldstein-Lock analysis and 2-D airfoil data which 4-20 incorporate variations in airfoil lift and drag coef- ., ficients with Mach number. However, this computational method ignores two phenomena which may be important to .the actual performance: a) Three-dimensional flow near the blade tip: Radial flow near the blade tip (due to the tip vortices in the wake, and the proximity of the tip itself) reduces the effect of compressibility in the tip region.

Consequently, a 2-D analysis will tend to overestimate the compressibility effect.

b) ~he effect of compressible flow on the wake-induced velocity: Compressibility effects should be accounted for in application of the Biot-Savart law to the compu- tation of the velocity induced at each blade element by the wake.

The effects of these two phenomena on the performance should be assessed, and included in the analysis of pro- peller compressibility effects if necessary.

Full scale propeller tests will be required to give confidence in the use of any developed method for computing propeller com- pressibility effects.

Wind Effects: Equation 4.66 expresses the effect of wind on R* in terms of the Corrected Windspeed V .

w c Figure 4.7 shows variations in X,Y and R*W/W at the operating O condition for maximum R*W/W ' as corrected windspeed varies; for O 4-21 the LASA 60 airplane [h = h f = 0.3, f = 1, PAUX = 0, re comp c

c = 0.45 lb/BHP.hr]. Similar curves exist for the constraints

[h = constant f:. h f' f = constant f:. 1, PAUX = constant f:. 0, re comp c c = constant f:. 0.45 lb/BHP.hr].

The wind has no effect on ~ or B when X is fixed.

Engine Rotational Speed and Brake Torque The engine rotational speed NE (RPM) and brake torque Q (lb ft) E are required in Chapter 5 for the computation of engine brake specific fuel consumption c (lb/BHP.hr). It is convenient to compute these quantities here, in terms of the propeller shaft speed N (RPM) and torque ~ (lb ft). Figure A.2 shows the no- tation used in this derivation.

NE is simply determined by the transmission gear ratio G: (4.72)

NE = GN revolutions/minute

The engine brake torque Q is determined as follows: E horsepower AUX + P ] P =

s [1 P

s

= Q [ + 5252.1 P AUX ] a

. lb ft

Q G 1 N~ E Substitution for ~ (Equation 4.69), N (Equation 4.65), and PAUX (Equation 4.62) yields Q \ .

Q = ~ 1 + 5252.1 ... i

E G 4-22 Invoking Equation 4.68, Q becomes E lb ft (4.73) Input-Output Hodel The input-output model of the Airframe-Propeller-Atmosphere (APA) subsystem consists of the set of relationships which determine R*c and Q£ (the outputs of the model) in terms of the airplane operational variables (the inputs to the model). These relation- ships have all been formulated in the foregoing discussion. Figure 4.8 depicts this model, with its inputs and outputs, in block dia- gram form.

Implementation: .

The APA subsystem input-output model is well suited to imp1e- mentation in an airborne microprocessor, for the following reasons: 1. TIle X,Y,Z plot; the X,Y,6* plot; and presumably the f plots; comp may be stored as sets of coefficients of cubic polynomials.

The memory space required for this storage is very small.

2. All of the required equations are algebraic equations, in which the most complex functions are trigonometric func- tions.

Allocation of numerical values to the non-operational variables in the model, for a particular airplane, is readily accomplished by the airframe manufacturer. In particular: 1. The X,Y,Z plot is constructed from propeller shaft torquemeter readings of Q , in conjunction with Equation 4~69.

a 4-23 2. The X, Y, S* plot is computed from the propeller manu- facturer's data. The parameters K. 1/1 and e required by Equation 4.71 for t.S are obtained from a C~:J2 plot o.f the same propeller data.

3. The f plots could be computed for the airframe manu- comp facturer by the propeller manufacturer.

4. The value of ~ may be estimated by the airframe manu- facturer from propeller shaft torquemeter readings of Q • in conjunction wi th Equation 4 .. 69.

a SU~1ARY A propeller performance model has been discussed. The APA subsystem input-output model has been developed. This model has been presented in block diagram form in Figure 4.8, and appears suited to microprocessor applications due to its simplicity and minimal storage requirements.

4-24 I i

I

!

i TABLE 4.1 COMPRESSIBILITY CORRECTION FACTOR f comp

Flight Condition: Lockheed LASA 60, W = 3400 LB

I'

I

CD = 0.0402 + 0.052 cl (power-off)

I -j

h = h = 0.3 f = 0.98

ref J

P = 0 fD = 1.08

AUX Standard Atmosphere

I i

& _ ~ I ....

Entries in this Table are .J.. - 'I I 'I comp p p

I

DENSITY PROPELLER RPM ALTITUDE EAS ft knots 2000 2300 2600 Sea Level 80 1.0 1.0 1.0 100 1.0 1.0 1.0 10,000 80 1.0 1.0 0.994

I

1.0 1.0 0.976 Values of f were computed using the Hamilton Standard Note: comp Method of Propeller Performance Calculation, 1941 (21).

4-25

8 = 3.5 ..Iejrec$

K.,= 2 Jl!:!Jreu

"-- __ ---L-_--'- ___ C (.

o c. ~

R. a -~ - /(., Cos 1/1 Sill (?/l :!: 8) .:

C:. e 0/1'0

.L

(/ + 5 C Jh )4 RoM EIJUAlI_ ~ 53

Now L

AN)> + dh - +.aC~ }

- clh -+ -;4~"

. &.

.'. llf3· = -fC, C4a 1f 51;"("'11 - 8 I~') C: [< 1+ S C Jh)t - ,]

L

C:. B7rjlBo

= - K, CoS V' sin (1/1- ~) [( I + ! C Jh i-I] ....

L 8 rr/180 .'. SJ)IlSftl'II'(u.r, FD~ 11) ., Ad K,; Af3· = -32.74 CDS(/.75,6·-2)~(1.1S~*-Z-3.5~)[(' ... !CLJ,f-IJ FIGURE 4.1 EFFECT OF C.G. POSITION ON PROPELLER ELADE AN6LE.

11-?f; ._-------_. __ ... _ .. __ ._<_ . .-.-=, \ .

. ~ ....

lit. ",,11 ,n" HI H~ TilE CF.Nl'~'Ftrn

KI , IF I r t. A. ,':.' T I~ (" .. ~. '.' I' • "r, 1 rc,13

-

'Jf

Q* AN]) (3* CoNTOUR.S AT SEA LEVEL WITH

S, '5252.1 ~ o J(Nors / HoRSEPOWER " PROPE.LLER

RPM

i. , ., .. , .. , , I" KNOT.5 = AIRSPEED, EQUIVALENT TRUE AfRSPEf:D Vr Vc: i 0 0 I , ,

' , , ;" ,"I ' ' I'

' I . , ~ , l' "I " I;t'''''·, " ' .. ",: I 'I

:: f:":" t' '.:'! ": 'I 1" I "I' i' I' ,. • ", I '.1 .'~ I" X 't> '1) 1111 ,U~IIt.lt III' 46 1513 hi I If I I.l. ti. 1','.1 H CO . ~ .. , , I~" ..

I .• , '1' I' : .

., ... ..., .... ~ '1' ~ . I' "I'! I' 1 . . I , I ' I . I ., ~. r .• ,.... 1 _. I ." l' I

· I "'-""'r'

Sc· , Z AND f3* CONTOURS

. I I: .---~~~~~~~~~~'

*= (7* 'vJ = 5252.1 X

CoK.RECTED 'FkoPELLE12.

S HORSEPoWEIl

c J w;, 'E Y2

51-1f1F=r ToRcWE ····,····I·· .. \'··J·II' .... ,' .. , ........ "1'\'" · ': . . ;':: ill: ., ... ':: '.,: : .

LL ;1: :::1_ __ z ~ if '0 i' •.. " . ". '.

;-'''-- ....... -.- -:" I·· .. · :::: '~T; .': . . , , , I ~r-~, ~~~~~~~

./ . . .!. ..... J.. ~--+--r-"'i-~~

'

Y=

.1 " !

. , ~ • N · CoRRECT£D ; PRoPELLfR SHAFT SPEED

RPM

"T. ii" "I:' ," 8 : I' i 'I I:; I ' ,.' i' " .' ';':' :,. ".

, 'I' I' I '., . 0 :1, . ', .. :. . .90 i'.. ,.: :'.1. i· ':;'3

! 'ff I j'I',:j

. I . .: ... : . j" x = \ I 'Wo CoRRECT£D AfR5PffD ... !:; :~0 .. : 1 ,I Vr . I ,I .

E .. :.. . i. L .. 1 ... __ ._ .. _"!. ______________ ~ __ !5.'!~'!._~,_~_~~,~_ ......... [ .. ..l L .Jl.~;.

.., '-.....,..-'--------_._-----_._---._----,_._._.

10 '( 1(1 'If) rt'r r.t f'Jllt..1J 'f"f) ':' . ' ,- I I II , '1 H r ~ I~ I " "'.' • '. " "r:, 1513

-

., , , ,!'~r.-:-l'·'1 .. II ·'II:;n::1 ::,. ·I"i ,··:'T -·1' -'1'·"1-: 1'" I I' I '1 . I j . . . "\'-1"1 . I 'r- r--.,-" .. ,,-- :~;~ U: :..1;: .. ~:.: .. ' " ... ,. X" Y. Z '\;; . :: \:::. .: 'j: .:. j"' : \.

~: ,i:'! \' : "PL.OT . , ". . ... :-- ..... , ...... \..... ..... . .... " ....

j~:: I:. , C'l: ::11 ;;Tl m:r,.:: :\1 ,::1 i' I :'.: l'PI··:1 :---:-: 1'n n:'I"1 .: : .... "II:" !···U: .. ~·1"·: :'T : . i[":" . j . ,I. \ I: i: i j:j i i:: Ii!· j::: e: . ;; '::: ::. ; :. . .!: i i' .' iii . ! : : ' :; " ,:'., . I," 60 . , j 4 0 " , ;" i· : . ; '1' ~+lIf+8!I'" f7; h·;: ff,'I'::: :7!~ -_. ,": ~'- .. t! 1": ,'" .... :~' I"'I!' , ..... 1 .... i' t..DC, HE .~A A. . .. II' II' (J. LB .. ... , ...... 1 ... ,:: :: .. -'" .: .... --, .• - - ... _ .

. :1 :1 ,I:: loll 1'1: I',!' ':\'1 'I:. I.. II: .:1', ' .. ' .1; : ,! ,'. II' I ': \.. I·'; 'H,' J h' , o! . ,",' . , .' .

"I II iill I, ,I I " II ., I, I " I" ." ., ,. "I" " . . I " I....'· I " , ,I , to.'

' • I" I'" .o. ....... ,,, .... ' I" '''1 ,. . 'I ,., '" .". .,. ,,: .. I' . . "[":""'" '.' ,.... i"'" . . .• .

II I i I: ,:: I':: ~I: lUI :: 11:: :'1: :'1' 'I: "I ,1:' III 'II ' I.. 'II I ,: I • ,; • I ~ I l;fa . "', . l." : ,::' ~.. ,I .. ':: ! 11 I:: 'I!. 'jll: ::111: 1: I,;i \,.: ,:11 I ,I ' :1 ::~: !I: I"! I' "":1 . I' , I,' ":. I, I .:: "J I'i.· tl.. -0 J . () ~~ ... )' [" I,: ,:' I j •. t

oz

'111 Ii I !l i; t7i~ I'· .tJ~~ ;it~;:: TIT: rTf: ~:t'I' 'i" i : ": I';:' 'I'~: I :'1, i ;, 1" I:': ":+1';' . :-1"·:' ,': ...... 'I'" ... : .. :: .. : -II .• :: '" j,' "f'"".D'· I':' l 4 +-: ~'~>7&''' L 1'---: t ~i!; :;-. :.... . .... ~~: --:~ 1 "" i:'l I;' :,,' ... 1 I,:! I';: 1I11 'I' ::'1· I" ,'I" ",I . ::', .' ',' ":1" '. '. :. "'1 t' * 0 a..J. .£ LJD I' !,. :1' .;' ! ;.:

~

I ··!·, .. ", "Ii .... ''-, .". I .. ,. 01., 'I .,,' .. :; ,-, "I" ..... '.. . 'I"" ". f,J:" .. ,,' .. : '::w." I .7lr . 1<, 1, .' ", ..... ." ... .

fl t I 'iii 1'1"11 .,., "I ",. '1' ., III 1" I' 1'11'\ "I :: ',., I ., ''', II • I • '.I~ ., ' ... "1 !.,.". I' .. , ... .

\' idl I!: Iii "\UI' ::i i;1 I;:! !::I IIi! ,1 IJ :i ,.i.hi!" :!.l i /: .:.;, 1:;,11":, ':',':' \::. :.' .. :Ir:,' N.·,k' .. :':'~·:l/j,:.;· .,';1_!.., "JI~/....,;!. ..... i . ',,oK ",J. .. ';' 'Ii i!' .:'. :;; .. V :, '.: ,~ nl' 'Iir'~ ~+- ..... t~I! ..... t ......... " I-"t f ''1' .... -l. Ht- I ...... to. • ... ··t··· .......... ··t' p., .urrKJ.) .•. ~ .... rr"N::~ ''''~U,"'''' ~r:, 'EJi!c.;) -:!~ 1. ' " ,I!..; •. 1... .~.:..:' 1:1' I: I,;: I':: !, .. :, ,,:. ';1' I!:: liil' .~' I": I !"I 'j;' :1'1: " ." I:' ,I'. :1' . :, .... ,. 1":1 ' . . ::1: !i'~ .~ ... ::.- - ... - -;.[ ::1 lj' Itt! t L:: : :: d. ' . I. ;: II .: ! i : I I ~ I I!,' : , : L .; ! " I." ':" , 1, : I, " I: , :. '::': I j : , • I'" I .' , :. I . I I , I .. , l" I I I ~ I " I , , , .. I :TTl Jll! m :1:· ::11 I::, :.I! I!:: Il:j :111 ~!'I : 'I I::' I:;! :'1: I:': j:' ~::: ::1 : .. :.... ':,.:' .::: :: ... ,::1: .:~. :: .. :i·; I:· . i: i·· .. : ". :;'1 'i ... : .: : I: H< ::I:I:iii UJbO R I'r l 1 , 1'1 'H' ~:! tl:' ;1:: :Pi :!:t ::: iii:! I liii i :i Ii;: Jilil', I :' ':; ii!',:i! ':'1',": ,I;:':; ;\ '1: ' ,: ;, : :,,:: ::i. ,',:::, :i:~! ;i' ': .1,:: ii·:, : I':' :;1; .IIl;~::: ~ , ,:

t

"I' \. I'lt ,. ~ •. :~t' 'U .. ··~·tthi " +-.: : •. ~ '1''' rl'ti~:4. "" ~." :--- .. ~~'~. ';-"~ '_ .. , .... ~ .. -'- ... - .. - H-h-7 ":~I-'~: .:.: :~: ~.:.. '1- - ..... - _·t··- ~j-''':llf'- .. 1 "'.tH,# . -: ..... -.- --·1·...l I!' 1 I I I I : ' :; 1'1 : I I: ': 11'1 ii" I" I . "I ! I !; I 1111' ! I . l' I !. I I" " • " "i I ' ''', " , , ., ,I. I, I',': • I '. " I ., ' ,: ' ; : I I' " : ' 1. : ~ , : : 1'1 ~Pl 11·:· !j; :;',' ;:!l H;: :1,) :~;I 1::lj':: ij::';, ;:lli :.:. I,:: :.:.\'!1: .. ~ : .. , .. !I': . :.:i :::. :. :.:: ::::I;i:1 .::! ::. ::;:! I: .. : ··.Ii .. : ::.:. : : ... I:: ~ ,Ij .. ii, i':::: i ... :i; .ii: 1 dil' !i1:lll/i;:: :.::: 'I :::1 ,:, Il!I':' ::1!.; IIi'! Itt:· , ,;;: I.: :;1 ·i:. ':l''';' :'" :: ,:i " ::' :1;, '1'1 ," , '*:' I' 'I:, .. I:. :. 1. ,:,' "';l 1 :il Ii, ! I' It "; ,n I II:" '; 'u;r::1! ;:': !:: 1,::' ! ':; ff+';'i j'l j' .,1: ,I: j,':' ::': ,I: " .:: :'1" , : il['I: ":;1' ::': '!I' :!'I :', .:: III '!',':.: :~: I ,tl! i'l: ' I: :1:, I.:~· iH!' .Ii ' ..... m!'1~J.: I - ~,I ~ +1 ~I' .- .. tT , ......... - .................. ". -'-' • .L;.;j.l~ .. 4··· .......... , .. I. :-.;.. -- •• :~ ._. . ... :.. .. ,~l+t~ $~ ~009-· H; I I tI ii I'" '::1 :~.: :I :i, jI:1 :1' ,1:11,:'1 ::i :Ii 1: 1;;:", ',': :!: ;1 .:.:<1 l~' ::1 ,li:. ::; !:ll 'I:' ':. :1 ,:,: 'I .' . 1:,' I :lllrIW'''~ ,,', ," il I '11 til::'! ::!I :,i; :;! ,'I!: \1: tl:, 'II: i I' ~ ';:; ': ': :1:1: .:,' : ,. ::.: :., 'I; ," :1: :1:: :::1 1'! ,'j'" l! :....,:~ , : ,I: '. !J,lilil I .. ;)" J" ::,1 ,[:' 1 W,!!

1 1 :, "1'I-Hjl+':li:ll: ::l! ;:llj :::: !:jil ;l:,l:-I ,::! ',.;: 1;1: l,dl:: I ":. J::: !:::f:t:. ';;' ... : .' '!';":': t ", :::: :!:;::II ':.: ::·:1iJ:: :!: .. ::k"~' :;:!-'::~.':' '::.I;:U@.!':::::;:"''':':::'1:;01 ' . t 1'!'p'l ."11" Il" g.l '1 1" 'l"l··'1 'I" 1 :1, "I' " I, ,,, ,I . II' ,'II "" ,",, "I I'" 'I I •• ~. I ... " ~,! I I .t'l ,,,:. ,!,.

111 I "4-H+I'''!o4+i'-'-4f#'~I' !.1.'11. I '" H· I I~ ,. I II, t ,. It' 'I " "'" ,I, •••• " ! I , •• " • t. I I I' '11' , " ,I::~ :: .. ". ,. '::Ii~'" ...... , ' .... U~· , .. :1.... .' ... -:t ..... - •• '"'1''' ........ , ~~. "" - ......... " .- ....... -'-' ......... +~ •••• ".~ ...... ~ •• -.- .. :~ - .... - -~~ ,.-.W+!+,l >~ .L UV .-. -".

l'll lilljil Hi' :1'1: 1:;'1 I',:: I::: :d. ,\1 1; i i :'1'111 "I' "~I' ,'1 1,1,,1'1:' :1 • 'I':: ;1 ,: :: :!;, :ii' ::Ii I:' ; .. :" ", I ;;. ::. 'I" ~", . , ,'11·1' . "111"~"" 1.1' .. , II' '11" 1"'1'''1 .. 11,·,1", ,11,1 I., "1 • ., .'1' I 'III" I", "I'I!I:LI;~jj, " I"":' I ,. 'I': ." ,It, ,,11,.11 il 1*'11 If m': ':.j: :ILt +: l-jlj"i: t I:: ':1' lji~, "'I' .,;. I::: :':l,U' I: : .. :.: .... ':. I::: :,:1 .i: iii. :.:I;::tl~~: .. :: :". "I' :,:.I;:i~ ... , ... 1:;::Ul.J.i.' ".i.Hf,'l:':i. 2:4110 .. :.1 .::!

llil ;' Ii:! I: :;,: ;I!'i' :;;!lil ! .:;1 ! Ii :ii.t' Ii 1'1' II 'I ;'1 .Ii~'i:: ":. !I, :::'1 :: i::. ~ .. -: .'ii .i:!:.:'t!!l.-;, ,:' .. ':'; ;: ·1::.:l~P ~i::I :.:~.: J.·;"lilil '.,,~: I I,i! ,,:1 I 1 .t=o. 011 . I., , ll.. .• '"'' ." ,., ", :II! H-l f8t ~l!l .t;.l. ;;.4 ':. ~~. ",. :~.: .,-;~ ... ~;,; .... :: ." .. ~~I";'i: .~ __ ,,,_.':":J.:.fil"'~ •• ..;. _.:. •. '" . _ ._.: -_._' , . ,~~ .. , " 2:4aCO :;lj~ , Iii:, i~ I;;: H'I: '1.' :;, .;:: II;; iii: i,l: 'I!I :,' I.: IT;, I' 1 I:': ·:i: :1 ::: I;,::.: 1 ·T:lill.i. ,"",:", i·: m'·: ,::·It~j:::~~ :.;. ,,1-Ii~[JJ.4':~@' ·1:li':'P:;;?. I' ;iTT I:: l ... " I!U I,i: :'.1 I I' .. :i. :·:t ::;: I " ::.; ,I. l'l 1,:1 ::!1 1111 ;:1: j' : I::' ;~i:ll: I. iiI :.!..~: ·I!i .' ,j,; ~j:; "'~ :', l;il1~r.....-:--! ::i' ,~I '~'" ~ ,1, iii, ::', ., :'1, 'I; ..... ,fIT ": ;::: ,tt ;1, .::: !:11 ::'1 til' ::!; : :l :1: .. : p:! 1,:1;:: ' ;,1: :" ."ili!"~ I.::' ... : .,;.;.:;:I:~:~ ... ~ ... :'.: :1::':'~~ . I 1·~r:ili.P' .:. .... :.'i I::: ':1: I:!' ":'1 ,I. :i 1-:" ID ii' !I: " .. ::!. 1 .. 'lj' " ... , .. ';j'!i" ,I"" 101 " II:, ,.1' . "·1 ~~~, .1'::1 "., . ..--- I· 1:"'-'--"--":;' ,. ,. , .. i' '11' ,,' 'II" fl· "'1 .,' I :1:llll,lil:ltl"';~4' . II ''':_~: .. .:..: +-i ..... +++.-4l •• ...;l..; •. :l.1~ll.-:::.:..: .. ':~,~".J. .. 1J4t1,I:,t,d':L_ ...... _.:· ,i ~~ "~'d1~ : . .:'~~ .. ~+-4":J.il~":~ju:; ~~: 1iJ , I ~' 'iif !f'l ·Ii. :'1" :·11 I::: :::. I'il ·:'II'j·,·1 ':-::1'+1 :;,: in I;!: :;, :.:. "'. I .. 1.,::1: i-H""" ", ':". "~i;i"l-'-'~ ... :, I,' ".. I:~ :: .. l7;t7 .i:: :1"'" : It! :," 'I jl"!i " .. ,', .. " .. , ,. 01,,· .. , .,11,,,,, "~I . I . ,.: .. Il':;i-'""":~~, .. "iL."I.;,.,;,~ . '" "., .. " .. " ii" ,', ,,,.1,,, .... ' ., ,. ".1 1 q' ·'Ilt!.. , IIi " , II • H" 'I I ....... ~·;; I ' " • ,...-,.....-:--., ,l .. '" oj,. 1"1'" ., 1'1 ." 't" 01 r r" ,,1,1 " , • '1 t. l' .. t...... ., , ,'" '. .,. . j,. ., . Ii ,., I , ....I. ,. , ... 'I' , ,r, I' •• i •• I.' • t· .. r. •••• I,~ •• , •• " , I, ., r ••• , j ,. ,. • 1\ W

n

iii .. Hi: ,i:1 I!' ":, .. ,j .. j: Ii," .iii '1, i; ill'lii, : L I:"~ ,.,. :: .... ·i . , . .. . ...... : ,: .:iI·i'l:i! ii: pil! :.!i:~ii :;i: ·iii :.: :,:. i::'!I1~'''' '.i~ .':: ::i. ~i!: : ..

:. I , .: It.: III". :~k'" .. , :..., ... ".I+. .... I"'. • • I' • ,.:' .: .. -~~ HH ~~+t ·H~ '~J1~~~ ~~ H~"1'4P+~ r'+ ;t!~~~~ ;~.!. 1~ .' ~' -:~~0~ ":'L~ ' .... : oI'II~"I'W.:· II:I~ . . ,. I·· .. "·" .. · "II "II "II I II , .... '1' "I· II .. ,' I" "Y1::1 ,~ .. , ,I'iliji'" .,. "II I::. "I.i.~; I:: ;', ,'1 ., '" 1, ; " ·,',·tlt .. 1: ... l ::1: : ii' .;1: li,1 :IJ' :::1 : :, .':, 'I;~ !' ':! .': I ":: .:: ::1i ;'h ~'i . ';. w '1' I' .... ,.,.: .• '"'''' , ......... " , .. · .. ,,·:,·,,1,,·, .. ·, ... , ....... ",,: .... ""1,,, .. ,,.,,·1.1"""'" ."." ... ,. '-, ........ :I ." ... 1, "'I~ I·· .. , ..

~~!l ~ .i~~ !!j!:l: :i: .. ::1". ~;, ::: :j;;: 'I' 1;1 !!:i IiI! ::j! :'1: j': ';,;1:1< .;:,j .; i·: 'i': !';i ,,:! ::~llJii ~!:: ;:1: :;:'~;: j': :1:' :,:j ::1~ i!i ::;~ :;:]1:::: :',::. ',: ,:, :j:i :: , ·'11: ~:l'l .

I-=:~' _. ~""'H" ... - .... ;";"f'._ ..... <+.... ..l-q.: •• , '11. _ , .... ,,, ..... \ ........ , ........ ".+ .". "" .-+-, ... -~- LH' •• - .-. '" ., .... L :~.;.; . .!.~ .... w.· ~H .... ~ - •• 1. -~-~~,..j-:.:-" ~.~* ~+ ... .

p:., . i:i !1~: ii .:! :·:il·!i: ::i: iii! !l!!, I i·J 1i, i 11 ;11 i,;: j,' : ;; :i; 1':1 fi' ,;:' ;'/1 '1:' ;.! Ifi~ i:l; ll:! ;;; ::, ,I I: '~; :':. ~~ :.' );:\.:.:;" ,:' ,ii. !;i~ )1.: 1:;,·1::;: ::i! 'I: t "I' .. jIr, .. , t· ... oo ., .............. ".1 .1" ! , "'1 I .. , ,!.I I'l l .. ,' , .. , '.'~!'... ., ,. .... "", "., I.,. '." "I, ..... ,. ..., ., ".. .. .. , ............... "1' ,,,' .. , ......... ". "" .

~ :.; I , : .: Ii! I :;: ' : I :: ii :::, :::' :' I ' i ; ii' : II : : I ~::: : J Ij :, 1 1 :, i; i, : I ; ; ! : ; i, : ~ . : ; I! ,. I: : : I II: I :!:: ; 11. ':: ; • , : :: ;: !,:,'; :: '!: l : :: ".: : '. 11 : :: ,; 1: ,: I; .::, ::., ': . : i' :' II .: I 1+i-4!l-! 'f.!-!.:.~~: '·;':'I~f-: "fi+:-:H .. llfl.,· 1::;W'" .Il "· '1+:" .... l~" 1" f-:.' 'j' .• .1 .j.L;1.J~'.:.l"" ... '" " ':;.:.!"'" .... .t.:.J.;.; ~~ "j' .' . " f:';';'; ... , ::.: t.~~ !::: " .. ~". '!! : ': ;:17 ~:;, ::~~ 'tl: l!~~ :;1 It: ~~il J t !:Tt I~: ... :, :,~ .. "'::j"':i ~::'I-':- ,"j ~ ~ .:~: 1. ! :1> ;~~: '::: !:: ':: :7:' ~~: .. ~":. " ',:: .': ot''''~ ii, :1; ::1;::1 :i;, 7T: :,:-;1: -0.

tiht

::! I : II ".: I::, " : 1; I :; II .'; I: ~: ::: I • 'II ':, I I, II I .. I I: 1'\ : '! I ': '! Ii'! : \: ,'!" : .. , I ;:' ,,"': I ;'; II:: i I!: ; 1" ! I .:" .:: ,1 .::, '" : : il':': :! t i: j.' t:!, ; i \' 1,\;: I I .:.: ,:" '::, :, I: 'I"" l, ••• ;l ."',, .... ,o., ,,,I '1 "'1"1 11 '111 .". 'II I'" ' I· ""r' ,. ·1"" I.,. ". ,.,. I'" "" .• 11 .......... " .. , " ........... ' .,.: .- .. '''' I, .... lUll. "'1 "" , ... ,., .. '·1'· , 111 I 't' "" ! I. ii' II 11'1" ,. t, II "I" ' J I ,'" I 'II"" '\ .. , ,. ... '1 III 'I ", '1" "'I \,.'" . II .. .. , .. ,," ,., ... I.. I .,'" , "" I ::I'I~) ' .. ; 'II, ; ... ·lllli, ip: IP':li:I';n' IlL: I' IU' I '.:' .: ':" illl ::1, .":. :i:':', .,: :11: I,' "~!: it:, :::i :: .. ': :," :'. '.: I:: .:' :;, .!; :ji: I;:: 'lll II' il:; .:. ::!·I I:: ::1' ':"\ t fttt~I~' ::,; :: " I~ ';1'1: 1 :I'!; 'I;;: 11.1'1~II<L tl'I:}til'I"I:~ I ";t'-ll-I'~~l: ~I:·H Hf:I!4 'I: :f. .~ ~:;. :;:. ::~ll~ijh;; 11.;~rf'; f · ,·,: :71::-:-IYt:~ .::: jj .... ~; ';~~::+I: ';~; 77: , ~;: ::;: ;',';: ~:Ij ~, :H,i'" I;;' ~~. :1:;: ;:t .~ ..

I l 1 '111 I ' '1" I' ,., ~I Iii '" I 'I' 'I t"1 ,,' I' 1I"IiiL "1' ,1'1' ,I I •• , 11'['111 I 'I' ." ", t" 'I' , ..... "[' 'II ... 1'1' I ,. 'II ,t "I' ,I, '" I " ll :..:: ii': l.a +ii' I:'f 1 iii! u:; I 'i . I Ii!, ;~I ,I, I l!j 14 I Ii I I'; :1 :;1t. I'" :::, 1:1\ :;1 :"1 III I' I~'U'I ,UI ' .. ' .;:: '1'" .i:i ill; .• ,: :, • 'II ;;!1 ttl' t : it j ~ 1 !.l.! ;;:. :,l~ lj .. ,: ~!:lll!' !i:! !I. : :~i! 11 pu ~!:qi:li i;+l H l:~ nl: 11 i~ lW ~~ ~!4~~1 ~~ ::~, j~0~·!t \;11 w414!~ ~; I!~! !If 4;; ,;4 k .ili i~4l~~d! !II! ~~!ll~!~ill!!~ \11 Ut !I:~ !!!! !i:: J~l~ G+ 1 11 "I' 11/1 \' H I, .'11 1 ' I Iii' 'I' II" "'II "" II" '11 ' I "1 ". I'" '\1' ",j"., , .. 11" .. II 'ill "'I II" III I ,.ft ,,,, .," 'I' "I .,,1 ·11' 'II T,' '''1 01'1 I ... 'I "'I' "", .. , "~'I' .. II :'1' I:' I' t I' I'!' l " i f I Ii; '11 "I i " " ,:! II : 'I' : I Ij I :!; :: 1 i ! I : : :: ,:'; : :: :.: I, ~ : I 'II J' I 1" 1 !::' II!: i :. ': I I ;:" . ',! ,:. I :. I I !.: ~ II. 'I 'I'; j' Jii' I: : "I! :!:: I::' :', I :! 11 ;: I'tl rn In . 'Il" ,. 11 f I'" I' . "[I ,,' I.' I I'll! I ", I', I'" I , .. " ........ ,.,. ,," '11" <I !' ,Ill " ... ,,' 'I,' 'I "II " ." ... I. "'I'''' I, "i', ' I ,I, "" 'II' .'01 'i'll' "1 ::1 Ii, Ill: II ,!!i,: il' I;:' :,1 ':1 :i' :.j I'!I II" iI: Ii! 1:'1 : :T::I : :.; ::,1 :.t!. :Ii! :, II: iii' :i!1 it:; I::: I,:: :: I .. : :1, ;iI' 'p' iii! ;::i 'ill Ii I I iii :!:: :11' I,,' ':i I' .i,: I' tlilltl If : !!H 't I '.1 {i' (1:&1:1 ";1 !'. :11 11" !'I ilt 1'1 I ::1 ;,:1' .;, t" :. ::: !! "Itil Ifll :!:! !:: ':: I!: II ',d :,,1 .11 ':1' ''11 ';1 ".1 I I ,." ,"i :", :tl: " : i I,nl !!III! 1" '111 iI'; i ;i:4:'b:·::~: :;:;1 I:;; i;:; ,I,i i;.,: :'ii Ii: II!' ::~·~:··I:I 'Ii i I:, j;!. ::' :.I:li ':;-'JI :::i \il:l, i',:i :'I'l :.·,i ::.:: \i; ·;:\:,.:0·:' ·i;l: ;:".::, ::::'\:;: ;" :;::1:: :'~: .~ •.. ::\\: il\' :\1':1 '" I Il!l ,. 'I ,. . "I ,., " .. ··1' I" "I ... ,. . . .,. I" 'I ""I·':· . .,' , .'" 1'1 I " ... ,. .... " ., , ...... , ...... ". ,.,. .... .., I' \ 1"1 I .. '\'" .... ,.,' "" , .. " ,., " 'I , .... oo ., , .. , , •• , ., .. "', .. .'" ... I'" " " " ... ' ". ..... . ... ,,, .• " "" .. " I'" "" .,,' ."." .,. 1 I', ·t:· '1 t'h!: ~/!r' 8l :: i, if!!! III j Ii,: i: ,;::'1 ;:ll 'L: I,: i; ~!!! '1: iii: : 'l i i : I\,! : \"\ ::!! !:: ::::1!:: i ! ;. ~ :1 : :: I ;! : : : i, ;;!! III :,. ;! 1: :: 1, : i : '1' :;;: ;:: I:! i : . . . :: ,;:; :::; ;: i; ': i !::; .! I: ! Iii; ;: :: .:': ! Iii ! '[1 : 'rjl i i l . , . " "",,, .. ,, W:· ,,' .. j . ..," , . I J ,. " j' ,.".... " ."!' ,,' 1 .,,' ,!. I' .. , I ' . , .. .. ... . . . . . ,. ". , .. ."",.. .... ,. ..::....'. .. 1 :.u 1:'. + , ... n I' ~ ~-tt~rF··· ........... t 1~'11'~"" . .1 '''r-'' ..... J. •• • •••• ••. • • • • ....... + n'" too.·; I· .f .......... ",~, •• , .................... 00-++ ~- ................... ~; ..1-041 _J;.. ........ .. ..... "trot-, :.

H ::IIII'II;u'lli '; 'i,:1 :1;1 "";;:'!'I':; ;1':;; I'::I::':I'!: ':'11 .,: .:: .. :·1: :1i:':;'M:;::::'··'·: .. ..: .'::. ':1:::'::·:1":::::::::;·:::::'::· :".,.: ·;1

t

l l' . !. I ill I' 'I!' "II"" II., I.., "I l' Ii' : I • I· I" . ,11 t:; " I"'" .' I ,.; I ,I I' t I o! !;" ;, I' • I ., ,I' j , ... " ", . I: " ,,'.' , ' "It "I' ": ." i!' ~':: :, I :iii I !il: !II II! I, !;: i.iii [Ii: l'd: :1 ' il:j !·I Ii I 'I iill ;:;i I':. jI :ql: ." .; : t ::j'i ;;:: II:;: i':; \j .::; :::~: Ii . IV .. I :: I:: ::':::,:'.: ::I~:': :1': Ii:: :i': :::. I::' :i:; dll :it) i! :1' ill,! i llJd II: i! iii \!t ~:!: ;: !! I ;:' j ::' " 1 -: I : I; Ii: :!,!:!:: i '1, .: ' : ;! . : ' I i ~ : . ~! i ,:;::.- ::;t :;::: :. ....:L:.!:J. ': ; ;; :uL .... ~: .::' 1 ~ :" :: Iii: i: ': i: ;::: : i ;: : II: :! l :':: l I'" 1 • ,. t 1-, u. ... 'In "r' ... '" ... " ... 1 , .... I. . " ,.1 .. ,.t ' ....... ;~... :1:, " ,,_ •• ,., ......... 1" ~ .... \Ie J I .... _.1 •. In.'''''''.:):, ._._.- .'~.H-:" ........... ~- ... I.!-:*, ~ 'i'll!il II:i ':i'I~::: Iq: :1: I,'·i :: .. ,:1" : :'1'1 '11 1 :! ,I' :: I:' ., .,:! ·:·1: 'I':· "1:::' ··'i ;: Ito :. '(V : .. I: I, ... 'I .,,:., 1:'.· ::' .. :1' .: l :: I" ,1.1": p'::,:":: "~'. !!i . I: 'ili ! 1 ':1 ,:' 1 :11,. ,i ':1 :Ii' II.il \:::i::!:l'::l:, I '0 .'1'., .li::;' 11': ';.' "':", ,',: .I,I",! ,1\ ,\ ... " ''': I,· '~.GUR; ,:~,.Li 4 . , .. , , ". 'I' ,iI •. '\1. ... ; .. I '''I "" , , ... " . " " . ., 1 'I '" , ........ " ",. I, ... , ........ ,.: .... : ...

. ,., "I',·· 11' .. r . ,. , ., ."" I' .. II .. 1'1' "1'1'·· ,... . . , ........ , .... .... I ' .

::~: l;:i :::'!l: .. ' ~ ,,' Jo. ;:1 Lli Ui jJ[ !l L; : . ; ': '[I: , .. : '::i l~_: :;:::: ::.'[ :: • . i··' .': :~!.:' .. ,.:. ':::.C .. !. .~.' .. i.:!

III 't "', ' • I 10 X 10 TO THF. erNl1 M[ Tn?

KI un "L.A rC;'·I n ((I "")' ,'III' ~ li T " :.;: :.:. !I: li :.\ !1TT1!1!1!1IF ~nrn1!! :;lI!I: ',f!]., 'Ja:: TJT 1:" :-~'r:'j~r~! --t)O> "Tl-~ll- 'T"-j".-r'-r·- ·'-r ! "l--T' :1: ';': iii; :1:: I!.: ::, ......... I" '. ::!

........ ,., ,'I , "I'" 11" .,.. . . .. .. p' .,. L-. I' ,. \ .... " ... .1, "I. ... ,.' ...

'1 I,: ,'!' ':' "~J :;', I:.l~:.' I::' jJ' :! " ; ~ t I ':; ;.;. :!'::' ,,' I: . '~

I

• ,;:.: '! I .• :i. I;;, 1.1, ; I' ", .: I' i : I'. . \ I " I :: J I ,J', ::,: :d::: II: . ': ... p ~ ... :~ .. -'~1":: ::-1' t-:t .. 4. H." .... T··'· .... · .'" '. . .... : . .... I· . ,.. , ! ... : ......... ~ ;i,l ~.~ .~~.~. -~ -'-1"- _.- .'-~ i '.': '::: !!;·i: :11 '\.'I'I'!I!!:!:!)'I·:!I: .' 'I . f" 'I : I' ,I t· . I: " u" ·:·I"I<i.;·:ii:!::··· I .': .;: ................ '''' '"~ ...... t' ....... I ....... ' .,... • •. • .. . .. . I ,. . ............. , ...... ,. ,... .... ....... , .. ,., I ': ::!: ii : :~.iA~':::!I!:: ;'.: t ;: I';: Ill! :1 : 1 : ,Ii:; , I 1'1'" ~," , ~i Mil .... 34' () ,I : :,' !:: !I: ;;;: ;: :.:':: I ,; .1i .,ii .... ,1,/ 1.1 1'\. II I" I. . 'I· •• I " ,I ,.Jt~ sA k I - ',. 'I .11 I::" 'OJ ., ,'I,d . ',: .-~!:: :;[ 1:~' r~' ::-;. ":.,':'; . :- .~. 'Tr: .~! · .. c· " .:: ... :: ... ~ :: ..... UW\. .' : ., o· ", . -:-:- .:;' ~::: ::'-··:t:~· .,,~ -...: +. '7 ~tt . , .... ,., , 1'1' , ... " .. , . ,.1... . 1 ' ,11" .. hi - \() .... .. . .. "~I ... , . y '" . 'I 101 I'll I I ,,, 'I I II I I ",.. ,'' '- hi -, .... ' " . '. 1,1 " I I It. ••• • I I I' I' 11 ., I' I'" .' ,\.... , • I· " ." I 1 I • , .' ,.. "" • • I , I , • • I • ," , , " •• 1. I I, I. •• • •••• •• • • I • i ~ I'!: '11.:1, II ': iii: I :1 '1:1:. ' 'I:. ,', . I , I. • I I Il ,I' , I I:j' ;, ::1 " ,) .;' ,!, 1, d' "I' .'" J." "I \'," :::.l '.~ ,'; I', ::',. I'" ,: '" • : I::::: I. t+'. I:; I' " : i!' . ::.: . ,.1 !l!: jii :ill iii i ii~!i.ii liii :·;1 ~:'i !: i !.:: .:::1 .. :1 .. ' :::. :::. :i:::::: :: ': ,:. ::: ; .'1:- .. !.: h f1' :~l{H~B .. f~~t()~.·: i!!u:ll~~ .. :, ,:~:,.::i Ii i;: ;'il IiI' ~:4:i 1::1.:;: i:: !:::::1 !:.: !::t' i: . ;.:. ,:: :Ii: ~.: N~·LI.;~ .' I •• ;·~i ~.'. !"er: .. .J.. ... ~ -: :.,]IS'!: .:' .i': :"'''7:' ",: ,iii ;:: :. r .. · ;: .:[1 lit; .. .... .1 4 ....... ~ ......... , ..... ~ ... ··.·'T .j .. ;:) :Y..&"~pc. .'fVt} . Uf I" tMaSP. 'E~ .... . i~ ._.. ..·",..d *~~~I··.: -; , -ill

rw

Ii, :j. :;: i!! ;~ ::i: :~ii ,,;1: I' It I:,' <:1 ,:' . ',:i:" I " "', ,: I, ,I I, I I I i,.'L.!, I , ;,' ;1" ,;:: 1'1:: ':;;::: ",: I~U ll '1'1," "1'1 1 .,'11'1"1"\1 .,,' I,' •• '1\' ,I I, II I, 1 '1 .. , I_~~ I .. tll ." III 'all ,:, ... I ,,:" ..

" , "., ... I'" , .... , "', .. , ......... ,.. ... , ... ··1 .. ' .. • ........ ,. .... .. .... ........ -- , ............ ,' ....... 1. I' · .. ·1 . : ..... ..

;.' ,.! \11' I I"~ .1;: ;::, I II' ,: : :.i '; : I/t 'I .' , ',' ! :; I.', ' I ; I ' 'I: :!I ,I! :1/1 : 11'1 ":1'" I . 'l I: • ::: II . d I: t. I ,I .:1' :, ' ' .. " , ': '\ ~: " ,:'." " I 11, •. f:, .: : I: : I:' ": ~ I:: i : I I I ::! L ; .' , . : I ii: ,I .. ::: 'I'! I':: ,i.: i!.: ::'1'::' , .. '; I;" , ' .. :.1 :, . ,: . :' J..- :,' I;:. :;: .::! :1: !i::I:i:~ .. : ... 'll :,.I,i

"I'I'Ll"" "\"1"" I •• , '1""'1' ," I' 10" ~::....;.~' • I' ", ,,·111' ;,;~~ 'II': "I "1

., ., r"1 I' • , .. ,'1' .. ,' .......... ,.. ... .......,. ";.:~ -- . . . .... ., ..... '" .... ,.~~ ..... , ... : .... :: .. .

'1 :: ~:'. . !, .:, : ,!! Ii. i \. !:: .. : ; L: "'i .' . :, ': I .:. .. i; .,;".,...- Ii. l . I .': . <:i ! I ....... ,...... .: I:. .':: ;::: ... ..' " , :;1 '; ::'; :1" ,:!' I;:; '1,01', ': I:.: :;. -: I"~" : ~ i 1 : . I' ' .'!':u.~~':. "., 'IIi ,II; ,1 '11:: I' II :! ;'P ~I' .... 1H .• ~1~;;1 .. ·,.. ...... .I.L ..... ,... .'-' ....... : •.... \ .. 1. ..... ., . ·il· .. · "'-I"~ ....... - .,. ~ ... , ..... ~~ ......... Jj~ l..I.!.: U1 ... , , .. _ .•• JJ.l :: ,:: d, i·· \ : "1: : ::., ":'. I: ':." I .,........ .'. . I I' : !.,' .. :': I::; .:" ::"PITWf::' I.:." ,: :,', ::, :;':: ,I;"::' I l,'! I' II'i':1 " I ' - '" .t .~f:~~·, , ,,', ",: ; ',;: .,1 : I ":~' ',:~~, I., :L: "1' ,;:llli'WW':!rUillI 11 !,II I, ~2 I!': l 1 ·1 1 ." ... I." ... 1j I .. ·····,.. . . .-~ ... , .. , .. I .. · ..... , ........ , ...... --. I .. ·""I •. ,.".1, .. ,., " l' ,"1 I :1 ,:~ .. , ':1' II I : ,. : .. , ,I .. :. " I" ., '.'. 'I':~ \' btJ·: :",' t'I:' Il:i::'I:;~ , . '.:";" I :.:: ::J : :,: 'I I I" - " " 1: .1 •• : ,j I : ",' ~~ 1 J '~:, ,',:, !' ",'~~ :'1,;11 ,;:j/::f; " " .. I ':1 " II 'rr .~+~: .. j' ;:: :i:: :;1: :~'1 :.:: l:'::n; ::;: .. ~.; .... :" .t;; "':, ';;~~~ltP-' i j': ·Lt:t:~· ";·1'" ~:. ''':~P~!~I' ::. ;;i: ,',':; fill ::\i\::i: ·:~:J:·'--~t:tr~l •• '1::: I:: ".:::;1 I.:, ':::li'I:: ;.!; ; .. : I':; I.:! ::.: .::1 .. :, .. I~lt.!.~, I " .... :..... '. ; .. ; I·':,~ ,.1: : .. ::. "::~. 1!!!::;rt8.. . ...,., :!J: ..

