Methods for comparative evaluation of propulsion system designs for supersonic aircraft

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Final Report Project Manager: D r . Edward A. Killis 16- Absm The pmpulsion ? - s t e t , comparative evaluatian study had tug objectives: ( 1 ) to define a rapid, approximate l s c t h o d for evaluating the effects of prepulsion s y s t a changes for n advanred suprunic cruise airphw, and ( 2 ) verification of the approbte m e t W by - r i n g i t s mission perfcmmce results w i t h those frau a eon detailed analysis.

A table look-rp coaputer pmgram was developed to determine nacelle drag k m w n t s for r range of paramtric mcelle shapec, and sizes. ' Aircraft sensitivities to plPprtsion paraatters urn &finedi -Nacelle shapes, installed wights, and installed perfomice w e n detemined for four study engines selected fran tb ?d\St\ Supersonic rruise Aircraft Rcscarch (SCAR) engine studies progm. Bath rapid evaluation method (using sensitivities) and traditional preliminary d e s i s ethods #re then used to assess the four twines. Ihe leth hod was fornd t o carp.-e e l l with the mre detailed analyses.

17. am war^ ( s - t c d bv A U ~ ~ ( J ) t a w i i kitmnt Propulsion integration Unclassified, tmlimited Perfonrace sensitivities Njcelle drag Advanced supersonic transport technology Engine evahtion 22. hit*' 10. Securitv asif. (of this pagr! .

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For U t e by the Njl;aca! Tecbn~cnl Icforlti~t~on Si.:vse, $pri~gfielrf. Virgin13 ??I61 This docualent presents results of the study 'Nethods for Conparative

Evaluation of Propulsion System .Wsigns Cor Supersonic Aircraft ." The NASA

In addition to the authors technical repxvsentative was Dr. Edward A . Nillis.

noted, significant contributions to this study and report were? made by Ellwood Bonner, aerdynaarics; Henry K. Chin and Louis C . Yomg, propulsion.

Page Estimation of Supersonic Cruise Drag Estimation of P r o p ~ l s i o n System f n s t a l l a t i o n lieight Estimation of Airplane Takeoff Gross lieight Validation of the Approximate #ethod Conclric ims and Recamendat ions - - \ P P F ~ ~ Baseline .G rplane Definition Basepoint -4irplm-e Design ?lission .Altelnate ?lission Balanced Field T3keof f Thrust- to- Drag Ratio Base 1 ine -4 i l-plaqe Prop.11~ ion \lass Properties .Aetrd!nanics - tstimation o f S u p e r s o ~ i c Drag Parametric Drag h a l y s i s Drag Table Lwk-Up c'owuter Program Sacel le Shape E s t inat ion Estimation of Sacelle/ Jnlet lieight TKO Dimensional I n l e t s . k . i s ! m t r i c I n l e t s Et ination o f .ii.,plane Takeoff Gross lieight licight Sensitj \-it? Analysis Application of S e n s i t i v i t i e s

Validation of t b m - t e Nethod

Propulsion Mass Properties Aerodynaeics krfomance and Sizing Sensitivity Method Verification LIST OF ILLWTRATIONS Figure T i t le page

Nacelle Laywt . . . . . . . . . . . . . . . . . . . . . . 7

h-mr Characteristics of Appmxhate ~ e - . . . . . . . 10

Xomalized Xacellt? C m s s - k t i o n a l Area

. . . . . . . . . . Variation f o r VSCE 502B and VCE 11?C

&epoint A i r p 1 . m ~ . . . . . . . . . . . . . . . . . . . . 17

Vehicle Sizing and P e r f o m n c e Evaluation Program . . . . .

Reference blission . . . . . . . . . . . . . . . . . . . . . 21

Altem~te Mission . . . . . . . . . . . . . . . . . . . . . 23

Balanced Field Length Definition . . . . . . . . . . . . . 25

. . . Gross Weight Versus Thrust-to-Weight and king Loading

Ralanced Field length Versus Thrust-to-Neight . . . . . . . . . . . . . . . . . . . .

ad Wing Loading 27 ThrustfDrag b t i o C;crstis Thrust- t o - k i g h t and

Wing Lading . . . . . . . . . . . . . . . . . . . . . . 28

. . . . . . . . . . . . . . . Baseline Airplane Climb Path 34

. . . . . . . . . . . . . . . . . . . . . Basepifit 'Xacel le 35

Comparison of Reference aild base,^ i n t Nacelle..; . . . . . . 40

. . . . . . . . . . 41

bcelle Cross-Sectional .I rea Variation

R a s e p i n t Vehicle Cross-Sectional Area Variation . . . . . 43

Basepoint Jncremental Nacelle !)rag Versus Bbch h~onber . . . 45

Rawpoint have h a g Sizing Data . . . . . . . . . . . . . . 47

. . . . . . . . . . . . . . . . . .

C I . ~ Versus Mach Shmber 48

(:k Versus Mach Su&r . . . . . . . . . . . 49

. . . . . . . . . . . . . . .

'h;' Factor Versus Mach Smber 50

h s c l i n e Vehicle (.ro.;s..Scctional Area Variation . . . . . . 51

Nacelle Parametric Cross-Sectional Area Fxtremes . . . . . 57

Typical .?k c e l le I ncremcntal \hve Drag Vari a t ions with Mach Number .& = 2.79 sq n ! (30 sq f t )

. . . . . . . . . . . . . . . . . . . . . . . I / d , = 5 . 5 59

. . . . . . . . . . . . . . . . 6 1

S i m l a t ion of Naccllc Shape

. . . . . . . . . . . . . . Nacel l e Drag Sensi t i\- i t y Tradc 69

Propulsion keight and SFC Sensitivity Trades . . . . . . . 70

Sizing Point Thrust Sensitivity Trade . . . . . . . . . . 72

. . . . . . . . . . . . . . . . . . . . .

VCE 112CNacellc 73

VSCE 502B and VCE 11 2 C Takcof f Thrust . . . . . . . . . . . 75

Installed IJerformance Comparison of Baseline and

. . . . . . . VCIi 112CatIrlach 2.32, 19 800111 (65000 f t )

Baseline and VCtl 112C Performance, bhch 0.9, . . . . . . . . . . . . . . . . . . .

13 700111 (45 000 f t ) 77 irCE 5028 and VCE 112C k r f o ~ m a n c c , Mach 0.9,

13 700m (45 000 f t ) . . . . . . . . . . . . . . . . . . . 81

V X E 5028 and VCE 112C Installed Performance a t

k c h 2.32, 19 800111 (65 000 f t ) . . . . . . . . . . . . . 82

Figure Title VSCE 502R Nacelle . . . . . . . . . . . . . . . . .

GEZl/J10 01 and GE21/Jll B3 Takeoff Thrust . . . .

GEZl/J10 81 and GE21/J11 83 Perfonaance. k c h 0 . 9 ,

. . . . . . . . . . . . . . . 13 700 m (45000 ft)

GE21/J10 B 1 and GE21/J11 B3 Installed Perfo~mance at kch 2 . 3 2 . 19 800 ar (65 W0 ft) . . . . . . .

GEZl/JlO B1 Nacelle . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . GEZl/Jll B3 Nacelle

VSCE 502B and VCE 112C Nacelle Cross-Sectional Area Variation . . . . . . . . . . . . . . . . .

GE 21/J1@ B1 and GE 21/J11 B3 Nacelle

. . . . . . . . . Cross-Sectimal Area Variation

. . . . . . . . . . . . .

Economic Mission Profile Design Mission Range Versus Engine Size . . . . . .

Balanced Field Length Versus hgine Size . . . . .

Sizing with W E S02B Engines . . . . . . . . . . .

Sizing with VCE 112C Engines . . . . . . . . . . .

Sizing with GE21/J10 B 1 m i n e s . . . . . . . . . .

Sizing with GEZl/Jll B3 Engines . . . . . . . . . .

LIST OF T A B L E S Table Title page Baseline Airplane . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . Sample C)utput

Coaparison of Approximate and Detailed Gross Weights . . .

Drag and Takeoff Gross Weight Increments h e to

. . . . . . . . . . . . . . . . . Changes in Engine Shape

. . . . . . . . . . . . . . . . . Airp1m.e Characteristics

Baseline Design Mission Sumnary . International Units . . .

Baseline Design M.ission Smmv . English Units . . . . . .

Base1 ine Alternate Mission Sprmnry . International Mits . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Baseline Alternate blission !3mnary . English Units . . . .

. . . . . . . . . . . . . . . . . . Vehicle Weight Sumnary

. . . . . . . . . . . . . . . . . . Basepoint Engine Weight

Basepoint Nacelle height . . . . . . . . . . . . . . . . .

ksepint Configurat i m Estimated Profile and Wing Drag Characteristics SREF = 929 sq m

. . . . . . . . . . . . . . . . . . . . . (10 000 sq ft)

Baseline Ccnfigurat ion Surface -4rea and Length Sumnary . . . . . . . . . . . . . . . . . . . . . . . . .

Baseline Configuration Skin Friction and Wake Dr?g Characteristics . . . . . . . . . . . . . . . .

Nacelle Parameter Values . . . . . . . . . . . . . . . . .

Compariso D. of Eascline and LrCE llZC Nacelle Drag I r . c remen t s . . . . . . . . . . . . . . . . . . . . . . .

Fmgine Sumnary . . . . . . . . . . . . . . . . . . . . . .

C;lgine Weights, International Units . . . . . . . . . . . .

F~gjne Weights, English Units . . . . . . . . . . . . . . : Sacelle/Inlet Weights, International Units . . . . . . . .

Nacelle/Inlet Weights, Ekglish h i t s . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . Drag Conpar i son

Airplane Characteristics with Refined VSCE 5028 Fagines . .

Airplane Characteristics with VCE 112C Er.gines . . . . . .

.4 irplane Characteristics with GE21/JlO B1 Engines . . . . .

Airplane Characteristics with r j E 2 l / . Jll B3 Engines . . . . .