:." ,.,. R·;:~·:· II: :.\ ::1 ::.: t': ::11 :;.: ... : :,': :1 t·:: . :; I--~. :\1 .1 .. : .' : ." .~, I. , :::: i :'::I::~:: p- . . I ~.I .::1 v, !' I' ,; ii '!; I '! ill I :::::',::.:: .:,' " I :, ,I ' ·.l '; I , " ' : I, ,I ; j ,,' ::: '~~ ,,,:':' 'i!:, : ': I, .;c:;. LU .. H' .\' ... ·-:tt7 ,. , " .. ~... \":' ......... t·· ..... ! ...... :l.'~ .... . ; .... : '.'.1-- .... Lb'; ... ~ .. :.......... ~.~.. ,.-, ..... :' :'," illS --:- .. " f:'+l I • • • ,........ ,,, , ... 11. , . I' . . '. \ '" . . " , .....-, ., '11" I' '1' 2. .. _.... .

8.. l • ~. 11 ~ I ; :, ::' : ' ,l ""'" :.W ..; • ' ~ ; : I ,I ' , ' I , I : ~ • ': ': I ~ I I \' I' l I ;, :: l: ',I I : ~. ' • '""" ! '~ I ..,.. -I Q:! Jill'" ... J,:... ,it! I. .... , ....... · .. :1 ...... · ...... 1 .. ";::'i'.~1--" ' .,.... I . .., .. . ,. ':'i';;: ." · .. ·I;~~ .. . I' .. ..

o ,L \!J !!:Li.:. ::i :;:" ,. ii,' :::; .'!! .; :'.~ i;:: ::l{!: '.: ....... ~~ i PF: .:,.; .: .'.: I! !' :~P~r-:;I:' . '[':::: .! ';1 :!!!

r.: ~. Hf~~~·l •• , •• ,. l.;J... • ... 'HI" ........ I· .. · .. I ........... ~~ ~ ......... '1' -~- ............... - .. ~ ' __ 4 .. j...:. •• ,.J._+:......

:, ~ .!i!: I: .i!: ":1 : :,\i:·· 'i:' :., ... .: I I·. :;; :") ill' , L!1' .: ' '.: .: :~. :': .:' i::' ,;!, :i:: .i:! i:· ,·:f· I':: ::i!

i. I ....., I....... . ;~.~. ~l" ··'j·.I'·· ili-:. . ..;.;.:~ I' .. ..... . I' I .. ' .. , .. I'" .......... '1...... .' ... , nu.: '::'J: i:. ;;: .. ::. : ... : .. : :::1 .:: '.: ". -. : II.' .' ...... : ,,:\ ' , ' " .;i: .'i ,;1: I!! rl' I ,', 'Itf' 'r '::::.. :(1 :1:: ~", .... ~ .... I. , ... , ... '" - •• -. " . I .. :i ... · .. 1 • I... . , .•. ·1· .. · ... ( ........... j ... _. .... . ... "';~V"·· ,! .• (. ··~H~· ..ilfl-:+!-!

W

',' ,:...... .. . I : :' i \ :: '~ ..... , I I '1' i .. I '.. .'; Wt,: i; ~IPM' .. ::! I,'

II" 'I ' I :1 I <i 'I : I ' : " ,;w ,~', " , , ,I 'I' .1 I..... .. I' ., ... .... .: ... \ ... , .......... j.... :1 Iw' .,.. . ... .

'1 m i' .. 1 '. ; ',. .. ... 1': ' ..• :' I' '\. :·t· .: \ : .. :.

H 'I..l.-. .l~:I' ... :. ''1 ... ! ...... , .... i·· ... : ..... \'. . ! ....... :, .... :: ........ : .. :.;:.: "~'I ..... 1 ............. : ... ! ................ '1::, .. ,: ...... J:.... "--1";" --:-~·:h

*

:\];::Il!: :: ::~l'j-:. ii·:li;:! ;.:J ::. ;L':::I:: : 1',-:1-:::) : . ii: ,:j: ):.' ,::~ ::.! ... J. :.1: ·1 : i':: :;:1" ; :T :: ....... :' ::l::: :-:1:> <\ :::i J. ~:f!L.. :., .. ," ..;.. t'·~h··· .... ,) ...... ··f ...... 1.1._ ...... ,........ , • .1 .... .1. ... ····1 .............. , ...... ·--·1--· ..... , .. _ ... ...\... . ... , ..... ~- .... · .. ·1(:·: "".~" .- ... - -, ....... - ... ~ ;1 m· IF iii;:! !:!! Lii illi li:1 ::1j "') :.:1\: ·:i:I·J .. ;:':J!i: :::.,1 ::,!l: :.:' .';: :'; !--: ';::1'/ .. :[1:::.\ " :.: : ":1) :·fir:. d:. I;:: :li: :;;,;·I·· : .. ~::: :,-; :::~ H ..;. lfu.l..I. ·JI ~4H·I+ ~~ I .. , ... I .. , c··· ....... , ........ , ....... I·'·" "' ..... >' .. " ............... ~ ....... ,. - ... ~ ....... ! ....... , ...... ,- ., ............ , .,H j.;.j.;.....;.;.;. 'H ---I ..... - ~~, ... -:- H __ '; , Ii: ; i;: .! j I iii I' ;: i! 11;! ;::. : !! !.: : ;: Ii'::: 11 y .: i;..:.: i. :;: I' .. : :. :::;::::,':::::::::.:::. i: .. . .:: J::;::::: i!!: ! iii i!: l i:: I::: . . ::::;:!! i!

.. "t. '" '1\ .. 1 ... , I'" ,... . .. .... .... .... .... .... . ..................... , .... , ... , , ............... 1 .... '. .. ,.. '" .... " ..... , .... ' •. 1. I,,, '\1' H!' ................ , ... , : ':l~'~~ ~~!:I):;~~,:; 'il ~:t!r !iii ::~ ;;:;:::: ':- ~ :,-: !;:::~ j: :.~: ~!!; ':~:I : !)':: ,: 'i \: , I:.: ,; ;. I' -: .;::: '; .':il~::~ .~I\ .::i ~!:li iH~ ~IIL!!lj d~! ;~.: -:': ~;:~ .:\; ;;!l ' ... ;. .. ~;-f·~~ ;, .....••• ~ .... j:.; ........ I···· ''''1'''' .................... ,. ,.,,, ............ ;i.; ................ , ........................................... ... l .. J.'4 ."l.~.,. ~-, ......... ~ .• ;~ !.;:,: : !!:i: ::; :l: :;;, l:l~ Ii:' :;,' ;:1 .: .':: .;:il . , .... : I:; '.·1' . :: :::i ;.'.:; .. "1.\ .. :: i .. : .i::: ::':1<:: .;;; .:;l .~!: ll~~ ·li~ ::t~ j~~ ::: .< ;~:: :::1 :~!!

!:.:: :.,;l!: I:: ::: ::!I i'~: !!;: :;:;:-:: .: ... :: :'::::':i . .:: I:::: .• ;i·· :. ::': ;';:'.: '::,": ::',::::':: ::::/:i:··j:::; :.:::::.!::; iii: i' 1: :1;:;': :::.::: iii: ::;1' ":1 ,. :.. , .! I:, ........ ... ,,:. ".. . .: I .... . , , . ." . : l· . . . .I , , . J . . .i- .. , .. : I .. ; I . : i . .. , I . , ; i" "... .: I" r .. ··.. .• I' ." ~i4

il

t.' m' !l <l!>: •.•• i:' • I-I':: .~ .. r.·.<.··.:. ,::. I' ,. .. \.:' "::i~b >::. :','1 :1: . '!!Il>.' •• :: . ·'\.".k ..• #'(!'t')!\ ... l.... .... .." , ... I.... ..., .... ,... .... . ... I.. . .. , I. .. . . . !' ... .:'. .... I': . :.:: I ::..: i. . :.. i .:. l '; .:. .:~ .. : .I.. . .. .. .. . , .. .. ... .... r . :. .:8.~+

rr!'~/6UkJ'~1 ~J 1'[ ....'! ~ 1=' ~' i jl J.r·',I· '1'/,'1:'

_ ............ _-.---._ ........ _ ..

10 X 10 TO THE C"NTIMETFR '" 'I( ;"i r fl.'

r Kftlrf Fl ,,, Fc.. ·.( R (0 ~'AIII ,·1" , 46 1513 fTI !l!!llll!!!iIUfTllrmHnl.!~'I'"jll!!r!II!" lin '\, :::1 .:11 iii!!!", 'i'l! ':!I':I!'; :.i:lli::l 8'1: ~":] :/T:l '· I::: :8.: : i ' :!: I:!: : T:p':'~'sm' 'I']'YR F:I I!!I'!II; ,:;i :1,· 1,1 ~\;~~IFf1 I,,: . : I :1. 1 Hl '11 1 11111:1,,' Ii! J' : I' ~'I . It· 1',\ l!l, I' t' ., '"'''' , , ,. ,;:1:, " 1"" ., I :!~ :,:: .. I., '" '1:' :,:; , il dl,I!: ':" ill: 1.1: \' :11' I:':" .' :;1 "I' Hi tl,l 'I:j "~i I:I~ .,. I~' I'll' 'I ! i!: I:'; ;:;1 t::, :1': ,: • ::,: !~I: ::i: :." ,~: '!,~ ~ I'~ :' .. :':: .. , . , .. " ... ,,4.4 .", ",I .... ~4 .+1 .,., t·· ,II, 1 , .. ~I 't,· .,1 ..•. 1 ,. ~ 1, I.I i,', I: 'I I jI I: 'I I II 1+ trill!' ::: : .1 .. ' .",': : ,II'" : ,: 1'1, ,:'!I. ! .",: ,11," "i. " ;: ".' : ,: ,: .. ; ':"'.: I : ,: ".' .', II 1 .. " : l ,,: i :: i: 'I:!;! i 'I; I ,:,': I:': : i 1 11 ! I 1'1:' : I:: :'. :.1: " '!l' lw: , I: 1.:1 : I i,:, I 1 I ., I "1" "II . I 'I' " I I ,I. 'I If I I 1 '1 .. ,., ... , I I, :: :J:' .:~1 it I :: ::1' it:: : :; t~t7 ·t+ !: ....... ~: :~q 'I: ~::. :::~ ~'"!~ 'r:' ~ ... "i"!"" ..... j !" :~"l"~' .. , . . .. ," ;.~. :.,,:, 4:~1 :, '.~:.:!: .. ;L~~':' !~+t ,!~ ,~t1 p~~ ... ~~~

n

Iii, I' 1"1 1 ,,, 'I' '\" I'll ,," 'I t ""'1"; i' 'i' III "II:~ . ,,'

Iii II ~f!tiji! ::j~~~\lil ::n Ii' VARIATION OF PROPULSIVE EFFICIENCY n* iii iilili;:i < :1!1 I~II i Iii: ::.':>:::~ ::11 I! ' ,* .. ;~cr.c.; '!t:i ;·::14 't" ... rtt:":':"~.a ~r' ,".' :.l:~':';':'~:. r-: l

ill i LI!!llliVL:: 'il! !:jll;~ L'ITII X A Y : :,,:~b~;±~~i~: ! :~ k~ > d..;ii: :j

UI I ':/il!' , ~",' I:: ': d VV 1M Nb : VI. - 3400 ::: . :: r 1 11 I jill !j~;j r:~:i: ';illj;~ iT I'! !!i! l'1Jll!!'llfTlI!1 ill! IH1 ~P! !!P q;! f\n[~'J!!\lrlllrr~nprm':'::l' !!'~I~~rn'!lIl)J'~,:!' UP m r " 1fIlITfflUfJ;!t~Hll' tr!JWjll't"""~~"~"'f"':'~~ i~ u ft t iii! filii:: :: .. ; j:;: i I: ll:: :'1: :1:: :,11 :.: W' I: I::: ::1: :i:! ::.: !II: I :'1 ,:'. ., . . t-" , : 8k"'" ,I,! l!i:IU:~'" .. 0 'i fIr", IPofm~,,! ·I,n .. n .. ~- ~.v 1 , ilil !ij.ll:l .. iirr I ::ii iI::":.' : ::.: .. :! ii: I Ilili i:li iii: .;:i !.:i .,. , .. '.;' .. .: .' .. : :' .. ,' ,.~: :" f"') 'iL' ~ :1: '~W' !.l.I(@,: II.i#w.oolij~ll! .j;tl . Ii l ·· ~:tt~~I+t-"t. t· "'!-'''+ +~ • .u.UJ··;l'·i-H';';""'''''1 ", .. " .•..• ~ 'r:- " ................ I... .... . .. ".r.-'d .. , fIr.. '. ~ B. -~.~. +~ . :.:. I :;: :: j: 1:;1 ,:: Ii", ',::,,: I: !\': :. ~: ,::: '::; ~ " .: i .',::,,';.': ~: ';.: :;:: ': j: ;:: ": I • : • "', • • , ' ... .. ,I" II I, + ", • i' ~ 1'1: .:,. '! :::1 :\li ,'10 ::1' ::1: :1/ 'I;' ,;1' :.11 ;:Ii .. !: .:~, I . "I, :'[1 I:!: It:· 11,1 :1:: ::" :;!\ :::' 11:1 ':'1 1': .!:. 'I I~I .~~'. ::'~ f = O.QO ~ '" I OBi! it 1 1 ft m' ",,'" ""j'\I' III "1'1'" "11 ,,1"1 j'" ",·V","·I .... 'i"'I' " ....... ,,, ,I" .,1. "" ,II, ., .. 1.1, , ... "., .. '.. . ,,,I ,,: .70 .:: ,.

~ I j' ":: ;ili :;: l:i;I:!l! :::; :1:, :;. !Hlllii' l;: .:' , :';, 1:1: ,Ill ':!i ~!.' !!:. ,;:: t:i! !1:: :::! ::i! 1:'1 ::1: :lil ::, , .... ,', I,: J" h: . q .. r-- ' ., ,III 1.1 11"11,, ';.j.;. ",: '1I'C:lll U' 1." ~'. .,01, 'm 'lll ". , . ""I":' ". 'l.:.!. '." '" iJ· "" '11.:.1r. " , ,,,., .. . !.

I i1

*

•. ' C"-Ili' I::~ .I!';: II:: I'.':: i'l: ;;:: ;; 'Ti: " :!11 In) ~";ll" ":~:try II: :lp r: ;: .. 1r:.rrTTT~7:::·:,1 ::~tl m: ':lr~I':7' f ':;;: :1; ~t+:I'I";:n ... ~ ':~T . '. 'ft :'II~I' ttl: 1""'f;l1l T!' ,'j l l II '1' :,'11 ,I' II' I::: i: ! ~Ii. :11 I~I II·: WI.' : ":1 ;. :il' ! I~ :1.1 :1:1 !,': .t.· ill: ,:[! ;I.! ::: :1!\ :1.1 :,! I'!: : : \1" :;Ii :li! ; '! •. , ': .. ', ..,;.".:; ,~ ! 4: ',':!.' ~.: ,I; j I ... ~.:I' , 11'1" ,01, ,.iI·1 I" "., ". ,', "" ... , , " "I' ,,', "" 'I" .1" " .• ,,' ,'" 'I" "I' ,II. '''1 " ." .". "" "I, I'" .... ".' 1'--"" ···~O'O Ii.~'

~

; ~ , :: : \' : H '11 : i II: 1 : Ii 11 i ; I': ,'d I ~ j : t • I • : , : : l .::: , . t • 'I ~ I :' .: I: iI'" '11.: ! :: l:: I ;::; :::: "I: I' H'I : J :: : I j: ! ~ :! i .~: : I: ': i: II 'I ': II i:: Iii 'I: !: . :: 1 'I' I 1*= II I ~, " , , /I , I Ii i I' II: Ii . I , ' 'II' " , . , , " ., " , ,. 'I' ... 11 . II i:; ",. 'I' I ., " , , I '" . I ' I" " "I' I, ' ., . ,. . . . , ., . ,

X

AA .' I ~~~·tJ; . ", .. , ....... ,. .... '':'';''.¢;j'' , t~:~ !!..!: ~~r~ Il.l.: '~' ,I' ,I " 1+~' '_J.;-'~.4. l1! . .l' I, ......... ~~ .. l~ln".!..: 1 I' ., ~~,~~ ......... ·.~.11

>-

II "'lI I' '!I"' ... ~... ~ I ~~' . " . '1'1 . " ''', ", iI 111'1'1" II II' .1., '1'\ "'I .. , ""'1' II "jj' '.' , !l ,.1, '. '1 r;~Tl ' "" 'I! 'I' I'" ,,,' " . 'V: ". , . f4..,. 'I '1/ .. " "" "1'["'1' ."" , ," '" ,,' "Ill' j"1 "I' 'j]' "!H' '" .. , 1 ...... " ~ 1' 'ill.' "1 'II "~'I' '. .,01 "'I ,.,' "" L[I I" , ,t I • I"" "" • I "I ,", I ""'Ii' otl' '''I "I ," , ",.1 11 H 1J'I' :. , '1' -.., "j"" . ~'" ,. " .. ,,',,', "'1"" ",." I '-'I! "" "" "'11' "I "1 '11' , 'I"'" "Ii ,,' 'I" ", '"ii''' . n· ",' ,,,I,.,, .e::: .. t,4 q LI;' . :"'I:~ .. ,':; ,.~: ~::: ,., '~::. t! 'Itt '1:.. :"': ~~~: :::' !r: '1tl:\ t :1 ~ : I::~ :," " ... , .. , ... .HI. ~ ,4.. ....... "'! i:t: :~tt

U

I

lLI ~ .. 1:;h::t L:l, .. ~.~. ~;~; ;!"v,;';,;i :l~i :iii ':!: ::; .. :.i ll:; lJi ::j} ::-:I:L. iLI:\~I::~ ':!: ; LILlI!i!li'!1 !!~. iiL jj;I"~ NtiIlki:L N:t.llii~~i 1i.i..Lij ,I,I.:~I~ i ;: :!!i :11 - I' 'I • 1'" ,." " •• ""I.~ " I I fl~ltn'l "111!1 ", "1' ",I .. I' ' •• "" ,., .• g "I ,·'1 'I!' I" tt "FP':~. '. I.., ·"ffi}.IlTI''' ." 'lll" ~.. K;li ill; i, H:jl j'il: i!:;[l)::::~ : \', 1'I't' il I'i'" 1','1 , I :' :!:I'I!.'I illii '!:I' " I';' :! .. il·. ~' Ii:: :ijl"::"~; ::I! ; :i I,,'j. I:;: ;:,\ ii ;iil I::; !v ... ·; "i.W.",.!"lI.~;.l.,~ I: I l:d;]'l:,:;:: i :: !ii; !,:~ l 1 J ~ l' •• ~. ~.il '~I .. ' I .. ·' .. " t 1 r t ~ I' .U •• , I" il' '''','' ,. , .. , ...... " ,,,.j:.~K:..! ... I, ,II :1 ~ !H flU ,It (I."" .. ,:-na::!C'ti, -4 14; fH-+- .. ;.1., ' l '-1.. ( '::: I:iild! 11j!:ll) :;::1:;:: 'ii' !:ii i il t'mll ill! Hii :1:iIIJ'i! iii! :1;;I:·:·l:; u:' i·:i: ':.:. ":: :::: :,:;1 .... ~: :!l 1:1: .::! :iii .::1 :;.' '" I;::" . : . Ii iii' ii' ;::. :':'\1;:: :ii :!

u: I';: f.Hittt+::·~:; ;~Hr:ttt :i, :1:, >lIl" 1 in,; ;;;: ;i;· Iitt iWr·hrl1::t,::·: ::~~ .. ::~ :~I ;;~ ;!77 ::;: ~Tt+r~;! ~~~. :';!; ;!i! :", '~i r~t:fTI~t+;:C: tlil I ~; h ;;H .;:: i< i:!:'" I ::: :i:. ',1: I;':: Ill' t!:! I' I:!I II', 'I \ 1':1 1 :':\ 'I"~ :II; '::1 !!':~! , :'1' :1;, : :: ::'1 '1,1 :'" ::I!' il" N:: ,II ::1 ll!' !;.: ::i. ,i:1 ::11 111 ~1 1'1' I,!: 'I!; :!;: :,,1 ..... "" "I ... , .... ,.! .. " .. "". I. I 'I .t't " ..... I., 't" "" " .. I .. , '1' .. " ... ", ...... .. ,,,,, ..... "1'"'' I I'" 1'" H, ..... ,,,. tI" 1.+ •• ~ .. 1'" , .. , ., Lu 'I!' ':. ", : " : 'I:: Iii:" :1:: ::\ ,il 'm'll Ii, 'ii' I::: ::!'\'II: ijl II :':1 ':.' :: .:, I,:' .:: :.:, I:"~ .1:1 .',: . .: 'I. N" 'II :!Ii ':1: I:: i'll .::' :i'l ,II I'I!I ::.! ,:j. ::!:~.' I 'j • , .. "I.,h "'Iii Iii I'" J 'I ,,', 'II"." I 1", "~I." '" ,,·o\HI. ,," ",," "I 'iii ,I" ". "., . "'" I 'I" .1, ,,01 ,oil I'li ' i"" , .. ,',. I • ::. ...... ~.t rt-tt!' .. , I' 1 '4 t'lL!. ~lill...L+.! :ll.! U.1.!. ' 1.1 . Jj~ ':.;~.' ':'l':"'~~ '.l!.!. III " I " • :~.~ .. :.. t.!: .. ~ .. N' :. 1.1 ", "" ,'11 ., . ' .... !..+..L. .:J..l.' , I I::, ,:;'. II:: I: Ii: I: I, : ~ 1II1I11 I ,.! i, i!:: rl::' i" I '! j I I I: l 'I .': i;.: 'I:' •.• i I: j' .:., ':TI' 11"1 I: 'I ': : ,: ' ,,' i; I, .: 1 I! I !!:: ! d i 'I: :: : il' I '1: I : !:': . :. : i 'I: : If "1'" 11' 'I' \1'1" "1' II" 'I ,,', 1'11,01'1 "jl '!lllli' , I' 'Iii '" "" I'" ,II, ",I ""." 'I 1111 'I I "" ,.... 'I N .. ,I I'" 'I" '1'1 'I' II "I, "" I,. ",., ,. "" '1 I ' ','I ,. , I "I I ,,\ I I I "'I I"'P 11'11 I .\'111' \., I' I , .• , I'" . ,. I "II,.,. ,,! , I" , •• , , ••• I I I I ,I" 'I" "" .' \ '1 _

W

-...;;:' .' "" '1/ •• II" "t·· I'" I' , '" 'I' I" '" 1 III" .. , ...• t ., ·w .", ." '''1 '" II I . I' "" " "1"" "" '1" "1' "". 'I' "t' "I' tI'· "1 . , - jl~' ":::: ::i.,!l ::: Ii;! II!! III :1 ill! i:I': i' 'I Li] :11: i l' ,I' :! i iii; ll··! iI:i i' I ::i! I;!: :'1 :,il till -:t:ln i~·.: ,'i:: ::1: ':i: .. Nl :": iii: i::! !lll!l! I ! ::;1 :i:: i:'; :1,: !:HI r: d· ,,1:\:::1 I., I""""",,, 'll lIT 1 it llr~ 'lL L,"-: oil, 'I; U I'.I.[ ,I., ,.1111". \ ',:U ,ill ,,,i .,,' I II: I II, , .,. ':D"!! .. 1"1:,,1 ,." " , 'I", ,"" ,I" .1" "I. 'il r ''';-r: . ". ~t~ tr:- I~P"t.i!'~~ -:, , , .. t I • 7, r.:.~ ~I It-:t :-; 1~~~ " I+f'. ~" -:-i!i , .. , -:-H", ... ~-i ~'I ~ I' .' 7' I"'~ '11 ~'nl ~:: ...... i'~."'~~" ~;i~ ~'+ IT" . ~r" . " ,'" "I," II "I ~1"I' 'I'''' , .. II;; 1"< 1'1, ,II 1,1 'I" d I 1. \ ,·1 ",I '1'1 'III III " II' \'" I," "" 1111 "'1 'It! '''It,l .. , ,.1, l' ,\ "I , .. I I ... ,'"'' ,1'1 t· lit! I.J, "".01 , •. ,.1 I:; :,' ~I :'1' 'I:: Ill: .:i: :i" :i! '::1 ~ 11 1:11 ':1. 1:!1 'i:1 I !. I 1'1 :;:. II : II:: I:H ::,. ii:i !!!, I:!! '!I ,tl' t:.1 il! Iii. i:li . II I!!: j' I' ',:1 11 '1, Ii '1'1 :'1: ::: :;: Ii:' it ..J !.~.,.... t'j' 1'1' ." •• ". "" "'I \.1 "I' 1. "I' "" ,," . 1\ I '1' .,,' "" 'I" '11' ",' "'1 ",' ",' .. , ",I "It '" 1'1'" I " ..•. ,.. K"I'" I' ' I I. 01,. , ... ", ..... " , ' : :J . :'" : 1 I :::i d!: Iii: i; H :!:; : n I ;;; I,' Ii: i! 1 '! ; ~ i i; ,: q III I i H' I: : Iii :: i: . I:: i' l' : 111 .:; I' ,i: ! 1 :: I:: i ; j i : i ! i : I;: Ii: ' I' Ii :: I ::! i ; I '" . , I ., : .. ~: t I:: U 1'1 :: J! :' i· ! i· : : ; J H+f: 11

t

;:. "" ~.. ~!l . " .... '11 ,." ",t "ll I", , '.\. ,.,. ti; ,,,' ,I, t" '11 "U .. , ,I. ,I .. lWi "~L !.lllf!,l'll," ":L ':.lJ, II" ,,' "!I'~~!I 'JI.. . I ,,,. ,.", .. " !:4'.ll+;' ,I ~ ....... I:~. :~ .. ::i j:.: :;:: It!: Si :r: ~:I jt;t :111 ;1;-: :::: ~~; '::: .,'! . ,:::TT :::: ;!~! rl:~ :::: .;-;, ~::I ::!~ lni ::li i,:: :r~ r:"~T~t~ ::11 !:1i~:!i ... ~" .. ,. ." ....... I~:t·~· ~ !:; :::: :1.\ , !i'I": I; :::' ;:1' Ii: :;!: ]!'I !:·II,·I ;:1 I':: till ::d ;:1 d:: !lll ::11 I,:: I!. :', ;1/: .:' :::. I,:: ~'~' :;il ;,:t ::I:!' d; :'1; ::11 ":i .:,: :" ~" . I ',': .::. Hi, 0 ,'" ... " .... 1 .. ,1 .. , .. " "., .. 1 "1.,,1.1,, "" "" .," "" " , "I' I ... "" 01, I'" . 'I .... ,,,' "t· '11'"'' ... ,,, " .. ,II' ",. " .. " .... I 1 . , I" . ", ... , . ""'::. "i ':~: l'!; 'I:' ;::, ;1:: :'H" ,11' '\'\ lilt lit .:i; :'!:: !; .. :lil ,',I :::1 1:': :',' :!: .. 1 :.i: ;;j' q'l :ll! i::' ,: ::. ;,': \I ',:; ! I: ::,: ,I • ,. : 1 I I j LI..:'~::' d i ;,:. : ~ j: !;', ;; I; :!,: I 1 ;: i! ! I, 'I,: ::': ,:;: ::;. ~:' i' I :! ~: :::: ~::' I; f': :: I: '::! I: ~ :,:! I d ,! ~. :: i .. :: ~ 01. !. ~: 11" I .:: ,!. :,'. .; .' X.' II d~ 'JI-'~if'

f

ftf n . .;,A:._ ...... :.1 ~ ......... ,..... ''+1- .,.1.. l •• '~" ~I-' •••• ,t', :.t,. " ....... , .. ~ ...... - '''f~ ... ~ ".' " ... ~ .... " ••... -. .••• .~- .+ •• \ ........ , ·';C;1\·tjt~l !L I-L i!:~";: \: ::;~ j~l: ;:::.;':: :;; <'~ 'll: ;:~: ~:~ :::i !:! !!1,:i1 :!:l ;.:::, . ;i:: ::;~ ,';, 'j:! :11i :~;! :~l; :;;: :::'1:' ;.;, ::;; ;; j ':,::;' .;~. ': ::; i:- ::1111::: ::','; I., i ,:i • II .. .,. . . ,I .. ,' ,.,. .,.. . .. .. . .. I • , " 1 ' , , I. '.. I •• , I' 1 " ., ,. I' "'1 I.,. 1 ~ " "" •• ,' •• " , ", "" .,., • ., •• , "., • ,. I ' , ., "" " . .., .. , . . . . . . .. I ' ." • ;1 J!~ I:: .:11 :;:~:: I:~~: :': .1, '.:, .. 11.. ~.~~ :: ,! ~1:. :L' :' :1: ;:1; !l;i :~p ;:;. '::: : : :' '1 :;~ p ,:1 :\:'\" :\1;1'.·; ,;1:lll ,;i~'I:' ::. 'i :11 •. , •.. :.:. .... ~!""' .. "1'''' ..... ,., "II "" ..... " ....... ,.... ~ .... I· " ,,~ , ... • ... 14:·· ··T· ......... ",,,,, " .............. ;..;.. -I,',' "~;'rt1 •• :t' -, .. -1--:"7- :'1 ;:::'ff1: q!,'nn j:j,i:i' :; '., .:' .:::: ,:! l ! ~!ij !::. <i; :::1 ::,' :1:' i;,,": I .~ .. : ';, ,;:i ::: :~:, ,i: :,:: i:: ~. : t ,;! ::j: Iii: :'::, .. ' " .. ill >Ih:: I:;: il:! I:Hh:' :;l; :':i : .. : :". : ::... ": : ... '~'; I::: I:: I::: .::1 Ii:: :il:! ·I!j·" ..: !'--<.i.~: .:: ,:,; . ;1 :::: ':1':':' , .. :: : .:;. : ... ": I :;: :::: 'I'!: \:/;:1::'; ,''' ;:,' .;:; :ii!

",. '"'''I''~''' "1'''1'' . I . , .. ,,, .... "·"1'· .. ,. .......... ' ,,, " , ... , ,"'" I,: I'::': . .! I::. '" ;;:: ;!i:fU ;l~t !;,.~; :rt;~;~ :1;,::.:. ";'\"" !.:; :;~::;:j::1\ .. :: !::1 /) !;:. :ji:!'::: ,,:. :'::;;; 1::t .. :: :i:: ~ .. \ " ".:: '" .. :,: ":~ .... ;::: ;i" :::t~ :~jt~tj1l~: .::~:: ~~:;m "" .,,, "" ,\,1'''·1·'' .. ,I ... , .... 1 .. " .. ·1 "'"'' " .. ' .. ,., ... , ." ,'" '1,.1 ". , ...... ! "'. "" '''''J ~ X "'60 kt~ .. .. I· .. i':: .::: I::· ';:',". " :."' .. ',., !,t~·' !iliIJii: ll:'!,"!~~ ::'~I.·.'I;j .. ~ .i~~~ .. !.t,~ ····I~~~,: •.• i~::'1 i.2'~ .i~6~'," .. ~r"l: c.!: 'It!

Yl,.::· :::-\;::: : .. t·::· ·:,:l· " ·1:"":" ·':I:,,·:J .. ·;f:: ·l:·I .. ! l.. y _ N1 'IN. 'tT- C/JflUtT£J> PlW'ELLER +"

W

I- ·.II.Li.bl~; j 6 i' iii' .... ... - I'. " ", 'I · '1' S~A;{~~PEEDI "., .. I.' :1:: I II- loUrill.. :.qr. . " : . \ \" '1': .. I ' I , IR ~. ; ... ("'.1 10 X 10 TO THE CENT1Mf:TFR 46 1513 KFUf'r EL 1\ E GClr p co MAl" If" II '. /I' III! ::,.IW~:u u rll iPll1ill~ :: !=~~W:Oll1',rD,il::lJ"'ij!JJjI~jj\:jrw:B ,;i; Ii:: :~,: ,:(~ ~: ~;0:-r:r~i ,ii il:;: ,ill liI;lll IIPI 1111"1 P~I!Pj! 11:)'1 !i!1 ':1111 '1111 II '~11 !' .. ~~~ ~i~i~:~~'~~.H !~~. ,':; :~ .~:~~~,;~ " ~~!i!i;~I~/"I'.D~':V,~~ ,I. ;':;' r::' '::: :::: ':+; :';' i';: " '!: <I :; ittj ~ t 1 H1;t H·t:. ~ ·if H· HL :~.: ::~!~"f ;H~ ilii 11 I" ii'ul1 "I, 'Ii' ". Iii II' .,. 'I "I' ''1i1 I, 'I" " :1' 'Iii '1'J.il" I' ,,' ,. '''' , ,"" ,.1 "" ",' " "Hili ,I l·lI I; ,I III d [1,1. :~~::: ,iiji ,:1, I :t :':: J~El' , "P'!i~ 'J: 1:;iJt' ~j"liJiiM~io1i:i~~:~I:AiJ: I: i~;1 ;~: ~I~; t:i: ;1:1; :f:~I:i:~;.~1ti; 'i~l~lt: ;1++ :::, .;:. '-~~I 'i~I:I:; ';, ii' II 1 ;1' II'~I :.' ~. ~go¥:""I: i*,'1 'l '" :, 1IIli11!1TUi~ 1111' :i:i i:. ,~rfViU/lfJ: I !:1iJ ':1' Itl!i I 'I !:I' :~ ,:il; I;, :/:i Ii:: 1'1 l't: :':'1 ;r,. ,I. ,,', II j'l I !:1 ' llj 11:1 ~1.IPll " .: ;1 I 1:1 l j !1I1!! 1 •.. ,. ~~~f1;~ ',.'!" .... Il" ".'- .' " I • r\, ", " I'" '''1'''' 'I" j'" '''' .... " • , .. ,.1. ,,", "I' '-H • t ,l •. I' lIJii j t 'il . .t~. ",. 'I m' '1,.

I: ; II' lit, .. I' 11 I: " I;": t; :;: i i . .; : j, , i ~: !:!, III :; I' t :: 1 I' III;:: I ! :1" ::!: : [: 1 .! I :::' ~ i ~ t 1 t I' I:' I, "! I II 'I ,: I III Ii' I:! '. '.:; I:" :::: 'I' I' I !I' I ,. , ,,! i I" I , ; i' " I . " , ,,' """" ~' '~ , I' 'Ill .' 'I" Ij" ,I t IlJ I 'I II ' '''. I '" -'" '"'; I i I! " , ",' lit. : i ' d' I' ~ II' lj , I 'I'" , I i I ,..,-; , I .

I11 ',: I t •• 11 '+;.'::",:: ::In::~::':lj,,-~:I', f+i~~; +Hl -: ':~'~r~'~~i 1:::::'~~:-t~~+,:~J~.~jt~;L~~:H"Jt ~~+, ., II.,: ,I'::', . " .

1t , I,' I It iii' '. i.i.i..u 'I'~iil II ~i" I I. 1'1' III I 1 1 '1' 'I~ "I '" 'III "I' '11'''1,,01 'II' "" "j'''' 1,1;1. 1: l(!j~I' ,p; IIIIU,:'I' , 'llil ~ I I ! 1/1 .! ~ I. !'OJ '~:' II !~. ~!j ~[l~i ~c; Ii- II,: 1\ lId iI' :'1: Ii: It ::: !I'!I: I ~.tl i ,t :'1 IJjJ jltlW,1 !: ~ Ijlt' Ii! Dill i,l :::; ! III=!' : 11111 1 I r Ii liT I. l~~'!"i~~!: I' Wll ~,.,: ~ :i;:' 2 'i~' ~1.1 I :~~::~'::': :1 Ill; 11!'II·1f '1,,1;'1 1'; :;1': 1;11 !':1'; III''': I 1 ,:n no. II' In: :::tflil' I'll

t

, I ,ii' '1 iJi "~I" """11 ,,, .. 1"11 1'1"11'1' j' Ii ,,, .. '''I I"!" . "1', "I:·'H.)l' I I ' "';',! . +!.,_ i~~ ~' I I. ' _:. ,,:11+1 J.ll+~++#!.U,-~:ljl~:I;I.!~l~iLIL:-::~~:..illt:l~';.t J:'lii: :illll'I~I"L! • 1 1 1 I':IFI, I I ., 'I 1111 '! ",,' :'::~: '::.: , ~' ~~'~: I'~' :,:i'" '" l.!i.J' 1111 !:j'i '1 : :i:::;:: ;:11 1::f :Ii , I' ::,1 i ::!I iTfT I' .1'1 il:IIJ i '11 1 :\!\liI' " ,jil " ill' " pi 11 I t I j III fill ,: ....... ., .. : IrurJll' n,' 'if.! : 1*lh 1i'J: V' "~' i: I II! ilil' ill: :111 I:;. I I: :'1 :::i ,I: U': UW'I ,: 'Ii ill'!;1 [I ~' il'" 'I:' ;:;, Illi ~' I'H' " ,1'1 i', It' '1 :~~f:': "',~l "-'-''''-fJ,I''';: I ~ '111'\' ;'f .'''' t :111', If:;·.t :t~! ~n ltd '11 I' :1:' '::: :~: " 'I; : I I +-1 • '1, t • II~ Iti~ '!:: ~ It il- I, I !:I !!.' I,! I ! !! 11.1 i!,~ rI~~i"w.~~I~ i ~} ~'/1/1cr~~:I+l4 ~ lu W;~I:.i; i:ir :4 i t!~ ~+~~ ;!i! :4~1~+4 :;~; :, I :~' ::~ :~~ .Iiil!li: : _!~ Ii!! ~ ,I !U~~~ ~: 'if wi I) i !!

t

l ' \ .. "11 ~.fT '" "1 1"1 A "~~.' ,.!ill:. "" '~WJJ' ~ "ci ' , I'" ""I" ,," 111 "'I ".1 '1'.ijJ."lU?' .,,' "tm1 II., Wi di1· , '" It· '" 'I', II : li' 1m': I:: : It if' 1'1 III JUt I ~! . :1 ,IU~~ '; 1~1 III ::1'1 !:'~ ,'lilli' '::. :!l;~"i·' '., I:' "1111 ttl! 1\' '1'; III :l'! '::. ::. II': I I.

~t H-ITil :11:. It:' 1:l tt: ;, ,> ',' Yo '-:1- ..... r .... '~". . ,I: 1111"':" ,: ' 1,,1 :I~ I::, r:: ':" ".! :,,~ " " .. : ":' "1.l1i ::':' :! 1:·. : "h I::' .:: r II '1:1

i

l · ~:' I 'I 'n "I I '" III ~i~~j4il~' ~1. tt1JliP-ll ',~ " ~ 'Vk" l' I I, I 4~"""" I I" ~~ k ' . 'II I lil.j·I' I" I ... 1 .. I., .1" I" 2'Wlli' 'Iii I •• 1. I 1'1 I, • 'II" ~, .1 ",! ttl -/ I '\1*.'" I'I! 'III I, TI' I I I "I Iii III' .", "'I I' '. "'''' U-.

I ••• 1' , I 'U! . .!J ' j 1.' Ir;':'" II :11' ,t! 'I 1 I I l'i.L.:.!...U. ,. . I~~ , !. I .;~l:_ 1.1 r t '." iI' I' 'I' I • 'fI!~ .:. I I ii ;T'j j;,: ,,:, j:;1 If: :j"I:'1I ~. )'I'ry;o: I, ;',: r~:i, ':.- :;:'1 . , :' ,'in; (~I :i,,::,: II;: :::;1'1;1' .~ 'i: :':: "'T-~:([T ::1', I ;1;, 'I':' Il'i 11':/ljI: 'I!' :.' ''-. :ill ::1 :11' 1 1 , il!!' 11"\11:: ,!It !! ' Iii: 'l 1 I. 1 '11 ~~. L' : it I.J.:JIl " ',,:, ":J'I'I ::1'1 ::111 "I' I~: II :'11 :,:: I::: ;::1 :j;; ,~:~ ';'J ,!,' i,( ; ~ ::': II 'II :111 ',!II': ::1: i.i' '!111: j' ~'I 'II " : 1 T! ~l:: '!I: :t 1 : lU'l 11t!1~ Jij :.:: ! .. :~~~' i!]1 .':: I:i: :;"H,j: ::1 '1. !,:: it': ~ .. , ',,1 :;:i I't' I::, l'I:I:::JVii ,'1 I::, i',: '.:' ,::1 :1:: :. i :11 :":, i!;4 I',: w!'" II:: '::' 'II: : .~~ :1 'I I I 'Ii 1::, ':1': 1 ' .. :11 . :1 liiil'~" II,liJo. ·U..:.i.U:" Ill.ill'IIi.' ,01, ULI '1 '111' LH' I . '1 IO'H' 1'::: ,I:! I: 1~'I: ~ I::' :/; I'll' I:t':! "1 :Ui': ,ill: 11' 1';,1 li: :1:' 1 1 ";/ ,i!il I::: ~: II': I ::~ 1 " il ." "'!I'II " f+!+.t' • ';.o:JM 1&'I'Ii1l',;~ '.II JAN If. pI':;-;-f.j-t-;.:"." ":u: ." ,',' ',I • fJ.' "4'14 ". "'Ii' 'I' , .. ,', ~ 1 • " lIT' Ir~liH I::, i:j! +I : II I;' 'II rr ,:,:., ~~", :.:, ;:'1: ',,:i I, '", ~: ~:I: 11:'l7::;'; :, ; ;::; ·:ITT :!I~ -:.~' 4'~~ ... ~: i::, +~~I' Til"" 'I:' 'I': :r'j ,'I !: .. 'I':T t 11 '" HI'I' '1"1 1' 'I' 'II l·.j I' ~"'Il" I""" ·,1. 1.1, 'I" " ,II "I "1[' , , . ,II' ,II I,d, "'" "II'" 'I" 'I' .", " '1' " .. Ii I ' ,I,ll.", I, 1'1. ,1", .. I' I" 1 ll' t~' I' . 'I . I ' II II" '~" "I' 1"1 '11' 1'1' '''I ' ," 'II "I 'I 'I' "" I'" ,,' "'Ii:j; I"" ," "II'" ,," ", I . ,'" ", 'I "" 1"1 ",. "Ii' 'd,,,, 'III' " .1:: I;: u:;; ::1: :1 !nhl:1 Iii 1'1 ';p, ;'i :::i iiI ::d :; , ":, !ii' ',;: :!Ji ~!q ~I' !: 1[:: ,;;: ;ij1 ;::r~ :,: :iH '!f !:: I!!: ~ll' ,'il :', ::'1 :1:' :!l: :1' :::im4I!: lji'l i\ 'illl' ;:1 ,':: ,: t" ®~i l l:iI I MIJ 'i':: 1'*':: !I il: II ::l~~ .. LWll~.l!@l:l1 ~~WL.;:. !U~ttil'll llt !I;~ i U IUI~:j'l~ i.:, !Uimt'!IL~J. 'rm,!j, 1i lL~:~l ~~~! jj:l;J Lill!-dllW,l 'I: ii" iii ',!lI!:, .Ij.i.41iii! I ""~'l' '''j' il" H' , II 11'1 II "I' " I~r.:s" ",. ~11 " I" " l'j'I' " ,;' II" ~'" "", 'I"'" " " I" 'I '1' " '" ,T", 'ill" ''', 1'1' "I' '1'1"" '1,lt:tt!I" l 1'1 ttll :i. d I t·il I)' 'I 'Ill :itt Ii': I " dl: ;:1' ,.\, 1:':1' II I I :lll ;1: ! I'IV': I'i; I:" ! 'i 'II ii' :! I ,'tIl !I,i ::1'1 :" :q 'I:: ,l!1 ,:11 :tp ,:,j '11 :.1, ~i'll !i,' " '1 l l l ;t ': 11 1 ~It, .. pI. 1~11 !li: .;: I Ifr I .. Ii I':' ..... , ~l: ': :::' L:' .:.; .. ' "II :.11 :1:· iI': ,. til ,;l! ~LI .::, 1.t..: :1,1!.: ,1:1:: ,:.1 ,I. '1:' '" ,j! .1.1 ['Pl :11 'iii .. il,: :,:: ,I, il :dl rf! f :,1: Il:' ,!ti I:" I I ~i It!' II' ,I ;1:: I':: : " .. I ~k.i!i ;' 1: , I:!' :; 'I:, :::, II :::J '~'II ::11111:' :I:: =1:' .:1, ;,p II', ~'~. 1:/1 :1 : 11'1 I;: il' !!Ii ti':.;: J: ,11 II!,. :': !f:' ;!;' ']'1 1 !I'll ". "Ii "" ,', III " iii' "II " ",.. 1~Li.:::·'· ".' ,'" I'"~ " '~'I' ,II' " ,I, '1"",,, , .. , Iii "" I'" d" ", 'I" ", '" I, ,,,' ", "" ,1'1 "I! ' ·i:.. ;lil~' , :.:: ': I':' '::, :11: I" • ::: , :' •• : ~~~~ ±"'~~I~~:~ ~ ~~11 ~!+t I I ,ol .. r~'~ '1,1 ~': ,:': ,:: :'" ·-qH~r~~!.t q~ .. !.~~ ~,< .. ;t~LLL ~~~ "I~!J.~~+':: ::' : ':' ',~' _, . I "" . .1,." ... .II."j "'~II'I'I' ".,1"", "1'" '~I".II::U I,., ""1 ""''''''1''1' "1"""""1'" . '"'' li'I"'I",II:;!'I,,·tll I'l,,, ~' , ·11 1 1 :!,' It'll :,:' .. :: "'~ 'HI I :j '. j:'I' dl ::li ~:.: ,,', ;, : ~il: i il l' . :!!IV. ' ::: loL. : 11 'i, ::;: ~!:I .II! .:~I i:l! :i:: il:. 1~!' .':, i :II: :,~ 1:: ~III 11'1 ,I: :111 f~1 I:' .:. ,;, ','I "il" Wi .. ·.' .. · ~l. .,' I I' 't· .. I .............. "'I "'." " • ~ ,", II" ", .. , ",. I'" " • "', -"1 ... ,.,. ,,' "I. '". , '. ,," I'''''' ",' "",, .. , .. ,I ro" " , .. :: Hti ... .

. ~ :IH '; ,::: ~:'ll1i :: ;:. ~I:: PI! :'"1:;': :": ;:.; :Ili ::~ '. fl ~:! " Ll.!il~~I; ::;' I ,I ,Ill ::;: :!:: :;:; :llt ~,:;:; d!' .l:: :t;: :;1 'i ;~.: .;:. :i!' :::i li;i :i1: :::: .i!: I::: . : :il~~'~1Q ~q '. :::r\ F ll-;1tt'L.:..:J. uh ,'it:i~,J.'" 'J-l~!.:H"'''' "lJ ,,, "" I~' '~' . 'I "j' '''J-l~';''; "~.i ,," I'LL'" ;.lll ," I", ! ". ,11-: ""I~ '. ", .. "" .. I·" I ,,, L "1: ',,~l t :~ " .... : I 1,', r:-:r I::i ~ ~trr! ;,~:-~ ::: '~ .. -:;-7":1 ": ~.::.:o- "';:r ". ~ 1:il4Jj'II-: :-11; :1:, :-!: ;t"l '~I:~;: :::t Hi-' Ir:: ~-~~~ ... ~ :1., ;~t: :!I' r::r ~I!:" ,:i: :;1: :!I ':1' ::n~ .~~ l : ... '" " ':11' "I 1'1' , . 'I"',' I, II' "I' ,IiI.;'; ", 'I' " I t+l.4, I I'" "" "" ,I I~ ,,,' '1'1 ,I.. ,,,I ' 'I ,.1, "'I ,,,, I" .. " 1'1' 'I '-' 'I~' lliH'l I!

",,':;1, I::, :.:. ; i.l: -:11 ,;,j I:"., ~"::;:' :';; ,; ; :; I ': I/:;.J~ "'i1: .i:: ,;II:~ '" :. J.J.!JlIn:: ::1; iI" " ~:I ;,1, ;,:, :,,: ' ,1 ,:,\ :,:: ill: ::'1 I:, I." .::: .1 j :!.1 ~: .. ,,, .. " :!I :U:~ Hi: 1::: l:i: ::i' III: :1 ,q! Ii': :;, '.::;:,:, i I: : i~!!~': Iv.- I, .• :: :lll: !!:! ,;: 'l, :1'.:., !j:I;;~~I;!\;, I::;: :I!i ::1: ;:' :, ,: :!'i :l:: :1:'1 ;", ::ti ::~: ii 1 ':11 !!:. ,> !:;'ItJ! ;\ llilil:: "" "" "I, ~ l' ,I, ";1 ." I V' .. 1 ,I, "," • ,,', ,,', , d, .. ,,, ,,]'!tt! ",,,. li" 1', "" , ':: 'I" ,." ," ".,. II:' ,II, .:i; ·,;,,1::: ~'I' ,," 4 ~~~ .. 'i' I~' jl ,"-" ..... \'-.. ~-:i: ..• ~. i·-:- ........ :~ • ... r .. t .... ~· £,1: ',,';'~ .. ; ... ! ~t· .~ .. i ..... ·,~ -;-:·1 :~ ... :"~I"'''''''': . ,~l.!t!~ :~ .. : ...... , •. ~: I"~ it" ~-+ ~~~ .: .... ~~ ~r.-:-" ~.~ ., ~ .:..~ ,',' " " ,1'1 ." ,', 't ' , • I ~ II ., ,,\1 ,!,' "I, II, """ ., I" .... '" , I.l..:,r--' . ""., II '" ,t, ,'I I II .j" , 'M4 "II .:- I:,: I: ' . : ,::',,: :.:, ,,!. r> :' II :' ,':1.1 '1;:1 :'1 ;1" \'., " , ,\11 . it ::.' ,::; ,:;: ,. '~: 'I:: ' ' I· II , .; i', ;:.' ,.;::: :': :" : .::1 .1, " ' .... " .. , "" ,,, .... ", ,," '''I' , - , .. ,' ,. " ,I" "" .",.1 ,I I", t' " ' , ...... , "'. d' " " .. I '" '" , ,,",," I .", ,., " , ~" "II ']!"~", ~'I, ::1'1 i'i' I i;!'~::! ...... , I:: ;:jl : ,:" ,;1; :::1 ,:;1 ;:, :/, 1,,: :11,:; ::': :;ii :!!i ,':1 I;:' :::1 :i, '" ,: ' :(";';' I:' ."" t"j ':,1 "I: ." '!:' 1,1 .,,1, :"""'~""'I'" ,'II'lj ,I"" '1",·,1 ".,[, .• , ,.11", ,I! I'll "'I I' ':' 'I, ,I, "',., , .. ,,' 1." , lIt [ _. ._. _ .. '.1'-''' "J+:" , , '" N J .. -, .... ,'-, • , ,,., ' .. ' ... , .... ·i., .' •• ++- .H' .-.-" •. ~~ "4' "'-' !. '''·F·~' ... , .•. , ",. ~ ...... Ii .. '1' ,H' "_'j-:-' ., ....!l . " I: ,t :' '''d~iiJ ! . ~' ~ ;'1' 'Ii; :. ,';: I;':, ill :,,' I;', ,:: "I: ,d: I'!' , ,. '\ \' .: " .::! , I~" ., ::; :: ,', 'I:,!: ~ :d , ,:,,: II: II! ,;:1 ',i: '1:I~ ',';', '. ,',' ~:. I:, ,I :1/1 III .1:1 II" 1'" I 1: 1 .1 ',;:: ,:;1 Iii ;t' :,' , 'II' ,I . " ,: ,;" 'I:! ""W1' :i' :::' ;:1 ': :';' ':1 ,I" .. , " t, "" "rl~' '~"" '. ", "" .. , -, I~~I j:~1 , ,. I .. ,' " ,Ii" " T ,," ....... , ... "ti II"~ ,.,1 '.,,, , "", " ..... "" .. , ,,,. "" .. ,' .. , ." "'I .. ;:;: :: .. :. "":i' i:;' d .. !:':::,' ;, !:,: !i::, '. ~!' :~!q ~:i::l' II:, ;: ' ,il! ::: j:!. ';:; :!l :!! ::,; ;:: ,: .', , : ::,~ ,~i' :;,1 ':, : ::, ::!l 'H ,:' '.1;:: ,:1 :[11 , .1 "" 1;" "" l.u,.l "L!J...!_'Jli' 'c!.l " ~.i' " it ,. " !:i;';.1 t' I"" . " ';1 .". "[,, .. '11' ,. ",,, ,~:' '" 1;' Lil-il-;..;.!..l" .. ,I ... ", ,. " t!C .. I, • :ill rt ,: ,;.! :,: :: ~~;~ •• r~· ":: r;._4 ·1~ :-f;' .-: :4. . ---: .... : ~:r ;., .. ;~ ~~: ;:!; : I;' , ' ~~: I iP~ r::~ "i~ :0.: tr~ rtTi 1!1 ':: i .... : .~~~ '~,' r.~. -.~~ .~ :;-:T I~' : 1'1 :--; 1::. ~7~ ,:: ,::: I.' I~;:; ~~r ·:Tn :: :::: 1:': ,,;' I:!! :,:: :;.; I,!l :! .:. !,,! . ':!! :m' ,ii \:[' :;11 1:1 :11' ':'II~~L.i;: II! iiI ;11: '::' 'II' :~. ::' '1',1, ,: ::,: I' ,:~ ::,! ,::: :::. :;! ::1:" , .1:: :\1 ,::1 1 I 1 ., :7'11'~:::;: :::' :: ~: ': li't ~':j: 1111:'p::gl: :::1' ;:" , ... :'11: \'1 I 1"1 I': :i 4 :!' II IiI) 'i;1 I:' I" ~l.LliiU;li~kl I'lil :II: ': ~'.' ," " "::': ''', !I'l: :1~11 'I:; :1:' I::; :1;: :;1"1 -:iI I:' ... 'ill ::t\ ';'1' " 'i;';" 'I" I' '" • I~'l ' " '" :" , '" I:' 1'1'11'" "'f ", I' '''I~~ Uiiilili;' I' , ". '"'''' I ''''. ,,, II" ''''fill'' .,. ", , ''':: 'II l ~ ~" I. ! i; ,~ : 'I 1i 1 ,;1 J.dl Eli i'ii HllHJ ;~+ ~1 .. ~i. 11 ~lJ:ii !i.: ;~: ~::,.i.U .,:-. :: .... ~t-4iJ. .. _ t .+~ .~: •• ,:: :.. .. ! .;j UilW.u ::; 'I:: I:; :111:: ' ;.:;.:lt~ iI.. 1;1\ ;,1 ,:11 I :'11' 'I', I' Ill"; 'I I! n '11,:,:1:':. ,: ,I :i!llill , .. : 1'/: 1'1'" I' i['I" ,:; III II' i' : :::1 "i! 'I" Li ,I r--.:.li..i'Jl:li:,; ;::1 :!:I :1'11 I,. :1:: 1\:, il'\: iii ,:::'::' ,:'1: I" :!l1 1' :i :1:' :11' !l I' I:: I: I :'1 ::::,::: ',1 ,I, ;::: I" I: I I: ":\ It i I: Ii,' III' lid 11:1 li: 1 ,t:, .!, ;~~~::I ,': ;ll: II :1; I::: 1:1 I ::, :!U ;:: ':: :1 ,II ::\ :\., ii:: !::' 1m i1i t ~i I ,!;~:!~ ':1: ::'; :':: :::' j'1ll.!il !:~ ::i; ;li 1\ ;! 1 Wi!lll !!Ui' il! I,': !::l!:lj i:i\I;!'!l :1:1 H'li iii 1::: ,I., ~~ ,,-4 " .. d Iii: M::'1tp }l iii tiij ii:, ':'~ :1'1 t!i :i , 11,1 .. ,. "!~ 'Iii 1:1 iii' 'I ." "" , .. ,., 'I I; ::J; l;il ill I I I '1' 'I" 'I"'" 'il 11I1IIi ' , " lin IH .", , " , , , , 'I ' , , " ", ... :, 'I' 'II !il ~ ~H-H-: :::: j.' ,t 1++ lilt ~·H ~~; ~;~ ~.:.:: )' t+ ~~ rrh l, t, J,' !~~ I',;! ~~L : I' " ,,:"!t ~tl Hj; :t+; :i;: .. : :-' ~. ~~ q;r ·ti~h+t,8~~ ,,""!"~" :., ,,':' Jr.~ ~"11' I: , 111 1 /1 "" ,", .. ' f~'~.l I III ,,, 1. "., .. , 1. 'I I "I' II, III, 1 11.'1 .. ,' I""" 'II '~rrI1T'llliI'll "I 1.11 "I' " I '" "'II II'" I '1" '" "I' '1 .. ,' " II "1 .:1 l ~~; :1 1 ~i:, t : \; I III II ";. I,,, :'., :'. ~ II!, ::,1 :: I:: 1'1 :1: I:: I,:, :111 : 1'/' Ii!' IjJ', ,: ! ';', 'I.' : I, .t r ;':: . ;: ~ " : II ::: 1.:1 !!j' ;!,: I: J ::t ,:' .::: ,:1 Ii!

~ •• .j., If • tt· ,I 'I .. ,' " , .... ,.,' I I '. ,'t, "I I' '1' II 't" "" 'I ' ... ,., I ,It· lit· "\ 1,1. ,,01 . " " , "" ... , '1'" "I' -I" I'" 'II' I' '''' .". , .. "I··!j . ./ :: Iil'~U;'lij::lliiii ~! !I Iti~'1 i'\, , j: ' .' 'I,' :1:: ;; I :::: Iii: I I I I It i!l! ii, :1: ::i! :i !Ui·i8.+i!:1 1111 :I!i ::1 ::ii :il: ' ":: : ::'i !I:: i ! il: ii!: Ilil :lli ;i \ ::il i;:'I~ 'ii: III iii ~tq t~ ~uv~~: : ~,: ,'I ~~ t :·~:l:"·· :~ ... :~..:; 'n· ~ ~jt ":; 4~! 1111~ +!it HH!';-d :i:· I:: 11·:·t 1 t t ;':, ~ln:t +tH :H+ tH~ '1;~' ,,~. ·:·t ~.~ !~'H , :, :', :!:~ tH ~4i +! .~~~.: I'" :"1 ,', :' .. " ,I . ..", 'ii' ,I f I 'I II' .. " " ,,', "1 "I'" 1'1111 , .. , .. ,. II II' I, II '1'11'11', 1:11 'I' "', "'I .. ..I .. , II ill II" '1" .1, ,111 '''I .. .j" "l " : \ : I I,. i: : i I: : j j' I I :! II 1 : : ~ I : l. ,;", ; " t: I ' I , It:·,: I 'I : I ' : ! I !, I I : , : " : ; ,,\ ,,;, ,:: I ,; • : \ I ! I j! ; i : , : i' " :: :! t l I . . ,P';:: I ): :! ~ I . : 1 ::. : : II 'I !: ; !

'~:: !I:: ., ::ll: t.1 1:1 . 1! ,'1: ":: ":'" : :!. :',1 I::: 1':: I': I, 'I'!!i ::,1 ::: I" ", 'i'j iI: ':1: :1:: ::1: ", ~:': :1": " . ' " '1:' ~. I :.t. :~', I.:: I::' :::: 'I: : .. 'I:' iI., :1 ! :: " , ,,' " 'fUJI' .' , Ii 'II I I I ' , • " ".' I:! I '" , I" 1;1 I111I 'III " , .. ,,' "i I "" I HI ~ '!" II i' "II , I", '" , ii": ,,: i ,,, II",.. '" ",', ., w.~ .. "I, .

I' • t·, "1 ' I'! t I' II' I' ,., I 'j ,II ',1"" 11'11 ' I,'" I ,', t : I ": I I 11 : 1'1 i! I " I " ' " ' . .'1: •. ' .".' I i I ": I '" III'" .', "I' ., I 'I "" I' , .. , ~t; ~j!: ,~:' ~~n; t:r:tji~~' :::, I:: ::', ",' .. ; '. : "i' ::" ':,: i':, .. · '" '" : ' "', :,,'. ::,: :,:, ," "i ::: " 'I, "';,:~:',,',', ',.:' .'" -:.; :;1: rtf ~l" 'I:' I:i: :::: II:: :1,pllml'V: 1111 u::: !~.~ .!. , i'-';I£t :1 ',I!~~! :I!:.; ,.~~ Ii' .: ,:ijf;., H:: ';': :;i~~~:i ,:: ,I' 21:) I &: ,jr,l:!! :::1: '~' fI ::: :;~:i ::::I'S.~ . .1. HI .1:', " . .... "1'IIHffi' I II!' if I,ll '" "I I' ]1 ,I ... , \" ,II , '" I"" "" I ' "" ,,, - .., , '''I "I ::; :;'!::. 1: I 'I. 1 : 1 I' I' II:," , , ' , ' , . , :':' ! \1' I, ,I , : :', : I I ~": " ., II ':': d ' : " , r~h ,_ ~ .. : '!:' :: I: i I: "I".' :: t', . :; I .... ttt' _ •.• ll.: I+H" 11 "'"'''' ,-", .. '''''1 ... >-", •• , '" "" "" ... ' ':.1 ,,, ni:' d:4 I... ....... Ij'" , - -' ... ' iiV- ~" . ·i .... ~·· ,_1- ......... :~ _.'-!1 > !:;i iii: Hi; lilillILl,~l~ ~ I~! l;~ '7 i .! ,I :' V ii:1 d!:: 1 ,to~kJ~c,~,: \:w~~tr tb v..!i; wJ W' ',:, ~roi' :i,::- -: I',: ') :: ~'I':::: 1"~rG(,·~,.lt,L"'''. I .• : [1" ';, i: : 1 i, _ .1,1'! Ie:!. :,,[: ! I I : I I I i

i

INPUT - OUTPUT MODEL

APA SUBSYSTEM

J SrllNDARD IINI> NON - STflN1:JIl~D A'lfYlO5.1'HERJC CONDITIONS

j

f ·ct ~~Sl'E£D

V

W AL(){G 1KIICK PLoj' I.

I

Pr.ODucr OF i r EQUIVAL EHI

v

E SPECIFIt! RAWGE

I' '*

2. * Rc

X, 1, f3 PLDT

A"'D ENGINE.

Bt.AKE S'PE.CIFIC.

W a.RO.ss

i ,.

FlJEL CONS,O!l)P1I1JN WE./GHT PLOTS

I 3. t

comp

h C.G.

POSITtON

4. EQUATIONS 4.62 - 4. 73, C.II

E.NGIN£

P. AUXILLIARY

BRAJ::E 101:&Uf.

flUX EQU/PMENr PO\IJER.

ENGINE SHAFT SPUD -r:.tmos IrrMOS'PHE.RiC ·r:.:tmos Rf/fii.IE rII A rre.

T

0-= oi:mos ( 1E.MPUflTIJR.E.

~ R CL rc,.,OS

Yo

P

a:t",os STANDARD' ATMOSPHERE

H=

Hp

"PusSU'RE.

J-I

p RLTI"rVDf.

fIJUAT!ONS

B.3 , B. 4-~

B.6 ) B.B NDTE. : THE. INPtrr ~+-_ :: iHE A1'IIJOSPHUJC AN81ENI TEMP£RRTURE "'-UPIO$ IS RE~lJli.~ FoR THE CoIIJPUTAiiOAJ of THE.

SPc£2> OF ~OI1Nb IAI 71#£ ltf1t1oSPHEIlE.

I>UiWJG tHE CoflTrllTA1iow ~ 1.

Tcomp •

FIGURE 4.8

4-33

CHAPTER 5 THE ENGINE-ATMOSPHERE SUBSYSTEM Table of Contents Page INTRODUCTIO!'-l ........................................... _ .................. .. <: :: = = 5-1 THE NATURALLY ASPIRATED ENGINE PERFORMANCE MODEL ••••••••••••• 5-3 Parameters Included in the NMBTE Performance ModeL ••••• 5-3 Desi gn Parameters.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5-3 Opera tional Parameters.............................. 5-4 Parameters and Phenomena Excluded from the NMBTE Performance Model. • • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 5-5 NATURALLY ASPIRATED ENGINE PERFORMANCE: FIXED IGNITION TIMI NG. . . • . . • . • . • • . • . • . . . • • . • • . • • • • • • • • • • • . • • • • • • • • • • • • • • • . •. 5 -10 Brake Horsepower ••.•.••••••••••••••••••••••••••••••••••• 5-10 Leanout Performance •.••••••.•••.••••••••.••••••••••••••• 5-11 Fuel Metering Requirements .••.••.••••••••••••.•••••••••• 5-15 NAnJRALLY ASPIRATED ENGINE-ATMOSPHERE SUBSYSTEM PERFORMANCE: MBT IGNITI ON TIMING •••.•••••••••••••.•••••••••• 5-16 Brake Hors epower ....................... ~ . . . . . . . . . . . . . . .. 5-17 Leanout Performance ••••••••••••••••••••••••••••••••••••• 5-18 Constant P and Constant BHP Leanouts ••••••••••••••• . 5-18 m F for Minimum BSFC During Constant BHP Leanouts ••••• 5-22 F for Maximum BHP During Constant P Leanouts ••••••• 5-24 m Cons tant P and Constant BHP Leanouts from F • • • •• 5-26 m max Performance with Specified Fuel Metering Schedule ••••••• 5-28 BSFC Performance Maps at Sea Level •••••••••••••••••• 5-28 BSFC Performance Maps at Altitude ••••••••••••••••••• 5-30 A1 ti tude Variations of BSFC with Constraints ••••••••••••• 5-30 Corrected Quantities .................................... 5-32 Corrected Brake Torque.............................. 5-33 Corrected Air Mass Flow Rate •••••••••••••••••••••••• 5-35 Table of Contents (concluded) Page Corrected Part-Throttle Performance Model of p mand IDa' 5-36 Input-Output Model ••••.••.•••••.•••••••••.•••.•••••.••• 5-37 ..

5-37 Formulation for the Standard Atmosphere •••••••••••• Computational Scheme (Standard Atrrr>sphere) ••••••••• 5-42 Formulation and Comp.utations (Non-Standard Atrrospilere) • ..••••••.•.•.••..•••.••.••. a, ••••..•.••••. e-. 5-44 5-47 Implementation • •••••••••••••••••••••••••••••••••••• 5-48 Summary ................. ~ ............... e· •• ., ................ .

5-48 TURBOCHARGED ENGINES •..••••.••••.••..••••••.•••••••..•••.••.

Performance Comparison: Naturally Aspirated and Turbocharged Engines ...•..•..•••••••••..••••••..•.•..•••• 5-51 Brak.e Torque .•...•.......•• _ ...................... e_ •• 5-51 5-52 Brake Specific Fuel Consumption •••••••••••••••••••• Recommendations: TEA Subsystem Input-Output Mode1. •••. 5-54 SUMMARY. . . . . . . . . . • . . . . • • . . • • • . . . . •.• • • . • • • • . • • • . •. • •.• . • • • • •• 5-55 TABLES 5.1 - 5.4 ........•....•........................•..... '.' 5-57 FI GURES 5. 1 - 5.31.......................................... 5 -62 !

i

I

I

I

i

OiAPTER 5 THE ENGINE-ATMOSPHERE SUBSYSTEM

I

INTRODUCTION This chapter develops an input-output model for the cruise performance of the engine-atmosphere subsystem. The engine-

I

atmosphere subsystem considered here consists of a naturally aspirated,

I

spark-ignition, inlet port fuel injection, four-stroke piston aero engine; operating in the standard atmosphere or in a non-standard atmosphere.

In this development, the engine is assumed to be of fixed design. We consider only steady state operation of the engine: no attempt is made to develop a dynamic engine model. In addition, no account is taken of engine exhaust emission controls.

The tasks of the engine-atmosphere subsystem input-output model are: 1. To compute the engine control inputs required to minimize the engine Brake Specific Fuel Consumption (BSFC) at any engine operating point demanded by the APA subsystem (Chapter 4).

2. To compute the engine BSFC,c (lbm/BHP.hr). The airplane R* may then be computed from c and the value of R*c (knots/BHP) provided by the APA subsystem input-output model.

The input-output model developed here reflects current General Aviation piston engine technology in all respects but one: that of 5-1 ignition timing. All commercially available General Avia1:ionpiston engines employ fixed ignition timing. According to Chirivella (16): The magnetos are wired to ignite the mixture ata certain fixed advanced timing. Thi s feature is different from the variable timing that automobile engines areprovide.d with. The reasanfor this resides mostly in simplicity and the fact that "the engine regimes in an airplane are not subj ect to drastic changes during .flight. The optimum timing is selected for inhibiting detonation during take- off power situations. No attempt is made lateran to vary the timing for cruise power . . . The normal timing varies somewhat from engine to engine, but is on the order of 20° BTDC [before top dead center].

In the pursuit of good fuel economy,the ignition timing incorporated in the input-output model developed here is optimized for maximum brake torque in every engine operating condition. This optimum igni tion timing is called Minimum ignition advance for Best Torque (MBT), and is discussed in detail in AppendixE.

The engine-atmosphere subsystem input-output modeldevelope~ here is referred to as theNEA (Naturall yaspi ra tedMBT ignition timing Engine-Atmosphere) subsystem input-output model. This model is developed from computationsperforrned by the Naturally aspirated MBT ignition timing Engine (NMBTE) performanc.e model presented in Appendix E.

The content of the NMBTE performance model is first examined.

The performance of current technology, naturally aspirated (fixed ignition timing) General Aviation piston engines is then discussed.

We then discuss in detail the performance predictions of the NMBTE performance model, and develop the NEA subsystem input-output model.

5-2 !

I· I

I

I

, Finally, turbocharged spark-ignition piston engines are discussed briefly, and some recommendations offered for the development of a Turbocharged MBT ignition timing Engine-Atmosphere (TEA) subsystem input-output model: this model is not developed in this work.

I

TIlE NATURALLY ASPIRATED ENGINE PERFORMANCE MODEL The naturally aspirated engine performance model used in this

I

work is presented in Appendix E. That model will here be referred to as the Naturally aspirated MBT ignition timing Engine (NMBTE) performance model.

The NMBTE performance model is an analytical-experimental hybrid which computes naturally aspirated piston engine performance in terms of Brake Horsepower (BHP) and Brake Specific Fuel Con- sumption (BSFC) Ibm/BHP.hr. The parameters included in this model are discussed brieflY below. Parameters and phenomena which affect engine performance but which have been excluded from this model are also discussed below.

Parameters Included in the NMBTE Performance Model I !

I , The parameters included in the NMBTE performance model fall into two groups: design parameters and operational parameters.

Design Parameters: Design parameters are those fixed by engine design. Since we consider engines of fixed design, these parameters are modelled 5-3 as constants. The design parameters included in theNMBTE perfonnance model, and the values given them in the present work, are presented in Table 5.1.

!

Operational Parameters: Operational parameters are those under the control of the pilot. Those included in the NMBTE performance model are listed below as inputs to and outputs from the computations of that model: Inputs: F Fuel-dry air mass ratio P Inlet manifold absolute pressure, inches Hg m T Inlet manifold temperature, degrees Kelvin m P Exhaust absolute back-pressure, inches Hg e Engine shaft speed, R-PM NE Outputs: Air mass m flow rate, lbm/hr a

m Fuel mass flow rate, lbm/hr

f BHP Brake hors epower, horsepower Ibm/BHP. hr c Brake specific fuel consumption, Brake torque, Ib ft.

Q E The quanti ties F, P , T , P are common to all cylinders. The m m e quantities lit and m are equally divided between all cylinders.

. a f The NMBTE performance model assumes that: 1. Inlet manifold temperature T is equal to the atmos'pheric m ambient air temperature Ts computed from the standard atmosphere model of Apperidix B.

2. Exhaust absolute back-pressure P is equal to the e 5-4 ------------------------------------------------------------------------------------------------------ I i ,

I

t

I

I

atmospheric ambient air absolute pressure P t computed

I

amos

r -

from the standard atmosphere model of Appendix B (with

I

appropriate units conversion).

3. The ignition timing is the Minimum ignition advance for

I

Best Torque (MBT) at all times. This ensures the maximum

r

r possible brake torque and the minimum possible BSFC for

t

all operating points defined by the above set of inputs.

t

For computations performed by the NMBTE performance model in this work: 1. The computational scheme is given on pages E-39 through E-43.

2. The fuel metering schedules used are discussed on pages E-38 and E-39, and illustrated in Figure E.18.

3. The Reference Operating Point and the Fuel Schedule l Datum Conditions are listed in Table 5.2.

4. The engine delivers maximum continuous BHP at the Reference Operating Point.

Parameters and Phenomena Excluded from the NMBTE Performance Model The parameters and phenomena excluded from the NMBTE performance model are listed below.

1. Ignition timing T: The assumption of MET ignition timing obviates the need to include ignition timing T explicitly in the NMBTE performance model: the ~~T ignition timing T at any operating point is unknown in this model.

o 5-5 Taylor (13) presents some automobile data, here repro- duced as Figure 5.1, which shows the effect on Brake Mean Effecti ve Pressure (BMEP) of variations in ignition timing L from L. Acco.rding to Taylor (13), o variations in spark timing, from that for maximum power • have the same percentage effect on brakemep at all loads and speeds. This correlation makes it pos- sible to predict the effect .ofa given departure from best-power spark advance on both output and fuel economy.

In the light of Figure E.3, however, these data would appear inapplicable to all usable equivalence ratios.

I t is unclear from Taylor (13) if the data of Figure 5.1 apply to all values of {¢, T , P , CHT ,h} .

m e With a knowledge of l and the effect on BMEPof variations o in l from L , thep.erformance of fixed ignition timing o engines might be easily modelled. Such performance has not been modelled here.

2. Cylinder Head Temperature (CHT): CHT Masnotrequi red for any performance computations. Monts (23) shows that for fixed ignition timing engines, leanouts at .constant inlet manifold pressure and constant RPM result in a maximum CHT at ¢ = 1 (see Figure 5.4) . It is assumed that the same behavior is demonstrated by engines employing MBT ignition timing. CurtiSS-Wright (IS) state that for their TC18 engine, in which the spark was advanced from 25 BTDC to 5-6 30° BTDC for cruise power settings (resulting in improved fuel economy): There is one disadvantage to using spark advance; if the mixture is ignited sooner, then the duration of the combustion period is longer; the burning takes place over a longer period of time inside the combustion chamber; the result is more heat generated inside the cylinder and higher cylinder head temperature. So spark advance requires the use of a little more cowl flap to main- tain a given cylinder head temperature.

In the NMBTE performance model, it is assumed that CHT remains within operational limits at all times.

3. Exhaust Gas Temperature (EGT): EGT was not required for any performance computations.

With regard to operating limits on EGT, Monts (2~ shows that for fixed ignition timing engines, leanouts at con- stant inlet manifold pressure and constant RPM result in a peak EGT slightly lean of ~ = I (see Figure 5.4).

When leaning at constant BHP and constant RPM with approximately MBT ignition timing, Chirivella (l~ found that ,for the Lycoming TIO=S41-E engine: . the engine temperatures do not necessarily become higher than those obtained at the best power point if one is able to lean sufficiently to the left of the TIT [Turbine Inlet Temperature] peak.

Curtiss-Wright (15) state that for the TC18 engine, when the spark was advan~ed from 25° BTDC to 30° BTDC: 5-7 since the burning takes place fora longer period of time, inside the cylinder, the resulting exhaust gas temperatures are lower. This is the main reason for using spark advance. Ex.haust gas temperatures are reduced, with resulting benefits to turbine and parts in the exhaust system.

From these observations it is concluded that MBT ignition timing will probably yield acceptably low values of EGT in all ultralean operating conditions. For simplicity in the NMBTE performance model, it is assumed that EGT never exceeds engine operational limits in any operating condition.

4. Detonation: No attempt is made in the NMBTE performance model t.o either predict the .occurrence .of detonati.on or to model its effects on engine performance. The interested reader is referred to Appendix F where these matters are briefly discussed.

S. N.on-Uniform Distributi.on of Air and Fuel to Each Cylinder: Unif.orm distribution of inducti.on air and fuel flow to all cylinders is assumed in the NMBTE perf.ormance model.

6. Atm.ospheric humidity: The NMBTE performance model assumes that the inducted air is dry.

7. Ram Effects: Inlet manifold temperature changes due to ram are neglected. Similarly, at wide open throttle (WOT), inlet manif.old absolute pressure changes due to ram are ., neglected (clearly at a given inlet manif.old absolute pressure at part throttle, ram air pressure need not be considered) .

.4 5-8 In all WOT operations, the NMBTE performance model con- siders inlet manifold absolute pressure P to be a function m of engine shaft speed NE and atmospheric ambient air abso- lute pressure P t (Appendix B) as follows: amos N , RPM at WOT (Pm/Patmos) E

•

I: 2,000 0.969

"

2,200 0.963

I

2,400 0.956 2,600 0.950 At WOT, increasing engine shaft speed results in: in- creasing absolute pressure losses in the inlet manifold, due to friction; and hence decreasing P IP t (see Ref.

m amos 24, p. 19).

8. Inlet Manifold Heat Exchanger Effects: Variations in the temperature of the cooling air surrounding the inlet mani- fold, from the atmospheric ambient temperature, may sig- nificantly affect the inlet manifold air temperature.

The relatively long length and large diameter of the modern air cooled aircraft engine's intake air manifolding make an excellent heat exchanger. In fact, we find that the inlet port temperature may be more influenced by the temperature of the air surrounding the inlet manifold than it is by the temperature of the ~onsumed air (25).

The complexity involved in modelling this installation effect has been avoided. The inlet manifold temperature T is assumed (for simplicity) equal to the atmospheric m ambient air temperature T (Appendix B) at all times in s the NMBTE performance model.

5-9 9. Inlet Manifold and Exhaust Manifold Pressure Acoustic Effects: In the NMBTE performancemodel,P (P )is taken me t.o be the mean value of the inlet (exhaust) mani fold absolute pressure .atthe inlet (exhaust) valve: variations in {Pm' P e} in time and from cylinder to cylinder, due to inlet and exhaust manifold dynamics, are ignored. The interested reader is referred to Reference 26 for a study of these phenomena.

·10. Exhaust Absolute Back-Pressure Variations from Atmospheric Ambient Air Absolute Pressure: The NMBTE performance model sets the exhaust absolute back-pressure P equal to the e atmospheric ambient air absolute pressure P t of Appendix amos B (with appropriate units conversion): variations in this condi tiondue to exhaust manifold acoustic effects, flight speed, the installation of an exhaust augmentor(24) etc.

are ignored.

NATURALLY ASPIRATED ENGINE .PERFORMANCE:FIXED IGNITION TIMING All commercially .available General Aviation piston engines employ fixed ignition timing. Before .discussing the performance predictions of the Nf..1BTE performance mode1,i t is instructive to consider the performance of these fixed igni tion timing engines.

Brake Horsepower Atypical plot ofBHP versus inlet Manifold Absolute Pre~sure 5-10 (MAP) for various constant values of engine RPM, is shown in Figure 5.2 (24). This figure was "developed from the performance of Continental 0-470-K and -L engines" (24) at standard sea level con- di tions.

Figure 5.3 (24) shows a typical sea level and altitude per- formance plot of BHP vs. inlet MAP and RPM. This Figure is (24): . used to determine the power output of a Continental 0-470-M engine at altitude. The chart at the left shows engine output at sea- level standard conditions with no ram air pres- sure applied to the carburetor intake. The chart at the right shows the effect of altitude and. is used in conjunction with the first chart.

The po:.nts corresponding to engine rpm and mani- fold pressure are located on both charts. The horsepower indicated on the sea-level chart is transferred to an equivalent point C on the altitude chart. Then a straight line is drawn from the point A to the point C to establish the altitude correction. The intersection of this line with the density altitude line (0 in the example) establishes the power output of the engine. The horsepower should be corrected by adding I percent for each 6°C . .. temperature

decrease below T [T = standard atmospheric

s s ambient temperature] and subtracting I percent for each 6°C temperature increase above T .

s The fuel-air mass ratio appropriate to each point on the power charts of Figures 5.2 and 5.3 are not given by Bent and McKinley (24).

Leanout Performance The General Aviation piston engine manufacturers usually pre- sent variations in engine power and specific fuel consumption with fuel-air mass ratio, for conditions of fixed throttle position (constant inlet MAP) and constant RPM.

5-11 Figure 5.4 (23) shows generaliz.ed mixture strength (fuel-air mass ratio) characteristics for General Aviation piston engines t with fixed ignition timing. According to Monts (23), Figure 5.4 : is a classic fixed-throttle [and fixed RPM) mixture control curve, and it depicts the relation of power (BHP or IHP), specific fuel consumption ... , cylinder head temperature (CHT), and ex- haust gas temperature (EGT) as a function of fuel/ air ratio (F/A). Although the data presented here was developed at Teledyne Continental Motors, this same rather precise relationship is valid for all aircraft piston engines regardless of manufacturer.

The F/ A at which power peaks is called "best power" and the F /A at which specific fuel consump- tion minimizes is known as "maximum economy". It is obvious from an examination of this mixture control curve that maximum fuel economy occurs at approximately .060 F/A.· Therefore, for most efficient operation and maximum energy conservation, all operation should be carried out at this mix- ture strength, unless limited by other factors.

Figure 5.5 (27) shows generalized data similar to that of Figure 5.4. With regard to Figure 5.5, Ref. 27 states: While the absolute values of [BSFC, BHP, CHT, EGT) . . . change with engine power, the re- lationship shown here is approximately true for operation over the normal flight regime of the engine from 40-100% power. Best power occurs at about 0.076 fuel-air ratio, peak cylinder head temperature at 0.067 which is the stoichiometric (chemically correct) fuel-air ratio, peak exhaust o gas temperature at 0.062, and best economy at 25F lean of peak EGT at a fuel-air ratio in the vicini ty of 0.059 . .. . While the "lean misfire limit" has been variously defined •.• , it will , t The original figure of Ref. 23 does not include the BHP curve shown in Figure 5.4; but treats the IHP curve of Figure 5.4 as both IHP and BHP, and treats the indicated specific fuel consumption curve of Figure 5.4 as both ISFC and BSFC. The modifications to the original figure of Ref. 23, presented here in Figure 5.4, were performed by Mr. F. Monts (28).

5-12 I !

i

I

i be defined here as a point at which the engine operator detects audible roughness in engine operation. This point is characterized by a

I '

sudden decrease in EGT and usually occurs between fuel-air ratios of .052 and .042 depending on the engine, ignition timing and fuel system.

A comparison of Figures 5.4 and 5.5 confirms that the relationships

I'

therein are not precise in general.

I

Current practice in General Aviation is to lean at constant inlet MAP and constant RPM (when a constant speed propeller is installed) in cruise. As shown above, the minimum BSFC is obtained at a fuel-air mass ratio of about 0.060 using this leaning tech- nique. However, it is not always practical to lean to this fue1- air mass ratio because of engine temperature limits, detonation limits or other limits (see Ref. 27 and the discussion of Fuel Metering Requirements below). The General Aviation airframe manu- facturers recommend leaning procedures which enable the pilot to establish a safe minimum fuel-air mass ratio between "best power" and "maximum economy" (as defined above) : 1. In the absence of a fuel flow gauge, fuel pressure gauge or EGT gauge, the mixture is usually leaned until rough running is encountered, and then enrichened to re- establish smooth running.

2. An EGT gauge, fuel flow gauge or fuel pressure gauge permits the fuel-air mass ratio to be established more accurately than in (1) above. The fuel-air mass ratio may be established most precisely using an EGT gauge, by varying the fuel flow rate until the exhaust gas temperature 5-13 is a specified increment below peak EGT on the rich or lean side of peak EGT (see Figure 5.4).

The loss in BHPwhich occurs during leaning at constant inlet MAP and constant RPM is often undesirable. Constant BHP can be maintained during leaning by continuously opening the throttle and thereby increasing inlet MAP. According to Monts (23): During the late 1940 I sand 1950 I s when the air- lines operated piston engine powered aircraft, they were naturally interested in economy of operation and extended service life. To promote both of them, Wright and Pratt & Whi tney each published methods for economical cruise operation. Both were based on the use of torque meters (or BMEP gauge) and the mixture strength/power relation-

ship ... Pratt & Whitney called it the torque

drop method of setting cruise mixture . . . Simply stated, the approximate desired power was set and the mixture leaned to peak the torque reading.

The torque value was then reduced approximately 9 percent by leaning, thus establishing cruise economy mixture setting. The throttle was then opened to regain the 9 percent torque loss. The Wright method [(15)] ... was the same except a 10 percent torque drop was used . . . It should be noted that there is no loss in performance from this operation and increased service life resulted.

Although general aviation piston engines are not equipped with torque meters, approximately the same resul ts can be obtained using an EGT gauge . . . [It) is possible to identifyniixture strength from relative EGT 's. Aft.er leaning to the desired mixture strength, the throttle may be opened to regain the power lost in the fixed throttle leaning. [The only measure of power recovery for the GA pilot is Indicated Airspeed.} There seems to be no hesitation about correcting throttle settings to compensate for ambient temperatures, but there seems to be reluctance to mov~ the throttle (increase manifold pressure) td compensate for mixture strength. Obviously, if the operation is at an altitude requiring full throttle for the desired power setting, it will be necessary to suffer the airspeed loss.

5-14 I j

I

I

i

Note that such power recovery by opening the throttle is only.

feasible if:

I

1. The fuel metering system maintains constant fuel-air I mass ratio as the throttle is opened; 2. The absolute value of EGT does not exceed engine limits I as the throttle is opened.

With regard to the constancy of fuel-air mass ratio in the TC18

I

engine as the throttle is opened or closed, Curtiss-Wright (15) states: . if you set 10% BMEP drop mixture, leave the mixture control where it is and then move the throttle (up and down), the BMEP will change, as will the fuel flow, but the fuel-air ratio will remain about the same. It should be noted that present day carburetors are not quite capable of holding the same fuel-air ratio if the changes in airflow are substantial.

According to Curtiss-Wright (15), the 10% B~ffiP drop mixture used for cruise power settings with the TC18 engine corresponds to a fuel- air mass ratio of about 0.053, which fuel-air mass ratio was used for cruise in conjunction with a spark advanced 5° from the normal spark timing of 25° BTDC. The leaning procedure used for the TC18 engine in c·ruise wa.s equivalent to leaning at constant RPH and con- stant BHP to a fuel-air mass ratio of about 0.053.

Power recovery by opening the throttle during or after leaning in cruise is not common practice at present in General Aviation.

Fuel Metering Requirements Figure 5.6 (23) shows generalized fuel-air mass ratio requirements 5-15 of General Aviation piston engines with fixed ignition timing.

At power levels appropriate to idle, taxi and approach: arich fuel-air mass ratio is required for starting, idling (29) and smooth transient response. In the cruise power range: operationnear the "maximum economy" fuel~air -mass ratio is possible. At the higher power levels: the fuel-air mass ratio must be increased to permit the development of high power, to cool the engine and to prevent detonation.

It is emphasized that the curve of Figure 5.6 varies from engine to engine. Figure E .16 (23) shows the fuel-airmass ratio metered to the Continental IO-540-Nengine by the Beech Single Lever Power Control (23,30): the Desirable Schedule in Figure E.17 is the generalized curve of Figure 5.6.

NATURALLY ASPIRATED ENGINE-ATMOSPHERE SUBSYSTEM PERFOru.1A.~CE :MBT IGNITION TIMING We here develop the Naturally aspirated MBT igni tion timing Engine-Atmosphere (NEA) subsystem input-output model. Thismode1 is developed using the Naturally aspirated MBT ignition timing Engine (NMBTE) perfol;1Jlance model described on pages 5-3 through 5-10.

The discussion in this section proceeds as follows: 1. For the NMBTEperformance model a) A typical p1otofBHP vs. inlet MAP and RPM is pre- sented ,and compared with corresponding 'd'ata fOT fixed ignition timing engines.

5-16 I i I

I

i

I b) The leanoutperformance predictions are examined, and compared with corresponding generalized leanout data for fixed ignition timing engines.

I

I "

An indication of the reliability of the NMBTE performance model is obtained by the above comparisons of its per-

j

formance predictions with the performance of fixed ignition

t

timing engines.

I

c) For various fuel metering schedules: variations in BSFC, Pm and ro with brake torque, RPM and altitude f are presented.

d) Altitude variations of BSFC with various constraints are examined.

e) Corrected quantities are identified.

f) Corrected part-throttle performance plots are developed and presented.

2. The input-output model of the NEA subsystem is presented.

Figures 5.7 - 5.26 were drawn from computations performed using the NMBTE performance model. In these figures, engine operation at wide open throttle is denoted W.O.T.

Brake Horsepower Figure 5.7 shows the variation of BHP with inlet MAP and RPM at sea level, with fuel metering schedule A, as predicted by the NMBTE performance model. Figure 5.7 is similar to the fixed ignition timing, s~a level data of Figures 5.2 and 5.3. Each of these three figures applies to a naturally aspirated engine with a displacement 5-17 of 470 cubic inches. Comparing these three (sea level) figures: 1. The rate of change ofBHP with inlet MAP at constant RPM is approximately the same.

1., 2. The smaller rat'e of -Change of BHP with RPM at constant inlet MAP in Figure '5.7 is attributed toth'e MET ignition timing in the latter figure .

Leanout Performance Constant P and Constant BHP Leanouts: m Leanout performance of the NMBTE performance model is here examined under the following conditions: 1. At constant inlet MAP and constant RPM, at 'sea level 2. At constant BHPandconstantRPM, at sea level.