Refined VSCE 502B Baseline Design Mission Sumnary , International Units . . . . . . . . . . . . . . . . . . .

Refined VSCE 502B Baseline Design Mission Sumnary , English Units . . . . . . . . . . . . . . . . . . . . . .

VCE 112C Baseline Design Mission S m r y , International Units . . . . . . . . . . . . . . . . . . .

VCE li2C Baseline Design Mission, Surmary English Units . . . . . . . . . . . . . . . . . . . . . .

Table Title W e 3 2 GE 21/J10 R1 Baseline Design Mission Sumary, International Units. . . . . . . . . . . . . . . . . . .

33 GE 211510 B1 Baseline Design Mission Sumnary, English Units. . . . . . . . . . . . . . . . . . . . . .

34 GE21/J11 B3 Baseline Design Mission !hmary, International Units. . . . . - . . . . . . . . . . . . .

35 GEZl/J11 B3 Baseline Design Mission !Summary, EkglishUnits.. . . . . . . . . . . . . . . . . . . - .

36 Economic Mission Characteristic5 with Refined VSCE 502B Engines. . . . . . . . . . . . . . . . . . . . . . . . .

37 Economic Mission Characteristics with VCE 11X Engines. . . . . . . . . . . . . . . . - . . - . . . . .

38 Economic Mission Charzcteristics with GE21/JIO

Bl Fasines . . . . . . . . . . . . . . . . . . . . - -

3 9 Economic Mission Characteristics w i t h C;E21/JI 1 B3 Engines . . . . . . . . . . . . . . - . - . . . . .

40 a3C, IOC, and ROI. . . . . . . . . . . . . . . . . . . . .

VSCE 502B Baseline Economic Mission Surmary, 4 1 International Units. . . . . . . . . . . . . . . . . . .

4 2 EXE SO2B Baseline Economic Mission Simnary,

English Units. . . . . . . . . . . . . . . . . . . . . -

4 3 VCE 112C Baseline Economic Mission Surmary, International Units. . . . . . . . . . . . . . . . . . .

44 VCE 1 1 2 ' : Baseline Economic Mission Sumnary, English Units. . . . . . . . . . . . . . . . . . . . . .

4 5 CE21/J10 El Baseline Economic Missior. Starmary, International Units. . . . . . . . . . . . . . . . . . .

46 GE21/J10 B1 Baseline Economic Mission b W r y , English Units. . . . . . . . . . . . . . . . . . . . ., .

4 7 GE21/Jl1 B3 bseline Economic Mission Smmrrry, International'hits. . . . . . . . . . - . . . . - . . .

48 G21/Jll B3 Baseline Economic Mission -Sumary, English Units. . . . . . . . . . . . . . . . - . . . . .

Takeoff G~noss Weight Sensitivity Calculations. . . . . . .

METHCDS K)R UliWARATIVE EVAWATICN

O F mPUtS1ON S Y m DESIGNS m

S U P ~ I C A I W By Ray M. Tyson, Ronald Y. Mairs, Floyd D. Halferty, Jr.,

B r u c e E . Moore, David Chalof f , and Amold W. budsen

Los Angeles Aircraft Division, Rockwell International The National Aeronautics and Space Administration is conducting a continuing program of idvanced supersonic technology studies with the objective of developing an adequate technology base t o support development of future supersonic cruising aircraft. I t is recognized in this program t h a t one of the more sensitive problews in the synthesis of a successful supersonic cruis- ing aircraft is that of airframe/engine integration. This process must inves- tigate and properly manage the interactibns between the technical disciplines of external aemdynamics, internal aerodynamics, engine cycle design, acous- tics, nrass properties, and structural &sign; and, it must Le responsive to the practical considerat ians of fabricat ion, maintenance, and operation.

h e results of a recently canpleted study, reference 1, of the effects of nacelle size and nacelle shape on the drag, weight, and wing camber plane warping of a supersonic transport illustrated the sensitivity of these param- eters t o relatively small changes in nacelle shape. The resultant shape of a nacelle is dependent on the geometry of the engine (inlet area, mounting pro- visions, accessory location, nozzle area, etc.) since this establishes certain control points i n the design of the nacelle. I t is important, therefore, that the engine designer be aware of t h i s sensitivity t o engine geanetry, and be provided with sane guidelines for favorable geometry relationships.

I t is probable that some engine geometry control can be achieved by the designer with no penalty in engine performance, although on a t o t a l system basis some engine performance degradation could be accepted in trade for reduced drag.

Although considerable effort has been expended on the problem of airframe/ engine integration, it has been mostly i n the nature of point designs. The study of reference 1 produced results for two specific nacelle shapes which resulted from instal1at:on of a dry turbojet engine and a duct heating tmbo- fan engine. A comparison of these results shows the superiority of one nacelle .

shape over the other, but gives no information directly applicable t o other ins t a l l a t ions having differing nacelle shapes. ?his report therefore t r e a t s nacelle shape and size i n a parmetric fashion so that a range of propulsion systems can be readily compared on a consistent basis. To meet the user's needs, it was clear that methodology faster and more convenient than the traditional a i r c r a f t -preliminary -design process would be required- -even at some cost in terms of accuracy. Therefore, the approach was taken of organiz- ing a relevant, existing s e t of nacelle drag data (reference 2 ) , together with supplementary data points as required t o cover the parametric range, into a computer table- lookup program. The program then yields supersonic wave and friction drag increments a s function of size and shape parameters for 3 representative supersonic cruise airplane configuration (reference 3). The drag code, c d i n e d with linear sensitivity factors (derived frm perturbation studies of the reference 2 airplane), provides the desired rapid approximate methodology for comparing a1 ternative propulsion sys tern designs .

The methods of analysis and major results of t h i s s t d y are described herein in. the "SIUDY PRtDXME" section. User's iilformation for the code, program listings and mathematical details arb presented in the Appendix.

rnkIARY OF RESULTS The present work is an extension of a previous study performed f o r NASA Langley Research Center (contract NAS1- 13906) and docunented in reference 2.

In that program, a baseline airplane was defined. Under the current contract, the baseline was revised slightly as described on page 71 f o r consistency in validating the approximate method; the revised baseline is used when perturbat- ing and comparing airplanes with other engines. The baseline and revised baseline airplanes are described i n Table 1. The baseline airplane was based on the NASA modified S C A T 15F vehicle described i n reference 3. Parametric data were generated showing the effects of variations of nacelle shape on cruise drag for a range of shapes tllat reasonably cover engine designs applicable t o supersonic cruising aircraft. Generally, it has found that nacelles shaped such that the maximum cross-sectional area occurred a t or near the nozzle exit and having l i t t l e or no boattail resulted in the lowest wave drag. In fact, nacelle shapes were found that produce favorable interference effects (drag reciuction) of such magnitude as t o nearly offset the friction drag of the nacelle. These results are valid only for vehicles of t h i s general configura- t ion and nacelle locat ion. Different vehicle configurations or nacelle locations could results i n different "best" shapes. In considering possible trades of reduced drag through design changes i n the engine for some penalty i n engine wzight and specific fuel consumption (SFC), it is necessary t o have v i s i b i l i t y of the net impact of a l l three effects on the t o t a l airplane i n order to make a comparative evaluation. Therefore, sensitivity data were developed for the effects of changes i n drag, propulsion system weight, takeoff thrust, and SFC on the takeoff gross weight as a figure of merit. Results of the weifit sensitivity trades showed that the airplane gross weight is highly TABLE 1. - B4SELINE AIRPLANES REVISED BASUINE NASA Langley study

--

7 408 7 408 ( 4 000) (?. 000) Design Mission Rhnge, Ian (n m i ) 2 . 4 2 . 4 2 . 4 2 . 4 Design Cruise Mach N h r (61 028j 27 682 (61 028) 27 682 Payload (292 passengers), kg ( l b ] 3 190 3 190 (10 500) (10 500) Balanced Field Leqth, m Cft) VSCE 502B VSC€ 502B VSCE 502B VSCE S02B h r g w ~ 4 1 (698 375) (712 188) 516 783 322 046 Takeoff Gross Weight, kg (lb) J

&*.** -

sensitive t o both drag and engine SFC a t supersonic cruise. A one-drag-count 'change (approximately 1 percent of airplane drag) results in a 1-percent takeoff gross weight change; a 1-percent change is SFC also results i n a 1- 'percent change i n takeoff gross e i g h t . Changes in drag o r SFC at other flight conditions a d changes in propulsian system weight had relatively sllaall effects on takeoff gross weight.

The follcw-an program, described in t h i s report, was intended t o render the above-mentioned parametric data into a convenient, useable form. The objective was t o develop a reasonably accurate method for the rapid, prelimin- ary evaluation of the effects of variations i n propulsion system design parameters on the total system performance of an integrated engine/airframe system. The figure of merit used was the airplane takeoff gross weight to perform a design reference mission. The effort was organized around the following five tasks: Estimation of supersonic cruise drag increments reflecting nacelle (1) shape and size (in the form of a computer table look-up program) Estimation of propulsion system installation weight (2) (3) Estimation of airplane takeoff gross weight Validation of the approximate method (4) (5) Reporting Estimation of Supersonic Cruise Drag A computer table look-up program was &veloped (see appendix) which yields the incremental wave and friction drags of nacelles as functions of five nacelle geometry variables and airplane mach nunber. The drag increments are for the t o t a l vehicle relative t o the vehicle with nacelles removed. The five nacelle shape parameters used as inputs to the program are: Inlet capture area Ac Nacelle maximum cross-sectional area Nozzle exit area (supersonic cruise position) An Distance from inlet cowl leading t o m a x h cross-sectional area L Nacelle total length SREF Reference wing area I t has been found that the table look-IT results correlate best with more detailed analyses when the maximum cross-sectional area and its position are based on the area that occurs a t the intersection of straight lines originating from the inlet and nozzle and whose slopes nearly mtcl the slopes of the actual nacelle. A sample output from the computer program i s shown i n table 2.