Figure 5.8 shows typical leanout performance under each of these conditions. In Figure 5.'8: curves bhelled A pertain to

leanout at constant inlet MAP = 23 in. Hgand 230'0 RPM; and curves

labelled B pertain to leanout at constant BHP = 132.S5BHPand 230'0 RPM. DUTing the constant inlet 'MAP leanout A, the minimum BSFC occurred at a fue1-'airmass ratio of 0.'058 (point 1 on the right

hand side of Figure 5.8): at this ptiint the BHP = 13'2.55 which value

was used to perfonn the constant £HP 1eanout B.

Consider first the left hand side of Fi,gure 5.8, which shows the variation of BHPduring leanout A, and the variation of inlet MAP during 1 eanout B. Peak BHP on curve 'A, and minimum P on curve m B ,both occur at a f'le1-airJila~;-s'ratioF= 0.08'0. Each experimental 5-18 i i I

I

I

!

I

BHP data point added to Figure 5.8 (denoted 0) was obtained from the generalized BHP curve of Figure 5.4 in the following manner:

I

1. In Figure 5.4, let the best power fuel-air ratio be

FB = 0.078

2. In Figure 5.4, determine y% = percent best BHP at a fuel-

air ratio = x% x FB

I

3. In Figure 5.8, let the peak BHP fuel-air ratio be

I

Fp = 0.08, and the peak BHP be BHP = 157.97 p 4. Compute F

,BHP = y% x BHP

p and mark the point (F, BHP) as 0 in Figure 5.8.

For F ~ 0.08, the BHP curve A and the experimental data points show close agreement. [For the fixed ignition timing data, BHP tends to decrease more rapidly with decreasing F (at ultralean values of F) than the MBT ignition timing model predicts: this is an expected trend.] For F > 0.08, the model does not show close agreement with the experimental data: this discrepancy is attributed to the fact that a cubic polynominal in equivalence ratio ¢ was used to repre- sent the indicated thermal efficiency n! in the'model (see Equation 1 ' E.4l and Figure E.7). Such representation of n! may not be suf- ficiently accurate over the whole of the usable range of ¢: a table lookup of n! may prove to be more accurate.

Curve B on the left hand side of Figure 5.8 shows the extent to which the throttle must be opened, as the fuel-air mass ratio is decreased below F = 0.08, during the constant BHP leanout.

5-19 Consider now the right hand side. of Figure 5.8. First: comparing curve A with the gener.ali zed (fixed ignition timing) curve of Figure 5.5; we se.e that on the former curve the fuel-air mass ratio yielding mininrumBSFC (point 1) is 0.058, while on the latter curve it is 0.059. On curve A, the minimum BSFC = 0.4631

is 86.4% of the BSFC = 0.5360 obtained at the peak BHP fuel-air

mass ratio of 0.08; while in Figure 5.5, the minimum BSFC is approxi- mately 85% of the best power BSFC. Thus for this case of leanout at constant inlet MAP and constant RPM, the variations in both BHP and BSFC predi cted by the NMBTE performance model are quite close to those given by the generali z.ed (constant inlet MAP, constant RPH) leanout data for fixed ignition timing engines.

Second: consider the BSFC variation along the constant BHP leanout curve B in Figure 5.8. While the general shape of this

curve is s imil ar to that of curve A, the minimum BSFC = 0.4556

(point 2) is lower than the minimum BSFC = 0.4631 on curve A (point

1), and occurs at a lower fuel-air. mass ratio = 0.0495 than does

point 1. The BSFC decreases by 1. 62% along curve B front point 1 to point 2. Consequently, if the mixture is leaned at constant inlet MAP and constant RPH to the nominal "maximum economy" point 1, a further decrease in BSFC of 1.62% is possible with no loss in BHP by leaning along curve B to the true minimum BSFC point 2. In leaning at constant BHP from point 1 to point 2, the inlet MAP must be increased from 23 inches Hg to 26.17 inches Hg. Note that

the minimum BSFC point 2 at F = 0.0495 is slightly lean of the peak

5-20 , of the n! curve at F = 0.0514 (<I> = 0.7667: see Figure E. 7).

i 1

Consider now a series of leanout pairs similar to the pair I on the right hand side of Figure 5.8. At sea level and 2300 RPM, a number of constant inlet MAP leanouts were performed [P = 28, m 25, 23,20,16, 13, 10 inches Hg). From the point of minimum BSFC

I'

(point 1: F , BSFC , BHP ) each of these leanouts was continued at

I

l 1 1 cons tant BHP = BHP 1 until the point of minimum BSFC (point 2:

I

F , BSFC , BHP ) was reached. Figure 5.9 shows for each leanout 2 2 l sequence: 1. Fl and F2

2. t.BSFC % = 100 [BSFC - BSFCl)/BSFC

min 2 l plotted against percent maximum continuous (me) BHP = 100 [BHP /230).

l The increase in inlet MAP from point 1 to point 2 may also be ob- served in Figure 5.9. As the inlet MAP of point 1 decreases, the value of FI increases, reaching the stoichiometric fuel-air mass

ratio at Pm = 10"Hg. In comparison, the value of F 2 is virtually

The value of t.BSFC . % decreases as the constant at F2 = 0.0494.

ml.n percent mc BHP decreases.

As discussed previously, the current practice in General Aviation is to lean at constant inlet MAP and constant RPM. Once the "maximum economy" point is reached by this leaning technique, a further decrease in BSFC is possible with no further loss in BHP: Figure 5.9 indicates that for the engine represented therein (at sea level, 2300 RPM) this BSFC decrease is less than 2% for BHP values (at the "maximum economy" point) greater than 50% mc BHP [this is the BHP range in which General Aviation airplanes generally 5-21 operate in cruise].

For BHP values (at the "maxim1..Ull economy" point) less than 50% mc BHP, the dec.rease in BSFC from point 1 to point 2 is substantial.

This BHP range is appropriate to automobiles in constant speed dri ving conditions. From Figure 5.9, an automobile cruising at say 25% mc BHP would achieve a 4.5% decrease in BSFC if its fuel metering schedule was established on the basis of 1eanouts at {constant BHP, constant RPM} rather than at {constant inlet MAP, constant RPM}.

F for Minimum BSFC During Const.ant BHP Leanouts: Woods (31) discusses the procedures for establishing optimum fuel metering schedules. He shows that fuel-air mass ratio schedules for minimum BSFC must be obtained by leaning at constan.t BHP (rather than at constant inlet MAP) and constant RPM. This has been confirmed by the NMBTE performance model in the foregoing . t su sectlon. Woods (31) concl:udes that approximately a 4% decrease b in BSFC is achieved, wi th the Jee:p engine at constant RPM, by leaning from point 1 to point 2 in the manner described in the foregoing

subsection; and that the true minimum BSFC = BSFC occ.urs at a fuel-

. t' F = 0.9 Fltt.

(rn Figure 5.9, a dec.rease in BSFt alr mass ra 10 2 of 4% corresponds to F 2 ::: 0.78 F 1 and to BHP ::: 27.5% mc BHP) .

t Woods also shows that an equivalent correct metho.d for obtaining optimum fuel metering schedules is to: "Maximize torq:ue for a con- stant fuel consumption [fuel mass flow rate] and constant speed" (31).

ttw d (31) d h . ... ... d' 00 s oes not s.tate t e 19U1 tlOO tlDUng corre.spon .1 .. ng to· these results, but from the context of his discussion t:hat timing is assumed to be MBT.

5-22 In the present work, we are interested in determining the fuel-air mass ratio schedule yielding the minimum possible BSFC over the operational envelope {BHP, RPM, altitude} of the engine. To determine this schedule, a series of leanouts at {constant BHP, constant RPM, constant altitude} was performed using the NMBTE performance model. The results of these leanouts are shown in Table 5.3.

On the basis of these results it is proposed that, for General Aviation naturally aspirated piston engines employing MBT ignition timing:

A single value of F = F. will yield minimum BSFC in all

mln steady state operating conditions {BHP, N , H} (when F is E not constrained by other considerations). In the present

work, F. = 0.05 is used.+ The choice of a single value

mln of F. is expected to yield negligable variation in BSFC wn from the true mininrum BSFC at any operating point {BHP, N , E H} due to the flatness of the (F, BSFC) curve at such an operating point.

It is assumed in the present work that in all steady state operating conditions {BHP, N , H} of General Aviation naturally E aspirated piston engines employing MBT ignition timing, BSFC in-

creases continuously as F increases from F. = 0.05 through

mln F = 0.08 (F is defined in the next subsection).

max max t cf . CurtiSS-Wright TC18 leanout discussed on pp. 5-14 through 5-15.

5-23 In the (NMBTE perfo,nnancem0(i'e1) constantSHP Ie-anont'S de- f scribed above, inlet M;t\P P was found to reach itsmi:nimum at F = m

F = 0.08 and t:o inc:reasec:ontinuouslyas F decreasc:edfrom F =

max . max O.ost through F;. '=. 0 .•. 0.5:. In th.e 'pe,r.es:ent' work·., 'tni.:s·· s'ame b'ehavior nun of P isa:ssumed to be true of" GelYeral AViation naturally aspirated m pis ton engines employing MBT ignition timing.

Note that the value of F. = 0.05 determined above is about

mIn 16.7% leaner than the valueF = O .. Oi6.currentl.y recogniz.ed (23) as offering maximum economy for fi-xed i.gnitiontimtrrg engines. TIre

value F. = 0.05 predicted by the NMB'fE perfo:rmancemodel may .not

mln be the value found to pertain to real engines using MBT ignition timing, since it res-ul'tS from the part,tcular design parameter values used in the Nr-UnE modeL The true importance of these constant BHP lean- out resul ts is tha·t the mini1lf.um valu'e ·o.f BSFC, throughout the engine operational envel:o,pe, occursatessenti,allY'a constant v,a:lue of F. On the other hand, the value f. :; O.DS is sunn'ort'ed by the fact that: for lIun rr the leanouts at {cons'tant inl.ett-1A'P, constant RPM, se:a level} in Fi gure 5.9, the NMBTE perrormancre mod'el predicts l1Iinimum BSFC to occur in the range 0.05'65 <F < 0.059 rOT P in the rang~ 28 >P - -- m . - m inches Hg ~ 20;. This" F.rarrg;e. is s'l.ightly lean of the. l"inaximum economy" val ueF=0.06 (2.3) and F=O. 0 59 (27) for fixed ignition timing engines.

F for Maximum BHP During consta:rl't P Leanouts-: m The NMBTE perfomance l1l0del was used t!odetemi~-e the variation in fuel-air mass rati'o yielding maximum BUP, duriing leanouts at two h· 0 1 t ln .01 inches Hg.

5-24' {constant inlet MAP, constant RPM, constant altitude}, over the operational envelope of the engine. The results of these leanouts

I

are shown in Table 5.4.

On the basis of these results it is proposed that, for General Aviation naturally aspirated piston engines employing MBT ignition timing:

I

A single value of F = F will yield maximum BHP in all

max

I

steady state operating conditions {Pm' N , H} (when F is E not constrained by other considerations). In the present

work, F = 0.08 is used. The choice of a single value of

max .

F is expected to yield negligible variation in BHP from max the true maximum BHP at any operating point {Pm' N , H} due E to the flatness of the (F, BHP) curve at such an operating point.

It is assumed in the present work that, in all steady state operating conditions {Pm' N , H} of General Aviation naturally E aspirated piston engines employing }oiBT ignition timing, BHP de-

cre.ases continuously as F decreases from F = 0.08 through

max F. = 0.05.

m1n

The value of F = 0.08 predicted by the NMBTE performance

max model may not be the value found to pertain to real engines using MBT ignition timing, since it results from the particular design parameter values used in the NMBTE model. The importance of these constant P leanout results is that the maximum value of BHP, m throughout the engine operational envelope, occurs at essentially

a constant value of F. The value F = 0.08 is slightly rich of

max 5-25 J the "best power" value F = 0.078 (23) 'and F =0.076 (27) for fixed , ignition timing engines.

Cons tantPand Constant BH? L.e;anouts from F m ~x Chirivel1a (16) identifies th,e "best pow-er poi.nt" .a5 .a fuel- air mass ratio cOllDllonly sele'cted by General Aviation pilots in cruise operations: . . the "best power point" is an enginecondi tion well known to pilots and easy to reach. Further- more, and in spite ·of the power set'tings offered by the manufacturer for airpl anes provided with TIT and fuel flow gauges ,most pilots do like to operate the engine at such a point because of the safe margin in TIT and/ol' the absence of engine roughness (16).

We shall thereforee.xamine some typical cases of leanout from the fuel-air mass ratio F = 0.08, using the NMBTE performance max model. These leanouts will provide, for naturally aspirated MBT igni tion timing engines, an indication of the BSFC improvements possible relative to the BSFC values obtained using a fuel-'air mass ratio typical in current Gene.ral Aviation practice.

Figure 5.10 shows four leanouts from F = 0.08: the left

max half of this figure shows sea level performance at 2450 RPM; and the right half of this figure shows perlormanc-e at 6000 ftand 2450 RPM.

Consider the left half of Figure 5.10. At the ope.ratin'g

point 1 [F = F = 0.08, P = 17.72 inches H,g, BHP = 115= 50% mc

max m BHP] the BSFC is BSFC . Two leanouts are show,n ori:ginating from I point 1.

5-26

1. Leaning at cconstant Pm = 17.72 in. Hg, from point 1

to the minimum BSFC = BSFC at point 2, yields a decrease

in BSFC of 12.15% BSFC and a drop in BHP of 16 BHP.

I "

2. Leaning at constant BHP = 115, from point 1 to the minimum

BSFC = BSFC at point 3, yields a decrease in BSFC of

17.84% BSFC , and requires the inlet MAP to be increased l to 22.93 in. Hg.

3. Operation at point 3 rather than at point 2 yields a decrease in BSFC of 6.48% BSFC and an increase in BHP of 16 BHP.

The right half of Figure 5.10 is similar to the left half of the same figure. At point 6, the inlet MAP has been increased to 21.51 inches Hg which is almost the wide open throttle value P ~ 22.9 inches Hg.

DWOT Figure 5.10 clearly shows that significant decreases in BSFC may be achieved by leaning from the "best power" fuel-air mass ratio. The constant BHP leanouts from the "best power" point in Figure 5.10 show a maximum possible decrease in BSFC of about 17.8% of tIle "best power" BSFC. This result compares well with the ex- perimental results reported by Chirivella (16) for similar leanouts of a turbocharged Lycoming TIO-54l-E engine in flight. Chirivella's tabulated resul ts of leaning at constant BHP from the "best power" fuel-airmass ratio, with the ignition timing advanced from the standard setting of 20° BTDC to 30° BTDC, show that BSFC decreases (16) : 5-27 · .. from 11.8 up to 20.8% if s'evere roughness is allowed. The numbers become limited to 17.4% if only incipient roughness is tolerated. I f on the other hand the engine is not allowed to operate with any trace of roughness,. the best fuel economy [BSFC] improvement is identified as 14.4% at 15,000 ft altitude and 75% rated power.

When leaning from the "best power" fuel-air mass ratio, the advantages of leaning, at constant BHP rather than at constant inlet MAP are tha t : 1. No loss in BHP is suffered - 2. A substantially lower minimum BSFC is achieved: about 6% lower in the cases shown in Figure 5.10.

Of course, if WOT is encountered during a constant BHP leanout,. the full BSFC advantage of this leaning technique cannot be realized.

I I I I Performance with Specified Fuel Metering Schedule We here examine the manner in which BSFC, inlet MAP and fuel mass flow rate vary with brake torque" RPM and altitude; when fuel is metered to the engine according to the fuel metering schedules A, Band C shown in Figure E .18.

BSFC Performance Maps at SeC1. Level: Figures 5.11 - 5.13 show BSFC versus engine brake torque, for constant values of P and RPM at sea level; as computed by the m NMBTE performance model. Lines of constant percent maximum con- tinuous BHP are superimposed on these figures. Figures 5.11, 5.12, L' I I 5.13 correspond to fuel metering schedules A. B. C res'pectively.

5-28 In each of p'igures 5.11 - 5.13: • 19.:s. inl et MAP, inches Hg < 29 • 2000 < RPM < 2600 The following may be observed in Figures 5.11 - 5.13: .~ 1. At constant fuel-air mass ratio a) Brake torque increases with increasing P , at constant RPM m b) Brake torque decreases with increasing RPH, at constant P m c) BSFC decreases with increasing P , at constant RPt-1 m d) BSFC increases with increasing RPH, at constant P .

m 2. The diagrams generally move to lower BSFC and lower brake torque ranges, as the fuel metering schedule varies from A to B to C. This is to be expected from the foregoing discussion of leanout performance.

In Figures 5.11 and 5.12, the rising values of BSFC with in- creasing brake torque (at constant RPM and high BHP) are due to the rising value of F with increasing air mass fraction at high values of the latter.

With fuel metering schedule A (Figure 5.11) at any fixed RPM, minimum BSFC occurs at about 85% maximum continuous BHP. With fuel metering scheduleB (Figure 5.12) at any fixed RPM, minimum BSFC occurs at about 64% maximum continuous BHP. With fuel metering schedule C (Figure 5.13) at any fixed RPM, minimum BSFC occurs at WOT: note that fuel metering schedule C meters the fuel-air mass .J ratio F. to the engine at all times.

m~n Figures 5.14 and 5.15 correspond to Figure 5.11: • Figure 5.14 shows inl et tolAP vs. brake torque for various constant values of RPM; for fuel metering schedule A.

5-29 • Figure 5.15 shows fuel mass flow ratevs. brake torque for various constant values of RPM; for fuel metering schedule A.

• All of the information in Figure 5.11 is contained in Figures 5.14 and 5.15. In particular, fOT any brake torque and RPM in Figure 5.15, the BSFC is computed ftom Equations E.3 and E.8.

Likewise, Figures 5.16 and 5.17 correspond to Figure 5.12; and Figures 5.18 and 5.19 correspon'd to Figure 5.13.

BSFC Performance Maps at Altitude: Figure 5.20 shows BSFC versus engine brake torque, for constant values of P and· RPM at 6,000 ft al ti tude; as computed by the M>1BTE m performance model using fuel metering schedule B. Lines of constant percent maximum continuous BHP are superimposed on this figure.

Figure 5.20 may be compared to its sea level counterpart Figure 5.12. Note that in Figure 5.20: at any fixed RPM, minimum BSFC occurs at about 65% maximum continuous BHP.

Figures 5.21 and 5.22 correspond to Figure 5.20, and may be compared respectively to their sea level counterparts Figures 5.16 and 5.17.

Al ti tude Variations of BSFC with Constraints We now examine al ti tude variations in BSFC when various con- straints are imposed uppn the engine operation.

5-30 Beginning at the operating point • Sea level • P = 21.56 inches Hg m • RPM = 2100

• BHP = 55% maximum continuous (mc) BHP

• F = 0.067

five constrained altitude variations in BSFC were computed using the NMBTE performance model. The constraints imposed and the results of the computations are shown in Figure 5.23.

The constraints BHP~ = constant and RPM;a- = constant were

selected for the computations of Figure 5.23 because: Straight and level steady flight of a fixed-pitch propeller airplane with • Fixed gross weight • Fixed center of gravity position • No propeller compressi bi Ii ty effects at constant equivalent airspeed (EAS) and at various altitudes requires tha t BHP~ = constant and RPMIcr = constant (see Chapter 4) .

In Figure 5.23: 1. Compare curves A and C: the greater values of P required m for curve C result in greater decreases in BSFC with alti- tude for curve C than occur for curve A.

2. Compare curves C and B: the greater values of RPM for curve B result in sma11e~ decreases in BSFC with altitude 5-31 for curve B than occur for curveC (or curve A). Note "(: that curve B, which corresponds to the fixed-pitch pro- peller airplane at constant EAS described above, reaches a minimum BSFC at an altitude of about 8,000 ft.

3. Curves C and D are not identical, but are almost indis- tinguishabl e and are shown as a single curve. The al ti tude variations in BSFC for curve D are attributed solely to the al ti tude variations in inlet manifold temperature and exhaust absolute back-pressure.

4. Compare curves D and E: the increas ed values of RPM for curve E result in smaller decreases in BSFC with altitude for curve E than occur for curve D.

Figure 5.23 clearly shows the extent to which al ti tude. variations in BSFC depend upon the engine operational constraints. The co- location of curves C and D in Figure 5.23 is further discussed in the next subsection.

Corrected Quantities , In order to formulate a compact engine-atmosphere subsystem input-output model, we do well to make use of corrected quantities; as we did in Chapter 4 in the formulation of the APA subsystem input- output model. We here develop such corrected quanti ties using the NMBTE performance model.

5-32 Corrected Brake Torque: The co-location of curves C and D in Figure 5.23 stimulated the search for an expression for corrected brake torque in part-throttle operating conditions.

Examination of the computer computations which produced curve D (Figure 5.23) revealed that: At constant Pm = 21.56 inches Hg, constant NE = 2100 RPM,

and constant F = 0.067; BHP;';- varied from the sea level

value BHP by no more than 0.5% of BHP ' for altitude O O variations from sea level through 10,000 ft (standard atmosphere) .

To check the reality of these computations, the cruise per- formance charts in the Information Manual for the Cessna 1980 Centurion were examined, and it was found that:

For the Cessna 1980 Centurion at constant P = 22 inches

m Hg, constant NE = 2300 RPM and recommended lean mixture; the value of BHP~ at 2000 ft, 4000 ft, 6000 ft and 8000 ft (standard atmosphere) varied from the mean value BHP~ by no more than 1% BHP~. The value of the fuel-air mass ratio F for the "recommended lean mixture" is unknown to the author.

These data agree with the NMBTE performance model computations for v curve D (Figure 5.23).

Extensive computations using the NMBTE performance model were then performed to determine an expression for Corrected Brake Torque in part-throttle operating conditions. These computations revealed that: 5-33 Operation of the naturally aspirated MBT ignition timing engine here modelled, in the standard atmosphere, with con- stant values of • Inlet MAP P 1 inches Hg m • Engine speed N , RPN E • Fuel-air mass ratio F yields a brake torque Q 1b ft which is a function of altitude E H (ft) only. At sea level, Q takes the value QE' The Cor- E a rected Brake Torque Q given by E c n

Q = Q CJ 1b ft (5.1)

E E c varies from Q by less than :::..1% of Q ' for altitudes in the E E

o a

range 0 .::. H (ft) < 10,000; for constant values of {Pm' N , F} E in the ranges • 19 < P (inches Hg) < [p at WOT] - m - m • 2000.::. NE (RPN) .::. 2600 • 0.05 < F < 0.08

where CJ = atmospheric ai r density ratio at al ti tude H Cft)

(Appendix B) n = Density Index = n(F). The Density Index n is a function of the fuel-air mass ratio F only: this functional relationship is shown in Figure 5.24.

Equation 5.1 is illustrated in Figure 5.25.

It is emphasized that constancy of the corrected brake torque Q with variations in altitude applies only to engine operation E c at constant inlet MAP. Q is not constant with variations in E c altitude when the engine is run at wide open throttle at each 5-34 altitude, since inlet MAP varies with altitude in this case.

Corrected Air Mass Flow Rate: Equation E.42 shows the relationship between the air mass flow rates at any two operating points 1 and 2. Consider two operating points. one represented by the subscript 0 and the other by the absence of any subscript: for these two operating points, Equation.

E.42 becomes (5.2) lbm/hr The following assumptions are now made: 1. The operating point represented by subscript 0 is at sea level in the standard atmosphere (Appendix B), where

P = Po = ambient atmospheric absolute pressure =

atmos O 29 .92 inches Hg , .

T = TO = ambient atmospheric temperature =

atmos O 288.15 degrees Kelvin.

2. The operating point represented by the absence of'a sub- script is at any altitude in the standard atmosphere, or in a non-standard atmosphere, where

P = ambient atmospheric absolute pressure, inches Hg

atmos

Tatmos = ambient atmospheric temperature, degrees Kelvin

P P 3.

=

m mO (5.3) = NE NE 5-35 4. T T m atmos -- =< T 288.15 -i~ mO (5.4) P P e atmos -- =< P 29.92 eO With these asstmlptions, Equation 5.2 becomes T ] (1 - e: ) t p P atmos ] e:

m = m atmos

lbm/hr (5.5) [ [ a a 288.15 29.92 O

We now define the Corrected Air Mass Flow Rate m

to be a c

m :: m lbm/hr (5.6)

a a O c Substituting this definition in Equation 5.5 yields t • . . [T atmos ] (1 - E: ) [P atmos ] E:p m -m -m lbm/hr (5.7) a - a - a 288.15 29.92 c O When m is known for any conditions {P ,N }'· the value of E a mO 0 O

rn in any other operating condition {P = P ,N = N P

E E' atmos' a m ~

o

T t } may be computed using Equation 5.7. Note that Equation 5.7 amos is independent of the fuel-air mass ratio F metered to the engine.

Corrected Part-Throttle Performance Model of P and rn

m a The foregoing discussion of corrected quanti ties permi ts the fonnulation of a corrected part-throttle perfonnance model of P and m

rn. Figure 5.26 shows such a model, computed uSing the NMBTE

a performance model.

Consider the left half of Figure 5.26, which shows P versus m

this has been drawn for F = F. = 0.05 and standard

mIn 5-36 atmosphere conditions, for which the density index n = 0.57 (Figure 5.24); and is applicable to all altitudes in the standard atm0sphere.

The sea level wide open throttle line is shown. At altitudes above sea level, the WOT line moves to lower values of P than indi- m cated by this sea level WOT line. The left half of Figure 5.26 was drawn by plotting P versus Q and NE ' and relabelling the E mn n

U v o

resulting diagram in accordance with Equations 5.1 and 5.3. Dia- grams similar to the left half of Figure 5.26 may be drawn for fuel-air mass ratios F = constant ~ 0.05.

Consider the right half of Figure 5.26, which shows P versus m m and N : this diagram applies to all fuel-air mass ratios F; E a c and to all altitudes in either the standard atmosphere or any non- standard atmosphere. The sea level wide open throttle line is shown. At pressure altitudes other than sea level, the position of the WOT line varies from the position of this sea level WOT line.

The right half of Figure 5.26 was drawn by plotting P versus m a mO O and NE ' and relabelling the resulting diagram in accordance with

o

Equations 5.3 and 5.7.

Input-Output Model We now formulate the input-output model of the Naturally aspirated MBT ignition timing Engine-Atmosphere (NEA) subsystem.

Formulation for the Standard Atmosphere": The NEA subsystem input-output model is required: 5-37 1. To be co.mpatible wi th the input-output model o.f the APA subsystem (Chapter 4). This requires that {N , QE' E Ta tmos' P a tmos} be inputs to. the mode 1 (see Figure, 4. 8) .

I t will be shown that H is also separately required as an input to the NEA subsystem input-o.utput model. t 2. To output the values of fp ,F} required to. minimize BSFC, m at the operating point {N , QE' H}. The values of P E m and F are required as control inputs to the engine.

3. To output values of BHP and m in order that BSFC may be f computed. R* may then be co.mputed from this BSFC and the value o,f R*c provided by the APA subsystem input-output model.

4. To be suitable for airborne microprocessor implementation.

The required inputs and outputs of the NEA subsystem input- output model are: Brake torque, lb ft Inputs: Q E Engine shaft speed, RPM NE H Altitude, ft T Atmospheric ambient air temperature, atmos Kelvin' degrees P Atmospheric ambient air absolute pres- atmos inches Hg sure, MAP, inches Hg Outputs: P Inlet m ,,' tIn the standard atmosphere, Tatmos :Ts and P atmos are uniquely determined by H in the manner described by Appendix B.

5-38 F Fuel-air mass ratio Fuel mass flow lbm/hr m rate, f c Brake specific fuel consumption, ';- lbm/BHP.hr.

Previous discussion in this chapter (pp. 5-22 through 5-26) has shown that, for naturally aspirated MBT ignition timing engines operating in the standard atmosphere: 1. In all steady state operating conditions {QE' N , H} E requiring part-throttle or WOT: a) BSFC is minimized by operating the engine at a fuel-air

mass ratio F = F. = 0.05 (when F is not constrained

m~n by other considerations)

b) BSFC increases continuously as F increases from F =

F = 0.05 through F = F 0.08.

=

min max c) P decreases continuously as F is increased from F = m

. F. = 0.05 through F

= F = 0.08.

m~n max 2. In all steady state operating conditions {P , N , H}: E m a) Q increases continuously as F increases from F = F = E min 0.05 through F = F = 0.08.

max b) Q reaches its maximum value at F = F = 0.08.

max E [These same results lea) through 2(b) are assumed to be true for naturally aspirated MBT ignition timing engines in all operating conditions {Hp' Tatmos' Patmos} in any non-standard atmosphere.)

The cruise operating condition {QE' N , H} of the engine is E 5-39 prescribed by the APA subsystem, which subsystem also establishes the value of R*c. In order to maximize R* in every such cruise operating condition of the engine, we would like to operate the en-

g ine at the fuel-air mass ratio F = F. at all times in cruise

. m~n (see 1 (a) above). However, it may be impossible for the engine to

deliver the required value of QE' even at WOT, when F = F .. In

mln the latter case, the only way to obtain the required value of Q E is to increase F above F . :. the minimum possible BSFC will then m~n be obtained with a value of F which yields the required value of Q E at WaT (see 1 (b, c) and 2(a) above). In the operating condition {NE' H}, the engine delivers maximtml brake torque Q when operating E at WaT and F = F (see 2(b) above, and Equations E .43, E. 57}.

max In the light of these considerations, we proceed as follows in the formulation of the NEA subsystem input-output model:

1. Fuel-air mass ratios in the range (F. = 0.05) < F <

m~n (F = 0.08) only are considered.

max 2. The engine part-throttle performance is modelled at a constant fuel-air mass ratio F = F. = 0.05.

m~n

3. At fuel-air mass ratios F > (F. = 0.05) ,the engine

m~n waT perfonnance only is modelled.

The NEA subsystem input-output model consists of: 1. A corrected part-throttle performance plot such as that ~ I shown in Figure 5.26.

2. A set of five Wide Open Throttle performance plots such as those shown in Figures 5.27 and 5.28.

5-40 3 .. Equations andS.7.

S.l 5.10, following; 4. Equations 5.8 - Fuel mass flow rate Ih : f (5.8)

Ih = F m lbm/hr

f a Brake horsepower BHP: (5.9)

BHP = [33 ~~oo ] Q NE

E Brake Specific Fuel Consumption c: Ih f lbm/BHP .hr (5.10)

c = BHP

Figure 5.26 shows the part-throttle performance in terms of the corrected quantities Q The left half of Figure 5.26 E c applies to F = F. = 0.05 and to the standard atmosphere. The right m1n half of Figure 5.26 applies to all values of F, to the standard atmosphere and to all non-standard atmospheres.

Figure 5.27 shows schematic WOT performance at four values of F in the range F. < F < F [The WOT performance is presented m1n - - max at four values of F in order to permit cubic interpolation in Figure 5.29.] Each of the four Figures 5.27 (a-d) shows Q as a E function of NE and H at WOT,in the standard atmosphere, for a fixed value of F.

Figure 5.28 is a schematic WOT performance plot of P as a m function of NE and H. This figure applies to the standard atmosphere, to all non-standard atmospheres (in non-standard atmospheres, H is read as pressure altitude H ) and to all values of F.

p Note that Figures 5.27 and 5.28 are schematic: they have not 5-41 been computed using 'an accurate waT performance model. The minimtun and maximum values ef NE shown in -Figures 5.27 and 5.28 represent WaT the RPM limi ts for continuous .eperatien of the engine .

Schmidt (32) gives a numbe-r of formulae for computing the waT altitude performance (BHP , BSFC) of naturally aspirated aerO' engines frem the WaT perfermance (BHP, BSFC) ef these engines at sea level. WOT perfermance has not been fermulated in terms ef Cerrected Quanti ties in the present work and the data storage penal ty for this omission is small.

Computational Scheme (Standard Atmosphere): The use of the NEA subsystem input-output model for computing the set {Pm' F, Ih } which yields minimum BSFC for any set of inputs f {Q N H T P } is now described. The standard atmos- E' E" atmos' atmos .

phere is ass tuned. so that T :Ts (Appendix B) .

atmos

1. Enter Figure 5.27(a) with {N = N H. = H} and

EWOT E' -:waT determine Q EWOT a) If Q ~ Q it is possible to' eperate the engine with E E WOT

F = F. = 0.05, at ei'ther part-threttle or WOT. GO' to

m1n Step 2.

b) If Q < Q it is not possible to operate the engine E E WOT with F = F. = 0.05. Go to Step 3.

m1n 2. F = F . : m1n a) Cempute Q (Squation 5.1).

E c 5-42 b) Enter Figure 5.26 with {QE ' N } and determine {Pm' ma }.

E c c (Equation 5.7)

c) Compute m

a d) Compute m = F. m, Ibm/hr.

f m1n a e) The required quantities {Pm' F, m } have now been f evaluated.

fj Compute BSFC (Equations 5.9 and 5.10). Stop.

3. F > F. and WOT: m1n a) Enter each of Figures 5.27 (a, b, c, d) in turn with {QE = QE' N = N } and determine the value of the E EWOT WOT corresponding wide open throttle altitude HwOT' In Figure 5.27 (a, b, c, d) the value of HwOT is HI' H , H , H4 respectively. Store the four co-ordinate pairs [(H., F.), i = I, 2, 3, 4] so obtained.

1 1 This step is illustrated in Figure 5.27 by the points A, B, C, D each of which corresponds to the S~T.e b) Interpolate between the four co-ordinate pairs [(H., F.), i =1, 2, 3, 4] to determine the value of 1 1 F corresponding to the required altitude ii. This step is illustrated in Figure 5.29. This value of F yields the required value of Q at {N , H} and WOT. Note that E E if H exceeds the value of ~OT obtained from Figure 5.27(d) (in which F = F ) then the engine is incapable . max of developing the required value of Q at {N , H}.

E E 5-43 c) Enter Figul"e 5 .• 28 with {oN = N_, BWOT ~= B}and EWOT ~r: detenninethe requi red iril.et'f.1AP p=p m1DwOT .d) Enter the right half of rigure5.26 with {Pm' N } E .anddetennine m a c e) Compute m (£quati on 5.7).

a f) Computem (Equation 5.8).

f g) The required quantities {Pm' F, mf}have now been evaluated. P is not required for output since the m throttle is wide open.

h) Compute BSFC (Equations 5.9 and 5.10). Stop.

In the above computations, interpolations (linear, parabolic, cubic) may be performed using L.agrange's Interpolation fonnula (33).

Formulation and Computations (Non-Standard Atmosphere): In non-standard atmospheric conditions, the operating con- di tion of the engine (as demand~edby the APA sUbsystem) is defined by the set {Q N H TP } ·E' E' p' ·atmos· atm05 where H- pressure al titude, ft p

Tatmos = atmospheric ambient air temperature at H '

p degrees Kelvin P - atmospheric a11lbient air absolute pressure at atmos ",. i B , inches Hg.

P The only change in the above Formulation for the Standard Atmosphere required to account for non-standard temperature T atmos a t pressure alti tude H is: p 5-44 Altitude H must be read as pressure altitude H in the p text and in Figures 5.27 - 5.29.

The computational scheme listed in the foregoing subsection for the standard atmosphere is retained for non-standard atmos- pheres, with the following adjustments.

1. H is read as pressure altitudeH in the text and in Figures p 5.27 - 5.29.

2. It is necessary to adjust the value of Q required by the E APA subsystem, to account for non-standard temperature at H , prior to entry into the computational scheme.

p Let:

~Tatmos = [atmospheric ambient temperature (degrees

Kelvin) in the non-standard atmosphere at pres- sure altitude H ] - [atmospheric ambient . p temperature (degrees Kelvin) in the standard

atmosphere at H = H ] = T - T

P atmos s

= [rate of change of Q with

E T t when {H , Pm' N , F} are invariant: L E amos p 0 denotes that MBT ignition timing is maintained during perturbations in Tatmos]' lb ft/degree Kelvin.

brake torque (lb ft) required by the APA sub- system in the non-standard atmosphere, and 5-45 developed by the engine in the operating con- dition {H , T , P , N , F, l } in the same E p atmos m 0 non-standard atmosphere ~ brake torque (lb ft) developed by the engine in <' the standard atmosphere, in the operating con- di ti on {H = H , P , N , F, l } E P m 0 where l denotes MBT ignition timing.

o Then, liT aT atmos atmos H , P , N , F, l E P m 0 + (higher order terms in ~T t ) (5.11) amos We retain only the first 'two terms on the right hand side of Equation 5.11. The functional dependence of the derivative aQE/aTatmOS! on the variables {Hp' Pm' N , F} E H • P , N , F, l E P m 0 at l has not been determined in this work. I t may be found o that sufficient accuracy in the computations is obtained l?y allocating a constant value to this derivative: if this is not the case, some iteration may have to be incorporated into the computational scheme.

The brake torque Q = [QE]NEA is used in the computational

E scheme when computing Q and when entering Figure 5.27.

E c ,.

However, when computing BHP (Equation 5.9) and BSFC (Equation 5.10), the brake torque value used must be Q = [QEl .

E JAPA 5-46 n In computing Q =Q a for entry into Figure 5.26, the 3.

E E c density ratio a used must be the standard atmosphere value of a at the altitude H =·H ft.

P 4. The non-standard atmosphere values of T t and P tare a mos amos used to compute m (Equation 5.7).

a The NEA subsystem input-output model, appropriate to standard and non-standard atmospheric conditions, is presented in block dia- gram form in Figure 5.30.

Implementation: The principal hardware items required for implementation of the NEA subsystem input-output model are: 1. An ignition timing regulator providing MBT ignition timi ng and retarding this i gni tion timing as necessary to control detonation.

2. A fuel-air mass ratio controller providing F as commanded by the NEA subsystem input-output model. It is desirable that this controller provides a value of F within 1% of any command value of F.

3. Microprocessor.

Items 1 and 2 should be automatic control systems.

The NEA subsystem input-output model is well suited to imple- mentation in an airborne microprocessor for the following reasons: 1. Figures 5.26 - S.28 require very little memory space for data storage.

5-47 2 . The requiredcomput-ations are few and simple.

Figures 5.26 - S.28nrust be compiled from flight test data in order that installation effects may be properly accounted for.

The data requirements of thes-e "figures are self-evident, perhaps with the following exceptions: The 'flight test datanrust establish 1. The values of F to be used for the compilation of ,Figures 5'.26 and 5.27 .

2. The value of the Density Index nfor Figure 5.26.

3. The values of e:tand e:pfor Figure 5.26.

Flight test data are also required to establish the functional aT and to quantify this function

nature of aQE/ t I

amos H , P, NE,F, T pm 0 for use in the input-output model.

Summary The performance predictions of the NMBTE perforrnancemodel have been discussed. The NEAsubsys:tem input-output model has been formulated, and the use of this model 'for performance compu- tations has been discussed. This input-output model is compatible with the APA subsystem input-output model developed in Chapter 4.

The NEA subsystem input-output model issumrnarized in block diagram form in Figure 5.30.

TURBOCHARGED ENGINES The turbocharger is a mechanical device, consisting of a rotating turbine and a rotating c-ompressor, which is used in 5-48 conjunction with a piston engine. The turbine extracts power from the exhaust gas of the engine, and with this power drives the com- pressor by means of a rotating shaft. The compressor uses this power to increase the pressure (and temperature) of the engine induction air. A piston engine and turbocharger are shown schemat- ica1ly in Figure 5.31.

The shaft power output of the turbine is often controlled by means of a Waste-Gate, which is used to direct a portion of the engine exhaust gas through the turbine and to discharge the remainder of this exhaust gas directly to the atmosphere. The waste-gate is located in the Exhaust Manifold (the region of the exhaust system between the exhaust valves and the Turbine Inlet). When the waste- gate is closed, all of the engine exhaust gas passes through the turbine; and when the waste-gate is wide open, most of the engine exhaust gas is discharged directly to the atmosphere without passing through the turbine.

A throttle is placed in the engine induction system downstream of the compressor outlet. The portion of the engine induction ·system between the compressor outlet and the throttle is called the Deck; and the portion of the engine induction system downstream of the throttle is called the Inlet Manifold.

The relationships between the absolute pressures and tempera- tures of the atmosphere, deck and exhaust manifold are determined by the performance characteristics of the compressor and turbine.

In general, however, when {H , T t ' N , F, waste-gate position} E p a mos 5-49 are constants and T = constant or MBT, opening the throttle increases: 1. Inlet MAP 2. Exhaust manifold absolute pressure (this is the exhaust ".

back-pressure on the engine) 3. Turbocharger shaft rotational speed 4. Deck absolute pressure 5. Deck temperature 6. Inlet manifold temperature.

In general, these same six quanti ties are increased by closing the waste-gate, when {H , T t ' N , F~ throttle position} are con- E p a mos stants and T = constant or MBT.

Therefore both the throttle and the waste-gate may be used to control the BHP and Q of the engine, since both influence the inlet E ~~. However, an increase in inlet MAP is achieved at the expense of: an increase in inlet manifold temperature (which increases engine temperatures generally, decreases the engine indicated horsepower which decrease contributes to increasing the engine B5FC, and increases the likelihood of detonation); and an increase in engine back-pressure (which decreases volumetric efficiency and increases the engine pumping losses, both of which effects con- tribute to an increase in engine B5FC).

The performance of turbocharged spark-ignition (51) piston engines employing MBT ignition timing may be modelled by incorporating a performance model of the turbocharger compressor and turbine in the model of the naturally aspirated engine given in Appendix E.

5-50 Such modelling is a necessary prerequisite to the construction of a fuel-efficient input-output performance model of the Turbocharged MBT ignition timing Engine-Atmosphere (TEA) subsystem. The author was able to obtain the compressor performance data for a turbo- charger used in General Aviation, but was unable to obtain the corresponding turbine performance data. Consequently, turbocharged SI piston engine performance is not modelled in this work.

The author was also unable to obtain experimental performance data for naturally aspirated and turbocharged SI piston aero engines usingMBT ignition timing. In the absence of such data, and in the absence of a turbocharger performance model, no rigorous comparison of naturally aspirated and turbocharged engine performance is presented in this work.

The following remarks concerning turbocharged engine performance and the construction of a TEA subsystem input-output model are offered on the basis of the foregoing sections in this chapter.

Performance Comparison: Naturally Aspirated and Turbocharged Engines Brake Torque: The maximum brake torque Q of a naturally aspirated engine E at any operating point {H , T N , F} is limited by the maximum E p atmos' available inlet MAP P. As altitude increases, the fall in atmos- . m pheric ambient air pressure and the resultant fall in maximum {Pm' QE} for any {N , F}, seriously diminishes the performance E [decreased maximum: cruise equivalent airspeed (EAS), rate of 5-51 climb (RC), angle of climb (AC) lof an airplane powered bya naturally aspirated engine.

A turbocharger enables the P of a given engine at any {H , m p T , N , F} to be significantly increased (boosted) above the E atmos maximum P available to that engine with natural aspiration at m the same {n , T t ~ N , F}. Associated with such increases in E p amos Pm are significant increases in QE' The airplane performance improvements [increased maximum EAS, RC, AC at any {Hp' Tatmos' oNE' F}] resulting from this increase in QE' especially at altitude, has been the historical motivation for turbocharging airplane piston engines.

Brake Specific Fuel Consumption: On the basis of the discussions of naturally aspirated engines earlier in this chapter, it is assumed here that: in all steady state operating conditions {H , T t ' BHP, N } of General Aviation E p amos turbocharged piston engines employing MBT ignition timing A single value of F = F. will yield minimum BSFC (when 1.

m1n F is not constrained by other considerations) 2. BSFC increases continuously as F increases above F = F . • ID1n The ability of the turbocharger to boost P , above the maximum m P that would be available to the engine with natural aspiration, m has important consequences for the BSFC of turbocharged engines.

Consider an airplane powered by a naturally aspirated engine, and assume that the APA subsystem demands that the engine operates in the condition {H , T t ' QE' N }. It is desirable to operate E p amos 5-52

I the engine at F = F. in order to minimize BSFC. If the engine

mJ.n

cannot develop the required Q at WOT when F = F . , the only way

E mJ.n

I

I the engine can increase the brake torque to the desired value Q E I, is to increase F above F . . The maximum brake torque will be ffiJ.n developed at F = F and WOT. Increasing brake torque by mixture max

I

enrichment is accompanied by an increase in BSFC. For the naturally aspirated engine, this BSFC increase is an unavoidable penalty for operation at high brake torque: it has been demonstrated (Figure

I

5.10) that BSFC increases of about 21% may be sustained [at constant {H, QE' N } and MBT ignition timing] by mixture enrichment from E F = F. = 0.05 to F = F = 0.08.

mJ.n max Now consider an airplane powered by a turbocharged engine, and assume that the APA subsystem demands that the engine operates in the condition {H , T t ,QE' N }. I t is desirable to operate E p amos

the engine at F = F. in order to minimize BSFC. The ability of

mJ.n the turbocharged engine to boost inlet MAP to high values means that high brake torque can be developed at F = F . . Consequently, mJ.n the turbocharged engine can operate at F = F over a greater range min of flight conditions than can the naturally aspirated engine, with attendant increases in R*. The feasibility of operating turbo- charged engines ul tralean up to 75% rated BHP at high inlet MAP has been demonstrated by flight tests (16) of a Lycoming TIO-54l-E engine.

5-53 Recommendations: TEA Subsystem Input-Output Model As stated above, the performance of turbocharged SI piston engines employing MBT ignition timing may be modelled by incorporating a performance model of the turbocharger compressor and turbine in the model of the naturally aspirated engine given in Appendix E.

Such modelling is a necessary prerequisite to the construction of a fuel-efficient input-output model of the TEA subsystem.

In constructing the TEA subsystem input-output model, attention should be paid to the following: 1. Leanout performance should be examined to determine the fuel-air mass ratio F. yielding minimum BSFC during mln constant BHP 1eanouts.

2. The engine should be operated at WOT at all times, and the inlet MAP controlled by a) Waste-gate position and/or b) Variable geometry turbine nozzle ring (34).

In this manner, a given inlet MAP can be achieved with a minimum engine back-pressure and a minimum inlet manifold temperature, which conditions contribute to minimizing engi ne BS FC .

3. The option of installing an aftercoo1er downstream of the turbocharger compressor should be examined. This device cools the induction air, thereby reducing engine temperatures, increasing indicated horsepower (and hence decreasing BSFC) and decreasing the likelihood of detonation.

5-54 SUMMARY The content of this chapter is summarized briefly below.

1. A performance model of naturally aspirated, spark-ignition, inlet port fuel injection, four-stroke piston aero engines employing MBT ignition timing (the NMBTE performance model) has been presented.

2. The performance of current technology General Aviation piston engines has been discussed.

3. The performance predictions of the NMBTE performance model have been presented and discussed.

a) The 1eanout perfonnance predictions of this model indicate that: (i) The fuel-air mass ratio yielding maximum BHP in all engine operating conditions { Pm' N , H} in E the standard atmosphere is approximately constant at F = F ~ 0.080.

max

(ii) When leaning from F = F . = 0.080 at constant

max {N , H}, a substantially lower minimum BSFC is E obtained when leaning at constant BHP than when leaning at constant inlet MAP. A 6% difference in minimum BSFC for these two leaning techniques has been demonstrated.

(iii) A decrease in BSFC of approximately 17% is possible

when leaning, at constant {BHP, N , H}, from F =

E

F = 0.080 to the fuel-air mass ratio yielding

max

minimum BSFC. F = F = 0.080 is a typical

max 5-55 operating fuel-air mass ratio for General Aviation pilots.

(iv) The fuel-air mass ratio yielding minimum BSFC in all engine operating conditions {QE' NE,H} in the standard atmosphere is appro:ximat'ely con- stant atF = 'P. == 0.050.

ml.n b) BSFC performance maps have been examined.

c) The altitude variation of BSFC has been shown to be strongly dependent upon engine oper,ating .constraints.

d) Corrected quantities for engine performance have been determined. Part-throttle performance has been presented in terms of these corrected quantities.

4. TheNEA subsystem input-output model has been presented, and its use for computing performance in the standard atmosphere and in a non-standard a-tmosphere described. Implementation of the NEA subsystem input-output model has been discussed: this input-output model is well suited t.O airborne micro- processor implementation due t.O its simpliei ty and minimal st,orage requirements.

5. Turbocharged engines and their 'performance have been briefly Recommendations for the construction of a TEA reviewed.

subsystem input-output model have been offered; but this input-output model has not been developed in this work.

5-56 TABLE 5.1 ENGINE DESIGN PARAMETERS INCLUDED IN TIlE NMBTE PERFORMANCE t.lODEL Engine displacement D 470 cubic inches

=

Indicated thermal efficiency e -0.0046322

=

n! cubic (Eq. E.4l) e 1. 063657

=

1. 1

(compression ratio = 7:1) e -0.9421708

=

e 0.2200205

=

TI Kelvin Reference temperature 305.556 degrees

=

m Data for correcting indicated thermal efficiency for inlet manifold

temperature (compression ratio = 7:1)

-1 degree Kelvin

~I aT

m SI -L 10- 0.6 -1.44 x x 10- 0.8 -1.44 10- 1.0 -2.16 x x 10- 1.2 -1.08

x io-

1.4 -0.54 R o -~- 0.6 0.7 0.8 0.73 0.9 0.81 1.0 0.83 1.2 0.83 1.5 0.81 aR l -1 -0.0004 degree Kelvin

=

aT

m S I J '0 5-57 TABLE 5.1 (concluded) Lost horsepower data: Motoring coefficients 30.99 a

=

o 10- (2000 ~ RPH ~ 2600) taken a -2.705 x

=

10- from Figure E. 15. a = 1.125 x Lost horsepower coefficients k = 1.667 x x 10- 2.112 = = 0.007 10- k = 5.111 x yn Volumetric efficiency correction indices E: 0.2 = t E: 0.1

=

P 5-58 TABLE 5.2 REFERENCE OPERATING POINT AND FUEL SCHEDULE DATUM CONDITIONS USED IN THE NMBTE PERFORMANCE MODEL Reference Operating Point Inlet manifold absolute pressure P 28.42 inches Hg

=

m, ...

T Inlet manifold temperature 288.15 degrees Kelvin

=

m l P inches Hg Exhaust absolute back-pressure 29.92

=

e l Fuel-dry air mass ratio 0.084

=

Fl Brake hors epower BHP 230 hors epower

=

I Engine shaft speed 2600 RPM

=

NE Fuel Schedule Datum P Inlet manifold absolute pressure 28.42 inches Hg

=

m fsd T Inlet manifold temperature 288.15 degrees Kelvin

=

m fsd p 29.92 inches Hg Exhaust absolute back-pressure

=

e fsd Engine shaft speed N 2600 RPM

=

E fsd 5-59 TABLE 5.3 NMBTE PERFORMM~CE MODEL: CONSTANT BHP LEANOUTS During leanouts at {constant BHP, constant RPM, constant altitude}: 1. Minimum BSFC occurred at a fuel-air mass ratio F.in the range 0.0485 < F < 0.0500 2. BSFC increased continuously as F increased from the value of F which yielded minimum BSFC through the value F = 0.0935 throughout the operational envelope:

• [45% mc BHP] < BHP < [BHP at WOT and F = 0.08]

• 2000 ~ N , RPM .:. 2600 E • 0.:. H, ft < 10,000 (standard atmosphere) 5-60 TABLE 5.4 NMBTE PERFORMANCE HODEL: CONSTANT INLET MAP LEANOUTS During 1eanouts at {constant inlet MAP, constant RPM, constant alti tude}: 1. Maximum BHP occurred at a fuel-air mass ratio F in the range 0.0795 < F < 0.0805 2. BHP decreased continuously as F decreased from the value of F which yielded maximum BHP through the value

F = 0.0470

throughout the operational envelope: • 10 < Pinches Hg < [P inches Hg at WOT) - m - m

-

• 2000 ~ N , RPM < 2600 E • 0 ~ H, ft < 10,000 (standard atmosphere) 5-61 ce'

s! s!~

t--~---+---rl---+------1~---+-<><~--+---.r.~ ---t-----1----;

-E :e

t~ ~~ ~~ A~ -10 o -20 -10 -20 +10 o +10 Retard Advance Retard Advance Effect of spark timing on bmep for a number of L"S passenger-car engines (Barber, ref 12.41)

[FROM IAYLoR (13)]

1.10

J

1.00 0.98

I

........ 1-7·-

/ 0.95

/~11.5'-

c. 0.90 '" .§

VL-16.5'-

E ::s E I.

20.3' .~ 0.80 --- -- .-- I.

'0 24' .~ ~

~ 0.70 If

.", -f: ..

~ :IE VI 0.60 0.50 -30 -20 -10 o +10 +20 Retard Advance Degrees from maximum power Correlation for all apeed.a and loads.

FIC;UR£ 5./

EFFE.CTS OF IGNITION T/MJI .. /{, ON BRAKE MEAN EFFECnV£ PR£5SLJR£ .. " ...

230 [171.SS1

y

220 [IM.121 /i 1\ 210 11SS.661 /" ~~ 1\ 200 [149.21 / ~ ,

JA~

/

\

.~~ , 10 [134.281

\ / ~ /

70 [126.821 I V / q.~ / L I., [119.361 II: ...

/V V

~ /

150 [111.901 ~ V

VI .I~,,~/

140 [104.441 ~ / ,/ II: / I~ V 130 [M"} ~ 1/ V ...

/ /' 120 [89.521 ~ L/ ,/ I .. ~Y 110 [82.061 ~ , V

~

100 [74.61 '/ /' 90 [87.141 /' 80 (59.881 ./ 70 (52.221 ., [44.761 17 19 21 23 25 27 29 [57.581 [M.351 [71.131 (77.91 [84.881 [91.451 [98.221 MANIFOLD PRESSURE-lnHg (kP.I Bhp vs. intake manifold pressure vs. revolutions per minute.

(REF. 2.l})

FIGURE 5.2

lEA-LEVEL PERFORMANCE ALTITUOE PERFORMANCE fIA.I.-THROTTL.E HP '\ '\.

AT ZERO 'l"M ....... t-....

/ :) V1 ~ o Z2 V 'I V V o

.'"

V V V /

i " 'I" ~.'!

&"!L~/ C ~ 1\o..1I'S~~ " ~ '"

~~V/ 18 ,t'- ~~

o ; t\.

~ ~ 1"", &>fb-9. ~ :I..!

~.;~~~/ 17

o ", / ~~~q:;&.

N~ ~ ~ ~OO-li ~NN ."

V.

'"' o V Iii ~ O,,~ t'- .......

//'l!'1.~~ v: c: o r- _28~) r-. .......

~ V V / ,/ry.;f.~ V "j.J o 14 26 ~ ......

'" V v: ..

'-".)

" IS o i . .1' ...... ~ ./.V ./ -" 2S I 20 !'..

~ 'r-- '/ C/ ./ l/ / ~ o \I 21 p 2:-" MANIFOLD PRESSURE. INHG V ~ V V V / V .--

v: ~+Ig 18

-" o I

•

'/ / "

i-25 o

•

,/ I o 7 ~-$O 17 II II 20 21 Z2 2) 24 25 ZI 27 ZI Zt lIO MANifOLD PREIIURE-INHG O!NSIT'I' ALTITUDf-p!n Finding actual horsepower from sea-level and altitude charts.

(~£F. 24)

t="1c,uRE ·5.3

5-63

(REF. 23, FIGURE J )

IT I~ l1~tUME.ll 111111 J'HESE GflfEt.IlLrZO m/xro(E S1't.ENGTH

CHAI.IlC:reI<15 'nes APr! Y 10 11IE. FIVE. CoN)) I TlOHS

L. l!oTEl> IN FIGullE 5.5 .

5-64

(1?~F_ 27)

Ii o~· A.

'eakExhaUst ~GIS t:E ·50 i 0, Temperature ~~u.

~!..: ·100 cjC1 - w -150

If

-200

JI

~~

\

'- 'eak Cylinder Head -40

.- ~~

Tomperature 3'- ~- c!% -80

_=u

-120

Ii

·160 ~

JI

\. Best 'ower _ 0

f!

0% ...

l-f

lID c ~~~ ________________________ ~ .g Q.

I ~ 260

A. g 220

ell 180 I

'O~ _.

n :? I~-Y\~-

I

~ 60 t II ---=::: I ====

ID .04 .05 .06 .07 .08 .09 Fuel - Air Ratio Effect of fuel-air ratio on power, brake specific fuel consumption, cylinder head temperature and exhaust gas temperature at constant engine speed, manifold press- .

ure and spark timing.

THESE GEN£RALIZED MIXTURE RATIO C.Uf!VE.5 f!PPLY (35) TO: I. NlrrLl~RLLY A5P/~fl'rE:b ANb luRBOCJIIU(GE:D .$1 Plf.TON ENGJNES.

Z. ALL CDNsrllNT SE.H {Pm) NE. ' H To.t,..,os ) /'umid.;1j} Wt1"HtN p , THE NO~IlL OPE.!e.R77N~ ENVELOPE. OF THE E.NtaINE..

3. FIXED IGNJ1'/ON TiMING 'to 4-. BJ.lP IN THE 1&fNt;,E +D1- 100Z OF mAXIMUM CONTINLlOUS BHP.

5 SfAN])R~b ANI> NON- 57'"ANMRD AIMoSPHERIC c.ofll1)/TJONS.

F/(;UR.E. 5. 5' GE/tIEKRLlZED /r1IX-rU~E. RR110 Cu~vE.s.

5-65 i

I

~.'.' =- .... l. l. .l. .• I ... ' .. 1 ... t .•• 1. L. .. 1.. ._L. _L =- 1--.------;.-.

I .. 1 :.: _: ... !

I

I r1 BHP VARIATION WITH INLET MAP AND 'RPM :r::'::::::-: .- ..

!

~:'~:~::::~-:~:;:J:~~}i~:8~~~q~f~~~!~F~~;~'~~----~'"

I

I

!. ;"1

. f----- ---:-':".' ., i i.C".'

-. t '- • ... ,

-- --.------ .: ~i:: _~~~ :~ir ;.~~ ~: ~~ ~r~: ~.:: ~ ~. t

.. - .............. .

-,'.- .......... _- ··-t-· ... -. ··:·:i: ....

.. :~--~ ::::'::1::" - ..

~'--.:~i~::-~~~;~::~:l~:~~::~::~~~~~~~i~~::_~:~-~:-::~ '~~~--~~~~~~~~~~~~~~~~-7~~~~~~~~~~~~~iri~~~~

r- ·:::.~:-~:F:--~:.:~:-:r::::--·

i:':~~~'~:~~~':-:~~;~~T~:~~~~~'~~~;~~~:;~;-.~'----~'~--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~£.=~~r~_,~~~.:~:~::~:~'.~:~_ .- .. -. -- ' ....

. - '.- - - .. -. ,--- . --

1---.- .... _--------------- l··y~:~:::T ' b: ~ ( ~-~.-~::~;~::~:~.~::~~-~.~----------------------------------------------------------.-.----

FIGURE 5.7

5-67 .In '"(. III TO ltU f r~JT IMI Tr ,OJ ,1(, 1 ',11 , !"! I I' H f' .j IJ I " "'. , "."

V1 , 0- i i i I I I (

I

.')

I

I

I

I

I

I

I I I

I

"': :- __________ --'_L-~ -.--:-.:-..:-~~~...;._--'-i--..:.--:..--..:.-~--:..~---:..-,,__~--+_'_--:..~-.:....:.:..f_.~JB1---,.__- -- ,...' -" .. ~." .. - ... ------~ ._-- - - ~ ______ ::2.

:·~3 ~--.-~~~~--~-~-~r_~;::t~~;:~~Tj~t-~~-~~~~~~~~::~~::J!~:t}!~

j- -~ ~~-:::-:- -4=~:!~:~:[ -

:--~__ - - ~:4 ___ .lS.7 -...., - ..

:- ---,£ ---- ;-:-,-- - -'.- - --'-'-"-'.:.:...;.-'-'-"---I---C-..;..------------ ------ ---------------'-'-~-'-'-_=_:~.::::::_~F..:.:.:.:~ ~~.--~ .. ~+~~:.:.:::..:.?-:"-~::::.f-::;.:.~-.-~: :~:.:::..:: :=-- -,.:-:.:_l_= ____ =: --=.-:':=-.".:::::=-:;:-:::-:-:.;.::::: .:.::.:::::=.:-::~c_; --'--=-'-'':':':':':':-=';';':~~~::;p'-:ltt-:---a:-~ ~:~_~_.=:.::~ '~:.: ::~i: ;~:.~~~~i ~~2~~~~~i:~~~~~~i~=~~ ~;: ~ ~~~::~;:i·: ~~~~~~~:.'

tJ) ------.-------.-. ----. --- ~_ ... _ .. _~_ .. -_ ---:-.--::-:--:c.Ji-"-:-:I"---,-",:::,,:::~:;±::~:~;::,;;~:-~:;~~:~~.::.;-;i:~::::::~:3~:-,,-":-~'::':':~:.:;.:.i~~::::;'·~~·E~~~-::'::::~~=::~~~~~:::C:~~~_=:~~_::=;;~·~'::':'·~~==--~~;::';;~:~~ =~;.;:.:~~:..:.;,;~::.:.~~-=~~::;::::=:-::::~·~:.::.~L=~~~::::;~~;:;:::~~:':::;.~~:,:,,:~~~.~=~~ =E~~=:::::':'~-=:~..:l;J: pz:::I;EOL-~-'_~~ :. ____ ~ _ ~.::.: ~ ::.::-:~~:~:~: ~::=1:-::::.::: :": 1-.::~=~:!:-:.~:-:::·::·~::::-:~~: :'!~::'~:::::=;-:~.=:::.::.:r.:=~::~=- r------- -~- ------------- " .. - .. '*--' - ....

... . -:.:=--:.::--.-:.r: • ~..:..:. :':'':::.: ::':~.:':' ..

. _ .... - . -- .. . ~ .

.. ..... ....... .

~--~----:----~-- :.:::::~~::-:::~:n __ ::::~_ ·>:i!p~::~::_~-~~~~:.::::~-~i~:::~:~-:;~:~:c~ =~;~:~~~~~:~f~~>=:~;~~:~=!::- j' l' ..... I _ ......... __ •.•.•.• 'V f~-- I: -- 5-69 , ~fi ,< " 11' 'w I! I , r) 1 I 1 F (I t-J 1 I ",'! r r I·' ·1 r, J r; 1 '1

-

r. .' " I : ' , ,I ; r' ; I~ , r' • U1 I --l o ---, ---------"-----,-,---- ---,--"'_ .. ""<---" ,,--, ............... .

R f.,"·· In". III I (l 11!r ,or tJ 1 If., 1 f P Ii ,.1 -:(11 !." (. '. .

CI1 I -...J ....