4 4 * f L.d* SF- > l z Y u 4 ~ z u a k ~ z r a u iL: & g U - I 2 0 , L . , ; o 3 r d d d e c N *.A r O - W U b 4 4 3 0 . 2 ru u r z a r - u .

u L Ibis t a s k also m l u & d preparation of design guidelines f o r t ? ?

installation of the engine in the nacelle so that consistewy i n definition of desigp awttrol points h r external nacelle shaping is achieved. h i d e - lines for establishing inlet ad i n l e t cowl shape, engine envelope definition (inclwiing pmvisium for wiring, p i d i n g , power takeoff, engine accessories, aircraft accessories, fluid rvoirs, air bleed ducts, and engine m t s ) , structural allawances, d engine awl .md nozzle fairing ,shapes were defined.

A satlple of + & nacelle shape b u i l w is s h in figure 1.

Estimation of Propulsion System Installation Weight X s i q l i f i e d procedure w a s developed for the prediction of nacelle struc- ture wight. Weight estimation of a i r c r a f t structure is a q l e x process and requires reore design detail than w i l l ordinal :ly be p e r f o n d in the type o f prel iminaq- studies being considered here; therefore, the procedure was keyed to gross e l m n t s of the propulsion system installation and yields only approximate wights. Ihe inportant aspect of having a well-defined p&m, e\en though consiJerable tolerance in the results rmst be accepted, is that consistenq is achieved in d i n g c q a r a t i v e analyses.

ktjmation of Aivlzne Takeoff Gross Weight -i method has been defined for the determination of the iqact of the propulsion system installation (cruise drag, SFC, weight) on t h e t o t a l system p r f o m c e utilizing takeoff gross weight as the figure of nrerit, lhis mthod b a s based- on results of sensitivity studies performed for Langley Research Center. Utilizing these sensitivity values, the drag and weight increments from tasks 1 and 2, and SFC's from engine performance estimates, this procedure yields the airplane takccff weight required t o accoapljsh tile design mission. The baseline vehicle is *h vehicle defined i q reference 2 with the lrSE 502B efiginz. The t o t a l change ~II vehicle takeoff gross weight due t o propulsion changes may be detemined from the equation:

=-baseline X R ~ ~ ~ X % "kXRFNETD new

D where "R" factors are the relative takeoff gross weight factors f o r each of the propulsion changes obtained f m a linear sensitivity analysis of the baseline system. The drag factor is based on a supersonic cruise incremnt.

@ Engine accessories. tjlcapsulated f o r cooling. I n c l d c s a l l teitperature - limited coqmnents.

@ -wine lube reservoii

@ Engine peripheral 1lar.kax-e.

Includes: engine f l u i d l i n e s (anti-ice a i r , fuel, lube o i l , hydraulic, drains, e t c ) , variable geolnetry mechanisms, e l e c t r i c a l harnesses, inst~uslentation, Local p r o t r u s i w s w i l l occur beyond this envelope.

@ Cnpresxlr bleed manifold.

@ Ehgine p e r takeoff f o r a i r c r a f t

accessories drive. Angle gearbox and

power transmission shaft t o uing -

mounted accessories drive gearbox.

@ fngine and nacelle support structure on wing, inside pylon.

@ Engine cowl. N o n s t m t u ~ a l , hinged

from pylon. Includes small doors for local access.

@ Main mount (front)

@ Stabilizer mount (rear)

Dimension in meters (inches) PRl?OTNG PAGE BLANK NOT Figure 1. - Nacelle layt ut

m L o o U T FBB168 7 2

Validatian of the Approximate Wthod Standanl preliminary design procedwes *re applied in the installatian of four representative engines selected from the NASA Supemmic Cruise Aircraft Research (SCAR) program engine studies, in the baseline supersonic transport airplane. Drag and weight estimates were raade utilizing carventiaml ~-.oceciUres. The airplanes were then sized t o the design mission utilizing an autaeated reiterative process. The results of this task grovi& a more exact evaluatian of the selected engines than is obtainable w i t h the spproximate slethod and thus serve as a reference for its evaluaticm.

The f o w engines considered were the refined (January 1476) Pratt and Uhitney Aircraft (PlrSC\) VSCE 502B and VCE 112C, and t h General Electric C c q m y (GE) GEU/J10 B1 and GE2l/J11 B 3 . These engines were chosen as representative examples which uould exercise tlre approximate nethod over a sizeable range, i n order t o determine its limits of validity. This can be done i n a cmsistent fashion by camparing the approximate m i detailed results shum in Table 3 ( C h the other hand, meaningful engine-to-engine collparisons

-

cannXTe each =%F m a on the basis of table 3 because the example engines do not

rscessarily reflect a consistent set of basic technology a s n a p t i a s , noise Hence, these characteristicc, or state of evolution within the SCAR program.

and similar results discussed later i n this report should not be interpreted as being indicative of the final out- of the ongoing SCAR engine studies.)

TABLE 3. - C(EPARIS0N OF APPWIXMTE AND D E T A I D VEHICLE TAKEOFF WEIGES I k i g h t Based on Night Based on Sensitivities Engine Detailed Analysis kg (lb) kg (lb) VSCE 502B 316 783 (698 375) Revised Baseline 320 146 (705 790) 320 046 (705 568) VSCE 502B (refined) VCE 112C 402 625 (887 622) 401 092 (884 258) GE21/J10 B1 514 450 (1 134 149) 463 708 (1 022 283) GE21/J11 B 3 629 306 (1 387 359) 510 136 (1 124 638) I By c q x i n g detailed and sensitivity results for each engine in table 3, it is inmediately clear that a good level of agreement has been reached. Tt~e relative error (nonnalized by the gross weight based on detailed results) is shown in Figure 2 as a fmction of the total increnental change i n TOGW

(normalized by the baseline value) . As might be expected fran theoretical

considerations, the error i s negligible for small perturbatian; in fact, it does not exceed 2 percent of the takeoff gross weight mtil the increment i t s e l f is in excess of 30 percent. It is important to note also that the error is consistent, i .e. always of the sane sign (the approximate method

urderpredicts) . Thus, even among highly-dissimilar engines, the correct

ranking is preserved. With these facts in mind, it is concluded that the approximite method is in fact a reliable and reasonably accurate tool for such purposes as engine evaluation a d corpariscm, over a range of about + 30 percent froa! the baseline W. Considerably larger in-ts also cbuld be accepted ( t rarily) as intenmidiate steps in an optimization

study, provided that % final case of interest is within tk - + 30 percent

band.

The user shwld never?hless observe several cautions i n applying these results. As a general practice, it is desirable to check the "final result" of a study by detailed laethods. This is strongly mxmmded for cases approaching o r passing beyond the accuracy band. The sensitivity values ( " R " factors) are t o sone extent dependent upon the engines sizing criteria, the ass& mission profile and flight rules. The user should therefire review these items carefully before beginning a study and generate a =re appropriate set of "R" factors if significant differences are noted. Ebre fimckmtally, it should be recognized that the wave drag data is s t r i c t l y applicable only to the reference 3 airplane mfiguratian d v t r i c a l l y similar scaled versions thereof. Trend results with nacelle shape fbr different airplanes of the same general arrangement are believed t o be representati:~, although detailed agreement b i d not be expected. l'he use of the pressit data for airplanes having significantly different shape, pmportions o r nacelle treatment is not indicated. Doubtful cases should be checked a t several points t o validate the data and/or establish corrections.

Cimclusiars and -tiom

Engine shape, a i r f l a r lapse rate with lrach nuber , thrust lapse rate

with lsach &r, SIC and noise characteristics have large irpacts an vehicle takeoff gross weight. As an exarple of engim shape effects, a comparison of cross sectional area variation o f nacelles with the VSCE 502B and VCE 112C tinghes is shawn in figure 3. The only significant difference in shape is that the VI=E 11X has a smaller aozzle exit area. lhis results in drag and takeoff gross wei&t changes as shorn in table 4. Thus, a nozzle that is 0.043 m ( 1 . 7 in) smaller results in takeoff gross weight inrreaent of 3 200 kg (7 100 lb) just due to the nacelle drag change.

Engine airflcw lapse rate with lnach &r directly affects inlet capture area. For exaqle, the GEZl/J10 B1 has approximately 16-percent 1-r n p e m i c cruise airflaw relative to takeoff airfltm than dues the VSCE 5028. nhe d l e r capture area results in approxirrttely 4-percent lmer inlet recovery a t static conditions and therefom miiced talreoff thrust.

In addition, the smaller capture area results i n a wore rapid incmase of nacelle cross-sect id area with nacelle length, and therefore higher

drag -

Engine takeoff thrust and thrust lapse rate with mach nuher have significant effectson engine size required t o meet takeoff distance require- ments. For exmple, the WE 112C has 6-percent laser takeoff thrust a t s t a t i c codit ions and 20-percent lauer thrust at mch 0 . 3 (at m h e d paJer t o mzet noise xquirwnents) than the VSCE 5U2B for a given s t a t i c takeoff airflow. This resulted i n an increase i n engine size of a p p r o x k t e l y 15 percent to meet bzlanced field length requirements.

A change of 1 percent in SFC a t supersonic cruise results in a 1-percent change in vehicle takeoff gross weight or about 3 200 kg (7 100 lb) .

Engine exhaust noise characteristics have a significant impact on vehicle takeoff gross weight. A l l four engines were assuned t o employ thrust cutback a t the takeoff noise measu=nt point. Haever, a l l the engines did not take f u l l advantage of the extra ground attenuatian while the air- For example, the C;E21/J11 I 3 3 has 26-percent craft was still on the ground.

lawer thrust-per-mit airflow than the VSCE 502B. Thus, the GE21/Jll B3 yields approximately 6 db lower sideline noise a t takeoff on the ground, but it nust be sized larger t o meet the takeoff distance requirement.

The sensitivity method has been shown t o be a valid method for prelimin- ary assessment of propulsion systan modifications, and it is therefore recomnended t o be used for this purpose. Continued airframe/prapulsion integration studies and coordination effort between engine and airframe manufacturers in the aforementioned high-sensitivity areas are also recomnended.

TABLE 4. - DRAG AND TAKEOFF GROSS WEI(HT INCRt- DUE 1D m G E S I N ENGINE SHAPE Takeoff Gmss Wei&t ACDs Supersonic Cruise Inc-nt lbelative NacelleDrag .

Engine to 502B Increraent Relative kg (lb) to Nacelles Off Base 0.00046

I I

A Area, sq m (sq f t or sq i n ) BLB Boundary layer bleed B K Boundary layer control BP Basepoint C Coefficient o r Chord, m ( f t o r i n ) d Diameter, m ( f t o r i n ) D h a g s daN (lb) db Decibel F Thrust, kg (lb) K Drag-due- t o - l i f t f a c t o r 1 Length, m ( f t or in) I. L i f t , N (lb) M ?tach number R Relative TaW f a c t o r S Area, sq m (sq f t or s q ir?)

SFC Specific fuel consclmption, kg/hr/N (lb/hr/lb) T Thrust, N ( l b )

rn Takeoff gross weight, kg jlb)

v Velocity, m/sec (ft/sec)

w Height, kg (lb)

X Nacelle s t a t i o n , m (ft o r in) A Increment Subscripts AM4X Maximrm cross-sectional area B Base C C a p - CD Drag coefficient D DraS

. F Friction

Fuel f i inlet throat Indicates l i f t coefficient a t m i n k drag K L i f t L LO b f t o f f hkxiaan MGY n Nozzle e x i t kt e f f c r t ne Profile P Reference REF R Root SFC Specific fuel c m s q t i o n SUB Subsonic SUPER Supersonic T @ Takeoff Wave W Weight WT

c ! Frees tream

1 C r i t i c a l engine failure Approach The general approach of t h i s study included using the baseline airplane, parametric nacelle drag results , and takeoff gross weight s e n s i t i v i t i e s devel- oped in the NASA I'angley Research Center contract of reference 2. -4 nacelle drag table look-up computer program and guidelines f o r determining nacelle A method shape were developed t o allow estimation of supersonic cruise drag.

t o assess the propulsion system installation weight was defined. A method of determining vehicle takeoff gross weight using vehicle s e n s i t i v i t i e s t o propul- sion changes was developed. IIhe method was verified by analyzing in d e t a i l four selected propulsion systems.

Because of the dependence of t h i s study on the baseline airplane and ground rules of the study of reference 2 , the definition of the baseline a i r - plane is included. In t h i s report, descriptions of the airplane configurations used are as follows : The reference airplane is the NASA-modified SCAT 1SF a r m ] wing (1) supersonic transport (defined i n reference 3) , The basepoint vehicle is the reference modified only as re~uiied t o (2) i n s t a l l the P r a t t and Whitney Aircraft (PWA) V!XE 502B engine, The baseline airplane is the basepoint resized t o the design q u i r e - (3) laents & a standard-plus-8" C day.

The s t m c t u r e design and operational enpty weight of the reference Weight and a e r o d ) d c airplane were ass& t o meet all design c r i t e r i a .

characteristics of the study a i q l m s were derived by increments from the reference configuration.

Weline Airplane Definition Basepoint airplane.- The "basepoint" airplane f o r t h i s study is based on the NASA modified SCAT 15F arrow wing reference configuration as described i n reference 3. The propulsion system of t h i s airplane has been replaced with PWA variable stream control engines (VSCE 502B) having 408 kg/sec (900 lb/sec) airflow each and witn axisymnetric variable geometry i n l e t s designed f o r mach 2.4 cruise conditions.

The resulting basepoint vehicle is shown i n f i g - ure 4. This airplane has a gross weight of 336 973 kg (742 890 l b ) , a range of ?471 km, (4031 n-mi.), and a balanced f i e l d length of 3017 m (9898 f t ) .

A l l performance and sizing calculations were made using the Rockwell

Vehicle Sizing and Performance Evaluation Program (VSPEP) . This conputer

program is a design tool capable of scaling a known basepoint vehicle accord- ing t o specified values of several different &sign parameters.

'Ihese include vehicle gross weight (or fuel weight) , thrust -to-weight r a t i o (or engine size) , wing-loading (or wing area), and p a y l ~ a d o r fixed equipment weight and volume.

Performance may be determined a t specified gross weight, o r alternatively, a search routine permits automatic sizing of the vehicle gross weight such th a t a specified radius o r raqge of the design mission is s a t i s f i e d .

Vehicle per- fonnance is calculated internally from a s e t of subroutines programed accord- ing t o a detailed performance analysis model. 'Ihe subroutines are general in nature and permit calculation of a wide variety of mission profiles. Several mission profiles may be calculated simultaneously.

Takeoff and landing d i s - tances and maneuvering capability may also be determined.

Figure 5 i l l u s t r a t e s the evaluation process.

m i c a 1 mission legs which may be calculated include warnnxp, t a x i , takeoff, climb, descent, cruise, and l o i t e r operations. C l i h and descent performance are determined by n m r i c a l integration of t h e equations of motion along a specified f l i g h t schedule.

Internally generated schedules are also available, including m i n i m t i m e and minimum fuel f l i g h t paths a s defined by the energy method. Constraints on the allowable f l i g h t regime are included. Cruises and l o i t e r s may be determined a t fixed o r o p t i m speeds and altitudes. Numerical o m I N A & PAGE I S OF POOR QUALlTy -.-.._- - _.

. - a Figure 4. - Basepoint airplane PREcmLsG PAGE BLANX NOT FWD searches are used to dcterrine opt- speods d altitudes a t the b e g - and end of each of t k s e legs, Data input to the VSPW for the . A S basepoint vehicle include:

Weights brokerr h by major t , along with scaling

infomtim an the wing, t a i l x i a g e , and engines.

Drags broken Qwn by major aqmmnt and by type (e.g., frictiar drag, waux drag, drag due to l i f t , base drag) .

Installed propulsion dat , including thrust and fuel flow as furctims of speed, a l t i d , and p e r setting.

Dinwsional data such as lengths, areas, and volgps for major a q m e n t s and the total vehicle, Perfomance items calculated by the VSPEP on the basepoint and baseline vehicles for this study cmsist of the following: (1) Design mission range (2) . M ternate m i s s ion range 3) Takeoff distance with FAR 36 (Federal Aviation Regulation, part 36) noise requirements (4) Balanced field takeoff distance (5) Ihrust-to-drag ratio at mach 2.32, 18 300 m (60 000 ft) (6) Ihrust-to-drag ratio at mach 1.2 during the cliat, leg A description of each of t!!ese perfonnance items is given in the follow- ing paragraphs. Because engine data were provided for a standard-plus-d°C (14.4OF) day, all airplane perfonnance characteristics were conputed for that atmospheric condition.

Ilesign mission.- A profile of the &sign mission is sham in figure 6. This mission consists mainly of a mach 2.32 cruise. Fuel reserves as recornsended i n reference 4 are calklated for an alternate airpcrt located 460 I a n (250 n.mi.1 from the destination airport.

The design mission consists cif: Warmup and takeoff - 10 minutes at 2le pc .,r plus 1 minute at (1) nraximun power.

(2) Clirt, - Maxiarr p e r cl- and accelerate to cruise altiturle o;ad

PBCh n h r .

(3) Cruise - Cruise a t mach 2.32 a t altitude for best cruise range.

(4) Descent - Descend d decelerate to 'mch 0.5 and 457 r (1500 ft) using idle power.

(5) Appmacb and land - Descend t o nach 0.3 a t sea level using

idle pauer.

(6) Taxi - 5 minutes a t idle pouer.

(7) Ibem all- - 5-percent of total fuel used in all previaus legs.

Resave cli& - C l i m b to sub~lnic cruise conditions.

(8)

Reserve cnrise - Subsonic cruise a t mach n m k r and altitude for

(9) best range.

Reserve descent - D e s c d and decelerate t o holding altitude and (la) mach n h r using idle pauer.

Reserve hold - Loiter for 30 Rirnrtes a t 3088 a (10 000 f t ) a t the (11) lnach nmber for best endurance.

(12) Reserve approach and land - Descend t o sea level using idle pauer.

Alternate mission.- A profile of the alternate mission is sham in figrpe 7.

The f i r s t half of the alternate is identical t o the f i r s t half of the design mission. A t the point corresponding t o the rd ipoint of the design mission, a failure is a s s d t o occur ic the mst c r i t i c a l engine. A t this point, the airplane descends and continues to cruise subsonically with one engine wind- milling. Ihe fuel reserve m i n i n g at the end of t h i s mission is equal t o the reserve fuel as calculated for the &sign mission.

Ihe alternate mission consists of: (I) Wannrp and takeoff - Same as design mission.

(2) Cli* - !he as desi* mission.

(3) Cruise - Same as &sip mission.

( 4 ) Descent - Deusad and decelerate to s u b d c cruise canditims using

idle parer, follwing failure of mst critical engine.

( 5 ) Cruise - Subsonic cruise at rach nuber ant altitude for best range

w i t h pie engine imperative.

( 6 ) D e M and land - I)escend to sea.leve1 using idle p e r .

(7) kserve - Allow total reser,? fuel q r a l to that calculated for design mission legs ? t h r o u g h 1 2 .

Balanced field takeoff. - Takeoff distance is calculated over a 1 0 . 7 r ( 3 5 f t )

I t is assued that a amchum usable lift coefficient o f 0.555 i s obstacle.

available for clirbaut. Balanced field length involves three re@-=: ( 1 ) Distance for a normal takeoff is calculated with all engines (throttled if neres-cary so that FAR 36 noise mpirepnts are not exceeded) and this distance i s nultiplied by 1 . 1 5 , ( 2 ) Distance i s calculated for a takeoff when an engine fails at t h In this instance, the critical speed md the airplane amtinues the takeoff, throttles may be advanced after the engine failure if they are not already at lPaKiaol v r (withut regard to noise requiresents).