111 Y ;-', , t ~ 10 X 10 TO TilE CENT! METFR 46 1513 KI \Ifr rl. A ft;..'·1 n () Lt.-,. ''I II ;

-------------,--- ._--- -------- ---

1 ! I .~ ~" l I' 1 I II ('''.: I I r- " 1 I I) I' Co ,.~ I' \ 1 I') 1 ... ~ I: ~ .

~~~~~1:;r1Flllrl!llE:n ::::I!!!lTI~]~l~T"~dJ'''lc'-:~'l,}'pi 'f :':'r' -":1' - .. '! -i - \ ~ I ! I T~~14to !(';U~ic,:,~:r/+~~~E~-·ll l .. :. :.:: : ... 1._ -lBttAk:1 : ~: .. S_Jt'E rl ! rl , .,JM nON CbMPUTER MOl>El I.: : ...... l. ... NA~'~y .. jlJS~IRATJU) ..

.. :. :..: : . .1:.: I:: !:;; IS!A. ~v(£11 ~ i S7'JINDAQ! A'TMOSPH£RS. : i i' II ! I I··J·· I·: IMST" IGNrr,OfII 1itft(tJ& I~~ml.::,!.:· ::.:,li: :!i ' .. ,;1." ' ... :. : .. " .' :1 .. ·· ;.. .... :.. ,I ': . I .. ' 'J .. I.. ,:.1.:: j: .... :i.:.' .. 1 I . -I .: . I :-i; .. r.-: ................... r.'O- . .., t Ii:: .;:! 1 .. Iii; ,,"1' Ii:'! . . ":" ,: : I" - • . .. ,'.:. I" ,'. .... I • : I' : I'· 'I, I. .i..: ·1'· I . I : ., •• ,,1', '",~" ,01 I" •• , • I. '"'1''' I" 'I, I '" I' '-, ., .. "'1'" .... ". , ..... N" ·1 ...... ' ... ., ., ........ " '1' ........ , ....... ...• ,- I . . I" .... . ... ,." ....... , J! il 1 j ! I !:;; q! 1 u~: ,I:. : i I : ~ i: ,'; ~ !;: i . iii i' r ; ; , .,' : .. ; j ; i : , '. i. i1 i !i :, ' :: ,: I • : I': ": ; , . .' I' ' ! , I· .1' !,; i : I : ! i : I : ; : : ;: i::' ::::: Ii. : .

_ ~,fl1 "1--'++ "'~; ·.1, ~. ~ .... - ......... I.H ............ '1' .. I. •. , .......................... 1 ....... 1 .. _ ...... - .. j. •••• 1 ... _ .~ .. ,- - -' '1"-' ... '-' ............ 1. ... ···t .. - i!1~I!\'9: l!i : :ii! ·!i.l!ii "\!;.:~. ~':i: :!i::: .,I:. :;;'j:l i :i;'! i, I::; ,.;: i. i:' , : .>1. : I;: .; ... 1.,. ,1 . ! .il' ': ):1 " . Ii:' ;: '!: .j:.:; '1" <I ,'1. " .. I: 1..1 :)n:Ii;:' . . .\ ...... ,...... d I'" .j 1"1. -. .. .. '1' ...... " I" •. ,. I' .. .•• .., ... "-1 .. -'" ..... "... ..... "" ." .. \ ........... .

!I:i r i: : i:jifi1~1 .::1:' .~. ':1;:' :1:\i:.; :::; :: : :i! j·:il .. '::: ::\; 'Ii' i' iii! ;';: I;:' ;i : I',: .::! :,:, I;:' .,' i:·: :·u::: -: ; .. ' .':;':: :1::1'.:: . ij:: ,.q ;1;: :;! .:. .j:: ::TIfu·: .: .

l . ~.f<'i! ._. ~"I'~ ... ~.;-:-t ........... .:tt ._ .......... , ... lJ ~,l""C+:"h'" Hi. ... 1-' - ... j .... -~ .. ~- .... , .................... -I".~ •.• _ .. - ...... ~.,~ ...... 1-- ... - ..... ~.;.- •• l ! f I;' : : ~ j I' I r':. I : .. I' : t t • I r' ';, :" !': :.,: 1 i : I . :, i: :, ; , :, I :: ! I : I !:: I I; I, ,] • .,' I : I: ";. I;:. . ; . i ; . I " '. I • . ,1 : ; I , : • I , , : : :, ; : I II': .:; .' : I: .; : t ' • ill :! "jl IH' ru ' ' 'Ij'" ~. '\" ".1 I ,. ,.j I. ", ,,,' 1'1 1" 1"11111 .1, "" I'" ,1'\ .. , 'II' '.1. oi, "tl'" J I" 'I .;., ". '" 'I'I II. ",. " ..•. I,.

jl · I-LI 11 • l' 'Wl ... 1 1:1: . ,.::: :::: .:.: .Ii: ;.1 .. :;. I.:: .. 'I r jll :Id i:: ,. : :.11 :1':: :.l: I.:: I::: :;1; ;;.\.: ... ::: .:,. ':::i.:: .1:. :1 1 ... i. :;.: I:;: I.:: .,:i :l!i ::.~ .... \: ... I::; .. ;.

I l ! I :n ~::i 'hi : I' '.! I:!: ':.! i· ::,'; :::1 ,: :i!, ;'Jl,1I I: ;:: :11; I I: lid ii:! I;;' i!'! I:!: : II ::1: Ii:: ':::1:::: ,1:: ::. :.; , :::; :.: d!i 'Ii: , ,i ': . I!!: ll!l jj!: '!~: :," ',.: ::.: :,'1 .:;.

m

·11·, .11 , ~j .I,·ll_,":: .. \. I ,,,.,, , .•... I ~~ ..... '~':LI1W-L;+I;" , .•. , .. ", ',U'!.j.j.: , .• \ .. , ~.. .' '., ' .. .:1 :-l' ""I:ll; '" . J!."L!.~11 Ii ... , . ":I'~:'''' .,.

:11" :~' ':' I! .:,: 'I ~'ll;ITT' H ~~ ... -: ~:~.. Nr-:::; .... --:~. '. ;,: .. :-:t· i : 11'11 : ~> ~~~ i;:" ;"n ~:r: ~,:: !Ii: ~~ ::; . :.:I:~· ,,:' +~01 04:~ 7~:: ~ .. : -;rr.r;w ":r r·-: ~r;::: :i!: :t, ~ ,~: ,::: ."

~: I I'; l!jl jllut1jll til, ':,1 :111 ,. ~ ::. I: ';, I';' oil '.,. ::' 1:, 1 : I!'! 'I~III::' I', I,:: :!Ii 1;,1 1 !; ::11 .1;: ;;' .:, ',ll,i' .:;:.' "; '::; '.,! ·~i :: :ii: ::,1 :111 11 : ' ::.: . :, ::;' ::': 1:; Ir 11' 't IllrwJ' ·'ot "t: .• _. ,'·i!ii.'" .. , '1' ... ,. .1 •• '1' .", ,., '" 11' .. ,. $' , '''1 II •. '." , ...... 1 .. ,- .... . .. ..... 1 '1' , ......... , .......... , II 'H .- ...... " ....... .

ld '.: iii 11 ii' I: :;p :i:; :: . ...l.t~ ';1i '''~. ;~! i· :·:1 :. i,: jii: 1 : !:i: Hi iii' I:; ;·i: .; i :i/j lili i;:i i:l! -:i! 'i:: .:;::: .. !i::; :;ii :1!!liIP ::; H :l::I;iii :dj ::1\ ;;:: :: :i:i :i;: :1: , .: I ~ ", ',~ ;': .. ::? ~.+,I. Bl'" ,.~ .. ~ .... :.;. ~F ijH H-++ t~+ j~,: d'~ ~·H: ,lti+t+t r~:' .:;: :::, :~:m !~ .. , ~~~b.4 ~4 :,~~H1': '~:1 ~~ ml::: rbn W* ::,' .:': :::. ::,' ':, .~.: Illi .\ ,,1 '1"'1 "II", \ •.. ~. ." 1"'lli lilll·III" ., ... ', 'I' ',' "I' "1 " •• , .... ,j ...... " ""'" .\ •• , .... ·1 .. , oil' ... ,.- .. , .. , ... \ .. 1.

I

' : I 11 lll~' I : j ~ j , ::;. .l. I I '; . i it\ . ,I i ' . :' I, ,I Ill; II ':: I,'::: 1 1'1 I;: 1 '~I: I; 1. : 1:: :; I :'.: ;;:: . I': I ~ : : :: :.::::,: !:. , : ~ 'II!: I : Ii 11111 ,::' :: : :;: i ; 1 j ·ll t ::': l,l. ,.1 I .,~ .1I. ','" , ~~" •. ~. ~~ • .. .......... ,., " j., I ", II' ." j" .I , .•• I ..... " )." .,' .... -'" "I" ·,1, '. d. "'.'. '."1", ,." "," H' "1 ",' •.•.• , ........ ", 11""" '.".'.

l " I , "1 II"'" . . -s \ . . ..... I 'II I' ., .. , I' I' .... '1" .. , .............. ,. "1' ... I' •. " .• , iii;' I ........ Ii' !

P Iii' 'I "Iiii: ". ." '-"'''''''1 ... , -',' "ilil'" '1"" .. I··· .. ·"··· '., '1 "1"1'11 -, ", ''':i lili'l!ii·· .... ij· 'li'li' ' . I • It .. j::: ·tl+HI·r:m;.;· ... N1\"I'\1'':i!' ~.; "~r- ;~j1Hti ~:l! ;:;! iq. p.: P;+:~ltl Hi-tH8~8i~: ::.: ::!' ::~:~:~::j" ":'}:~:::'. it:"U1I::~ .. ;'. I:;.' ~·"U"jl'~j' il~"~:': :::'.1.:: :1'1 :: ..

I I! p\'j ~ljii~"!:; H 1!d 'Ij:!:j Iii, : ,:~.: . """1 ~" ,l~ d:' :~li 1;:\ ll:'q" l:'l;,! :!!: j'j:; Iii! i!P 'I:; ::;:~, 'I. \ ~I,j;;~U "1,1. :: ;\: ,~::' ':W': :iii :;ti l!; ~llH·· til, :: 11 It~llltl -: I iij1f.:;!; '~";:I~ 'll' tW~ .. :~r i:~:li:'! i.' j!! . j::Ull iT i\!~ Tl :!il :f1: ::;: ~~.u.~ :'IA n.! ... ~.!-, .i:: '~~r:mt!:j: ~;~IIJt~:~Z· :iil~ T[ I' I" , , m.L'~' '4'~. ~.:\t '. ~ ! "' .. !J ..... ~ 1-0" ~-I"" ... l ~,~..L.;..!.! J.:":";' ;'1' I, ..... c:uru. -:~ t\...! ~'~I'P.~~" . 1~ •. _~ ~~.,,~~ ':M. ..

I t 1i \" I I': :~'.' . ,I 11:11 ,I .::1;, I' ~'-l ::: ' :, I" .;: '::; .::' :i:' :::: :1: 1;: ':' "I ' I.: I,~ ,"! '1,1 ,,: '" l:~ ,:'::, :. ,', .",' 1, :i:':: I 1 I 11 1111 I ~tl' ·t·· " .. '1\ II ',., '1' . -. K' ,. ~ 1'1" .. , "1 "" .... , .. 1 ." .... ' ... " .. ' .... "1'" ., "I" 'I'iI'" " .d, '''1 ,... .. ," ';Ii .. ,.

• : H ~ !. I'l ::~ t j" • ill.~~ !::, ~..., .:: 1 ,:.1\.:"" L :!. JII: :l~: 111: :.:: :1; ... :..!' , " 'Ii' i ,I ,. I' " .. 't I ,I I ,. , 'I ,I, ....... , ,,' , • •. I !!"" " , Iii·· r'111;1 "1 !"I""" \' ~~. ~ •. '." "'1' '" ".1...... •. ,., ..• "" .... , •.. , ... "., . -., "1' •.

ITt lill Ii: III: '1' i:: Ii !IIi ii.! i!jl:.::::: '~;'... . .. i\ft\ ... ,. '," . i :;11 :::;~iJli :!I: :i. :::; ::<i.Li.I:L.;,~::'--,.:j :u. ':;';I;ii :i) Ii:: iii. til. iii' ;ill I::: .;:: .i:' :1'1 .ii.

III'!! 1111I ,lij: iI' :. "I li!1 I I . t+1','j' :::1' ':-;:- C; '::! '1 - '\' : 1t' ::~.~:;;;.~; .. -,,, .. : :-rl'i ;m 1 .. Ii:; :.Ii '::1 :;:. ;;:; :.;c ::::": I : ;j! ~-::;';f:I: ~;:-"I' :. , j' :t: ;, 'I: Wli ': .. :: :.·::::i :::i ::; ll;! .: '1\; I I;' '[11 ,I I ' ill, II'; 4,;' l:j' "~~ ~' II, 1 'I~, ,i ::::,!: :'p ,:[~ '~l :::' !ji: d : :lii jl;1 ,::: ,1':: ; ::1 ij: I' 1,1 II "'I! ::.: .:, :;:; ,:11 .:.'

I

II

HI i 1 -1111 ~ IWl.·~ : d 11 III t ltil P .::: j::! 'II! : 'I: .!\ I· .. ~.I I, ,- . :tlJj:::,: iljti I~" :r!, .;: ::!: :I't ;::: I:;: ,:t ::j! 'lit :·'1: :;:1' :.': I.: '::1 1 ill- . ·!t :::. :: .. jli: liD .':' l iiI. '. 11: III: 'j1 : :' Ii Ii :ill":' i"I,:': 1'1·: I: I - . "., ", ~,.: 1. .: ... !. 'iLI :Ii' ':.: I':: ::q '.:, ':,: Ii:: )#Hi I •. :: I:': ill: :Iii 'iil :1: :.' ':. Ji.lli'd .:;: ,t ..... , :+.:L!l • ~ .::4!;:i I;~' .wJ!' I ._.,', ~'" "\'41 .. ~... ...~. '1 t ~ ;iii.!.t I ... , .. ·iL!. il:! ' .. ~ ,J..llH-U' I ;4 .... ,. 'II 1 ,I .t.:... .... ,I ,I 01" · ,~Ti "~III ,i,". ,.1 .,,!. ·T·,··,I 'I, ~.. ~'.-.~' "', ""~;"""""I"'~·'::I;J ;::1!11' 1"'11" "" .1'11'" ',' '" "t'· " ,. I ....... I.j: •. "1 'U'11 1'1 I I 1.1 I" " .. .I.: 'I" . II . , . ...~ . ,., ... 'I" "j .. , -"'J'" I" ...... I • I ..... ",. "" I' 'i"" '" "j' 'I' ... .

'

TIn

:::, :ill::ltl'~':!:'i ; I 1:,,1,'1: ;'::::,';11::,: ::,:, ~ .!I:' .::.11 ': :;:,:::~.':,:I:I,!, :1"'1'::,!·i:I:I II: ':;;;11:,'11:,,:::;' :::I,~::,I:: .... '\~""I'I" ;. II"" It' ...... 1 •..• I ... , ..•.• ,. 1 .• 1 .... , .. ," ." ~ ... '" ., ..... _ ... ,,, ....... , ...... I. It "" ........................... , ....... " .

• ,1. , oI,"" TI .,1,,· II' '1' I' "" I ", II .,' , I' I' '1" '" !'. I '" I 01 • 1,,1 ·"1" ,. Iii "'I 1,111" .. ' • '!' '1'1 ...

l :- ;:: ::::! i i" iJ.l : i ! 1 ii '! 1 i ! I I .: i i ;::! : i; ;:.: : I 1 I : I: :::: ! i : :. I.:, :....:~.L : I: (... I'.::!;:':!:!" : ," i :: . !: ! 1 ! I : p;; : II i: !: :: : 1 !! !:: Iii: :: "::: ;: :;!. ::: :;~': ~::~!!~ .::~.~~. ,', 1: '. ttif~I"irj 'r:: :::~'::; ;::' :;::"Tj '-I: t::· '::'1;'1; :-:. Iii. ~~' . "'-'\l,~" ··1· .. ··'· .. · .~ .. ! ..... :"1"': ~il i-ff.j':'~ ·: .. t~ ::~~f;T:: ":T .-' ,I: '::,1 : ,:1. '!~'" ::I:~' ::'~':" I' ::.! Ill' .11'11':" ; .. : .... '11:1 :, .':;.:: \' ::: I I' ... . ','., ... , '" ' .... ' ,: ... " ,j ....... 1'" .... 1 ....... t •• ·t .... 1 .·f' 1-' .". ". I' ........ , ..... ,'" p ...... , .... ~;. \ •.• ...... ..: ..... , , .•... ,.... . :'" .. : •. : .... ~.:: ::: .:.: ;,!; i ,i;i:+IH::;:. :i!l ifft li~~ 111; ::I!.: .' :': ,:~i' j;ili;~r;l' 'II , : !':;', ' k~\:- ,1,. \. :! l. ,.', :;.1 :!;I;::;~:: ~~:; '.: :i: -:' . -:', :::1 .

.. ~ .. ~ , .~ ., .... ~:. H~t' .~~! 7:" ...... ··1·:~· :~OG .. "1.C BH~. . ~'~.;.;' '-' ":" I . ·t .. •· ·: .. 1 .. ·· .. : •• ;~ :.;+ :-l++~~-:--:- 7-: ,,:~ ~: .. :----;-- .':--" ~- -++I'-8~~' l :.' .:~:::: '11,11"; :t "! :'I/':!' :1(' ::;;.:: i. , I: .'!' .1 t;l!! II IL. ; I' ~S ~~l I " ,. ,! '.: II:; ill' :\'! ".' 1:'1 "I :'1" ::; .. :: '."

1,':.;., ,Ill W'I ' 1,11'11 ,.,. I, ". , ,I .. II II ". " ,.11' "W' , 1'1 "" ,."" I 1'1" \' 'I' ", •• ,. '''1,'1 .: ,. ,.: 'I" .... I, ··i· I ........... ,11 .. 1 ! ... :.., I 1 '1 111 "" I. ·u ...... N· . ..- .. , " "t,· ;,~ .. t!: .•. I'" II" .. I: ..... :. ::.: .: :: .. :.: •....

iii: ill :::: II : ~::. I'I! II'i: I!H'! Ii' I::: ·.:l :.': :ili '.j :!:: :1: 1111 : ,;Ii 'l'lli .. j'. ' ':i I Iii: ;!" '-.! : ,'.' .• ". i I 1'1 ~llii'. :::1 I::: W.I: .:1: iii: .::: ... ' .::: I::! ,I .. '_j .• .1 II,. i!l!~j . .) jl L ...... I"J I:!!I -4; 1l11.1 'iii' '11" ." ill .. t i-ll+L~ . ,,' , ,/. Me 1.IHP ,r!-.I .. , ., .. ·~ .. ,dUilil.J.:';';.4 . • ;~.w '..ll~

~

::1' -:-:: :::: ::.' II' Tii: 1'1; ::11 1:-: :':: ;-;': ::'I::! r il'TPII:t t T: · : '::1 .:i· ;::: :::t;· i,'ll 1,[: :":: .:. -~I--:·· .,. :'1\ ,,:1 !I'llll: oJ}: j:: 1'1: ':i ;FfTflllli ::. ::" '. il:' .. :1 :.:.

W 1 I I l 11 1 1 i.:. :~ ,::1 I! '/ ":~ I ~ :1' ,j': j" " ':::1 : I it' tl' '1 ' ::,' I!~ :'I:~ j:ijll'·.1 1111 :Iji ;, .: ... 1,:" ::, :"; .;: Ilil I : Ij' \;11 1. :1'1 1 ' ,~::: ':,: 01'; :itl· .

O ::'; j.fi :1:: 1 1 I ,ilp 'II :lil Ii'; :.:! :;'i :U i it I;il' Will ~I II! I :li!'ti;: :U:; :i # llli:t: t : 'II.: ":: -:::J-,;' .": :::: "i: :':1 ::J' I:f!;,; iir id:llitl: ;'U ~1;lji .!j: :i:: :::: nl: !iiH :;:: 1 !:!i' 'j' i' liil I ..•. , . ·l', ., I" 'I' . '.1 ,1 ", II. H I II ,.1, :i' til' ." , .... 1., .. 1 .. 'i' lUi 'iii II' ii"IIII' I", ".i·: ;: :il: ill II' ~;,:. ri:1 '1 I I;' I::: ,i ,\ !:lli ::;: ;:~'I ::~~ :'11:1 '-r: If-I : I Ii-I I ~ t :,'-;fl ILl:: I.:r-t\!t- I'll -I'I'!' j'l! I I II~ ':7,t-ij:' '.~: :j:: ':i'I' ::~ ~;" :1, ;II!I' 'I; li;;IIII':·· "1-1- ~ ;.:, :i:: ;:11: :iij' ii'li I 111 'I" 1"1 ,Ii, !' 1\ !I'II II ' •. !,. q'" II I I M' ! I", I 1 " I I 11' 11: " ". ,'" I, .,' 1 Pi 1!!I' t I"fll" "j" ·tt·; ,,' I, " 1 it:! :::1 !::! ! i: .11. I. i ':l!::'::' 'I::!'I :: i' I ii, !:ill:!' tid ';Ii Ii. iii j : I .:l! ;.:. :::: I':: i!j! :::: :;i11j1 ! '1i 11i1~I"il J."]: iJ I ::.; 1::: ::::~: H iiI :tt!

l 1 ii :;:i Ij:1 ;i:1 IT II Ii:l! q:: ·il,:i· :; :::: 4' fl.: lill Ilfl W,! I::, IiI. 1'1:1 I111 II iii III 1\ :,1 'i;l '::: ·i. r"!~'" :.;~ ';ii . "f' iJ~1 M"e" HI' ... i.iI~.:.;,; .. :[~.' r~:1' ,:!I: 11 11 '~I'! 1'1~1:1' l.i'll ·· I!' :: '!I H ;+ll'l'j"1 ;;;: !::::--:1 ;.!.L 1'1 '1:+ 1, '1' I tth! lill ~ Ijt \+It pl~':llI tH1 ,iT :1 fl,'11 :1'11*11: :tttl ~~: ;~:.:- IT' 'I' ~,~~t: i~'''~:'II:~~''wn: I'" 'Ii U!~(~~c.I}.r~~l,~~:~ri ~t:;.~: I I I. ,I I ., I 't Itt I II I '1'1 t I. I • I , " ! i 1'1' I' I I" 1 . , I I " 1,1 'i! j!1 1 I 1!-1' , ! t • A '12 ' , ' I" F .. ,,"eM. '6M :.:! d: i : I! r' ii' :; " 11: II: I 1: Ii :::: ::.! I::: :' I : i I : i.: i I ! Ii i : i; Ii:: I!;: !.:: . II," !:' ~,: '. ; l!! !::;::' ::.... ' :: ;. :; .. : I .1 i . '1 .. . i ,. . .', · . 1'1' '<\1 I] ,1" ,tI; .1" !:I ... I'" I'" "1' 11 "'I :: II 'Ii ·Iil .... , .. I" ," I 1,:ll\li)" ,.1. II' 'i: j"', 'J " 1'.,".:' Int ." i. . • ,Ii" :::~ ,I.I ':'1 " :' jilt ,,, 11' ::1: ,::: ,:.: ' "I : 'II .. , Ii 11 ' II " , "" I j',; II Idtlt1 ,'" . 'd :: " 't .. 1' .,;" '; , :'11 " , :' ", ,;1, , il

U

;tr TIll PH I,!l m' I' I ill l'IIU u::: ii!.i!.."'·"j':" ' . ..;.1..": 1··11~· hi':; 'l1li:lllim' ~;j;: '2r.;.;..\' : .... ,1,; ··II:~L:.:' i:·~":~:l,,~;i ~ I ~ I tliL:..c:~;" "1·:"'L.-::·~r.'.I.~ f' ~t' j'. ,~~I .. :I ;::: Iii: I::! jil: I I: ~ .. P', da.~ I:jij~ :;~ " ... 80lIl. :~f""'l ''''''~:Il' ~:I:,jJIr- :~, :!""f'""'!: !:"'~: -'., :1' ,. "~.: :::4'11'- : ..... !""":j'. I . I :il ,:': I':, ;::: iiI I : ~!jl :;. I::i ii:: iii,:, " 1'<:I:'!1 "~:II!j ,'\': 111,:1' ,,'1'.: :1 ', :.,; ,:;: I': :l~1 " . " i~ I l. ':U: ":i ;',.:, ;1': ::: ,'\ l 1 1:.; l:: ill: 1-1" l ilrl A +itl i.:: t'i: -::j .: ..... : .... :;;i ::.Ji .. ;; W: ~1 : ,wj"· :.J I::" : :.,.1 ; ::~l .;~. ;.~! :!.: .. ~;, ....... ,.. . "!' .. ":' i:i' ;i._ ·:;i :.. .. ;;: ..... :;~ ... ... _." •. . .... J t :1:: Iii: '::i ::il IIi; ;lli 1;1; :'1111., ',:1: '.1' : ... :;::.\ :!1 I;: I!:! 'II: l. .: ':':! : 'il til ·.i: :::;i~~A:'" i""'dR~ ,;~ : :t" .~: >::i .. !:i . , I: ,:. '."

:::: :,!j .::: I,!: 1,1: IllIlPJ;' ~:l :t\/"t·~::· .' is'; 3" .:::! :11 ,::i .: II:. ' \' .::'1, . , : '.1:: : I:.: :::,,~, .:11' . ""IS ';, I " ;> 'i' . ,.. .. I' " . " ... ·:1 '. ::!: 1:\' .... : . i I I' :i , .. : 1:: :01': I': :1 ,'. I":" 1:'1 I '1: I I . I ,. ':' .: .. :: .

1 , < : ',.: !!~: .L. ~ ~ I, I." ... :, .J.! <1 :~.l. :.:1.: ~.! ! ... l \ ~l! 't:~' l:p ,'.', ,I _.1 ,. :~': ,. '. \ '. ~, 10 X 10 TO THE CtNT1MF.TfR 46 1513 Kf IH F-rl. A Fo.;<·rp t.n "".,'f ''II 11'_ '. 't' 11\ 111( f rtHI~.~1 1f no I I I • ~' , " .•. , III . ~ I Tn I'lf ('"fITIMI Irp Ir,'" \-,. rl't :'. I III r·' -" , ",f' I' , -----~~----- --~- 10)( In TO TilE: CEN1"METrn 46 1513 Kturrrl I\. ,o::~crn (0 "Ut'! ... n " 1 1 ,:10 !' "1'1 !l11~11 I~III i' 1111 II .. III ')~j j:1I I':' ,nl[w I!I~ ;1. "" ~I' I!" :1' .. ,'f,TJT:." ')'1': I:· : :~" "l~: ']lS' I:,; :::I'q"'r::'.r--:- ':', Ii:' 1,;1:::, !", '''' ~I!I!\I"I i~.i·:, ' :::1 ::1 Ii!: II 'I ' ',II l:! ~.' II!l it iilH :: :::I! ::~.,.:. I I i' :'!:~11!!' .:", II: .1 \1 :.: '!' \I:' ::::1: :: "I: li;; l: ::. '!':' ::. ',',: ; : Idi ' 1: .:,' ::l: l::: ,;1: :111 : .• :1 ::.' ::; ;,; .

• .. • HH'" ,,, ,. ~J' WIII~ rd ~ .. u.... ,. '~.... I;" U'~ , ., , ... ". "'·r<.t'·""· ,~ .... "'" I,.,. ",." ., ........ , 'I" ...... , ..... 't" .. I. ,~ .. :;. .,' , ........ ,I ••• III ~ i I Il i d:" .; f: .• ;:: ' ,:: "'1.; , ': Ii I:' , r-:. ~ 1 i .;: I I , I ' ':'.. ::. I ,,'I :;' " . I:" .:' i":'!!;:": I :' : '\: Ill: \I Iii': i: ,. . ::;:!'

II " 11I1I11'illi' . . '" . "":JI,j' r;~ I.' . ';:,' '., . . ... . "" ,., ,,, , .. ". 'i" ... " ... , , 'ii' ". " .. :. 1:;:1 '

k

[! i IP~UJ.jlj 41> : ~H ~)iH~r:~ ':'; pr ii:t ~;~JI/;n~~~ i!~ +.. ~~t;tl ;;H'H;~ill~:r0] rm ~m !~;: ~~: ;:~1 ~:); ;j;: iiii jj~ inj ili~ jjpJUlli' ~~ t~it ~1;rT , I 'I' lP , I, .. II .. ," .. , , ... "llllil I . I "1.:m'" I' In' 11j. !. i ";1 ., '1'1 ' .,Ii .,., I'" "" '1" ", .. ,I ·'·'d .. ·· ... , ... , iii: .1j,1~~~;lc~'-," H ... tS ..... C£/ltENr;~ l • , ,. I "!.j; i' i; 1 \;;1' I::,' jltH I' rl'IIli '; t 'i~ tTIl'ft +l:t!·,· ,t'I';:Iiltitilff:H~ ~;J: :iH "frtl:il.J.//'It++l'lffutt-;'1:1· :t· ;i f.1 ;,,; :;!:Irr:f81It:l~rui~iiilfitttW: tlliln11'j; j t .~~ 1: tl 111! 'i I I I I II II I' :j ld :j'1 ::IL~!!q il: i:q:, iI' '1 )'jl : :. ;:;~ ';: ::: :Ijl~ qp ,j :!i!J!tI~rl :J4t, ~,,~~~hJj)t ... 1 t I , II iT tl:' '\1 1 I, I' ':) . 1 Ii !: ,·d! ::;; 111' ti: 111 , ,III!:i If ,r 1',';:8:;i'j' ;ii :ijPII: ::d ::q:l rt:ilj'~:': ·it··. :::' r,:-:r:::; i;:. : .. :Si m l I UffiffitHffitttt!ftfHtttHffitHffitt tttHli+tit H#JfHi'fttiillfHti- il++' H+H~H+H+H+I' 11+fH.l.u.H+tilH-' H+HH- H'II++!+H++" m' '1"!! 1'1'1; H! I'"'' II. .:: 1:: .. ,......,,",' ;111 ... ';.,. l.:. 11,1.1 ~~w ...... ,. :1'lliiIiltd 'I:.

IT; • II ~ " m~+~~riTh H++ 4-H! 'il III !! 1 ". 'II , 'I" I,. iii ,I ,I, :LL i d Ilf \':1' H 1:11 "I" I! '1'1 i!l: I i; Jil: '\;ii ii'l I.!:, liii ill', :i!1 jill i,I:II::' :1;: ii:: ii: ,",'I' m: ~I :i:'1 !i::I!,::: .:Ii : II' it'H'l 11::lfn'I' :;" il't' :!i1 HfHlftHH-fHHfHmH Itl 'i " I I' Ii 'I I' II 1 \1 .. II' II' " ".. 'l'li' " Il,1 Ilt I' 'j" ,., ":':11 . ... "" all "I' I ,H" '!l .". '" ';4' i t 1 f! It II n 'iii!; " Idi 1, il 1 "iii'!ii I :j i::i :;;1 ri' Htt tli:1dd '1'1 II Iii 1,1; i:l: :':1 ;:'1 Ii ill: !::t :1il ;>"I·! n.i • nil' m if:': :n fit :Iif

I

I :, tii II ,. ,III ,I ,.. ",1' II' li'l lil' '!i: 'II till ::1 1I11 :. 'lj 'ii II: Iii '!:I '.: ,. iii: ... 1 '::1 '.1 .,'" I! ' . Iltl' 'ill !I: III ;11: I" I', I: ::1' ;:!l I;,: I:; :'j)"~" -::, ~j~: ,., ,: Ii .. , LO,t .: :i .;.;: ','j:'::, [.::, ... ::: ':!J'::: .. , :,.; i:.I:' ..... ".!: : Ii:' .1,1 •.. ,i:::: .. !i:I' .:il I:;: I;:' j:::!il! :II!

I I 1'1, Ifl\ : ~ II ~I I I • I • I I , I' ,I I ' \""." I • I' I ., I 1 1'1 "1 I'l' 'I ' .,., 1'" ., • I. • ,j I I ,. I ., ,,' I ~ j I '" 1'" II •• j ,I I I! It i I j tt ··+t~ti:'.f·" 1"" ~:, , ;'" I.. " ., ,.1, , ., .... "': " ...... ""'1 I "1 ",,,, ...... , ... , .... ,,, ......... \ ..... , .. n" "'1 t ...... tl" I, .....

If j ili': I jj.~l i;i ,i!li h:i .i:' :·!i I:,: ilii ili: i· ii' :.i; ;ill~:i;:'~ :": :. :~Jb~,:!~! JllH::::,;::: ;:[! ::\: :~ddiii ~Ji Iii' -: :1': ,.. . :".Gt·:;~:';::: iii! ::: liL :i:: :,i: liP :;(1 " , .. ,I 4,., ••.. ~, '" I 1 +-:-7, ~ t~ ~~~I ~-;;. ~:- •.. " t-;;-;-" , ..... ;~:o- .... :t ..... T.mn· ·li .... :~. -: -- . . ..... -- ",r;-:i. ITI "TT ... , .,,, I, ... ,,' , 11 '. 'I .j I'll '1'1 I.·. I' ll" Jill III " 'I 1 \' ' •• , II 1'" ",, 't ' ill' II, I ,. "I' ••• "I ,II 1,1' "" I., I , . """, 'l!, ,.:i I" ,I!" ",I ,.I.

" I II! I :'1:;1 lB'!':' I!~:.: I :~III ,it I 'III~ II 'I:!'~ll:' :' ,I:: it" 1: ~ ;, !II,JJ 1::1:"; 1::' ;'j' ,II! :,11 ,I, jl;i '" I:.:" . : :,:1 ill: It'l [nll ';/ .. ;;;; j l' ,"j' l H#lIHHIt+ l' ~I: • "f j' 1 .. 11~··' .... '" 'i'l . • , .. I '" W ' .. I "" .... f~··· ,." .... ,,,. , ... "1' "I' ., "1' .1. I" ,.. .. ... , ....... qj. ..' ., 'j" U,j H' I d I' Ii' :. Il Iii:: Ii!' :.1'1 :;::r!., :i ' ,I! :;[1 ,.:li: l:j I,!.' :;ll ", 11 ,1,l .;:: I::: I::: ::01.: IT 'I: '" ,~., .::, ., ,. :;', :lli :: , 'I:: .: : : :; '::: .::: !

f!'

, :~ .. !' .. ::!. ::11 Iii; II:: I': :'·:'~:~lli!. !'~ ~j~!+W' lf4l4f..:~ .. !~ :::>f.~H.4++~:4 ~ 4-4t;~:' '':':.~-.-t:~ .1; ...... ~I+-_ :;l; ::'!'I' 1::: ':::: I: !j11 :::: jI~ 'lil i!tiU ~Jlli'''' "1 u,'U Ul." jj' . "" "I' ,." " .. ,,1'1' ', .. 11' " I I, , . ,,', .. "ftHil., ....... '" 'I' '" ,,\1 '1":1,, I'" ., .. h ! ,. ,,' "\1 'I' iT,· .,,' \'1 ,;1 .,,1 1 1 ~l 'll ! 111' 'j'j , ;1 j;. il· 1:1 ILl 11:1 I I' :.1, '! , I::: ,I 1'\11, "'ill". \ :':I:P;I!:'~: :1': :;;1 II, ':1 : '/4H' '~., ,; I:: ,11,·!t ' \:i' .," i ,.1 II; :;:: I: .m: :i:' it ~. ... if '<1 H .. ' 1 .. "t,lIH '"II I ... 'ii'al'lil II,' II .... " .. "1' , .. , ,.1. -.1 '''1 .. Ii l' ,. "1"" , .. , .. • .... , , ........ '11' , .. , ,~ ...... j. . ~ h \

II

t

, ;. j"j, III jj •• :: I Ill; I'· ::!i t!q ':. 1'\: ii' ;;:: I:I::I! :11: 1:1: :~: " t~1 '!: tl:: j:;: ;';1' :!III :llll1:j,j. I:: lL .: .:,:: ,,,:Ii~: i ::!~, .': 1:::1 l':, :', :11: '1'1 :.'

li r illl I \I ii Ii I'll" 'ii' I" I". ,I 'ili'liil" 'lilli lili "i' ' a I' . "I· .. ,.,;::: '" I' 'ljjJ.i~i I"~ ., .. 'I' ,. 'I!~~ ...1.~; .... "I, ":i " .. "" !li" '''li

I 9

'W: 1'Illjl11 :,!' 1: H'i'tJ';llij'i::: '!j !lJ! ,:; 1:11:' '.': ::, : .. " '.. ".' I,,: :. 1"1»;" ':;~:i;; d f:: 'i:I:1 :±~~f:n~1~~p';i 1~:1' :jffi tW~:!.+:·~: i~:hft Q~ •. :~ ~!'+: :;1, '::: fu :::: ::l: :;11:: ::i' ,tl I If! :1 It !'j "lj ::iItI iIj.;1 tl~· 1'1' i-f.j;; :::.i ":. :114 Ij 1:-, :!; 1 1 !. :: : ,1!1 !:~:l:i:;~'!':' :ljl :,1: 1::' :' : II :::,11 . '," '::\ ::11l~ ,;: Ill. ;:1 ::li I Jll 'i)W' ::, r ~ 111 ::t:rt ::'jj':' "'j' !:JI' II:: ':~ ,! 11':;, ,:~ or:: :1l" ': !;'. I!' \; .:!.:,' "::jji . ,":: :: t h ~ : ;' 'i::' : ; ... : ;':::, . '.: :::' :::, 'i .::. 'r:' ::1: .j1 ::: 1: ", 1111', ,\ I ',:1 ,ii', ,Il', '11: ';:1 ::::'.010: !;1:1.1 I:f'~: 'ii' ~.I.J'Uml'I!hl+I": "Hi':11 '1: .':: ;:,: .':: . ::.::1 :. I !I,: :'I'!I:J.' ~: .'. :!.: :!.!,." . '. :1:. :: 'II,. 'I' :'1 :::', :'!

I VI ,,,..,,' ,..,; I . , .; I. ,,'.J 11~ ; ~ IItI .. l'<~Jlj,' ,rN, . L1.l.' ,'" • .." .. ,.' .. : l '" '" ,,, W7,' v.:.. ." .,.... ". .,'. ..... I!' . .., ... " ..

, I :e ::.: :.1: :',:".;,: '1' 1::; :.'; II;: .:: ::.' ,':: ;'.:~ ""-':-"f-:~'I;II; :i·I:':!:· :;:: ~I'- : ... ~:: lo~ .. :,:l::i; ,'ill'::' .:.: .;:- ..... ::: ·1iY' .. ~ - ). -: .,r: '-:J';f' .:: :1" 'ij! ::'1' ....., til 1:'N i;l: 1!1!'1'll~' i;', .' :1' I:: II';; :::. I:,; i.:: !ll'! iil:'1 .. :' 'I: It'· '1: '" :·:':1 ' .. ioI .:. ';::1 :" ·.!IIIlY. .: ," ':;' ,. 'L~v~. . :.' iI I .. :.:: I' :'" :.: .

....., 't!.I!ni ····m t.l .. 1. ·'1 t· I"') 1 " .. .1 ...... " , !~ ~I "1' i ... " '1" ..... ,." , .. I'" ..... -,,: ...... , .. "'1j::i1~:: '1" ..... "... . "J.oi'.. . ..... . "'j:'" .. -. "" ......... ,.~.- 11l'1 I'" iii: III' Ii" ''', '.' lii l Ii:: ill! i:il i;i; i<1 lUi!1 i d :;I:,lli: iiii ;111 iii) ;::l ,i;' iI .. tlJ,: . l!:: ';::Iuil~ II;' ':i: ;:1: .i: : .'~.-f ~:.:. . {:il.!ijti: .. ' iii: iilj .ii: !lll~l l'~> I;;; ':j,'i 1"1: ,i;; ':1' I'::; ;!;; ,Ii;; ::;1 ;:~; :~;! I::,: hi' :I·il ~~:~17,·: F1il: ~nl': DTi,: iT,!il~i~'li7"0':"~1 ;...,-:J~;;;~t~~~~ ;iTI : fi!; 'Ii: 1;~·t5.?1:··t: .. -.~;,~ :;'-,~; " .:": l~fltrl'1t ::::::- :!il ::;: ., ',.. ,I' I'i ' "I 'j' '" I··t "I' ,1. , '~I ' 1"')1 1'1.' II I " I'" , .. ~'1 "1' ,1\ t.!, •• ,~.. " . • • I'., ." II ",,1.1,,+ ",I l . ,., l' .... .. "1 ill I ., ·t, '1' ", "'" ~i ., .. ·1·· .. "·,,· "" ". . .,,, .... .. " ..... ,. '''''''' . I' .... p.... .. ... ,.. , ......... , ... , .....

iii L"Ulil! pI' ~.i :i :I,l i: lip ;;p iii: l:1\ lilt 'i I Ii 1·;1: :::: :ilj~:i!:~jI#ij:i;jj:. ':'!! till i '. ::1: ;:il' !:lIIi;Il~ .. UP" : ',:, ... , '. ;.:'.: :;:i :::1 ::: >; qt. ::;1 !:~;

t

:p, ;~ ;;;; qjll:I'.'~~:: 'ij 1::111;; :qj ;:'1 ',';'; fit~h '1" tl~~ 1 j:~ W; rm!! I ~ '~:W1WP'T';~:V;~ij~ ;~'::<iu :,Iil:+t#.i: .,:: .::: ... : .. :I:~;"P ':-~I!:: I.-·~I~· .:. ?I:;~tt~'~~~:ffu+lti III, I r. i1: I i .tl Ii: 1 1: I:!'I:' I', !. II ; .. ;:.: II: I I 1: I '::' ;:. :;!. I ,;:: ':, I,!::',' 1";:' " ~ ~ . l:-.n ilJ.f ~ :! 'L4.t1 '.;"~""- I:' .;': .. I "' .. :; ,'. i: I' :: i :,' ':;.,:'::: :: l, 'H' , ••. '."" I" \1' .~ ,,,., .I tl. .... "., ,." "I . 1 ,ii .. . .. I::i; .. ""I'''' ,., ." ."~~ .... ,' . "1" .. . " ".1. ..... J'.... ... . ... , ............... ,.

;lli"!~1 . :lii P,ll ,:'~;i "1 J:!: 1ll; :i!,!::: ;;;; ;,,:, il:l 'I, :;: 'l:;l.j.~~" :1;~'li! ' '1:'; .;;i :; ~ .. ~Ii ':!1 :;' ,:,:, I"; 1':'1:::: -::~ ,: :: ':, ::1: ::1 ii: .: :~:, :Ut 'j!

'I ,j II1ILL!.!J I. '.ul:':~ 11-, ;:il I '" , "I". ' l ~~ ",' ", ~".I -'~ ,·t I I,'.!.!. ' . . . ,It· I" '. "1 ,·l .~I .,;.!.I'·'· , •. '1'1 ... --1.

~j:: ;'~ ;;:~~'Ti! :llilli'" ,:Ii: ':,'G iT'::-t!: ;~:I<": :':. '''!~''''i "1-""" I'" ~ .. : ;!~ ... H+" ":. : ... , ,"""" :;1; -Ii !;:,,;.i..;~ ''1':'' •· .. I- .. ~ .. ~ ': ... :; -: .... i: ·· .. r7:f: ''7:':'''''7 I:;, :.;, ~::; ,.1, r~ ... I.lj I" II" I "II j •• , II', ,I'. , I ~ I . 'II. &if..J.. ~I" , ., ,j, . I' ,. I' ,., •. ,.j " :,::t ,:i.ll::!i';:':: 1~1::!:;,::1i1:;:1::: ~ .. 'I·J...;.;... """""'::'" ·1 .. :' .~~. :.,1::. ', ... :. ;1:·::·:::·:·: .. ·::·:· .... ·::;·:::::· : .. :i;·:::,·::!

~.Lt ;;:: iii! !(,::: ·.!I iT il:l :l~~~;:~~~ .. i:;LiilJ::ll~:P'" ;I!;;:il~~i~ .:i;;J;~ .. U L;; .;;. :~~ .J ..... ;f~li4..:.~ ~ .. L.:· -.:~~~ j~~ .- 4:' I::! ,~!

!!!; ·~:S::; iiil i!P i!i;':!:l :1 iii: !~i:I!:J;'i~~ ,;11: ;(1 .. 'i~~ ,~:::' t~ ; ; :!~i ~!:! Li! iii! :i:: ::!! i·~, I 'I : .!:: ·:lil;, ; l~::: .' :~I, .,1 ;1, :ii: !::l·::l l., .. ". "I' ttr' .. t, 'r" ... l ".. .. £,,1 ::I~~ ,,·I:i.u \.. I' ., .. , ... "I. "" '''I "'I"" . 'f" ........ , .. , .. " ....... " ........... , .. , .. " ..... , .:~.

;::, ~ ;;:, I ,I:;: I' n: ;', j •• ' I ~' I .t-ji.i.n-;; '''1: ';; ::. ,.' .. :: :.;! I111 :::1 'il, ::1: 'I ,. " r ,! :~' ',:: ,: .... ':,. iI"~ ,!jl .I! I.. ,:: ::.: '. I U .. "~.".,,, " '" '''.,:.: ,~... .., , ... ~~~ '.' ",., .. '" 'I .. ,. ,. oJ .. ,.llim'I" , .. " .. . ...... ", .. " ..... 1. .:;'r:th"'. ':;1 i . ", .. ", '" S, *": .. ': .:.; :+~~H .-: .. , .... , '. '-:It~~~' ~:'~ 'H~ ~ . !H' ;j~l HP ;1.' I:' .. ;.+~ .~;+~~: H+11 ~"H tP! 4f~ t,!, .... ~ ~ .... ~ ~~~J.~;! .:.!.+~: ~~~ ~~ :,,' ~'H"t";'~ -:~~~ :.': I:: "/1,, "'j' I I ,,!~,.TJ" II., .• , ·:--:L~~"""'-:i 1.1 I':' 'II' II "1. "I,' II!' "I ' .. , "1' ;;j'! I PI·I,' "; , , " , ... ", ., ........ I" '," 'I I ·1;1 '.' " <I '1. i Ii t !illl:;i Ill, I !l H "I !:W'ij:! ':::I~' ~; .·Ii ii' idi ,il: lli u;: Iqii i:;1 !:j: il:· '''; ,:1 iii:; ii:! :~i: jil~' i:j! i:q :Ii: ::. : .. : :.:! ::.: ill: :ii: :.q iE. !i~ ;!i: il~i :::1 ::: .. :: iii: :i:: .ii :!li ili1dlii I Ii III :Ii! I:: ::. : "'i Ilfll' lillll~' it d j' 'iiI! "I': i!1I Iii: iil: iP ,iii ':1 iii 't' ii\ lill :1:;\ i:' ':';.; Ii:; li:::ill ::!l il:, Hi: ili;!j :;H i I:: . :;i: :;1: 1:;, fht~hl"; I,:;! :1, ," :,:: ,:r~:'::ll:::: ;;'I' i,ii! 111 ,t; d11+:~I" 1 ,'tll I' I! ,ri+'ltt:ii 'l,r,:rp','1 Hif:: ""1 ~ ill: I !111tift j'l~r;!',:' :.:; i··j~~1 :'1: ::11" :/: ;;:: ;;;; ;r:+ ,;.f1. ~j ~I:'" -' :,:: ;'1:,,1 :;'1': i I '1 1 "II' I, 'll' I' If I" I' '1,1. "', 't I ,I , I , ". I 1111' 1"1 " I! 11 '," II I I, It!" 11 ' " • "'1 '" 'I I 'I' jt·, '" ,I, I ·,1 " , 'I"'! j l I:;, ill 1,·1 1: 1 [in It:: II I :::1 Ii:: !!! li::i' I; :I!! I: : lil!I'1 iii ::1: il:: ::1: I' 1 '\ :ii Ii lij'.dli I,:: ,I:, :.:: :.:: I:; • 11' iift :,: to. jlil Ii:; It· :ii ,: ... :!; H iii ~!i' lilll,! :~ i III Ilij Iilill!!! :.i!li'!' !;!illi:, 11 :1 1111 ilii iil : ,II:' illltlli: id: iii! ! Ii!' \11· ili' Ii iii .ilil .!!! !i:: ::.: :':1 I:!! iii !!iI !;:t it!! ;:;1 ::ii Pi!:) :1:; L~~t :I!i;i

'

IlLn liP!lj'!!' il:1 I i:i l!,i.; iii! iij~ "::I'i': liii: i,ULl Ii kJJl IUlill! :!ft~!!l :i.rilL::. !i~~l~:' L:L:! li ;; tL~ltit 'i~" ::~ . ;; .... 1.il: :~~Lii ::.u1liU !:"'U~ ii;)!;.·· Ii . :::; r :trt·llt· ;!!I f' 11!1 lit ~~ r::: ~'~i :~r-: !:~Itf': It ~ I!~~ dt'f~i !~~ !~~ ::)~ n~~ irf!r~ !:~~ :~ :"'r-: i~~ ;~~~; l~r-: i:~jI!~" '::: ::': :\: t n :/ l i rtlF"'1 ,:tt I I, ,1:'1 'i I ,? lfli~ ':i: ;:;: /';1 :1'1 il Ii Ji !l' 1111! ill'\t: 'T,-t'lll j;1 :':: ii" r ':R~: ~.:, ll"~' • 'i. ~~:1 .: .. ~ ...... 'JV:J"C: It::~'~jl.; :i!! S~ ::~. ::~: ::~~ J:: ';;1 :.:-: !:'- ;:I\' i::!\ ::: l : t I I 1'1: I , ,: Ii: t' : I !.:: I. i: ,: : l'::: I'! II : I. Ii! 'j I' I II 'I:::!' , : .j ~ , t I : , I t I: .! I": '::! \" ::; , : " ,j: t ::. I I;:' • I : : ~ .ll : I: I\i ,': I l' I' .. l't: I:' :';: : 1: ·i\! !:, : I:! I" : '\ 'I' !tl' '''I: : II: 'I . . : ... 'I:: . .. ... . .:::' :.:. I:: I::: :::' :: .. I!:: .:.: I::! '::1 ::: ..... :, ." I 'IU' 1 , , " 'I' ,I, '1 " ,., I .. "~It"." , .. , .. , I." II, 01 1 II i'll ' ,,' I . '1'" . , " .. ,. ,," .' , .. ,.\ I ,. ,,, .,,1 '. ".,. '. I' ... ,. : .:: 'I' .,' L Ii::' ,'Iii;: I ~' ~:I' P'! ,~, ,I', ,':: il:i 1 ~~ Ijll '\ \1 Il.l JI' I. II l~: It!. ':1 ;:;:~;;d :1 :!:: !! :':1 '" I ~ , I::. :i:~ t:: ':,' ::1, ':': !,I; :::IU': , :~' Wi ~.'

.. - Wif+i+i 1+ .... l.I..h \ .. , .............. ,; j"I, ,·tit·· , 't ·t" ' ... j ........ H I~'·rrr.o "r 1''' . ".I " ............... ,+ •• ~ ·-Ht~· -- ......... _+ .. _. ·'1 :., , t , ! :!! : '! : 'II II I \' : \ I .1; : :, :;::::,.:' i :: ': :, II' I ' : " : : I ;, I : 'I!' i i .i : .. ! 'I :..',:: j' I: I i!' i; .: I: '1::' . ,. 1 '.. I . : : : .: ':' .:;: : . '. I: : , . i : . : . .: I .:: : I ; i l : I ! • I II" I: I ! I ::.: ;,: . I. ::,", ,:' : I' : I ' ' .: I I ' \ : I ; I I ~ I I I'; I : ::,' : I I ! " It:' : I II ! i : .1 : ; '. ,', : l : i : II • ! ~ I :'.' .;:, : ; • ' l i: l , !

." .... , .1.. I, , "~ .. ··U .. ·, '~1'1.:·.' ';:;jf,i. "" "I ''1' II., , ", "II, " ... , ".,. I,ll ". "" ,," .... , ... , .,. ,," .. ,' .... ,. . ...... .' '," .!." '. , '''I :1', ': : : 11 1\:'1:' ,r~iI' . ,.....' I:.c.- I . t I ill, t ::1 :1:: ':t\ ~:i' :,;' :; .:, ":1 ':1 I;:: :;:: :!q ~I' '! '..I :: ""::1 iii:.: "'t ! 't : l .: : ' ·l:l:! .• : .. 11 J.a· j;." !;w.i. : , :. ,,': .LI' I;:, ., .'. I ," .'! .. l;lJ Ii:: ;'::: , .. :: . i I" !~: I'::: .. , .. '." '. .' .

1 f> • :~, I •• In X 10 ro TilE ,[NT' Me rrr~ 46 1513 I{j I If I I I. J, r •..• I P r. (l ~·A· , .• .,. 11' , il'II/PI \ 1 li':11 !,ilii ;:;: ;'~:: 1. ',::: ::I~ :1,' I,:: :i. 'lid !I'; 'Dll ::11' I:I!; \:' .. : I ,: >::, j: I :':: , : : iii,,: ::1 I ;;11 ;::, iiI: i:: ,:t ,; <Ii ::;:::' li:: :ll :::1 IIII I I I' 111111" 11,1 ·,1', ." F ,\ .1 I ',! I"'" It" '11' ' "I ' I ., "'." •• ' ... I I' ., . I • , ' I! 'I I" I' '11'" """" II , 'I"~ "'1 t' 'jll .It I d· t t, I' Itri It 11 I 1IIIi' :: tl:t ;::i it" ; .. : ,"; :;11 :::1 ':,' 1:1' IIi! i ," il 11': ~";' 'I" .::, ... . ,.' , ... il I::' .:: .. :': : ';:1 i';' :t i 1: ii:j !'Ii~ ;:1: :11 ' ;"I F:' :~'i I ,: l'li t;:1

t H

I ,,;:', III tI: I I. 'l;i '1"1 ,1. ':1. :': : 1':' ,II~ !II'1 .::: ::',1 i'I!: ,Jill Ii: I: I: :'1" .:i' " ~;.,r I' ,,:: : :1 ,i" :,''', "I, ,I:: '; , .:" :11, i'l ~'I"; :1 :;Ii ,II: i'I!' , I' d;III:: "if H '" , ,,' !I' tI, "" " .• " 'j.;' 'i'i!' "f+i-:"W' , II;.!' j " ., ...;~~I.L· .::Ic:l··" " .. , I: ' , ., ",' ". " ,. " .. il 'I "., . iii . " pT! n" ll1i II' I'! ·1' '~l H'II ': . ·n: ~:. :: ... ~ 4-:.: .~:: 71 ~:t::~ :i:~ :;'; i, t ;:,1 :1'111:[ 1 r I:,. __ yo ~..,.-....:. ':;~i! :~;, :~--.... -<-:~r;' : 7, 'J:l 01 : '~!: 'I', :!:' j", ;;I~ .:11 ',:1 :;:; ;!I:I!'j i::: !lnldlmltl:I::'r,lijl': 'il'ill!;I!:"".::. :::I',.I::::'::':':'I"I:!:I:'ll"::::.!';!' ~ ,. "'il':':";: '.!I'·i,I'::I';:I:;:::.·:;::.::;I:·;::,:'I":!;:::' d .. t .t~ .' [ttl It,l ". I r t·, l .. 1 ... ' " ...... ,'" .,~I •.• ""u'" .,,' I" "" ,1, ,,, d·· ,. i. •• ". ,." ,." ,,, " •• "., "'" I ... , .", 't' ... , ......... L ..... , ll~' - .. ..

ilP !':: ,':! :lil l~ 11 ::1 p.' 1'\:1(: ::!ii::': :,': .:; ::;1 :- ' :i,' ::i: "i: I!I: ::'i ,;:: II: ~:' ; I',: :: ,::i ;';' ,:: ,': iii: '!J1 :i:i :::. :::: ::- I·:;: ':i: ;:;: :1:; iii: :'11 ;:u Ii ' ,I .. ,;j1 .. , ,., I" ... , ,.. ~ '!!"l. ,,,I ,," ", .. " "~t I,W "it ,I·, "1 ,. 'I' . , ,.,. ".,:.. ." , ''''HI+.1 , .. , ... ". ". "" .,., "I ii, ,. I" " ..

••• I .", ,I I , •• ~I I! "'" "ii' -- ..... ~ .. :·· .. r-,O-t, ~t· ... ':--; ~~ I .. t-~ ·.lll' ~II -;-.0., t; .... ': -"~.. .", .... '~'~ +4-ti 4-~:-"":~ i~--r.:---- .1.4-. , ~4-~i it~ .• 1 ;t-:. "" -r"" ,\ .. I "I' 'II' I", 1 1 .1>,' I, •• 'I'II'I'I~'" "1 "" I," ,'" 11,_ • ,." '", ",I, '" , 1'1'1' "I' I I" "."1,,, """ ., ,I , " ,.,,, '" ,. " ..... " ':1 "1 !t" .,1, II! "I"'!

1" ::i. I. :~:: I:' I I : 'I i ilJI:1i 1: :.': :::! 'I'lt : " ' " ,,' '~ ,I 'I '.,1 "II :1:. ;,.: . [I::: ", I;~; ,I; .::: ,,,. :, : , : ,: t':: ':'1 I:: :~:, ';'i ! ;:' .!,I ,::~ 1:1: ;'t :1. ::', H·" I "1' ,.l 11~1 ,1'''1 J, '1'1'" ............. ,.,.. 1, .. 11 ""I .... ,., 'I "'1" ,.,." .. .." ' .... " .. " " ..... " ., ,. , .• , .. "11 ., .......... , .. 'H'lI '''1 H" .... rI"f! .. " UU ~ , ;;:i n:l i:! . j; ,11 'II! Ii'i:d::: :';'1:,: ;:,:: :, dl ,:11· :: i': :::: ;ll! :111 II:. 1;1 ~';:I,~ .':: U:: :::. :'li .':; ~iti ,:;: " 'II: I:;' .; I l/i :: .:!: ':, :;; :!i: Ii!: ::::! : ;dl ;!I~ "t' .. " 111 l! .,1" Iii, "11.(.:1'·.1.... "" Hl"'l'" , .. I. ""I' I, I,," , .. q ." pJ."':l ::",,:!: '1" ",~."" "I .... , ,,, ",. ,;i '''''' .Ii~i, "I.

Ii!! :, :t.,l!i,l:" "I: : IiI: III, ":: :~:. ~:.: ~4-:, j:t:'1 ~~l .::-: 'r:: .~.~ ;1 ; ::tl ::t1I~4-' " .. '; -'t, ::i' ,:;, ;;': ~;;rr~ ::; it'· :~:'I'~~r .:~ fl'T ;!l! 'I! '!! ::': :;~ ,II ;;:11:11 :!,: ~::. I I! ':11 'il:: 'ii' ':11' ,:.1:'1 I I!: Iii: i: ::.' .... I:,: ::1 :'" .. ,I, ;:1" ,:,' .:: t' , ., ::' ::' :::1 :':: II i :,' !; I .:;: II;, :':: : 't.. II;' :111 !" ,I;: :'" :::. ;Id .i· '1'1';:; ,! 11::1 :!;:: 'III:!:! flU :j' ::1 ,I Ii:;. ,'I': iii. ,,' . ; : .. : ;11 .:' ., ,I;. :::. , .: 'i'ilktl,:, . r? ,: !! :,,: II:' ': ,;11i 'II :tjl 'il I':; ::.'1' : ::!~.I:I :'~I~1 \:1 ::"W':: .:: ::i: :!,I Iii' iii: iii, ,III ~!:: u!.;..:. .:..:.u lIiI .10 "" "IIi' , .. '''1 ' .•. ,,,., '11 ' ',' ",. ILl, 'u '~j,i' " .. ,,,, 'V"" ":Ui.;.w . "'t-!-! " fl" 'i!j. ':L 1'1-:.41-4+; ""fi..i.' LL' .. 1,,1 " ;[11, ",.