( 3 ) Distance is calculated when an engine fails a t the critical speed and the takeoff is aborted. The ailplane i s stopped by applying brakes and mtting the remaining engines to idle. The critical speed for engine failure is deter- mined by varying the speed at which engine failure occurs (i-e., V l ) mtil the accelera'ie-continue distance is equal to the accelerate-stop distance ( i . e . , 4 2 s e , p e n t s B + C = D + E as s b i n figure 7 ) . Ihe balanced field length i s then defined as the greztest of i t & ( I ) , ( 2 ) , and ( 3 ) .

Ihrust-to-drag ratio.- The thrust-to-drag (TJD) ratio i s calculated tping max-

imaa available thrust a t 2 . 3 2 ma&, 18 300 IU (60 0 0 0 f t ) . Drag i s that for

level flight a t the same conditions. Airplane weight i s that at t h e start of the supersmic cruise as calculated for the design mission. Ihe thrust-to-drag ratio i s also calculated for the point i n the clinh-accelerate leg st which mch 1 . 2 i s mached. In this case the altitude and vehicle weight are the actual values during the clist, a t which the vehicle I eaches mach 1 . 2 .

Baseline airplane. - The *%baseline" airplane for this study i s a resized version

of the aforenentid '0asepoint." Resizing was accomplished by exercising the VSPEP for a matrix of thrust-to-weight and wing lmding values, and allowing the program t o search for the gross weight, i n each w e , that satisfies the design mission range requirenent of 7408 km (4000 n . m i . ) . Plots of the results are shown i n figures 9 through 1 1 . The parameters shown include vehicle gross weight as well as those perfommce item for which requiremts lnust be met.

Ihe balanced field length rcquirerrrrt is plotted on the airp- gnrss =ight plot in figure 9 . This all- a "baseline" airplane to be chcrsen khich is defined as the m i n i m a gross e i g h t vehicle that ~eets or e x & the follaNing perfomaim!! requilmE!nts: 7108 h (4000 n. m i . ) with 292 passengers Design rissiar range Babnced field l e n g t h 3200 r (10 500 f t ) .

bmmm T/D during c l * 1.2 or cruise A - Distance q to critical engine failure V B - 3-engine rceleratirn distance from V to Vm

C - 3-engine lift-off to barrier distance

D - Distance gained after engine failure before full brake applicatim

E - Stopping distance

- Critical engine failure speed

V ,

- Lift-off velocity

v~

Figure 8. - Balanced field length definition

2.0 3.0 4.0 Thrust- to-weight n/kg (lb/lb) Figure 9 . - Cross weight versus thrust-to-weight and wing loading.

Thnn t- to-weight n . Fg . ( l b . /lb. )

Figure 1 0 . - Balanced field length versus thrust- to-ueight and wing loading

: I . . : 2.2' . +--- . . . - - : - . .

l'hrust to weight- n./kg. (lb./lb. ) .gure 11. - Thrust/drag ratio versus thrust- to-weight and wing loading, Since the thrust-to-drag requirements are exceeded for all cases, figure 10, only the balanced fisld length requimaemts are included i n figure 9 .

The resulting '%baseline" airplane has a s weight of 323 046 k

(712 188 lb) ; a thrust-to-weight ratio of 3 . 1 r= n/kg (0.323 lb/lb) b a s e ! m

installed, static takeoff thrust; and a wing loading of 354 kg/sq m ( 7 2 . 5 lb/

sq ftl based on gross wing area. CAs discussed on page 71, the baseline was

revised slightly f o r cauistency i n validating the approximate methods, but the disc~ssion presented here is for the NCSA Langley study baseline. ) Further airplane design and performance characteristics f o r both the "base- point*' and "baseline" airplanes a r e shown i n t a b l e 5 . Design and a l t e r n a t e mission stimnaries a r e sham i n tables 6 through 9 f o r the baseline airplane.

In these tables, the f i r s t leg of the a l t e m a t e mission includes the first four legs of the design mission while leg f i v e of the alternate includes reserves f o r legs nine tnrl..igh 15 of the design mission. The path followed during the climb-accelerate Ieg is a m i n i m hrel path calculated internally by the VSPEP program. This path ac calculated f o r the baseline airplane i s shawn i n figure 12.

Propulsion.- Because many of the current and recently completed supersonic cruising a i r c r a f t studies have used axis;mnetric i n l e t s , a mixed-conpression, axisynmetric i n l e t was defined f o r use i n the basepoint a i r c r a f t f o r t h i s study. The i n l e t d i m t e r is 1.93 lneters (76 Inches) , and capture area is 2.926 square meters (4 536 square inches).

For takeoff, the basic centerbody is held i n the transonic position, but the fore and a f t conical segments a r e translated a f t t o create a centexbody auxiliary i n l e t . The auxiliary i n l e t opening i n the centerbody is 10 percent of capture area. I n l e t pressure recov- eries and spillage, bypass, and BLC drags were estimated, and t h e i r e f f e c t s were included i n instal led propulsion perfomance. Engine accessories were assumed t o be located i n the wing.

The nacel-le drawing i s shown i n figure 13.

The engine performance data available f o r the VSQ 502B engine included the effects of an i n l e t recovery schedule, nozzle external drags (base pliis boattail) , 0.45 kilogram-per-second (1.0 pound-per-second) high-pressure coin- pressor a i r bleed, and 149 kilowatts (200 horscpawer) power extraction.

Installed performance data were conputd by modifying the engine data t o include the e f f e c t s of changes i n i n l e t pressure recovery and i n l e t drags

(spill age, bypass, and boundary layer cont 1-01) . Because the amount of engine

data available was not sufficient t o conpute a i r c r a f t mission performance, additional installed perfonnance data were generated by calculating corrected thrust and fuel flow parameters and by extrapolating based on trends of engines with similar characteristics. Fortunately, these techniques were required only a t flight conditions where the airplane f l i e s f o r a short duration. rhus, any possible errors due t o data extrapolation should have minimal e f f e c t on a i r - A l l data were for s t a n d a r d - p l ~ s - 8 ~ C day.

plane performance.

TABLE 7 . - BASELINE IIESIGK !.1ISSION SUMMARY - ENGLISH UNITS

I

*

LEG. NO.

OPERATI ON WEIGHT, ALTITUDE, MACH NO. TIME FUEL USED, TOTAL TIME RANGE TOTAL l b s .

ft . l b s , min . min . n.m.

RANGE n.m.

INITIAL, WIGHT 712 188 10.0 0 0 0 0.305 8 5 3 4 703 653 10.0 1 W O G T O 5 5 1 500 0.500 4 631 1.3 699 022 11.3 2 C L T O 1500 1 2 * 8 155 161 54 943 2.320 54 090 3 A . 1 644 931 3 CLB-ACC 82.9 1 838 58 761 2.320 115 994 2 000 528 936 107.0 4 CRUISE 82.6 1 833 ti2 889 2.320 9 6 2 5 2 3 833 432 684 189.7 5 CRUISE 17.3 159 1 500 0.500 3 365 3 993 207.0 6 DESCEND 429 318 518 1.5 7 4 000 428 800 0 0.300 208.6 7 DES-LAM) 0 1 425 5.0 4 000 427 374 0.0 213.6 8 TAXI-ALL 0 0.0 14 240 0.0 4 000 413 134 213.6 9 5PCT ALL 1 500 0.500 1 251 0.7 4 0 0 3 411 882 214.3 1C Cl TO 1500 40 476 11 830 10.2 4 089 400 052 0.950 li C55-XC 224.5 40 773 0,950 5 2 7 6 10.8 98 4 187 1 2 CRUISE 394 775 235.3 10 000 0.470 1 921 4 253 392 853 9.5 13 DESCEND 244.9 10 000 0.454 14 221 30.0 4 253 378 632 14 LOITER 274.9 0 0.300 1 184 18 377 448 3.7 4 271 15 DES-LAND 278.6 TOTAL FUEL USED = 334 739 2.0 l.!

1 . ( O.!

0.1 Figure 12. -Baseline airplane dl* path A t takeoff, engine parer setting was scheduled so that the aircraft r r r e e t c FAR 36-traded noise levels. The SAE exhaust jet noise predictim aethod used with the dificatim t o overall s o d pressure level V by Bushell (reference 5 ) . This dification has no effect oar perceived noise

level at static conditions, but it results in approximately 4 decibels (a)

higher noise tian the standard SAE arethod at inach 0 . 3 .

A 1 . 5 db reductian in sideline noise was a s s d ~IE to sideline shielding while the airplane is on the grcmd. An 8-decibel reduction in noise level dw to t h e m u l a r nozzle effect was a s s t a d h r all flight conditions and pwer settings. Inforration from P U indicates that comnular configurctt ions reduce noise by 7 to 9 decibels hen the differace beteen core velocity d bypass velocity is 152 rpeters per second (500 feet per second) or =re, with the core streaa having the lawet- velocity.

M a s s properties.- The basepoint whicle weight s - r y is given in table 1 0 .

The . W A reference vehicle weight sumary (reference 3 ) f m a which the base- point was derived is also s b n . The differences between the weights of the t k a vehicles are b the engines and nacelles. Ihe basepoint whicle has LEiCE W2B 408 kg/sec ( 9 0 0 lbfsec) airflas engines i n lieu of the 363 kg/sec ( 8 0 0 lb/sec) engines in the M A reference vehicle.

?he kSCE S O B bare engine weight including nozzle m4 thrust reverser was slpplied by WA. Weight i n c m t s of 2 2 . 7 kg (50 l b ) for residual fluids and 22.7 kg (50 lb) for miscellaneous engine/airframe interfacing provisions were added to the bare weight to obtain an installed weight.

Table 11 shws the installed engine wight sumar-*- The basepoint nacelle weight estimate i s bast? 3n the nacelle dming, figure 1 3 . Far the k-eight evaluation, the nacelle was divided into three aft of the front face sections: foxward of the engine front face (inlet (engine cowl), and inlet spike. The engine cowl wight was estimated at 34.2 kg/sq m ( 7 lb/sq ft) of wetted area, Ibis weight incldes all the nacelle Ctnlcture that supports and surrounds the engine and was derived from prior kkwell I~rternational studies of a simi l3r type. ' I h e inlet - 1 and spike weights were calculated using statistical weight estimting equations obtained from the technical report SEG-TR-67- 1, Preliminary b s i w Methodology for Air- Fnzine mount weights were calculated sta- Induction Systems [reference 6 ) .

The mount weights are ixluded tistically at 1.5-percent of t k engine weight.

with the nacelle weight.

The weight sumnary of the bascpoint nacelle is presented in table 12.

TABLE 1 0 . - WfICE lEI(HT W M ! ! Y

N A s A m m C L E I BASpQIp3T

- m

LB I I IB

n bo5 83 347 37 805

W i n g 2 391 5 271 2 391 Horiumtal Toil 2 168 Vertical Tail 24 636

-

13 158 Lsnding* b l l e 8 625 Smucture Total (88 743 27 139 hgines Thrust Reversers 4 809 Efiscellaneous S y s t e ~ ~ 807 2 622 b l Systean-Tanks aQd Plubing Pmprlsian Total (35 377 ( 77 994 (27 923 (61 M 1 4 527 Surface Controls 9 982 4 527 9 981 I 542 3 400 3400 htnslents 1 542 2 540 5 600 2 540 5 600 Hydraulics 2 291 5 050 2 291 Electrical 5 050 1 2 2 9 2 690 1 220 2 690 Avionics Furnishings and Quipmist 25 ill 11 390 25 111 11 390 3 720 8 200 3 720 Air Gmditioning 8 206 Anti-icing 95 210 95 210 Systems and Ejquiprent Total (27 325 (60 242 ( 60 242 (27 325 314 771 333 883 142 776 k i g h t -tY 151 445 Crew and --Flight, 306 675 675 306 -Cabin, 744 1640 1610 744 Unusable Fuel 1 059 2 335 2 335 1 059 Engine Oil 361 795 795 361 8 852 8 852 4 015 Passenger Service 4 015 Cargo Containers 1 343 2960 2960 1343 Operatirrg Weight 332 028 351 140 150 604 159 273 21 454 48 180 21 854 pU=qFrs, (292) 48 180 P=='V!er W B a S 12 848 5 828 5 828 12 848 Z e r o - 1 Weight 186 955 412 168 178 286 393 056 !fission Fuel 158 680 349 834 349 832 158 681 DesiIpl Gmss Weight 345 635 742 890 762 000 336 973

TABLE 11. - BASEPOINI' ENGINE W E I m

ki&t/Vehicle I tee lb kg 24 312 53 600 Engines (including nozzle & thrust reverser) ( 4 ) Residual Fluids 200 Miscellaneous Provisions 9 1 200 Engines as I~talled 24 494 54 000 . 4 e ~ c s . - Friction drag estimates were made for a fully turbulent, hydrau- lically s m t h condition using the incoapressible von-Kaman-Sdroenhen nethod (reference 7 ) i n conjunction with the adiabatic coupressibility correctian of Solsaer and Short (reference 8). Coeponent characteristic lengths (e-g., the distance from the inlet lip to the exhaust nozzle exit, the exposed =an aero- dynamic chord of planar surfaces, e t c . ) and the altitude alang the mission clinb profile were used to evaluate length Reynolds nunbers. Flat plate values %ere inct-eased b y 3-percent to a c m t for form losses.

WeightjVehicle Item l b kg

-

Sacel les Engine - 1 6132 Inlet Cowl 1299 2864 Spike 2961 6528 Fngine ?bunts 812 Total Nacelle 7410 16 336 'Ihe wave drag due to thickness was estirated as a hnction of d ruaber using sqmscmic area rule theory (referenas 9 and 10) in amjutction with a trampanst wing simlation, an i n l e t aass flay ratio o f one, and the nozzle e x i t area 'held fired at its srpersonic cruise position. The e f k c t of i n l e t spill* and nozzle position is included in the installed thrust. A l l results rqmrted here are based on the use of a 51-mch-plane @X = 0.02 L (0) ) ), - 13-roll-angle (A4 = l S O ) analysis. Basepoint c m f i g u r a t i m msultc f o r increased s o l u t i m E& density did not indicate any appreciable c f t v .

Slpersonic cruise trim& drag-due-to-lift characteristics are assuned to be equal t o the reference configuration of reference 3 and amsequently inde- pendent of wing and engine size and nacelle shape. A different design wing aist and ca&er is required for each case to realize t h i s perfomaxe. The l i f t i n g efficiency may be conservative for soare of the =re favorably shaped nacelles of the parametric drag study i n that any increased b e f i t that may be realized frola f a m d l e nacelle thickness/uing l i f t interference over and above that of the reference configuration is neglected. Conversely, for the less favorably-shaped nacelles, the analysis may be soaaewhat optimistic. A t off d e s i p conditions, the above asstaption is necessary because the q u i d analysis is beyond the scope of the contract effort.

A comparison of the \?3I W2B (408 kg/sec, 900 lb/sec airflow) nacelle o f figure 13 t o that of the reference cmfiguration n o n a f t e h r n i n g single spool turbojet with variable geoaretry turbine (363 kg/sec, 800 lb/sec airflaw) o f reference 3 is presented on figure 14. The basepoint nacelle is 1.95 PPeters (6.4 feet) shorter and has a 0.14 mter (0.46 feet) smaller illaxilarn di-ter.

Ihe relative cross-sectional shape of the two nacelles is presented i n fig-

The basepoint t o t a l configuration nonaal cross-sect itma area d i s t r i b -

ure 15.

ution is sham in figure 16.

Estimated total and nacelle increolental skin friction and wake drag characteristics (relative t o nacelles off) for the basepoint configuration are presented i n table 13. The m e drag results a r e for the case i n which t k nozzle exit planes zre the s e as the reference configuration. A slightly

higher drag results (5 = 0.00006 a t mach 2.7) i f the i n l e t planes are

rsatched, The friction, wave, and t o t a l drag increments of the basepoint nacelle are The basepoint con- conpared t o those of the reference nacelle i n figure 17.

figuration has a slightly smaller installation drag in s p i t e of 12.5-percent greater airflow because of the mre favorable nacelle shape (no boattail) as shown in figure 14. I t was subsequently determined that a further reduction of 0.5 count could be realized by meridial contour optimization.

Figure 15. - Nacelle cross-sectional area variation.

i I

1 I I I 1

0 10 20 30 40 50 Fuselage stat ion

Figure 16. - Basepoint vehicle CrOS

PAGE BLANK NOT

Fuselage station - m . (ft.)

sepoint vehicle cross-sectional area variation.

#'t)LDOUT FRAME BECEEllii; 1'AGii BLANK NOT F L M D TABU 13. - BASEPOINT ~IGURATION ESTI)4ATED PROFILE AND WAVE DRAG W m R I S T I C S SREF = 929 sq m (10 000 sq ft) Nacelle Altitude A i r c r a f t M 0 m f t ""., - - - - --- - 0.00065 0.0061 457 1 500 0.4 - - - - ---- 0.8 0.00062 0.00572 6 400 21 000 0.00060 -0.00017 0.00545 0.00365 34 300

0.00058 -0.00018 0.00522 0.00316 37 800 i.4 i - 2 i 11 i 0 4 5 5 521

0.00055 -0.00019 0.00490 0.00254 44 600 1.8 13 533 0.00050 -0.00018 0.00450 0.00222 55 000 2.32 16 764 0.00046 -0.00014 0.00418 0.00217 60 000 2.7 18 288 The aerodynamic charact istics use2 in resizing the basepoint wing and engine size t o produce the baseline configuration used f o r a l l parametric nacelle drag studies w e r e established as fol LOWS.

Fully turbulent f r i c t i o n levels were adjusted f o r difference i n surface ?he wave drag varia- area and length Reynolds n u h e r of the wing and nacelle.

tion of the basepoint configuration as a function o f wing and engine size were parametrically evaluated f o r input t o the s i z i n g program. The r e s u l t s are pre- sented in figure 18. The e f f e c t of engine size was e s s e n t i a l l y n i l a t t h i s scale for the nacelle shape under consideration.

The trimned drag due t o l i f t characteristics were assumed t o be independent The s p e c i f i c levels used of wing s i z e and equal t o the reference configuration.

are presented in figures 19 t h r ~ u g h 21 and were taken d i r e c t l y from reference 3.

Sizing of the basepoint configuration produced the study baseline (table 5 ) which had a 12-percept smaller wing s i z e and a 3.5-percent smaller engine size.

The associated normal cross-sectic.~al area d i s t r i b u t i o n is presented i n f i g - A summary of the component surface areas and reference lengths is ure 22.

presented i n table 14, and table 15 p o s e n t s baseline drags.

Mach nuiber-Mo Figure 19- - C L ~ versus - k c h n&ber.

M a c h nmber Figure 20. - C versus Mach n h r .

='It Figure 21. - ' K ' factor versus Mach mnber.

L I I I 1 I

0 10 20 30 40 50 Fuselage station x n .

I I 8 I I I 53 60 70 80 90 100 elage station m. (ft.)

Figure 22. - Basel inc vehicle c r o s s - s ~ t ional area variation.

TABU 1 4 . - BaSELlNE OONFIWtATION SRFKE AREA ANDlENGM-Y - - Slllet

cxxmNmr w

s q . r . (sq.ft.) r . ( f t . ) I L % (315) 786 (8 450) -We 1 SO5 (16 987) 7.65-39.4 (25.1-129.)

wing 276. (3 388) 12.7 ( 3 5 . 1 ) Nacelles ( 4 ) 4 . 9 ( 1 6 . 2 ) Center Line Vertical 2 0 . 1 (219) 7 . 9 ( 2 5 . 9 ) Wing Verticals 9 1 . (992) 5 . 8 ( 1 8 . 9 ) 8 9 . 5 (921) H o r i zmt a1

TABLE 15. - BASELINE CONFIQJRATION E!jTIMATED SKIN

FRICTION AND WAVE DRAG CHARClERISTICS = 929 sq.n. (10 000 sq. f t . )

-

D ALTITUDE AIRCRAFr NACELIS 1 .