Ii::; 1~:1 1t!1 :iP i::li::::';: :;1: !::: I::: ' :: ~. ~ .. : ~~~~ '~rr :~:: ,. __ 0 fl~' ~:~. :d;~:~; ~"~:' ." ::~·I·~;! ~ f::: '~·:I:::; ~:;t :.H 'r~r i" :·~I·:·: ~l,j IF -:n.I:!!! :!:: :;:' ;:1 :11; :i! ii" :1·: :tI~ liP i::: t ,.J' l~.'!itl. ''ill'" 1'1' 'l '!I'I j" 1tll .• 1 , ., I. t·" '~" '~ I' ,"" ','. r \1"1' 1'1 I ,I '. '" "tl' '''' I'" III !J' 'J' "" t" 'I' ,011 •• tl It., ,II, ",I .. d .... ' fl .. "" lyt .. ,. H' , .... , ... , ............. " •• " ........ ,." ., ............. " .... ,." •• " .. " ••• ''''·· .... 1·'' , ••. , ......... ".,. .... ,." ..... , '·i·+· " t:;:· :;;, i::; '1 '~i"t :' I;:: :::: i::, .::. [',1'1: "'i ' '. ;',1 ~ . :: '\:~ , '. ;: : : ',": d: ,;:1 ''', :;' :., I, I " ',::' 1:· ::! ;:: ,::, ':' :'111 ,I: :1': .;:: .t . : :i :1" ,... .." ""Ii r;" 'd' I'" '1"1;::: " ., .. " ::U!;;I! . , "'" , I"" " , .... ,. ,,J ""'I ,.... I'''' . ' .. '1 .", . ;! .... ', .11 ,'" ... ' .,' ." .. " :::' , ~::: iI':~ ... '''I~ " .. :' :,:-:-m-;f .. ~~·~r~~ ~4+~ .~~ :~~ .1:, .. ~~' ;1- :!-H1;1:. ~L·1'·;.;..!. "" :': ,.: .::' L~;':u.;. ~. ': ," ., ',":", " ':11.Jlilii,· ':'.: : '.:, ' :' .:" .: . :, " .

CI1 , ""I~~ '1'" I' 1"'[1" W !"l I, .. ,,/1 .::1 .• , " .. , I, . I' '~~ "t '1 • ,,>, ',]'11 ... II '. ~'ItJ" '. ,! ,~i .'I~ ,I ii'I'II'I" , t"l. "t .,/' i::::~ :,;: 1.11 [W" :,' til :::: I;., . ::, .... ,11':: ,I, '::' .. ': :", "il ::' :, ::', ·t: ',; ;,': .:, ~':: : it l,l: I;,. 'II l. ' ..• 1~!J4 ,;; ,':: ~ <I:;' :11' ",: -..,J .

..... :~ ...... t.+, t .... " ..................... , •• ,.. . ...... '" . • .. " .. " , .. "'1 " •. , ........ , ... '''' ... , ...... ,. UJ ,·I .... ': .. ~ ••• r- ........ ~ ...... '''1 ~ ••..... 1-: ........ ..

J.i:~ :::; il!; i '~!i ~;ll44~:~~:: ::!", :.f ;:+:;u '; :I~" ' ,dl :!J ;:; Ii!: .: t·: ~J,l:: .::' ,;:; ~i~ iii ; :; l,.u~~~itli;MA$.r:!~-hQ· ., .. ii ::i: :aL~~ ~l .t' ::~::I'~~ ::W :!i: iHl::; ,'ii' iii: '::i Ie ~1'7~' '~~II:':: ':11 ~':!I~:;~' ,: , :i: :n! !:Ii ::::1(' ::':I":::~,:: (; '\ F ::!: ;:!: -~~ .; ... j ,,[:I1L~ .,:; T: .:.1:;; :; .. 1.:': .:i:~: " ,;;, :.:, :~ ~:;~:~,:, 2:T1ilii~!i; '\1:t! lH/:: . :f" : ::1 :; :dl(U~' ~ ·· .. [:lU i:ll :::: !':'IJ!:' ;: ';::11 <JU ::,~ ~:i: ::U in; .: 'j:. ,I:.:: 'j: :I,i.:li ::; " ,:~.,~. :::: ::ii i::: :··w: Jiul::: u ... : :. r::T: :1. I ;:: .o.:1r;;:r ::~·I~· ·'::i··_· ... ··I .... ··~·;.l7: :~::I·; t :>~ : .. ;: .:~> t·· .. ~-~I-'"t: :-:-:--. ::', ... :.~<t ':; ~ ... ··~I--~:- . ·ql-~ .. ·· -", -M-"~ oM; : I : 11~': r-: .... ·,.:,' ',::': -:- .J ' .,~,;;: "~I. "j'" '1',1'" 'j""'" ', .. '~" "I"!I' 1\,.,,1 i'" , " ,"., I'll If , ' .", ,. ",. , I ,.' .... t,., . ":~"" .... ,.'1 ..... ' ",I', ,. , I"~' ." "",1',,, " 'I I" ,. ""1' ,. 'I' ,. I' ", , •. ".,.. 1,·1 •. " ..... ' .. " ... ,. "" '. ,., .......... , . , ., ..... , , . .,..., "I"" ... , "'1'" " ....... ,, .... " "I' .. ,.. ., ". ,. "" .. t· ..... ··1 .... "','" ............ " "" " .

· • • • • I ,... '. I I " , I I • , • , '" I' " . I " • ~ 1 .' , , • , • I " , I " , I • I •

,.' 1:~1& ",I. t . ',"Il 'I '\ 1 't • ", ,I '" "" , ,I I "', t' l' t ,,, ." ,.'

.;..:1. ,_ .~~ '~:: .:1.::: : ... j.:.: .... : ... ~_ .. tIj<' ....... ,~ .. 11: ,:!:(:: !:: ... : .. : ., ... ~ .::: ll~ .~~: :L .... ,,~~ ... \:.. ,........ :: ... J.: .• :. :-.j~ .: .. l ... . _l . .:..... ·• .. I..l:·~':.. .~.

. .'.,: . .., ; , i ' ", i: .' I: ," I ~ " I . , . Ii· 'l I" I . i .:' 1

.. 1 Wi:. ',::. ;:: I.:. ::: : .. : :: .. ;, .. ::, r@,.[/).'i"::::'I·':::::ill"::'·':·:"'·'\'·';'::"::':'·1 i !: .. ,i: .. , i···· ! .... ;1 ... I·: .;;: .!'~:: rH;I;~:i.ij:" '! ,:~,., !',' : W' v: :: ,::. ',~:1 '.i: ,"i ::' i: . I; 'I~:; ':;1: ; :i:' I ! I: .;, , ;, It ,: ,I t:: d J .. _,;.~ .-.ht~ ..... ~, .... -~ .. !-~.~. .. -j,~~, l ••.••.. , ... ,\"L ".' .. c ..... t ......... - •••• r.-~ • .... -t.: ........... ,... ,.. .. .. r .. ~ .. t.+ '-' ._ ................ -t .. · · .. ·t·· .. ~··r·-· .: .. i:~· . :>Ii:il ;il:iU:i .. :j idJ :i:.'~ .. ;~.:'f . ii:.:!i ; to "':1 iii ii: ,.!:: '1< , ! ::··f: «L ::.. I ! ':: .. >j :.. ·I·~·· . !. .J:. 1··: ·.·:1· .

,:; :, :t,!!i1qUii1Ij,:i. iii! !~: :";W" i, 'i~,:l:; li:: ,.;~ :!I! ::d ' ;!;' : ; '.: ':::; ::; ::~i. L ' . , 'I ,', ,::1 :~. , ,.:: '.:1< I:~': '.

. -... .. .. ~i.fl~rL! ;~ :J.j.!~~~;;'" ... f: .......... ~; .......... " 'm ....... 01 .... , ...... , ...... - ... - ··8·_· .. · ... ..... , ......... , ~I-"~' ~ .... ~7'"! .~!- ... ·· .. t- .. f~ .. ..

'.~ :.' :fL i:fW.:'Qi1 i! :PI i:;:y'~ ,I" '!l1 ,i >, !;:; :I:!;I; ;;1: ' :~, , :: '." :: .::. j;:; i!: ::j~ . ,: ::' ! ;'" :I; .:.; .;. ::'.:. ::1:: ;:lili ' :! :;:: ::' .. ! . ::1'::: ;l,tt htl ::'1 'I rl l llG,l't2:' ,., ,'" :': ""1 ::~: "I:; I:!: ;,1, 'ill: '1 :' 'i' :':1 "'1 ';:1 :':: . :: ';:0 "1' :'1: :: ! :: : .. ;:1.::, .: ......... :;., .. :! :: ... ,. p':':' '1" .. ' t .. J "I Ui' '""'~' , . , ,.,,""'" "" "I ' ",. ".. ",,',. .. ""1'11'" .". I I' ," .. ,.' ,. '. "'1"" ,. ", ...

: . I.. . , t:,: 1 : I;! I; ': ~ "M ': ',~ : I .: i I :: ~ Iii, :: I' ! d :: ' : I'j , .: : I ; , II I :::, Ii .: I : i i: ,i I. ,,: I .,;. " . , ~ I:: 1: I ,; I: . ~, :: ' : .: :: tl f:: : i':.. :: :::::' ' .

.... t-. ........... .U •• ~ ·;.t:- ....... _ .............. H .... , .... ' tift ,tt .... ~ .. t , •• ,I ............ r;r~1 .. ~!.Jl.:~ ............... '" ....... ... .;.;.:.. .... ~. -- ·~l ~Jl.i...: ., ,::' I:::' :,:,jil': ,;' :::,' ,: t :1 ;:;1 ., .:,; 1:.1 :11' '1'1 j ,: I • " I ! :t,j; ': I "'j :!:: :. :::, ,'\ ;i :;, '::. :: . 'I !1:' '\: . '1" ;': .. ,, ~. : " ! I ,: I,':: : II ~ : I , ; :; :: '1' , ' I ',; :' ,~; I ' .' I; II : t I: 'j i !: ' ' .:; I : ; f 'i':!:! i :: ,:: I \.: I 'I:! " : " " . : : . ' . ! ' j :: t', : '.. ,;, • : t l , :; :::: ':: i I :'!'

.. , ... ' .... , .... , .. , ' .1 I... .... ... ,. ..' , ...... ' .... ,'" .. , "I' , .. ,' . " , I"" ,.,." .. , .... , ... , "..... " "" .... ", ,t.. " ...... , ............ " .. , ..... .

. . I I,; :. : Ii: i: 11: I ',I 1 : : : I 'I i i !' 'I': !, , '! ".! :', !':! . ~ I !,; I 'i I " ; :,:: • I : I I; I ' I:'; : !: ' , ' "; I : :: :.' : , ' :, ; ': : .. I·, : ! ' :: .': ' : "'1 ... , .. , I" II": I·" " ,! i I ... ". .., , ,"': i , .. " .. " U· .. , ':., .' . ,., ... , .... ,," I! i' . i i ,." ., ,... " ",.,. ,.,.... .., .. : I'" ... ,." ..... , " 'i,,'j "Ii!::~\~~i :~~I'.a .. .at :~~I&.~':~;" ;froi:i;'~ !;~ ! ~~,. i~~'I~";!1,4- I u..; '" ,~~ l'~~:ll::~~~ !':~~~:'I:~i'~~ :·ti ... 1""""\1'" ,ll, ,l'· .. ,1 .. ,. ,··1" . I , . 'I" .. ' "I, 'I I, ,I I ' ., ,,1'1'" "'li 1 I, I· I· I", " .

......... .... • t •• t· t "t · .. ·1 .... t'" .... .... . I ,.. ., .. ,. 01, ... , ·tl'· ',..... .. . ., ......... ·' .. 1 ......... ,··f ' ............... ·t .. · ....... , ........... \ .... -.~ ..

::';'1';: ;::' ii!iil'dlijil ::i :!i; (:,:'.: I':'! ::,; :;':I'il; ,i', r' Af':" ,: 1~~d.Jiji-h ',:' I,.,) _L I .: I . I. 1\::1' .. ;' .. :11 .';: :::; :,:,1:,:, : Ii ;':1' ::: jill,:::!::.: .. : I .:: , , : .. :::. I,:, 1. 1 'I 'I ' O· v, .~U'C: :., i fvaH~ ;.:, .... 1., . " 'I " :::: .:: · "1 ~.: : . ~ ,;:; :' I: '; . : , " :' '::. ':.. : : I, : "~::',' , 1 ' , ' .: 1 ' : , ,. I' . I I : .. , . : : •• 1" '''''i'' ,1" II, ".' II tl ,. I , 'III 'I"!' I ., I . I I, ' .. 'I ,....

:':'i;;:: :":I':!:~ !i:: 7tP .::;. h:+::~: :;.;.. ; "'I"; ... :1. ... 1;,'.:1 ':1":' . .. ... : .... : ..... ;; .. :. ! I· , .......... :... : '., "','" : ......... ;; : '.' ','::: :!::::::I: ':::: ;. t.: I':' !" . I ': I " I:"! . ' , 'I !! . ! i .

· ,:. '. ;:', ';::!i!;~ir.' 'rli IIM~ I~' ':. i' Ii:" I . : .. I" i' '. .• I ,.

, . ; , ::, ~ :; 'r. ~.l:) uM . • 0: ~ ! .. !; i ) I ! I ;.! I !

t .,.

\...:. . .i:'\ .~~-. ~~- ~-~ -~~- .----~'----.-------- -- If! x.". ' ~.1 ,n X ,n"TO THE CENTlMFTFR

~ I III 'JI Po ',-'.F R (, (l ..... ·1 ,,,. II',", - 46 1513

:11: !l! :j !i::I~! 1 1I11!!1 Ill! ~l! Ilt~'PW .. ;i ,"i!bW: . :I!;:j:~ L : ;i:: :;:: fld~0TI~irrm!i"'n,' :r~ :r.rrD; :::! :i': 'TfJr~ '"::~l~:- :~-r-~ -~.; :;" '11i ;i:! iii iT!!i: :[1 :::; T !: .

1J . t:: ::1~. :: ... . tn;. ti ~tnl I,. lila~' n":·L!..:lJ·· 0 .. ·· : I::' ~"j'fE' .\:. : 1: 'Ill :i: ':". '1<' "It:: "tt"~·R;.i,iL'Q:··l1IE::il:::: ';'.: , .. ": ::: .. : .::: :'1: ::l: :'!'I :'II! II: ... , .: ".

"I'!" ..... :,1' ,. 'I'" I:" ... . I" "0" '''' "1 [ 'I' 'j' ,. '1'" I" I' • 1

h:lt···,+:· f+!1:~ll~'++':i-l" ;1' I' . . l"·lI r . !' J ,;1.:,. !:, :!U .:' " I.' ! ,', ~I I :,1 11: .:': 1tH :~l! I:i: " :' r. -. ~j" '~I~~ . . ,;, , ,0. •••• .,.., .. ~ " ..... , -- ......... , ." ....... + .... ·.t ':-L:" .--I- ... ;.;.~' I : :: 1!' jll: j'll: :,'i,' \ d 1:1, ~ ',r. '::~ I " , ... L- .. 1~. ,I:, '~.' ~ #lI g'l, , I'" I'" I' ,1 J' ;1,1 il:: ':IT'" : I :,' '\ I' , .

... " ~:'" ".' ,. 'fl'" !'!i 1"",·.... .~ .. 01" ...... -. ",.' ~ft lit " • • ,,' ". 1 . 00 "1' ::,' "" "11 II I .,11 .. ' . ' .00 " , .. HI ,., I, J ,., I'J~'" I 1/'0 ,',' rj r;;. " I"', I I, ,I, "1 'I" \"" "," t.",. '"'' U .;: I' .~!. n: .''"1 It:· f;:' .:;:~ .... ,..,:. :":.: ..... _r I'.'. : . :: :':':" .:; .:: ':'.': I' ' .. ; ~.: ... : :.iI in::" "1.:11' .:!. :'''1':'' ".; .:.

d:: ~' ll'! I 'I !:IJ: I ~I ';' .. ; !~:1 .',. ':1:'.1: I': ',,,:,. :.u1: :": ~',:, .: . I ,,':: I:;, I: .;:: 'll":": " ~ ,I! ' ,J I I' 11,,\.,,.,, .;'1 ;:: .... Ii til. I ,·11. I I I." 1101 .1.... ..~ .. II ,J. , ..... ;0 •• '11' .,1., .. " .. , ... , ., '" '.' ... , '" ,. " "" " "B/~ I#JCH 9'IoIS""t.A .. ..,. ... £.... ..:;]1:::, ' ~ . pi .' . II ....... ".-t '11++ "tt ........ +-H_' I' 1 ... '···· '4 .. _., •••• " •••• '.- ,,- .. - ... '-' ~ ................. ' 't' .. ·... u r, "'."Fr· ... • lr:-=~ i i 11 li!llj:! Ii j 1:1' : l'li ;il: : ii I: II!! I: :::j' i!:! ill' j')'1 ~:i! II) Ilil!! 11 11'1/ iii 111'j: il;; :;;: ;;I!! iiill:l!! !::i :iii '.il .::: :~::: .:: ': ::! 'i: ::1 ;,1: :::1 !!,itll.GU1UU'I~1 tJlillJi,l t~P~!I::! :!;j' u 1 rt + ... ~ ~. rt t +, I 1+ I I ,,~ tl'l '1 IIHl "I' t tt ,H t I I II' . 1"\ 11 ,1 ,. J I,l~ t·~ !'I~ I'.· ··t' .,4t ,.,1 •. " , ••••. ,' II" , U-4:1 ,,~.tLi 'ilf I. r:1:!P ,,~ .. ,

ill

:li!l Ii . III I 11\ I i Iii Iii iii I i.!ilmi!ni'Jlj::1 Hi! !iIi ::i:'iU; iili~ I H+l" 'nl'l!!i: II,· l:j! i:'~1 P!i~.lli Ii!) :::::!1 :i:: :;:; .::, ,': :':: :::i iii; i ! :::~.t.~l!:ii.'oi;..v~~i' U-I'If/Arit!:- ::i/ !!, • I. It' 't· j~: 'I :": '~+H- T ~t:~t~~.!4~· ~ ~t+1'~+';';l: .±~~~~::: :r!~ ,~.~~~~~ ;H-f'H~~4'~"'I.DlT;ltl+~:trf~ , II' ~j ,::. ::: :~ I I "Il jll J ' 11 I II II I 01 liP II. "'11 ·ill ·1, tillllll' 11111 iii' ,I .. III.;' I", III. '1'1 dl. I, "I' .. , ",' .. ". , .... '" I ' 11'1 .... III' ·I·ll.·, . I'· .. ·!! .. I l: I 11' t' J I • It II I " 1'1 ,Ii,' 'j'l l' " • I' i I· .::, i ., I I'; I I : f i' I :,: 1 :: I i,'I,' :)1: 1 1.1'1 . 'I :: I :. : ,'.: ,::. :" : I ,:: I II:: : II' I:: I ::; I :". I I 'II Ii 111 ' : 1111':' :.:. ;;.: :: Of :: Il' ,1' 11' fi' . ! '''' "I' , I I 1'1 ., ... """ • I.... • ... ' ............. d.. ••• .. ..... ., ............ I 'Ii 1" lO" .... "r .-.

r! I;· I'i: I':j :: i Ii :Iii .. ;i I:': :iP ,"I .:, lid i'l' II" Iii' Ii:, I;:: :J:! iili' . :i i:' :li: I· :1:, ;:i':: :: :.': .::I,i::: : I': ii' ;;:'11';:; ;!iJiiJ/j: i'; ::. i·: . I:;: ',: It I il'li Ii il I 'I,t, ': t II:' d.; I ';' ill: I:' lit I 11,11' :1': :111 '1. I' tI, :1: ':1' ':': ';';).1': ,::: ;.;' ~:"II'" ~ , il:' iii! ill ill~lll 'I ",~i;':' ::n ::'

~ n

,·tllli;! 'Iii I H+! 1 J' II ::'1 iii: i:;i '1'1;; ::.:,:::: :.:; i!:: ·illli':'·: .iii:'.1 :ii'; ,:'1 : :'I'il ;:;1" , ';"I':'I! .. ,: iii: :i':';::: ::i,:;:: :'1' , : :',' . ,;;" ,ill: :: : :: : ;i:' :Ii: iil'l :;11 ;;i;: i. ,,:i,:; I 1 fl:!·q 1 L . "1 "'I 'P'rri't "'w"" .,,' ' .. !' ·'1' ... ~j.' 1"" I I 'II 'III" 1", ':";" :'01 t.:, ,.I! "I' "'ll~'" ,. . .,-' , t, ,. , 't' ,," ' ... ". I,',', "'I",, l .. " ...... ,., ~ . I 'I t :. II" i~Uii! ;/., '1!lljj:: ~!. ::t'l :l:: ::,: :',:: :i:: ::.! .::: :::: ,'II ; 11 HI Iii 'II: :1'" :::: ':,1 :::i H:' iii: :'·i :;:: I::: : .: ::" ''':,''': ":: :::: '.11 :::: ::" I::: t:I't 1"1' :'1'1 :::: .:.:\: ... ::::',' 1:t i 1: ,:. i!! I lJ..' I; :1'1 'I'i .. :: ,i;i ::1 ~:;: .::: j::j i!J1 :.:' .:;' i:;: 111:' ,~1:: II; !:' j,:' ::;: ::111'::1 :::: :4:: ~;II :':: ::;: .. :: :', .. :',: ,'; :;'; ::1: 'I::: ::'; I!:: :ld l i1liu :::; ::. t~::· :::: .. :: l Ilfl ' il iii ~. I . ,., "" ,oj • ...J ·.It "!.l..~~ . , It "1' .... ,iI "., t ill I ' .. 11'" "" ,.I,,, '+-~iiff· ."; ~~ '@"~ 'i"· ',' .,. ., ""' .. ~~ .. I , .. ' ll" 'h+ Ii:!! ,,,I !)~. ~ .",

w

~m ! H 1i l lil:]j llu::'~iijjl ;~ I j'jji ill! lilll ::ll F Ffi jT :lL :m ::~: iT ;[j; 11! jli~[ 1Dl ;1T in Tf;m )l Uj rG; [iii .} ;;:; .~~~<:. T: ":~:T iT [fli Ii:< l:li JIL 11 I jill !ill :H;;!· Uj :T l l 1111 jj'll PI. Ii '::; I" I::: !ill i:'! ::H ::ii U :w ': ::J! ::;: :::i iii! liji :1'1 !iii i!! il : ::,: ::ll H jil: ;i;1 ;:;:::: ;;:i ::i' .:. ;i:: i,:: .i: i' ;: ::1: ::i: :::: '1;:: ;'il ii :1/ !i:i ::: ::: .:ii :i;: I 00 . II 1/" , 1I ,.. lilj ... lill ,.1. '''j. iLl!.+.:.:.·1 I Sl' .... 'I;';'~ 'Wo' 1'111" • " ,1',;, "ft lhll.U..:1.";·' ' ... "" ,.' .. "'';';:~'"'' 4.' .", .... ; .. !i,lil ' ;11 '." ." ," .:1. , H 11jm l 11l I: j; il!! I :!!i! IWI: ilil :dl 'I~; ~;'j ::.: ;'1\ ~:;J ·~:;I:::: 11:1 I 11 i I :i:l ir:: rf;; 1;:1 ;;1: in: :r1P:·F-;- :Tt; i:;; ::::.r: .~:. ~:~ ,:;; :~.: ~t:; :111 ~::I :~:: i:;; :1.: I!II ,ill! 1:;:~:; .!: :t;' :::.

It't I. ,t!. " ~dtl .Iit '''I ., J 'I Ii +I I 11 Idl H" ,I ..... ". "~I, ; .• , 111 '~I! 'I" 1·1 , ., .. ,' .jll till .'1' ,d .. d. ··1' ,.1· "'I'" "1' '." .,'; \'''' . ': ,I" ," ... 11' 'II'!!] '1'1 .,., ," '"l'·· 1 l 1 ~hP • n, l'i lW';:j Ln " 11. ::1 I.:· :!'l]t:.:: ::.1': ::" :;:, I;:: :il'; I : :11' :f~I' :Ii: Ii.! .;:: :,:1 ::: :;:1 II:.: 'tl.! ,!.:! I::: :;:: '.:' :::: :,:: I,,; ::::: ! I:: :::: !,:t;: I I 1 ::iI1 'd! :::: :1:: :;:. ::.: I. ,I, II' , . I· I't ,. I 1 ., \ .• ,' 1"1 I •. t • ", .• ,,··.1· 'II' "I '1" 'I'· ,.1, -II I"~. II'·' I ••• ", ,"~ 1," " ... " .. I", 'I' "" .. " tl'. '·1" 'I 'I ,.t , .. '"~ ..•• ,,01 j!:: li.u ;:\ • .' ., • I:"" ". III' "I '" "'1 ':i:' " .. , 'I" . . .... , .. " .• 'III . 'lim' .. ;0 ,." .. ,' ... , "'I ;.' '''. ," .... '1:: ........ I'" . '" .' I· .. · .... " '''1 ""

til

;::! .. !iJ ':li " ".: ::. i;', H~~ I ':::: i~HH+~ :~~~ ~?~~~ qH Hf."HI~1~ j +" 11f. ~~~ +~~~k*~~t ',:: ~~ tm:~' ::;: :::: :~lli: :~~: ;~.~~-::~~.~.~~~~+ :.:~ :::: :::: :1:: ~t+ HI~ ::, :::: :::: :~,' ~++:::: 1. I:"; ,.!! III '" I}'" lilll 'II II. I' , 1\., .. .t I'" " .. ," I'''' 1. 1' '1'1 'ii I " I 'I' II"""""'" I '1" "I' III II' '''I ........ "" , .' '" ''', .. ,: II ii' ... , .. " :) .... ,,, IIj I . ·\i! \, .. ,'" ". " ..... .

1: !:1 I:,. jill II 11' , : ,1 IJ11 1 I to! i: J 1 11 :1:1 'i:; .1 ::1 ':l~ :'.; : 1, ~ "I :;! il:: lit: :l·: :1'[ :.:. 'I 1 1 ,1 :': ;:L ::.: :.:: ';:. :::: :':1 ; ,: I::: ;. ' 1::1 :::: 11:1 :'1: 'II :I~ ::: l;:: ~j:: ::!! :::: l It' ;;0., "H 11 'H'" ., t~l· I .". of .... I ., i ".. .". ,I .. "ti!! I I , .. , 1'" .,t. '.", dj' 1I·lt ... ,. i." . .1 •. 1" "" "" .". '"'' .... "iii .•.. "'" •• " ... , .+ ••• '-" .... ":1- ..... j ;j,I:;: 'Iii , ~ " ::1 :1111:; 111111' :::! J:I! jl:1 :!t,~: ;::! I'll :I.!; ;1 I ;:~I ;:, tl: :1:: :1I! '1'1' lHI ,II! 1!1: ;;'1 ::I ; ::1: .:., ':.; . :: ,:.: :1.; :\ j :1:; :::; 'III :11:; :1 J;I:.: .:: ;:;1 :~:: I ;il 'I" In:li d Mi' I I" 'iii Ii " 'tl' ... i II,. :j)1 "j; ,"', -+* "t" ill"";"" .' "" "III' 'liI'" .,1· I" ."" ." .. ,. "" '1 I .,,' 01 .. , ... " I' :i: II"'" ,,,. ",j .".

iiill:ii iii: iqj j' i; 'lli" I; :!.' p~; iill III iil\ i::i i:i~ i::i :ii: : i1 ~t :! i: ~tjf: ! i\t: rtfl :tt:1G~~ m:l:nl rittt n!: ;;ij ::ii iff :> /: t;~) "1 it(ii! ::~i f:: ;i;: : iii il' : Iii TT:~ :i:. :;::~:::: - ... ~ I .... !illi~ I 1,'1 ........ tl .. jl ., •. 1 .,,' , ... '1" ,I, ..... j .. I ... ,1, ·t'l 1'.1 II.. '.'" 0;" "q ,". ·'·t .. , ... , ......... , ... 1 .. " "" ......... , .. d ....... -' ... + ... ,. , f .l~ t ........, ... , ... ..

::1! '! ::1 tTIllt .:: 1.. ::': ' !:: :;11 1::: ::.! ;~l. :~: :::: Ill: it:: ~ ~ ~,: I;:: ~~; 1: ... ': .. j! :::: 1!!1 ,~:' 'j! .;~ !:;: '~~:: .. :: :.:, ;,;' ".! ".~ ':1 .", .... ~::! '!l' 'I ,OJ I'''" .... ::11 .:', ..... ,".' I,! I I : Ii'" .. I· Ij' till ,,,, .,,' I' , . Ii". . .. i::' .\ .. '~' I!ll ': iI . I • , . . 'I' " .." .. , ... ,:., ' I. .:;:: '.. ,,," .' .'

;;;; :~~ ;;; I; t ; :1l!:1' ,;:: :;:; I!' :~;: f1fH:f.-1 :t~~ 1: :, f~ if: tt! tt~ !I "~m !tft,; ~ .• ~. 'H~' ::'-I:·:·HI~~:l: 1i-Tf ~~f~7t~ ~t-H ~+;; :~~ :~; ~~: 1 . I rn !

I"" , .. I' i 11 \. 1'1 ':1:" .. ,. " ;, I' '1" ., I. ,... . ./ ... I. " .. "" .. I. I I II. ,. ,I .•. " ,. "'. ." I '.,. "I ., I ".. " .. ", "" ··,1 l.lh 1 .... ,J ~< 1111 .00 1!! 1";" ~u' ~ In ~1 :; :::! Hi'j l II!: l~:\ I::! :t I ::'1 ::;: :11: !Il~ I ~III :i:l !I .. :: , .. ,'.:; ,:;: ;1:; .l!~ '.:: :t! :;~~ :::: ,.:: :1!: ~!:l 1: l htl rm Immn~~~f!L:: ':.1 ~:;, '''I!~'''lljill '~"'I' "'I~W' l'I"''''''II'''l'*I''''II'''''I'''I'~''1 .. 11'" ,;, . ;'.;",",;,., .... ,." "."'""",, ",,, •. l"t, 1!fu:tmrltrltHlrrmrrr!f!l ... ,' "", ... ,01 I I If'" , ,I,. ..1' I'" ,I., '" I" 'I" I " ., I t I', ,I, "I; '1· I·, """ "II ·1,< .... ," .1" ... '·t' ,. , "~I' li.' I' ,. " .' .. ,."

;;;; ;~ ~;'I Illi~ I;::: I'! :1: ?l ;, :lH ;1:, 1j-1~11' if:t fH Ht i J! H , ::;~ :;;: 1~ ~!'frf~11WI Hlf ;~: :1'::I::j;II1::':::I~H :+ :~~ :::: -y :::: v; g.:: :: ,; ~n ::11 ::': ~.::: .:.: ;.:u:: ii:I'! ::1:1:::: I::. :~" :::~ ;::: :::: :::tt'~ . i:: 1, j':' 11:i ' ,;;~ .llil~: ':11 :::i j~ I ;4d :: ' .:;: 1;.: ;!1: i 1,lt! :.: ,I: :;. ~;. . ',' .~' ' •. ~j ;; ..•. :: ::: 'I~' : : ., •. t I ~l!:l:, : ... ,~. ;:;: ::

II

,.1.. • ... 'I' ,I I"" • t· .. , I' ..• I ....... I'" .". ",I ...... , .. ,,,. d" ""." .; .. ", • I'" "I .... ' .... ". ,", ,', ,;'.CoIl 1t.!U"" u.. , ""'w, .... ... : ' ... "I' '''.'

::;:'1" ;1::: III • j:l! 'jj" ·i:i II"! ;:q ;I:: ;::11':j ;11:[::11:: I::: :j:;. ,"Ii ::'., ,,;':""'; '.' ." .:. Ii .,:. !' : ~Jli.1 :'U,": ~~i"::: ~:.;j.ij:':1.j:[li"';:I.ii:: ;J.;;",;,~ :.

:::: :,., I::: ill:: ,:.! ':1 'j:;:' :: ::1, I;:; L:' .::: :W : il :;:, .::: :.: .!: '::, :': .~-- i' °d" 00 ;::; I : "ju,", :.-AWl:: ~O's:: Mf7O, ;~I.II'Sr,.i :LQ~i;"..IW'~ " ~Ti,;: iT? m~ :::.Irrr: ,:i: :' : :nmr ~T; G:: :::::1:1 :;:;I.:!::~: TT: :"';'~'::p-- ;,' ::. :,jl':; --i~"; '-::.":::";--: -:: I: : ~~l!I':;;I' "':'. i:,,' :,.: ::: .::~::'- r ,' ....

... ~' , ... " .. II;m;i1It ",1, ,I", ..... ,.t ",' I,. ,,,' 'II, ',.1" :.w.;'~"'~: : ,: i~~::" • ,.;,. I " '.", .... " I .... , i:,,·, .. ·1. .. 1 00" '"' "": :;~~l: :~:~ fin nq 1:1"1 :fi ;:;; l1i: i!il ~'n iP~ ;l~~ i~:; .!~~,"~! 2~~! .. ! I', :,:.i;L~~: : .. 'j:::: ::::1::, : ,i ~'i· :'\ : '1: ,I: .. :}:;'; ~:I! 'i.: ·::;1;;::: ,;,; :1'1: i:: '::; l· ;:,;1 : "";, .. ' :i) ,,, •. ,. ·:i! ." ..... i'" .,~. ""i~"'1."'~'" ,.~ 'P+'" ~~: . , ... i~, 00, 1,1· I . 'I"" , ... ;.u.; "" :~ ..... , ',,, ., ':~=. ~ ~~ " 7:1;.!:i :;:: :i'. ';::',:.' .: ,:11 II" i':~ ::'i: ~:~~. ": .:-.... ~ .. ill"'" :: ~:¥:I ": .:~~;: .. -. .;::::.... . ':',-" .:-':.:" ':",'" :~:I:!;~iI: ~"';7:1::~ :~:: :-::1 .':i j::~ ,"-,' - : .;:- :::'::"': ',;: ill' I'I:";'! ::t! ::i1 .. !: ,!:: ::,: ;;' .. ~..... : .' , ,,' :1.' ...-:'~': ,"'"'~ ".,' ,'! I', I:: ' : :,:1 .;:: ::1: I,: ': :::: ,I;! ::11 ill::: t" ';:: .'

.... " ... l ... ·!llll.~1 .~I'.I.. ... ,,, II.· i,·· ,,,. ;~-,,""" ::.iJ ' ., '. ;.:1; ,. • .. , ~ , ....... '" .. ' '" ", .. ' ," .,' .............. " ..... ," "I' , .. , , .... , .. I·· ..... , '... : oj::,:::: ,::: i'i' 'II' .!: i:1 I!' .j':.;j...... I """""'L.: :~~~ " i.-' .: :,:: II:: :i·:"·;'·I' i ': :';; I:!: oJ!: .:;; '.:, :::: ,i;::i i ':1: :;:' " .:; ::.,:, ~.t~;:' ~~~+W~ ,.' ';i f:!! :1: ~~i:"':j:' ': ~:~:: .. L:~ .:..:i..!:,,~--C··:,U4 it';'; I::: ::1: ;',;l .. :; ;~:i: .. ! .. :. :.:: .,,; -:;~4:;*;.i :::: :;:: i;:t+#i ,j;': :::, ',:.,::: :::, '.' I, ". H!j If::": 'I" '11 '1" ~ . .L-'., .. I~!:I. ~ , , , ... " "'1 .... /1.1 "I, ,Id .... ,,' 'I ."" " .. "It ,'" ",. "" .. I. "Ii "1 '!' 'j'" ::'1 :': ::"I.:~;::. 'ill' [.: I; \./ '; .~~ ... ,. jJJ'" ,·I.~ . ::,. i",: :.:. :';. ;',:.: t:~. 1'1 il!: ::;1 ::;; :,:: : ..... :::' ~.;: :::;::' :i:: :j';: I:;: I:!; t'l :'~I I.:, .. ::. ,,:. ' ..

l " .. ,. .. .. It I~IJ! ... d. I,..;.. . , , '. i., " .;!" .:~ ,', • , .. "', "'I"" II" d···· I.. 1 'llf'''to "" .... '." '" ".". "" 'I" "j' ., ... " I'" ...... ,I., ': .. :: .. :::- :~:' '::.' 00 ", "'" 'I .. ",,-, ' ... J-' --', """'1' I'· .... """"1 11 '" :i' " .. " .... , ,,' , "".,."., ... "" ".''' .... 1 .' •• I .

,::;1:, '''::1 1 : i:1 "!;:: ~ I . ' .' .,: .. ::: ii'II'): ,I:' :::: I,';. I!:: :::1 Ij' "I I liliij ::1: :"::1' ': :: :::! I::! ~i i ,::: p:: i:: iii: lit ' :';1::;: ::, :':: 'i;; .;:' l ~~.:.~:. ~::~ h¥- .: "~, !Ht H;; .r:-::~' " ... ,.,l. ~: .~:-~ t-Hf ~ltt ~ I tf! ~~!1'1~1~ L,:: H:: Htt t m' 'TT' :: j ~~1 ~~~l :;:':t·:·· : ... : .. ~ !~~ ~~:+ ~t~-P.-tl -4+~++H ~~-H:ll ;";~.p'~~. s::~ ,,;: I,., ." .~q I. I 'I" I I" I 1'1' .' .L .,,"., .. 1: I, • I' i ,. I ,.; I .,' I,. '''''1 I' I "I '1 , ' ,. ,... '1' . ., " ,I" ,,' 1 II', ., .. ,,, .,,, .. I '"'''' . t .. , 'i'" t' ::::!;:~; ii" : 1 I :; 1Ilil !,; ,::... : I I " ':1 ;;' ::'i 11!li! 11!1: III I :~i. I::. ~t~ :1::: I 1 ,1 II i!': 1 '1 : ·::l ,;:: ~ • ;, ... : :::: l:i, I' , ;,l, :1': il'; ~:;~ :'III! ;ii! !!,: " 'Ii!:. i.it .:!: ".:::,,::. ::.!!. t 1 jlll:1 '1' t I:i: Ii:: 'I ;' Ii! ::1 ;d:! I': :11: I:i: :!I :"::11; .::: :;:1 iii" :Ill' i ',i :·t.: :::: ::" :, ,,,.' . :':: :I:; III '1 Ii:: :111. 'I::: II::: : '::', !,,; ".: i ,:;' I::: :i:' ,.\." .". I ' H Ii".. . :I'i :li;1i .. " I " !, iii ""',1" ", ii' liii till 'Ii' II ' .' ".., .. ,,' jI" i: r .ili! i:" ii' ." " "::. :", ::jl:" :~j1IirW Wj Ii,; ~ l I~j ij~~Ul·I:;~'". :·;4.~·~I·:~i:,;·~iL;:: jrH :1<1 .~;: ::~~~ i'~.~: ]:I::U~;ii.1 ii~i:i:: ,,:r~:~l:~~~l'~l' ':,,:;: " :~ILJ: ::~~: :~~. ;~:: ~:~~\.t~.~: :.:' ". ' •.• I." 11'1 I. ~ :i#IIt- ,Q"jlla~,,! _1Itt .I~p"'" iR. fl.,,,, 1'"' '~I""" l.o..H.".:!fi 11,.-:· !~r-:' :!'I1l:-, . of"- UIO It,. ; 100M!"", ::OI>!'I ...... ,U'r-' . . :eel""" ,"'"",,1 oj , : ;: ~ i " :::: 'I' I I I' I' ;! I :" I " : I " '; ; , , ': I:. : ' :: :' , I ~ 'I I I, • I , :. ',.' II:' : I: !.: I : . : ill I " " , !' I ,,': • I ", : ,i "i !':: ii:J ::'1 ,1" IH~ '\ Il': ;j:, :,:' I:: I, ::1 " ;: 1 1 '! :ll; :! I "I .: "~'I' +;1 ~::! III/ 1:1: Ii', ,:' :i1!' , . I ,:;,'" ':::: ,;: ,:'!~ :' ::~,!:, ·· .. tr .. · .. 1 •• 1.1 H-! .. H·I+~ .. · I ............ 1 " .. " ... "t, .\.. ,. '1111 " .. ·,,1 .. , "" "'1 .... d+~;~: ... lltf· .. l.i "tl •••• ",," ." ..•• '''' .. 1 "" •••. '-'" ..... .,. ,,--- ...... ," .• ......, ':1.

i: :' ,;: I';; illj 1 ,1 :: !I[,'I!::' :i.: :,:' I':' li:,:1 ;::. :1:: :1'l i:I':' '~,' '" I" 1;';'·UiJ.I,'-I~ . ;1 ,·1' ! f k ,,' ::.: ;::1 .. : ",,:: : :. '1, I' .. :. ',:i ':':I:::~ :"! II! I: 'I I' I'" It:i I::' "!" ,:!: . II ,;! III: l!,1 I 'ill '; 1 I~ 'I il· , ' ., "I: . lIN 1_1 ,: I,,: ,I" !::' :: ". ";'1 . I . ': ':1 .... I"· .... II I' It '1 oI"~:I" 1'1 ... "". 11. ... ·'1· .... "'1 1 ,., . ",", 'j'" r1".,.~~~:. . .. . . n, ........ , , d ...... j' .... ' ." ", 'I' :: "1 .~I. .::' !~:: ij' :~ : l'lli ,I, ::., ~:. ;, II'::: ': : Ill' 1'1, l 1"1 'I ' . I;' 'I,;'I!:I" I :;t' 1:" i I + f ," :i: :., '::' :::' ' ~":::I ." 1 " , : ;, :::: :!:: 1 I II: ~ : i! li l: i : : t :!. : , " . , I : ! \. i 1 : ! Ii!: I I ; I " 1n I ;:.' I :! i : : 1 ,': I !: J: : i ' . : ': ' I I I,:: ~ " ~ I'! ,:: I :: , ~ L' '~', ; II , i 1..J i , .. 1!

- ... _ .. · .. ·1 !< tH+ ;l :1'Ht 11'1 .. • .. " ...... ; ...... t ..... t ,lttl ill I ". "'1'" '"1''' ..... ,I ....... -! •. 1.. -'" ..... , •. , ...... -. t+ - .................. 1j ............. " -:--: "rr I : : : : I ,'i: II' I' I jI I : I : ~ "I ! ,. 1,·' " :.; , , :; , I' I! I I ,! II I: '~ , :! , ij, ; : I ,'::; ::;: 'II,' ::. I' ' I ,,: ( : ' : ' : i', ' : : I t :.:: I:d I::: " I [I ilW ,: 1.' [:.~. I'; : I ).. '\1 1'1 : : :!!: :,j' :, I :1. ,j , !' 'I:; I.;~ ::1 :1'1:" ,;" I: 1, I'; ',: , II,:, ,;,,' :', I '!

.... I ....... '\1'\11 ~ ~'I ~I;. IU" ' .. ~' "I" '. '11' '1" " . 1'1' '" "1 ... , .. III •. Ii .... ' 'I I .. ' ........... ,. ",,, ", "'I' , ,::1 :::: :,j; :, t " I ,~\ .... ~ rnl" " i I :!:' 11;: 'I :. 'ill'!1 j,lI :,:: I:t: 'II.' I:! 'I ::,' It j I' I: l .. ,,:: : .. :,U!; _--.~~, .J' _ '. w.~ 1.:"".,. ,,; " ,I .' J;!: :~ll:!j, :';1 ,1 I"! :.:: !~j! ;':1. ~: I I I ' ". • : ,I' 'A In '. 1,1 T') 1.', ' f , J TI t,"f l f f~

-

I' I :,' 1 ,I' I' ;' ~. , ,.. . ,." , r·.::, '.: ·.:r.' :.,.' !I>": '~1lITr! !jl~.! !.:, ::I.': i !: :11,)1-~ T, :~]" rJ~}'L-'l" ·.·~rO··:N·--·[~-lJT 'J; 'r" ':''']1··· ~~~~~)£l .. , I T T"l.4-W~;~T;~6i1g~~~;; I fi; ~RA 1:.:. '£1 iCI P',Y ruE t Su,.1P,jON ~ MODEL .. ;. :)NA~L~j5~'~TE.b,: .... : ....

!: ~~~=,::.~I~i~'; (i 7 .. ;&1i4~J)fJl!l) I A7JI1o~ffi~ .. • ·11 .Iii ..'M .. l~/~~'f" L :."_: :;j: :l:! !:i. I;:! ili: :iii ij: ':;:' ,;., :.J"if!" .L_ .. L.;...~ .. : SC.! __ I .. _.... 'I' '~' 1:' "I I: I II ! : ',' ill' II I,.' I,: ,,:.i I .:; 'I" .... I ........... '1" '1 • .. t " .... " F'lI~, "JIIII!Il~taNQ.. If~,.a ,,' ., ""., , .. I ' ... ".". ,," ' , " I' "1' ... .

l '::'::':::·::':I!I.~:.I:" I:!,'",:'" I ' I " ':1'::' I'i: .:': , I I" I' I: ,::' '.: ,".' '.: : II! Ii!: !!:: :: L I"'" , ' ! I: : I I':: l: : , ; I: : i j 1V1: AI .. ,'8: , II : " ~ I, , • 'j I I: ' : ' : . : , : : . : :! ~ . :!

lL'+i~~ .• ~.1n ., ++1 , ...... ""r"" " .................. I... .. ..,' v . .... , .. ,. .,.. " ... ,,' .. ....... . . '" .• ,\ ....... ~ ....... , .......... .. J...... ...; ..

I'!: i::: I,:: ::'. .' '" , :.,: ,I:' I:: ":, ,,,, . :' 'I':i i: '" I ;" tt I' ,; '" , I : iii I' "I ' ,,::, , '1:' ,I: i I' '1 i .:': I:t: I':,: :11: :i:~'il: . 1:'l ':" :~' ",,, '." i" I,; "l)7' I ' :::, I" ' "::. "', I, I ": ,.: ., :i" ::'.' '.,.: • .1, I, ........... , ... " . 1'1 I,., I'" 'I" " .• , '''I .. .. .1" ""1 I' rl' "II "" " . ,,',.. ' ... ,,,,, .", ."1.,,. .. ... .. 1 iill ;::: I::: 'q:. !W. Ii.: 1;11!!;: I::' , [! i: ;,: i ,; : ':" ;':1 :~ .:' .!:::; I ,I ,! I:, ,II::' II I t: :!:' I:, , !. I : I ::: 1 :, i;:':,::: II : 11 I: 1 ,,:.:.::j .lL ,,', I ••. I." "'-0 ". lLilill, U'" '. ",I:i! I".. , .. J,'. "" .. , O·'bi6 ,1[" ,., ,t,·" '... "I ~:"., ,ii' :1:..'" ........ .

:fI' ')" I" ~ -, ... ~I "'Int" I +t II 1 . . .. ~ ........ :j~; ~lt~ .~:,.. i ~ "" · ... ~I ..... --- ::-:-:- ····1·.. "',". ': .... ,. ~ ''-'',--'''' .!'" +t--; .~:. ~ --:-1. ~ ......... ; ... ~~~ Pti'nt'!:: liP :U:': i;i'~I:: i !i!lli:: !I:: . I: ·:;i ;, : : ,: ::ll'j I' J" ,: :Iii ::Ii:j'" : I:' ' ;::1 I,,; !::: 'I .. ;A: I. i I . 1::-1., : i:::, iii! .::::: .. :; :'i::; tl ' !.l.1 I I, .... II • 'I!lll" II" "II q ...... " " ..... " ...... " ,," .d, ., ..... " .. 'Ii'" '1" 78'" ... iI"',. I I' , ... ,.. .. ........ "" ... .I ." , .... , .......

1: I 11 I:: i tI i I lW:' t !II !,: I d 1 t ;, .:,:: 1'!: :. (' :, I , ;!, . ",': ,II:' 'I! :. 'J":'!: I' :. : j j: . , ' " . .'.' . 1,::" ; (i: : I: ;:, j:'::': .;:; : Ii I 1 "'1 Ii Ii I I 'I II ii'" I " I' i., ·", .. 1. Ii' "; I ,.." I , '" ~ja' " "I""'''' I , I . I' ",' ,. ," . : i i' "I .... . ...

:'I:li !~: ;:;: :::i ::::1' ,.: ,I !'tlJl :.;: :Ii~:: "" 5" ';' ....... ,!.. ,'" I' ~:: 11 :'" ·tr·1 r~T~;:~", .. '. '1' .. ··1 ···~· .. .. ... : ~'-I';;~ .-.=. :~: ~r~: ;:,'; :;::;:. '-",:;: ;:'; ::;i I t: ;':! 111,ltil Ill! ,: I':: I' 'M't '.~ . ',:A~::! ,11+.7' .. a~:oa.:,! II! , ,; ,. "I :':: ':' I I I: , ;. "":,, ,:" I,ti ': I ::fl'l" " I:' .::1 ":1 111 t· J!I. I" h£" II I " 1 I'" I "P., I,Ll .! u ·"1 .... ~"G ... 7 .. ,+ . '. ' .. , ,.,' I'" ,.. ., . " ,. .. •. ", .. " ... , ",. I ..... ", ..... 1 ~ ......

"" '1:1: tI:: . 1 ' ': I :1':: !.: .. :: ;1,' ::lk.· Mij"" ... ri" :' .. '" I':'" ':'1' , :' ':: .. ', 1 I I"'" . :, . : .. ::: ':'1 ,I:, ':11 I'" ;, I;' ::1,;;: 'Ii! 'lOti -l.i" '1'1 " Ii "~:: !:., ",' I'" .... •. at! 1M • 'I" I "" , 'I ' ,I., '1" ,... , " "J" " .... ,. "1'1:';1" ,,, ..... 'I ip Ij~ iii: it:i ii!I~I!:ii ;il iiHi!I I:j ~~j'i~:l:tt WlljttTIr; ,:.: :i:.·· .: .. t:::'" , ,I'::~ ~t >! :~:. :; .. ~i"I::it !:~y .. :tl·~:~ .. \ .. :i,· .. · .... ·I·'·· .. ~ :" ··:~~11·~·7 f..1~~~~fl;r:?1>1 t- ")7' ti7f~ :.' f':I' II': Hi! 1 •• 1 II' :11 I. ! I. • t H jI ::~ .. ::: :::: :::! '" I:: :~": :Ii, ,:1: :.,; .,:' '~... :!:', , .:, : , . .. .: .... :,'. ' ..... : ... : :;:! II:: : I: !I! 11 .. ". :::. :! .. :Ll.

l

I! iI .: j :! Pill;:'! i.ii HI i :: \ ii, Ii III 't:, I! ii, ! i 1! i:; i : Ii : : !! 'i .; ; jI: ;: i: 'i' i; I' ; , :.. , ~ i hl" , . , I :. : I: [" ::, :: ::.: , i : :: i:!: !I j! : II : :: .: : ! : .. : i .i i!

;III;~ .... , !lli~!·W~ul' '!' ·:'1 IT: I [f·lm· mllt;~~IJf: :lt7~:f '.- .~. ::7~ tLlII~ ~Tr i~TI ::~ :r" ''';1·;11 :.' i I~'; ":'l~~: ~t-· ;.·-1 ...... ~·r'·-·· : .. ~; ; ... ·:~:il··;: ~:ftS ;~r. :JI" ::il:::- .~. ';1: :;.; :,;: I l '11 I t.l!:I:I I' tllll: I II IiI /iIi ::: ':1: ':!i ".,. ':; ~til ;'j: ,:: 'j:!": ;; : , "1 til.' . , .'.;. :', I ,:::' i:: :11\: ~ ::1 I:i . :;:' :';' ,i'l 111 , t.;, 1 .. i~'" tI·· t· . 1111 ,,'''' ... , I>., ... '" .... ". "1' "I' .,,' '" ". ~' I' ..... ''I. .., .............. " .• , ..... " ....... " l I'" ........... :,1.1 •• 1 :'1.:~ ;:;: fill J ': !', I Ii t: !lli !:I! 11.1!ji. ;i :',1::': ';, I,' ,~i':: I'; I. d ,1':. .! !':'~" :.: , ::' I:,: ':;1 :;:j '11\ ii' .~: ':.: ,:i!

1I1 ~;'I~:: ~ :~;; :;!! ;~:~I~:'li::: ilil 11:;~I;: ::n 1PI':;~~~!I'~I': < :~ ~::>t~: '~~I\':':! ,c-kl:~i' .. ' .. : i ~ '~H: '-41'~' ---f- ... ,:~,:-,,: :.: 7 _.:.! : ,:;: :::: :::: ;1:1:: ;:I~; :i·r::: ':;: I l~ , .. 'I'! d, I JI' ! t ., 11"1'" .,.\ "I 't· "I ·t·, 1"'1·,1 I I. ! 'I ',., " I" I fl' ,. t ... , . ,III ,I . I j '..1. •• , ••• \ , •• ,. t~ I t~I':I:~ ~n~~:11U: It 1 ,i Wi', I'P I':" ::" ::!; l;:~ ::':W''''! "'f'::'; ::;:''': :;~II ~" \t: i ,i, !''-':'. '::1::; "1-:' . ':" .. 1' : ':' :::: ;'j'::: :::' f::: :::: :ll: :::! rr" '!': :~:: :;i; ~~n ~ I , •• ~ I.! .U·iQl .. , '11 ,I , " ,,,. ~~:ll'l" :t ". ..I·" " ,. ,,0 a .:.I. ... '.:.J' h L ::.,.=8' " .~.L ,." ,I, II, .1" ,,, , ., .,., .. " l l iPi :'" ;i'i i':' ~'I~"I'i ,:' 1:1l t I' ;: :':: .,- ~ r!.Ui"T~~ ~! · .. ·I··~ :~!',; ~"~:r'i ~ J't 1"~1 i~ i :~~: ~:~~"~II:f': I'" ~":r-:':~' : :i:: :-;~ij'i~r :::'~llllil;i': T. iil iiil I;: ',,: :!; :ii! :itl;' ttl' !~ "" 1,11. 1 ., 1 .. 1 "l L 11'1 ,.1 ... ' ,:::~ .... " ...... , • c., I . ". " "" ..... ... 'L" ."" . ,. .. ................. '.', ".1 .,,~.. .. ... , ...... ..

rI:!! n·,. Ii;: !.~: t '; ': ,;1 iiI! l!:: J'l~: :~:: ' ': : ,.. "1.' ,l,i:" , I 1\'; ,II I A' .;:: .;: 11' ',: :' ~ :':: :::: ';~i :': ~::. !::' ;:1: !1I1 dl! !!. . ,;! :1:1 ;i, 1 1 1Ii11 ,,,. I... .... ,. ud'I"" U" .,i "I, " '" ~ """'" .. I ' ,. I'" .:\J. """~' 11"'''' . , ,~:.!.""., : .,:"".,:: . " '1. ::: .t.J.:."" ..... ,' ....

. :~, :1 ::': II:! "~:~':':ir;;:tr;;n '::; Ii: ~'~t t:· ~~ .... :. ;1' - tOO '~"'I":'I''':: ":'1 . I .. ': '\ :!r ;,r:!' ;,!':-- ~'I:" .... -: ~''T;':-~~'T~'T;:I:'I:: :::·ftf:1 :~:Ir;;· .... :'1 ::11 ::;: :1:: ~ ;.:. ::ti ':\1 :':i '!tll' :::l II.: :1' '.:: :, ,I :' I '1'1 I j, ,. ,: ' , '~j": iii .i 't.[.: , .. ,,1. . .: I:" , I; ::, 1: : I, . i;'; i.)1 ',; j:, ;' . ::;' l::f .,.,. .. ... ," t.~l ,I., ... '1" , ... II. I.,' .... "1.\ ~ .. \ .. " ... ,... ., / \.... t ".". ... . ...... " .. , .......... '''' ", .... I .... ", ·.It "., ". .. .. 1 .. , .. ~ .. ~ 2 :l:i: ;;::1;li' ' ]Hi";' i ,,! llii il:: .;;! :>I!;' . ~ .: .' "i:' I ' :' it K': ':'Ij':!: r ' : I:: .' :. ,: !::, :: '::':: +' 'p:': ::', :ill,2+:1:1 ::' ,: :!i. :1': I:!!

I'i' I ..... • ,'" Ll11: ~1!: '1111' I' ' , 'I \" ':/' ,.' '~ ,." ,. ,!" 1. ..,' I I:;, .,1 .1. ::_~L':'~!....:."":"":'l..l I ~+~ , ... F:"~" It c,~~ ;o~, ..... ",1++ ••. • ... \~. • ...... I "'''' .. [.:: T:it . ... ~ .. , ........................ ~ ........ , .-~ -' , ... ,.... - .... - '::;. 0::, 'C';; HE :'~: L:. :!~: ~:!l;~:i:;il':[j~1 Erf liL ['Iii i:ll :::' , ~. ··,tNS: . JJ.!~~i'; ~/.: ~ "1 ':, '~}4:: ~! ! ! 'i. 1;'":''' ..... L.: :". Ii :;lj li~ :.: 'JL :L ;:i[ :·;:r:t :::: :~:: ~ :: ! :; ::, ii , Ifi: i ;. :UJ I.:' I. ~.t~' 1 i2~~ , ! "': :;:; I'. (: '+'; :: i' ; I::: : .11: ::[ i. . ,:: .~. : ;: f Ii:;': ·,,·;··.h . .j I, " 11,1, i I I,,, . , lJ" ,,~,t ": .. I . L' .' .... ,," 1::.":: "," '." . ", ,.,',.

~t .. , ~.:-:-; .~II Iii. II" !!~ rr-i~tttt ,.... .... . ...... .,. I,. , ), I" ... '1'~r-1 "'~:.~ .• ,"- '0-4' .. ~.~ ...... , .. ,1·.,'" o-r,:-:--:----. - .... ~. 1·,1 ... .