(ft 1

A c ~

Mo c q , ,

=% F

----

----

0 . 4 0,00568 0.00065 ( 1

---- ----

0 . 8 6400 0.00537 (21000) 0.00061 10 455 1 . 2 0-00508 0.00339 0.00058 (34 300) -0.00009 1 . 4 11 S2l 0.00489 0.00305 0.00056 0.00003 (37 800) 1 . 8 13 594 0.00455 0.00237 0.00052 -0.00011 (44 600) 2 . 3 2 16 764 0.00420 0.00209 0.00049 -0.00012

(55 Od0)

2 . 7 18 288 0.00392 0.00200 (60 000) 0.00045 -0.00011 Esthtion of Supersonic Drag Parametric drag analysis.- The parametric nacelle wave drag analysis utilized the baseline configuration &scribed i n the previaus section. The installation grourd rules in order to pre- of the propulsion system follwed several serve the basic a r r a n - t concepts iPd provide consistent conpariscms w r n - ing the effect of nacelle size variations. They are: Nacelle overhang of t h e wing trailing edge and vertical nacelle-wing ( 1 ) separation was limited to the refemce configuration values for structural Teasons.

Ihe longitudinal and lateral separation distance between the inboard (2) and outboard nacelles was preserved i n order to faaintain inlet flw quality.

The reference configuration philosophy of locating the nacelle volui~?

(3) in a region of decreasing wing thickness was maintained.

Ihe maxirmm boattail angle considered was 10 degrees.

(4) The outboard nacelle is moved inboard a i i d forward as required along the rnidchord (approximate maxinun thickness) 1 ine of the wing until its trailing edge overhang does not exceed 3 meters (13 f e e t ) . The inboard nacelle is shifted laterally by the samc mount holding the longitudinal distance between the inboard and wtboard nacelle inlet p l : ?s the same as the reference configuration.

The nacelle parametric variables considered in the present analysis were the ratio of nozzle area to capture area .&/.%, the ratio of maxinun cross- sectional area to capture area .*/.+-, the relative axial position of m a x i m area SAuy/l, the ratio of nacelle length to capture diamter, I/&, and the nacelle absolute capture area .Ac. A sumnay of the nuher of variations and variable range analyzed is presented in table 1 6 . For purposes of computation, the nacellcs were assumed to be axis)mnetric and the inlet, m a x i m area, and nozzle planes to be connected by straight lines.

'CABLE 1 6 . - NACELLE PBRA)laEFER VAUiES

VAUIES PAmmER 1 . 2 , 2 . 3 2 Wech IIuber 1 . 0 , 1 . 2 5 , l . S , 2 . 0 1 . 0 , 1-25, 1 . 5 , 2 . 0 k / A C

*

0 . 4 , 0 . 6 , 0 . 8 , ~1.0 -

Xm/& 1.86, 2.79, 3 . 7 2 sq.ta.

*c (20, 30, 40 s q . f t . ) 5.S a d 7.0 e/dc I t Maxkm value considered correspads to a boattail angle of ten diegrees.

The paraetric nacelle friction drag analysis i s based an the use of Eully turbulent flat plate levels in conjunction with the expression for surface areas (for four nacelles) : lhe largest deviation between the exact and approximate express;on occurs for X w y / t approaching 0.4 and &/A, approaching 2 . 0 with the f o - r resulting i n 10-percent greater area. It will be subsequently fomd that these differences The are negligible in tern of the total installation drag for such cases.

parametric nacelle frictiim results are presented in reference 2.

ikcelle normalized cross-sectional area parametric extremes of the present study are presented in figure 23. fulaximm-to-capture area ratio of 1 to 2 at 40, 60, and 80 percent of the nacelle length are shown for nozzle-to-capture area rations of 1 and 2 . k v e drag results are discussd in detail in reference 2 .

Briefly, the increinental nacelle wave drag is a strong function of the

ratio of maxim- to-capture cross-sectionalarea, : \ & . k , boattail area, and

to a somewhat lesser extent relative axial position of maximun cross-sectional area, X m / t . Kacelle shapes with negative wave drag exist because of favor- able total system thickness interferences associated with the location of gmw- ing nacelle cross-sectional area in a region of decreasing wing thickness. The nacelle geometric variable behavior and sensitivity are unchanged by mach nun- The incremental wavc ber, nacelle capture area, or nacelle fineness ratio.

drag results are, i n general, weak functions of the latter two variables for efficient installations.

Jktailed nacelle wave drag variations with freestream mach nuher were defined for a range of levels covering high-positive, zero, and negative installation increments. These characteristics correspond to nacelles with large maxi- cross-sectional area relative to ' . h e capture and nozzle area Figure 24 illus- cylindrical, and near-truncated conical shapes, respectively.

Figure 23. - N . .-.elle parametric cross-sectional area extremes.

trates the mach nunber difference for these extremes for the fineness ratio 5 . 5 , d i m - s i z e nacelle. Examination of the results indicate that weak to & r a t e - mach nmber variations are associated with small nacelle installation drags.

Conversely, strong coapressibility variations are exhibited for inefficient installatians. The large benefit a t transonic speeds is somewhat illusory as the thrust mrst be progressively penalized foi nozzle contraction with decreasing mach nunbers.

Drag table look-up computer program. - A tab1 e look-up cquter proqrav was

developed ( appendix ) which yields the incremental wave and friction drags of nacelles as functions of nacelle geometry variables and airplane mach nunber.

The drag increments are for the total vehicle relative to the vehicle with nacelles removed. The nacelle shape parameters used as inputs to the program are : ( 1 ) Ac Inlet capture area

& Nacelle maximun cross-sectional area

( 2 ) Nozzle exit area (supersonic cruise position) ( 3 ) An

( 4 ) bX Distance from inlet cowl leading edge to naxinuo cross-sectional

area (5) e Nacelle total length ( 6 SREF Reference wing area ' I h e output of this program irlclwles for the nacelle of interest: ( 1 ) The aforementioned input data Drag coefficients at mach 1.2, mach 2.32, and the input mach number ( 2 ) for friction (CTF), wave (CDIJ), and total (0) drags The nondirnensional parameters of position of maximum c!'-ss- sectional (3)

area (XAMAX/P), nozzle- to-capture area ratim (An/Ac) , maxim- to-capture area

ration ( & / A c ) , and fineness ration (P/d,) I n addition, incremental drag coefficients of the reference airplane nacelle (reference 3 ) are printed. A sample output is shown i n table 2 .

It has been found that the table look-up results correlate best with more detailed analyses when the mirnum cross-sectionalarea and its position are based on the area that occurs at the intersection of straight lines originating frm the inlet 0.002 0.001 ' : . . 4 . .

0.000 . , i . . .

. . .

. . .

. , .

. -. - -0.001 - .

I i I . . - . - -. . . - . i 6 .. .

41Ax 41

xAMA?c -0.002

= 2.0, - =

1.0, - = 2.0 +'--I

a i . . i

j s -

. ; . .

I , . . .

. . - r ~ -: - .-.- - --.- + -.-- 1- -

. . , .

: i . ! 1 7 . . . I : . .

* . ..

. . I . . . . . . . . . . . - - . . . . . . . . - . . . 3 .

i" 1 : ; 1 i . 1 . ; 1 ; ¶ I I I : -0.003 0.6 1.0 1.4 1.8 2.2 2.6 3.0 Mo Figure 24. - m i c a 1 nacelle incremental wave drag variations with Mach number A , = 2.79 sq m (30 sq ft) &/dc = 5 . 5 .

which is tangent to the mimm slope of the forebody and from the nozzle which goes through the actual maximum area and whose slopes nearly match the slopes of the actual nacelle, as illustrated in figure 25. This method most closely approximates the parametric nacelle shape drag analysis because, in that study, Using this nacelle shapes were defined by two straight-line segments.

method will result in nacelle drag increments .at supersonic cruise within G.5 drag count of the drag resulting from a detailed analysis.

Nacelle shape estimation.- Nacelle external shapes are dete~mined by such installation items as engine accessories, compartment cooling, shrouds and insulation, aircraft accessories, engine clearance, engine mount geometry, nacelle structure, boundary layer gutters, etc. The engine configurations sup- plied by the engine manufacturers usually include only the engine case outline and nozzle dimensions. A method has been established to determine the engine exterr-a1 envelope and aircraft structure and equipment space allowances.

Guidelines are presented for determining the engine buildup envelope, engine cowl, nozzle fairing, and inlet and inlet cowl shapes. Those installation ite-s which have the largest effect on nacelle shape are then discussed. A n exaq - of the nacelle shape buildup is presented in figure 1.

Engine buildup envelope: The procedure to establish the engine buildup envelope is : Establish fan and gas generator case outline.

( 1 ) Add 5 a n (2 in.) constant to all surfaces of the preceding outline to 12) provide for wiring, plwbing, etc.

(3) Add 2.5 cm (1 in.) constant additional to outline for variable com- pressor geometry mechar~isms where applicable.

Establish mechanical power extraction drive station and radial loca- (4) tion for engine accessories drive and for aircraft accessories power takeoff.

Depending on engine configuration and accessory design, accessories may be on the engine or in the pylon or wing.

For engine accessories where encapsulation is required for cooling, provide 0.595 cu m (21 cu ft) of volume proximate to engine accessories drive of item ( 4 ) . Dimellsions of the capsule may be xraried for best packaging, but the capsule thickness at the gearbox should be 0.305 m (12 in. ) minimum. For o on encapsulated engine accessories, provide 0.51 cu m (18 cu ft) of volume proximate to engine scccssories drive of item ( 4 ) .