.. i, , " I,:: ; .. :, •. " '11l !,t I'" . "" I'" .... , , '" II· .. ·' I j' *' '. '11 .... 'I ' .•. .., ""'''1 , ' : • I ,,,. ., .:: 1 I I I ' • I I : ' I i I; . I 1 I ~ I I: • .. • ',' I 'I • ; ~ : .:. I. . I , .: : ,: ' :.:: :.: :: ; ::: ; : ", ! : : ': :':, "I· . .., ... '11t j .,' Ill' "U Id, ."',, '!ii "t f "," '1\ ... ",1, , " 'ij' '1' ...... " ..... I ..... ." .,., .

fj+r~I:·~; ;;;; il;; III'; iI :,' II l'lt: .r \Itf. TL:: ;~i: iit~t ':::~'>I .' , ' . .I. i ~:tt Mf.:t. ::t~ ::;; :-'1' "II. .. l"'~ ;: . ;::: ::;: ::; :;:: Ii;; :11' :Tli ::;1 ;:. :. ,;; :,':' ;;;1' ";: I I' :t'! .!n II I, II JI I'! ,:\1:" :'1. " :'1: :~'. :: ... ", . ! . ':..ll.""~~.:li :::1 .'; . I' , .: i;j: :.!i .::1 :1:: ,II; il'. 'I'I! ~t:: .;: ,; ::1 :::: ,., ,t .... f:.l. "t. ~l ~ 11 I p. I ... I ,." , ... '." ~I' i:I'I-' II. ""I -:... . .1 .'".... .... . ..... ' ................... I •.• 1. I ... ·1· .. · ....... Hit .l :;j l' :::; .ii!· 1 i :q! "I' j' , 'I::': . l.·~ '~i" .", ,. I'" ;.. ~( ,:.,' :::1 'I:: i:' ,: .:' / .. ':: lIil :i!i ii: :;'1: llU"i! il::~'I.': :ii :: ... : !;j'; :,ll ;'P" l li...:· Fliiil , !Ib i;!d+ .. :~~.;.:i: -:-!~~ 8HP ,..t,1 . ' •. '/. .. . :.11!.':: .. :: ... l.' ... : •. l:::l.U+:·:·' .. ~:.,:,,,~.~~: :U",*fi+!.::·::. :',,:: I I ., ,', 'j: IIH"'! II ~;" 1j! W~'· 01 I' ., 'l"ttltr@!ttllll"'I"I'II""""I I"' 'II'I"'I' "I "I'" . III, 'j' "It :'''1.1:".\.1111'' It.ildl.II." ... , ,,""""""""'1 ' • '~"I '" 'I' , "'!""I';'I"'I"II"'!"I'" ""i·i"1 ::!i. ::::! .11 , ,I • H :. ;'I! :;:, ':;: 1·:: :-i! !.;1 :::'P!:: II;! :il! !:i:' '.' i'; " . I:: !:i: .. i! :':'121' : .. , " ,I:: i :::! :,:: + :~!t :;H!j:;; :IIP il' '::. :i' ::" iH; :,il i:l ~:]lk: U~ fIll I.J . Ii I l~ 1ri~1" .:: ... ,I,j," dH~(jMc\1r .1+1 ;;l.i~t;~!.si~.:.. ,:.::' , ,;'L,i ... , ':';l::~ ,it . ~ Me. BUP :ll~:~ :lilH:ii UUll4 i.lillilL :11'1 ~, .. :~~ in; ::i! :!!!

. -:1" I' ~i '"I ,. " • ,. ~ffl-'~'I .;1,,,,,, '1:~.loCl· I k11 I,." I· r--'""":". l:A t "1' , .... til. , ..•• " .11" ". ,. 'I , .. I' I'" '" ii ::j: I:;i :Ii: d!i P't! :lil;iI 1. ii..;~ 1 .. :.tLi.~ ... ~ ,'.1L~' F· ... ·u,t '~;'i'I' ,~ ... "'rlJt • : ... ,," ,:; :i:i ,i:: ,:'1' .. i·1 .jl - 'I" ., : ':': iO:: :;Ili ;:: :i:' H:! ;:' '::! ' .. :: I: it:: :::!

DJIV, ::t! :1:! !!.: !f': It 'HI :i!' fIt; H ;IG "''i''': :~r"'lll .r..~. rt';!: ,H, ,"'1:.1"1 ... Cr., ;i~ ~::. I'!' :11' :1.: ',.,'" . . .. : :1.: ';1 1 ~! Ii:: ::" ';" ':I! ... ! ::. "·!:.:·1 :~ .• 'I" ,. I "III" I 11I1I I '. ,.. " , ,i, i ,!..", 'II'" .," I'·' ... I, . ; ",',,' I . ,., 'II' ,; i .. Ii' .'" , '1'" ,!.;" I"'" 1'" I .. " I I, ,. i I" I I 1'1 • '" I' . 'j I' , ; j' •• 1. I' " .• I" "I, I' j I! I ; I ' .' 'II'! j, ' . 'll. . I .,., ,I., .•. ,. II : I I" 1 1" .. I • t .".

l

:;7t f::1 :H; :0 itt II! rtF ' 'I~~~lil; 1!, ... I.i..,j ~:. , '1~.J.;I·~l~' .:'::i •• ,>·~.~ "~.I~' '1' ::jl~u'~: ': .. ':~l~'~'! : .... L: £w .,..~'.' Li.:;";.;.~' ~ I'~"" '''i~:' ·f.;+7-fi :T !!!: > :iii U: ;l~' :ill ~~~:; :iu~: J'~'I,a~~~I:~r-~ :~MI:! ~'I: i ~~~. A1 !T~>;: "~:~ :~Ji 5OfMJ ' : i 'J;;;J"PW' 1!'6iIWI~_I!fIV: ,: J·i:: I:::' :::+i 1::1 ;::1 .;~~~;: .":. ;'!,\l, ::l! ,;.: :~:, .:.: .. ; ..... ""j" .. :l:I .. :· ... :::: ,;,1,1: ",')" : ... " ... ~.)U :1 1 :::. :.:' ,; .. :;.:, ..... , .' .... ::~,.- ._., ...... j.l ... " ....... :-: ;,' ;~.

t ::;'1:1:' : .. :;: II.":. ',!I :o!::i ',' . 'ii, ,I ,:', :1':: I ',: It;R iJ,.:.: i::'"" ).l.j I' I ,i, i' i I, , ,.: ::':I!i:! ::" :::: :l;:i;,:; p'l 'i:U:::i'~:::: ;5'" .:. ::'1 ··i . :::: ,!, ::i I:! :. ...p tli I:: I~'" , OJ ~NOI. ! ::::: ,'''' J : i' . ,:- :I!!' I. : . : ,,,"': IIi : I 2.:" :. I ' ': ',.:: I' i: [ , i,:: I.:, I I . [ Ii' iii I! I I : •• ' ~'.:':' I . t:I . V '. t " ! ' ,~'.-:" • j - !, , • VI I ~ .....

III '''. til If) 111~ I rNllMI 'f r1 ~ J' . ".

,. I • r I 1 I!, f' "~'" .,. .

'''~~'l .. r '~~:!li~IA1II}L1~1'1-)Jrt I'~' !Bk~JiT~;~;~t' 'TTTFTT ····~··T

i · ... 1· :;:i:~~!~ ~~::. Ii;. i' . li!,!. illi:I,· •• ~+kt·lj

'-~-.: : .. ~.J~'.: :,~,ll: .. ~ J '-. ~':',I"'~. r~E : ... '1'" .... :,.: ---.j ..... i · .. · ... ''':~,'''' .... ; .... ";',' .. I, ... ;. "'1' 1 "70:: '.'7':: d·:'" ~ .... :~--:~. '.-'-:-1;: c .. :-:-· .:.:...JD l I' .: ;' 'I':' .". :;:,' .. : ,.\ .\ I.. . ..' . I . ,.' "'1 I' . . ... /. : ", .... .. '. " .. ")..' .'. T .,jOy tJ·:·.·"· . ,. .. '. .'. '.:.,: ............ ,." i. • ..... t' .. ,. , .. ,." .. ,.. . .. I" . . I . .., I . ..., . , ....... I... .... . I n... t, "'" :: :>: :::: iii: ill: ili; H::t I,:ili,jl:, i:!j I:,:. : ::::: 1: :::-1:: :~:II :. II:: .:: -: :'.. ,. '.' I I :1' ! ..... ' .... n~}I,iiy .:_1...,.~.6~ :i. ,:: :;:1 ~ ...... _-+-,_ ..... ~ t ...... +-!tt. t;i71""'" .·n ................. · .. ~·'I·--: '" ...... _ ...... -.: ............ ,. "1'--: '" ........... _.; .• - .... ,... ·-t· - l·vrfl.UI ,.,.,....,. IfSrli~tt:.JJ. ...J..;.:. 1---- ~.

il !: .: iii;: :l i1 ' :1',: ::11 ::1,1 I:" i:I': ;:1' :1" . I' I" : I:: ... ,. I' .\: '. ., " '1' lR>iri;r. ,,,i.,I;':"o.:·W .. Jr.ul~'''; c:' j.: :':; ";; .::.;:::: ::;: 11;: ,I:. ::.1 ;:/ lid I::: til! ' :: ::.. . .... ;:.,.. ';: ':1 .. . ... ;: ... : .. :.i. :j...\ ::.: !"LC!": .l1:Nf. d .:T»"I'IVQ:. I:::· :;:: :::; .. i::'!:: :.:' :'I.jj,li: ::IIi!1 Ii:",l!;: : I'. . .. .: I:: :. . ::. ,. i., i:,.,: : I :,1.1 j' . :i: i .. : .: . '.: .. ~i.:: .. I··:: I..;: : .. ; .': · , .. I '." .. 01 i I I ,II. ; I , '" . ." ., . . .. I.. •. J. .. ...• "I I... iI.... " .. ,,' .. .. . . . .: I. .. ,.. ... ...: I. ...: I", ... , ...... ;.!' .. .... d, ': .. 1::.: ;:;: ilii Iii: ;1:: :1'1 I::::" I': ,,'t"n1h I : .i.;,,;!,,"fJt. ~; . i· i" .. .: 'I 1 ': .! I:'" :'. I . I ... ::' :!

~"f::;: ::;: lit! 1 ill· '. f l.lll~:: I": :·fuIJ·" .~,rER'lM!t S : fD;:I" .' ,:1 ... :~: .. :: ':.: : ..... :1,. ..I. ..I.. I... ·1'. ';.1:; ... :.: .• : " ...... :.... : ./ ...... : .~;: l : j ;;:.Ii::! i::; iii: iW ~:~:li I;!! h: i: :l' .jl '.1:: \:':: .... b+7 '~f 'D~~; i .:i:.:! Ii:' ; ~k+ :.1' . l· ~I 8: .. · ::.j::.::~ ~L .~~ ::::~~ .f; ::.: :: > HH i~llIHilliji~jl~:li:; :111Itij'lr:ii J,I:; ~~rIT; > :~.~.~ :'n :':/: .. : I: I:. ;::;I~" :: l::" ;";,.':\: :::: di: ~~;'[.: ':r'I':~:' :~ .. ) ::':,::::1 ;~;c; r > ~[: C .. J;,:: .. ~ Ii .;. :~::J :.:: ::~: ::illl;!! i' I: :l'dill/ ;, i :; ":iI" ;::i : :: :': :.':. ;:1':":\.1"'" . . :i :::;: . :. ~i.i· , :q::i ii·. :i:: iii .:; .. :. . :~'::! ;,Ti':" ;:;. ":. i.i· .':' .': . ::: :: j .•.•• ' . II . 1 .. , It!UIII' .. .t .... , ...... II /1'--· ':.i.;.' .... ';:'; ~ r.f.CI ." .. , t.:.. ....... , '" .. .... .. , ' ... ,. H·:l.:.I-'-·· i.0l;.iiJ ...... ..

:~;~J~:;i uiilt!" !Iii; ijl~ ::II!il1~!I;; i:'~: :;1 i., .. ~ l, l~ ~'r~~' ~~~~ :i~ ~~" . 1:,' '-:~l~l! ~~ ~~,~ ~::: :1 :! ::: -r- t -' ,! . .IL •• -~ -.~ I~~~II:~;;i~;:~ ~~ ::1; '~. ::1; :~'I~- ---1,,' ~:;i :'I~ ""I:so!:lt'ttll -j1tiii!' , !.llll .. ill" ." ............ l. .... I' ..... I.... ·1 ........ ,,' ... I ... '''' .. , ... .... , ·t·· .. , , .... :, ... ,.".... ....... .... . I. ..... 1 : .• ~::'I; :1 !~::!i II '11i ~ itj f: ... : Ii ';:.: : .::::::':.;.. :, : I I: .. 1: '. I';: , ... ' . i·' 'I'!!: ~: :.... .:: . . , ...:.: ;;. I :'.I.;:! :; : ! :; .'::. :: ': .. ' : ::.:.:: f

tt

::it(~ :i!il!lii li " :ir: 'J:: ;;;: b p~ .• ~'.:' '(J' ~'l"~j~":'~~ : 'D a '~ ,', J": .. 0.'\'(14 ~.: --:) ''';; ~:: :3'<~'" : ·"I '" -:"1" "":?:II ·W:· ; ~.~: :(Lft ~l' ---+I'~~ :::; ::: :.::(::.,., I::: :t;: lqi Hi: .: ~ t:H I!:: .fV:T.:: :l ... ·1~ .... ~~.··I" 1f..,.0 . ~" :: ' ":1 .:': :i::'.' ·1· .. · .::.... ..:~: i:' ':. i;:: Ii: :::: .. ;. :::i :~~ .. : ..... :. I::: :.~~ : :.!:: . to:: 1111111 ':. / ji:i !::'liiil ii: . Awl" rJiJil· ."",.1:: .: .:'.' '1 I:. :' :: I:.! ·:'1":' . :.:: . -I. I ::.

ll

U1 >I}~ .. ;:;; I::: 'I. '" ':,' i;:; ::: '}~', ~:-:~. '. I , 7'~: :.;.;. ....;·"I·t .. : .... t·:~t~:... ·r··_·..· ,oo-~ .... -"'1-·:' :-. <,;;:::; ,;:::: . :'; .. +- -TS 7.

b --:.~. :.i: !LLiW.r'l~pi,W.'!i; :11!Ll b lid i:U ::: : .. I.. :\'.:.\ .. :; . :. .... .y: : i: :: ::: !: .. ~ .. : ;'::/1 .. ,1.: .... ; !' ....:! .' .. ~~~ :l.: :;;:~::': .:: ::i: .. ·l.. ..t ...... : ::: N .: I . :::: ill! : .. ":: :[ I';i I:;: iii ,,:I,i. '. II: . ":1:: . ::: . I:; .. ::.: .• :: .. , /., ..., ,i ·1 :t' :: :i" :i: i':; . :::1 ::,: .1. :.': : · I .... ,... •. :l:' ,I oil . i ill. . 'l..t~ .]. j.;'" " . ! .. ,... " . . ,I . , I' "I . . .. ;.:..;.;j.!..:....:. ,.. .. ." Bt· . . ., . ,: .': ;:JotIi ! :: 1itil'i," .:I! .: n II 1:::I!lil . ':1'1. .. 4- ........... ~i -:- " ·_"·14-o-~ ~ :~ ...... ~~- _'0, ;' '-:J: ~ ~- .. ~--:--- ... r~]- ... t- .... , _.-:- .. -: ..... _ ... ~': ":.: ::: j::: . :" .. :, .. . ...• '; .' ." 'I" ".. ',,, '1 .I: I I" 1'1 . .. .. .. ..... .. . I, ..... " " . I 'I .," ". ..., .. ". "". ... ... ......, .... I.;,;: I::: i.:: ;;1: ;!I: ., ':~l .:: tid; :i I::: : ... l: .. · .. :t" .... :.: ..... I·::· .. ! •. :.: . I:;:.. '[' .:1 .. "",. ':"1 .. I· .. · '. :. . I : .. : :.:, I.: ::;: ;:. :.: ... I:: .. : .. I:. .. .. :.: :::: '"--' :. ~:~ : :i ;:r Ii" . i; .'1 d:i! Wi iii! . :!I~:" : ~:".: :!. .::! : : .. ::. ii,.i- :1:Y :!!~,.. i I· . ": .' , I : ::t::·: I;: 'j:: ji:'!i::::,' :.' 4l::: : :::: ;:!

"~ ..... ,ii II Il._~..wp. __ _ .. ~ .. :;.; .~;.;..;~ _ .. I~,+,~ •• ~"""~".'-4''' ~v- .... + .... , .......... .. .. ~ .. " ........... ~ ::.: ._.[ ..... ~... . . .c_ ~.

:.~~ ::: !i~~ ~:~:":::: .![ i:ji 1:' ;1;(; ;[r;: '. '~~I:;:; .;.~~: I':: ,,~. : I ' ! !., I' "',: ':: ::,! i: ;:.; , '." I':' :-:i .::~ ..... .. ...... f" ,." " •• .1 It .. '''1 . "I ... . . .. ···1 .. . ":jl;,;#~ , ~". ..• I I"'" . I .\'., · .. 1··· .. ·......· .. I. ........" .

. ' ';::::' I:. Hi:!:!:: I;·... I :;:: ""v : ~ .. , I : I 1: "j: [. I 1 j' : .-.- .• ··~I :;'.' .• :. :!.t~~iH-i:~~;~ ..... j .... :"'1" ·~ .... l· ~~i .; .. I·"t.;,;..-;" ., .. '''':1''·'-' '1 "r- "'," .... t·· .... t.... I:~: _. · .. ··I~ .. · .. , ........ : ... - .... ~.'.-~ .~ !::'·I::'··:::' :! :::;11' i:': i ! . . 'I"~~ ....... V"! !,' i i . i . I ".:.1 ~. 'f;: !1~: iT 11 nir :~. r;::: ;:, '/ik' .' . ~. .'1-~, :' iiI ; 1 I I : .! 1'!' "r': \":' !. ..::. 'r . "\ : f-.t . ...;;f!.:.....:+~: . ~ .:. ,::: H~H-;~ .~[ .. :.... . ~' ~~.......-r.. 1 : ., '0.-:-- ~~~ ... ··t ...... ~ ..... t.. .: •. ~ .:.;~:~:-:- ~:'-- •. + .... OO~- "··!-_+·~r~· . < ;:I!~'l::: i;:i' '; 1::/ t;" i':; . :: 1 ~" I ' I . i: :::: ,,·1 : . I ii,': :;:':~' : ',,'- -I' : i :.

".:. . .. Iii::: iii;li: ! ii torr 1-: :!;t . :' : I::' .. l';tfIIlc1d...k+->~ I .: .. :.:; 1": ... :..... ::... . ! 'I' ... : .. ; .:., ::.: .!;. :;: .... :.' .·f· r'" ; ..... : t · .~~. If i iJf t!if ;1 :11: l!: !i:: : .~ ': : . . :: Le!::~, I . I . t !; : :: :;:; .::: ',: . . I .~ :;: :~I '; , :t:, :::' ':: ,,' I,' ',:l ': .

. _.. ..... ::n iT r.« ..... , - ... ---- .... , .... ~:.!~po- .. .. ........ 1.-. . I·· .. f-C- .. -~ r-~ .~~- ..... - .. ·f .......... oo· ...... ~ ~. __ li-q.;-:~r.-: F. _.1_.

: .!! il :,'! ! i· i : il I. illl : .' Jl: 1 ; , I; . f ~. : I :. :. t,:!; : : ~ :,' ,i i ~ I: :: ~ I ~ ~:: .. : i , ~. ! " i: ;:: : 1 ~ i : t: i : P: [;: ~ ::;: ;,:: .: I :::: . ~:: .

. .. ~ ... 1"'m41 tljjll j I .. , •.• '''1'' '1"" , ............. ,1. , ........ ·t· .. • .. d ... , tl .. ···t ...... , ...... 1 ........ , ..... " "" .,1, ·f ......... , .... . . ..' ..... .

. ;.L.\ . " lii! II 1!!:: ! !! ;j;i I :. • :: I, ~l. i; ilq :!~. ;il! :~!' . ::.' i :' ,: : I! ::!i l!ii :i11 ;;:~ .;::. 'I! . 1 :: ;;!i :!ii :1:1 i!i:d'I!~ :1': :;:: :.:1:: t.: l:~ .;:: ...... --- ~ .... ~.ul .W;: t ... 1 ·.'I~" ....... _.+ ... ·~4~· ..... ~·~ ........ " .... ~ .... :+t "itH-iii ... -~ "H·"'C~· ., .......... ~ .. ~.... ~f-,-.">~~;F-' . • ~~~ 1 ,: :":1IiP;~I!'l':!!! ,i ,: \'i:, ;:11 :::. I ::[/:II.::~: Ii! ;;;1 .!I:~ :.~: : : d· 'I,: ::P ~:;l ilU :~;~ dH ::~:' :,:./ ::: '" ,.: q ;~;\ ;ii~ :!,j dL ;!~; ;;~: ~::I :'il;: :;, ;;.i ;::~ · •. " .... Ittl d , I •• " • .1. .... .•. . '~i' ....... 1 ............ I·.... . ......... "1' ......... " •. ," ... "" .... , ............. 'In' ., .. '1" II ......... 1 ...... .. ........... .

,: ' . I: I : 10,., ,: ! :.; : : . i : i I :' 01: I':' ::: I : : ; , : ! ' : • ~ " ; 11 ; .: :::: .:: I : I : ' :; .. ' I ,: ' I:' : .'; ; : :. : ! ~ Ii t. i' :::; ::' : : . ; , , :. " : ' '. : I ~ : ~ : I .. . .. I! 'I • t!: t ., ! i I' "I i" .: I ..'. ,. ' .... , " . .. .111" •. . . " . .. :, i i" ; I" 'i" ., I. '" .. i' : I" : ii . iii : i i' i i" .... ... .". 1" . •.. ...

I

I~~": ~:::lrttt it ,Iij"'~;: :lliillLi;..i.; ' .. .l.~:' ... ~ 'lll~~'~ ';'~I ~,w..;.: .;;-l~ .·'.lll~: :iii'~ j:l.- '," ;' . ~~ .... .' '1~:I:";';I:.~rl·;"'w.: :.;.;.1.;.:... i' :.1" . '-r"~F.

,.:! :i H i'n ili III!I'! iI, II ;:I'II~lIfIII";1IR IJ(J i '~I ! -~i:.s41"f :~~. :~'I''''''''''' il·~k!""'J:·~jIW: [!"IW!:I; .... ~. ~k1il.;J"I-"-! 51_ ':.;;J4jGV; ;~~'1'6Of1U ',' fiiJ10IJ :: .. : j::" .;.: -+ l ""I. I. . I "." I'" ,I I I" I '! ' ". I 11' , ! ., '" I,. , , ' .. , , p .. ::; rOOT": .:~: 1: l~I1I'ilfTI·1 PHil :;f: :!-:-: ~;: .... j ........ " ... ;: .:;~ .. :: ~I-:-::r: ~Ii ::J' .. 'kA'" ... : ··~~.:Lii~~ .:.~ .. ;: "Li:;f~" "1'$'; ... :: :::: :~~I~~~~~: ~~;: .... I ....... _ ..... ' .. ~~.~ I:'" :l'!:'!:::f,: ::'!I[,::: ' ! l':I:!: :','::: 'i: ": r ':; 'II,!: i ,;' :::'::':'1::1" j. • ,: t .. , ... , .... " • , .. •• , .. II "I, ".. ". .. .1 •. .. 01 .. ........... .. ' •.. , . " ''''''t u .. . . .... .... ...... I .. ·· .. . .. , . . ,I·..·.. .

! : :' '1;!:11i:i1!j :il!!i!!" i: 'I i :j:: ';'i:~ :~;:'~l :,,1 ; I I;: I" I:' ! I . I :.' ~:~ ;';: t·: I 1, .'

L ........................... tt ... 1_. H' ...... ..... .. ...... - ............. H· • , ... '1 ... .... .... .... .... ..I.... .......... - ~ ....... ,- .. l ... , ..... - -.~ .. -- ... -

j ! .. ,::j:ii::!:!ii.:,\:j;:::i :: ~! !:;. ::., ':. ::.: : I'! :.' i'l ;! i .. t'::1 i i

.. II .... I. .. ,III· .... ·F··· '.' , ... 1. .... , ... , ' .... , I. I" .• j 1. ,I

::"!'!' I I :::: I U' ~ . " .. 11"" • , '," I .

I

; . :": I : .::.' .. :: ~. • c:. .:i:.. I:.. : : :: . i i; . .1

I ~ .- .'~ , '.'

10 )( 10 TO THE CENTI MfT[R 46 1513 J-.r,U·rll. '" 't.:,·.1 R CO ''''.''' ."1' • c-,-,c-- -cr "---=i-o" -+

(

(

;0

THE ~E.NSITr INDEX n /s COMPUTE

t, .

BRAKE TORQU£ THE CORRECTED L13 FT " ------_._- ----- - ,- ••• -- .. p-' ~ .•• - •• -_ .• - ._. ___ .•. ::-8~·::::~T-::::~~::1·:~::~:--~_' =:'::':: :~,:::.c:::.::: ; ,:.c.:: ; ::,

.. --- -_ .. - ... --- ---.-- .. _---_."-

,;,..- --_._.- .. ----.- -- "".-'"

(") ....

l .... ) ....

t----·- --1.:::::::':-: "~~~~<~~~~~:::~~~:::L~1~~j~:~=~;~~: ::--5= .~~?§F£f:==;~:"- ~-== --t= -~~=;~~::~~::::~~:~:~:-:;~::-

PJ:~

: '::T::::::~: ~~:~::::~C~~~~: :~:~~;::-:5?:~::~1f;;!~:;~ :~~~~:::~ ~::~.;;;rt~:~~§ _ ... ,;= :~~;~:~~r::~:::: :-:::'::-: ~:L=;J~~;~:~~~f::~= :::::=~~L~'::i~ : :~= ~r~:;:-=-:: :~::~~t::~:.::- -+=~:_:::i::~::::::i::::~:~~:: "' Ie >' = It :::--==--- -_.'- .. ----.-- - .... ---.

'" ... ----- -~: -- - - ...• '" ~ -c.;... -_ .... = :::::C' j:

- .. -_ ... - -

z~ .. ===r- :::- --::_ -~ __ .

"'~ u'" 1IJ!t :tv ~~, '" 0., ~.

0: -~ x~ c'" -'" IJJ ..

= ~~::~:.::=~:~j~~~i~:.ji~· .::::.. ~:. §;~ :-.:;;:;=- - :1' X

-' .. _--_.- ---- .. -

... " ...... - ..... -.- - ... -- .. _ .. - - .. .~ ... .

~:::~:r~: .. ~ :~--t::::?-:::- ~_:::--~=I--::::: ., --_ ... - .. ' '-'-' ... .

, ( - . . .. - -.- ._-'.

::~":. -- ... _- ... __ .. _-. __ .....

1:::=;: .,~ ..• --.::..:;-:..::-:.::.:.-~ ---=-:-:. ::- ::;~ ... ~ j:::::::::;r~~~::l7.:::t: :i=f."-- -:t=--.:_-:::_._- - .

-=

f--- --t---- _ --E:=~:~: -=r:-=:.:=~ -.- :::: :: .. _-:=4-. _:~:t~:~~:::

-- f--+--:::::~~.,.:L.I~:"':~f~:.;~lIf'::: = b..:;:r- -~= . ·::;~::~:~.::I~:~~:~~~~::<:'

~::-I=+--:-' =~ ._~_ t:;:- --,- -=-:-·:0r.~~~:~~:::~~::;;::~~:::

~-=E~::: __ ~~ ~~~t:::~~;ili~~:~:::!~~~:~::::~:;:::~:::~~: :::--

5-85 10 X In TO THE CENT! ME:T[R 46 1513 kfl'rrn 1\ P~(I~"("{) ·.H.t·· 'jll' ...

en I (1\

o-n

LB FT

Q

·e

!iii iii; I CO~ECrE1> RArE

B'RAKE ~.;~f :':1 !!";Jl::lil~'::! ",t',' I .:"':'J:~:~lL:"':_·.l:!::l::: !,:,:~'1':"":. 1::"1 '::1: :L.. I.....:-.I:l~.: .. J..:......~.klt;.1l.l..l.....JJ..U.l.r.Ll..l..u~.U_u. ... l...;_ll.:..L.W!;I. :!!:..!.I _~J!I.rJ:.Lt!lL!"[ULr:t..:.J.UJ.UU'iltrU!.J~Il:,::~q::'··I!: '1' ... 'nl:*r'll :

FIGURE 5.26

~ • j '. • • 1 . •. .. :.. • I . • • • . • .. '" ~. : j...:. .

- ... : .. _-_·.-_-_.·_::_:._·;_-:-_:~.:..t:_·· ... ·;_:_· 1;..: __ ·_';;.,· __ :._T_:_-:-_~_~..;l_-··_:_· _:-:- .. T-~·~:.:l.~:~·--:~;:_-_·-.....; ___ ·- _______ ··===::..;.-_- ___ -_., ~N~ - ; waT RPM .- ••• - • < ._---- , I , .

: - .. - ~- .. - .. ---- .

---.- -.- ... - ....... -----~------ ...... --.;-- .....

····· .. :·:·-:~-~·:H+~j~~~~ :~ fI1 .. -:-L.-- ... -~-.-:. : 1 I ; ~_ .. :. ..:_._..; ____ ~. _____ .... L._ .. _____ .......... __ ...... ___ ...... _ ... __ .... _ .. ., . __ ....... ___ . .. __ . ___ .. _ .. _ ._ .. _.'_ lEGUR£ ... EiT,~~·~t~~~-~.~~t'r-~0·-h-··.·.

---.----- .' . . .....•... 4 .......... , ..... ', .... - • . ..

. :_._.: .. _: ._·~:.:l.:L;:l.: _:::';J :> ;.,_~ .. '.:~:.-1:' ::L~:·! :Co.:::::;- ... :: ':.': :;C::::::':::1':-:-::::::T:~::::::: -::::::: ::... .

--~--- -- - ·':·-··~;~Tj~~;~}~~~~;;:}::::;~?;~'~:-:···

, ..... .. -- - ..... _ .. ,.----.- : .--:~.7t:::~~~:~-S-~~::::~-:~-:-::::: -:::: :-:'i:' ALL A.,.M~SPH£RE.S ............ ,_.

'~::::1: '.~~~:::~ -::'~::::'-':;~::-_' __ =~!~'_-:::~:-::" 'Jj'-- ~':-~ --:- .

..................... - .

~..NE.

~~.~.~ WDT --:-.;.;::.::r-~22.l....:c..:.-'-:-'1· .. -----!-- ..

RPM 5-87

NEA SUBSYSTEM INPUT - OUTPUT MODEL

~ STANDARD AND NON- STANDARD ArMOS;PHERIC CONDiTIONS ENGINE ENGINE.

ERRJCE

c

CORRECTED PART - THROiTLE 1.

Qe.

],RA~f SPECIFIC.

71JRaVE UM'F'TiON FUEL CONS PERFORMANCE PLOT: FIGUR£ 5.26 INL£T ENC,/NE. mANJFOLIJ

N£ r:n

SI1IlFT SPE.ED 'PRESSV£E 2. WIDE OPEN IHf?orr'l ... £ -PERFoRMANCE PLOTS: FIGURES 5.28 5.27, FUEL -1J8.Y AIR Rr mos 'PH E '(.I.e.

F

Ta.tmc?s 11MB lENT fllR Rlmo MASS TEf'II'PE RM Ll RE 3. EQUArtoN'S

5.1, 5.7 - 5..1I

.

mils;;, F'tJEL

m

f . FLOW RArt p .

oZmo.s STANDARD ATMOSPHERE

/-1,,1-1= /-I"

PREs.surE. flLT/TUDE. EQUIrTIONS B.3, B.4,

.B.l" B.7.,B. 8, B.9

~ ..

NOTE: I. !GNITlON"'-;/MING OPT/MaE]) FOR MAXIMUM Q E •

2. ENGINE. .BRAKESPECIFIC.Fu£L CONS.UMPTION c. c.tJNST1?RINfJ).f- To A MINIMJJM COMIIIE.NSuitAr£''WlrH tHE INPUTS.

3. K = 2~. ~21.2116.22 = C.ONVE.RSION FACTOR.: LB/FTZ. To INCHES HG.

FI(~URE 5.30

5-88

TURBOCHARGED PISTON £NGINE

SCI-I£MATIC

~ FUEL L,---.

5f>1/~K. - IGNtttON iHRorrLE COMPRH.SOR INDUCifON AIR PIS/ON ENGINE INLH DECK

y

MANIFOLD

I

VI I ID !;HIlF1 ~RgOCHRRGER --.;) C EXHRUST GAS EXHAUST MANIFOLD

¢=J

I TuRBIN£ I

FIGURE S.3/

CHAPTER 6 THE AIRPLANE-ATMOSPHERE SYSTEM Table of Contents Page INTRODUCTION. . . . . . . . . . . . . . . . .. • . . . . . . • . . • . . . ... . . . . • . • . . . • • • . • • . .. 6-1 THE INTEGRATED SUBSYSTEM CRUISE PERFORMANCE MODEL •.•••••••••••.• 6-1 Fomulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6-1 Implementation ............................................. 6-2 The ISCPM.............................................. 6- 2 I· The peripheral Compu~ational Package ••...•...•.•.•••.•• 6-2 Computations Using the ISCPM .........••..........••.••••... 6-3 Engine Control .......... 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 6-4 Increases in R* Relative to Current Practice ••..•.•.......•. 6-5 COMPARISON OF THE ISCPM WITH THE POH CRUISE PERFORMANCE MODEL ...•.......•••.•...•••••••••.•..•.•••••.••.•..•..•.•.•.•.•. 6-9 FIGURE 6.1 .•.................................. ·.................. 6 -11

CHAPTER 6 TIlE AIRPLANE-ATMOSPHERE SYSTEM INTRODUCTION This chapter integrates the APA and NEA subsystem input- output models (developed in Chapters 3 through 5) to form a cruise performance model of the airplane-atmosphere system. The latter model is referred to as the Integrated Subsystem Cruise Performance Model (ISCPM).

First: the ISCPM is formulated. Second: the implementation of the ISCPM, and the use of the ISCPM for performance computations and optimizations is discussed. Third: engine control requirements of the ISCPM are discuss ed.. Fourth: the potential increases in R* offered by the ISCPM, relative to current General Aviation practice, are examined. Finally: the ISCPM is compared with the Pilot Operating Handbook Cruise Performance Hodel developed in Chapter 2.

THE INTEGRATED SUBSYSTEM CRUISE PERFOru.fANCE MODEL Fonnu1ation The APA subsystem input-output mode~ has been summarized in the block diagram of Figure 4.8. Likewise, the NEA subsystem input-output model has been summarized in the block diagram of Figure 5.30. These two block diagrams are combined in Figure 6.1.

The ISCPM is the set of relationships which detennines the outputs 6-1

S = { R*. Pm' F, lil }

out f of Fi gure 6.1 in terms of the inputs

Sin = {V ' V , W, h, P ' N , Tatmos' Hp}

w E AUX E of Figure 6.1. The ISCPM yields the point performance of the complete airplane in cruise, in the standard atmosphere or in any non-standard atmosphere; when the engine is operating at the mininrum possible BSFC commensurate with S ..

1n Implementation It is proposed that the ISCPM forms the core of an airborne microprocessor computational package. Computational software contained in this package, but extra to the ISCPM core, is referred to here as the Peripheral Computational Package (PCP).

The ISCPM: For a discussion of implementation of the ISCPM: the reader is referred to pages 4-22 and 5-47 for a discussion of the implemen- tation of the APA and NEA subsystem input-output models.

The Peripheral Computational Package: The function of the PCP is to perform computations other than those which may be performed directly by the ISCPM. The ISCPH The PCP might be can only perform point performance computations.

designed to perform tasks such as: 6-2 i I I r 1. Use the ISCPM to compute the airplane operating point

i

which maximizes R* with or without contraints 2. Use the ISCPM and an APA subsystem climb-descent input- output model, together with navigation data, to compute

I

trajectories which minimize trip time' or M with or f without constraints.

In performing these tasks, the PCP must provide the inputs {V , w

I

v W h P NTH } to the ISCPM.These inputs are

E' , , AUX' E' a tmos ' p

I

obtained by the PCP either from sensors, from direct pilot input, or as computational outputs of the PCP itself (see following sub- section). The outputs of the PCP may be used in the aircraft: to drive displays (including appropriate fuel management displays); or as command inputs to automatic control systems.

The "architecture" of the PCP is task-dependent and is not addressed here.

Computations Using the ISCPM The point performance computation which may be performed directly by the ISCPM is:

I. Computation of the set Sout = {R*, Pm' F, fuf} for any

given set Sin = {V ' V , W, h, P ' N , Tatmos' Hp}'

W AUX E E A PCP may be designed to facilitate other computations. Fol- lowing is a list of the computations which may be performed by the PCPjISCPM to maximize R* with or without constraints: II. Computation of the set {Pm' F, ro , N } yielding maximum f E R* and computation of this R*, for any given set {V , V ' W, h, P ' T t ,H}. This requires that E AUX w a mos p 6-3 computation I be performed for a number of values of N : E the value of NE yielding maximum R* is determined by interpolation; and computation I is then performed using this value of N • E III. Computation of the set {Pm' F, m , V ' N } yielding f E E maximum R* and computation of this R*, for any given set {V W h P T H} This requires that w' , , AUX' atmos' p' computation I be performed for a number of sets {V ' N }: E E the values of {V , N } yielding maximum R* are determined E E by interpolation; and computation I is then performed using these values of {V ' N }.

E E

IV. Computation of the set {Pm' F, m , V ' N , Hp} yielding

f E E maximum R* and computation of this R*, for any given set {W, h, P AUX' vertical profi Ie of atmosphericcondi tions (H , T , V)}. This requires that computation I be p atmos w performed for a number of sets {V ' N , Hp}: the values E E of {V ' N , Hp} yielding maximum R* are determined by E E interpolation; and computation I is then performed using these values of {V ' N , Hp}' E E For a given airplane and atmosphere, computation IV constitutes an unconstrained optimization of R*.

Engine Control Formulation of the airplane-atmosphere system cruise performance model in the manner shown in Figure 6.1 facilitates optimizing 6-4 tmaxirnizing) R* under various constraints. From the above discussion and Chapters 4 and 5, it is clear that such optimizations require that: 1. The pilot or the airborne microprocessor system be able to allocate values to {N , Pm' F} independently.

E 2. The engine ignition timing T be maintained at the MBT value T , the spark being retarded as necessary to control o detonation. MBT ignition timing T has been functionally o " described by Equation E.33.

These requirements preclude controlling the engine with a "single power lever" in which {N , Pm' F, T} are prescheduled. Such a E "single power lever" has been advocated by Chiri vella (16). The ISCPM requires that the engine be controlled with independent: 1. Throttle 2. Engine speed controller (propeller governor) 3. Ignition timing regulator (see p. 5-47) 4. Fuel-air mass ratio controller (see p. 5-47).

Items 3 and 4 probably should be feedback control systems.

Increases in R* Relative to Current Practice Implementation of the ISCPM in any General Aviation airplane offers significant increases in R* relative to R* achieved when operating that airplane in accordance with current GA practice.

The following discussion is based on Chapters 3 through 5.

1. Choice of {V , N} for actual" gross weight and altitude: E 6-5 Consider the LASA 60 performance in Figure 4.3: S* might c reasonably be expected to increase from 0.71 to 0.75 in typical fuel-conscious operations, and from 0.71 to 0.81 in extreme cases. Hence the ISCPM is estimated to offer S* increases of c Typical S* increase 6%

=

c Maximum S* increase 14%.

=

c An accurate knowledge of the gross weight then permits an estimate of the corresponding R* increases. We assume that the ISCPM has an accurate value of the gross weight; that the gross weight varies from the take-off gross weight

by an average of -100 lb in 3,000 lb = -3%; and that the

pilot currently uses the take-off gross weight for per- formance computations. The ISCPM therefore offers R* increases of

Typical R* increase = 9%

Maximum R* increase = 17%.

2. Choice of al ti tude to maximize effect of wind: In currently choosing cruise. altitude, the pilot is assumed to fail to take advantage of an extra five knots tailwind component available at some other altitude. The ISCPM is assumed to have the correct altitude profile of wind V. Assuming a typical true airspeed of 110 knots, w and a minimum true airspeed of 90 knots, the ISCPM offers ~ i R* increases of 6-6

Typical R* increase = 4.5%

Maximum R* increase = 5.5%.

3. Center of gravity position, auxiliary equipment power and propeller compressibility: It is assumed (conservatively) that the ISCPM offers no R* advantage due to an accurate knowledge of the airplane center of gravity position he, auxiliary equipment power PAUX' or propeller compressibility effects reflected in variations in the value of f from unity.

comp 4. Engine brake sped fic fuel consumption: From Figure 5.10, the maximum possible BSFC improvement when leaning from best power mixture with MBT ignition timing is about 17%. On the basis of Figures E.3-E.5 it is assumed that operation with given {BHP, N , H, T t } p amos E at best power mixture and with MBT ignition timing yields· about the same BSFC as achieved by operating at the same {BHP, N , Hp' T } at best power mixture with a fixed E atmos ignition timing L typical of the values of T used in current GA practice. GA pilots typically operate their engines at the best power mixture. Hence, the maximum possible BSFC improvement offered by the ISCPM over cur- rent1y achieved BSFC is about 17%. However, due to the fact that BHP decreases significantly during 1eanout at wide open throttle with the result that the engine cannot always be leaned to the fuel-fir mass ratio yielding 6-7 minimum BSFC. the maximum BSFC improvement offered. by the ISCPM is taken to be 10%. This yields a maximum. increase in R* of 11%.

It has not.been possible to compare the minimum BSFC achieved with the ISCPM with the minimum BSFC achieved when current fixed ignition timing engines are leaned in accordance with the manufacturer's recommendations.

It is assumed here that this comparison results in a typical decrease in BSFC of 5% when using the ISCPM: this yields a 5% increase in R*.

Hence the ISCPM is as.sumed to offer R* increases of

Minimum R* increase = 5%

f-Iaximum R* increase = 11%.

The total percentage increase in R* offered by the ISCPM relative to R* achieved in current practice is 6R*% which is obtained from the above as follows: Typical 6R *% = [( 1. 09 x 1. 045 x 1. OS) - IJ x 100% to [(1.09 x 1.045 x 1.11) - IJ x 100%

= 20% to 26%

Maximum llR*% = [(1.17 x 1. 055 x 1.11) - 1J x 100%

= 37%.

These figures are taken to apply to all GA airplanes powered by naturally aspirated SI piston engines. The savings are per- ceived as significant. Implementation of a cruis~ performance model similar to the ISCPM. in GA airplanes powered by 6-8 turbocharged 51 piston engines, is expected to result in values of ~R*% which substantially exceed these figures. (The turbo-

I

charged engine can operate at the fuel-air mass ratio offering minimum B5FC over a greater range of flight conditions than can the naturally aspirated engine.)

I

CO~WARI50N OF THE I5CPM WITH THE POH CRUISE PERFORMANCE MODEL

I

The Pilot Operating Handbook Cruise Performance Model (POHCPH) has been developed in Chapter 2. The advantages of the ISCPM over the POHCPM are: 1. The ISCPM permits cruise performance to be computed for all values of {W, h, H , atmospheric conditions}. TIle POHCPt.1 p must interpolate between cruise performance specified for certain values of {W, h, II , atmospheric conditions}: in some p cases, cruise performance data appropriate to only one value of one or more of {W, h, atmospheric conditions} are available in the POH.

2. The ISCPM permits true optimization of R*, with the engine operating at the minimum possible B5FC at all times. The POHCPM permits optimization of R* subject to the opera- tional recommendations {Pm' RPM, m } .. of the manufacturer, f and with fixed ignition timing.

} 3. The ISCPM commands F which is established automatically by the fuel-air mass ratio controller. This precludes the fuel-inefficient operation which resul ts from poorl" executed manual leaning. The POHCPM requires manual leaning.

6-9 Consequently, the ISCPM is considered superior to the POHCPM as a tool for maximizing R*.

The ISCPM and the POHCPM have one problem in cOllllllon: both utilize calibrated cruise performance data appropriate to the airplane. However, the performance of new airplanes of the same type and model is not precisely the same; and the performance of a given airplane varies throughout its life, reflecting variations in the condition of the airframe, propeller and engine. Therefore, the cruise performance predictions of the ISCPM and the POHCPM must be expected always to vary from the actual airplane per- formance. The author has not addressed this issue, but it is one which will require study if calibrated cruise performance models are to be introduced into General Aviation.

6-10 ~-~~~~---:----~------ __ o ...... -:-.- ..... ------.-;----~-

INTEGRATED SUBSYSTEM CRUISE PERFORMANCE MODEL: ISCPM

STANDARl) AND NON-STANbRRJ> ArMOSPHERIC CONDITIONS -(RACK ""liND ~ PEE ]) IILON{; :

o X, y, Z

I. PLOT FlCURE 4.4 E!J.UIvIlLE..NI AIRf.P£E.D : 2.. PLOT FI(;UR£ 4.5 X, Y, f3

*

WEIGf.lr ~~s" : C.G. PoSmoN 3. PLOT!:. FIGURE ]).10 fe-amp

r--- R C

*

EaUIPME.NT' rOINER..

AllXfL LIAR Y +: EQUATIONS 4.62 -. 4.73, C.II 0- r;"tmos £N{;INE. SHRFT

NE

~

SPEEl> C') (]\ I .....

~

.....

.

f'l1 Q

Nt

"Pa.tmos -'J~ R*

E 5PE eiRe.

t~

tJ.E. 'RAN

<Jo Ra ~mos 1'0

0\ .

-

hrfV70!;'PHE~/C RMBI£Nr AIR.

T

atmos Ta., PERII1'/J R.E.

,.

C CORRECTED PA RT - THROTTLE PERFoRMANCE PLOT: FIGURE 5.26 STANDARD ATMOSPHERE INLE.T' t:.tmos MIII'I'FOLD

H-H

iBr

PRESSUJ!.E.

- P

WIDE OPEN rHRorrLE PERFoRMIINCE.

2.

Ts

[QUAT/ON!) PUffS: B.3, B.4, FIGURES 5.27, 5.2.8 fUEL <DRY !l11l.

..

F