Arrange- ment of the accessories package may vary, but the minimum thickness at the gearbox must be 25 cm (10 i n . ) . The dimensions of items (2) and ( 3 ) and (4) are additive and will usually establish the maximum radial dimensions of the gas generator section of the engine.

All other engine and aircraft equip- ment in this portion of the nacelle should be contained within the volme of Figure 25. - Simulation of nacelle shape.

revolutian e s t a b l i s h e d by t h i s l i n e o f r a d i i . For miniqum a i r c r a f t drag, l o c a t e a i r c r a f t accessories within pylon o r adjacent wing. Ihe engine Dower takeoff pad and angle d r i v e gearbox w i l l be within t h e pylon and t h i s w i l l not impact t h e n a c e l l e mold l i n e .

For engine f l u i d r e s e r v o i r s , add 0.0566 cu m ( 2 cu f t ' on l e f t o r ( 5 ) r i g h t s i d e o f engine. The r a d i a l dimension is 15.2 cm (6 in.) a d d i t i v e t o dimension of item (2j o r (3).

Equally space four compressor high-pressure bleed p o r t s around com- ( 6 ) The 12.7 c m (5 i n . ) diameter c o l l e c t o r manifold (with pressor r e a r frame.

f l e x i b l e sections) w i l l interconnczt t h e p o r t s and connect t o t h e airframe duct i n t h e pylon. The c o l l e c t o r manifold diameter is a d d i t i v e t o t h e a l l o k a ~ ' .

item (2). Low-pressure bleed p o r t s may be provided i n place o f o r i n ads4 t o the preceding. The same space allowance must be made f o r these. Or. o i more engine and i n l e t a n t i - i c i n g a i r d u c t s w i l l be routed from t h e bleec I : \ : fold forward t o t h e engine f r o n t frame. These ducts w i l l be 10.2 a n (4 111.; diameter and riill be a d d i t i v e t o tile allowance o f items ( 2 ) o r (3).

Determine location of engine mour.ting s t a t i o n s by engine i n t e r n a l ( 7 ) ::tructure. The nacellelwing r e l a t i o n s h i p should be considered i n t h e placement of the engine load-carrying frames and t h e mounting provisions on t h e frames f o r best weight effectiveness of t h e t o t a l system.

( 8 ) blain mounts - t r a n s f e r t h r u s t , s i d e , and v e r t i c a l loads: Provide 15.2 x 15.2 s 12.7 c m ( h s 6 s 5 i n . ) r a d i a l space a d d i t i v e t o items (2) o r (3) a t two posir;ons on engine main Rount frame, circumferentially spaced g r e a t e r thar! o r ecjual t o 90 degree:;.

( j S t a b i l i z e r mount - t r a n s f e ~ b v e r t i c a l loads: I.-ovide 10.2 x 10.2 s 20.1 c m (4 u 4 x 8 i n . ) r a d i a l space, a d d i t i v e t o items (2) and (3).

Locate local protrusions of mi.;cellaneous engine equipment beyond (10) envelope of items ( 2 ) and (3) t o occur a t random locations. These w i l l be r e l a t i v e l y small anJ will not cxceed the maximurr~ envelopc noted in item (4).

Engine Cowl : 'lhe engine cowl shape may I)e determined by the following: The cohil inncr skin mold l i n e must maintain a minimum 2.5 c m ( 1 in.)

(1) clearance from a l l points on the engine buildul~ cnvclopc developed i n t h e preceding discussion.

(2) Cowl structural requiresrents w i l l vary depending on t k arrangeaent and location of engine mtnmt points. *re mount points are i n the proximity of the pylon structure, the cowl can be made nonstnrtural; i-e., sufficient This to ~ i t h s t a n d internal and external airloads and flight dynamic forces.

w i l l require 5 a n (2 in.) of structure (constant) from the engine front face station to the cowl-to-nozzle fairing interface. Were o ~ o o n t points a r e widely s e p r a t e d f m the pylon structure a structural cowl arst be provided t o trans- f e r the engine loads. Caul thickness ir. the I d paths w i l l be 7 t o 10 a n (3 t o in.). In these areas the structure can i n t n d e into unoccupied space in the volune of revolution developed in the precediig items (4) and (5) , but 2 5 a a (1 in.) clearance anst be maintained frun xljacent engine buildup equiprent.

Areas of the cowl outside the load paths can be 5 aa (2 in.) thickness.

.Mzzle fairing: The nozzle fa'ring . m.t f a i r smoothly into t h e engine cowl m l d line developed in the preceding and f a i r srmotnly t o the 'base diameter dictated by the n ~ z i l e . The nozzle fairing leading edge step height fran the engine case k-ill vary depending upon the engine services (hydraulics, -tics, fuel, secondary airflow, etc) required t o pass through it.

This step height m y require adjusvtments t o the cowl outer mole line a s it appmches the nozzle fairing interface.

Inlet and inlet cowl: Inlet and cowl shape can be d e t e r m i d by tte fol- 'wing methd: Establish inlet length and captt:re area based on appropriate nacelle (1) design methodolo.gy and external constraints.

2 Establish inlet f l w path area geometry.

( 3 ) k f i n c inlet cokil external lines.

Fair from inlet l i p t o engine cowl. The faired mold line should provide m i n i m rat; of cross-sectional area increase.

(4) Establish requirement for the follming a i r f l w aths appropriate t o inlet geometry and engine cycle used: (a) Auxiliary a i r inlet (b) Bypass a i r (c) Engine seco~lctar). a i r (d) Roundary layer bleed (i) Centerbody or ramps ( i i ) Cowl inner wall Deternine cowl k ' 3 1 1 thickness by requirements of stnrtural integrity ( 5 ) plus space req~ired for flow paths and door mechanisms associated with quire-

ments established in item ( 4 ) - A minimum thickness of 1 S . Z a n ( 6 i n . ) is

suggested for the em-1 wall fm the inlet throat aft to the engine front face.

This ,nay be varied locally, but internal lines should be maintained. Thichtess of che caw1 structure bill vary from approximately 0.16 a n (1/16 i n . ) at t h e inlet lip to the throat thickness estshlished in the preceding.

Major nacelle shape elements: Three major elensents establish the engine external enve l q e : The allmance over the total surface of the gas gellerator of space (1) for engine variable geometry mechanism, plunbing, wiring, etc.

The space required for the engine accessory gearbox and assxiated ( 1 ; :iicessories. This package estahl ishes the locat ion and magnitude of the nacelle m;i\rlmtm c r o : ; s - sect i o n r t l area.

The location of the main engine mounts on ;he engine as defined by ! J ) t l l c engine mr~nufssturcr. kherc the main mwnrs are placed at the caapressor front or midf:-,me, suificicnt structure is available in the adjacent nacelle, pylon, :tnd \,ins to carry the multidirectional loads, and a simple, nonstructural \\here the main mounts are placed at the turbine frame, it is c0h.1 ma!- be used.

ncccssnp. to considcr the cokl as 3 structural cylinder uith penalties & the

nacelle : : i r e and weight.

: I l l other clancnts of the engine installation fall within the envelope defined hy tne preceding.

Weight estimation of nacelle and inlet systems is a compIes proczss and rcquires design detail not mnnally performed in the type of preliminary stdics being c,.midcred here. The estimating procedure described in this sec- tion uses 3 simplified aplxoach i~roducing a fil-st-ordel-type weight estimate keyed to gross def ini t ions of the nacel lc/inlct package. Thc procedure defined will provide the capability of maintaining consistency between nacelle weight cstimatcs while mking comparative analyses.

lbm dimensional inlets.- To estinrate the weights of eraine nacelles with tm-diarensional (2-D) inlets, the nacelle package is divided into the following ccmpments: ( 1 ) Engine cowl ( 2 ) Inlet cowl ( 4 ) Air induction special features (a) B,pass system (b) hiliar). inlet ( c 1 Secondazy air provisions (d) Inlet controls ( 5 ) Engine mts The methods used to estimate the weights of the nacelle canponents are primarily based on a prior Rockwell inlet stdv for the Boeing SST. This study was conducted for Roeing and consisted of designing a 2-D inlet as a contender to b e canpared to Boeing's axisymetric i r i l e t design in the inlet selection for the SST. Unit weights used to estinate weights of the nacelle canponents were derived fm data developed for this study.

The etgine c - 1 is defined as t k total nacelle structure Engine cowl: aft of the engine front face, including all structul-e that supports and sur- rounds the e~ine. The engine cwl ueight is estlrsattd at 34.2 kglsq la (7.0 lblsq ft) of nacelle external wetted area.

Inlet cml: The inlet caul i s defined as the total nacelle/inlet structure forward of the engine front face, exclusive of the variable-geanetry r a r a p s and special air induction features. The inlet cowl wight is estimated at 2 4 . 4 kg/ sq m (5.0 lbjsq ft) of wetted area.

Ramps: The ramps are defined to b e the movable pauels, including an actua- tion system, used to vary the inlet geometry in a 2-D variable-geametry inlet.

Weight of the variable-geanetry ranps i s estimated at 48.8 kg/sq m (10.0 lb/ sq ft) of movable ramp planfonn area.

Air induction special features: The bypass system consists o f inlet air 'he system weight is est israted bypass b r s , including actuation provisions.

a t 39.1 kg/sq m (8.0 lh/sq f t ) of door area.

The auxiliary i n l e t is defined as the auxiliary air i n l e t doors and i n l e t actuation system. The weight of t h i s system is estimated a t 29.3 kg/- r n (6.0 lbjsq f t ) ~f door area.

The secondary air provisions provide i n l e t a i r t o the engine c ~ ~ t The weights o f these provisions are estimated for e n g i w coafpartmcnt cooling.

u i t h t h ~ follok-ing equation: b.here h' a is efigine design airflok, kg/sec (lh/sec)- The i n l e t controls a r e defined a s the system provided t o monitor the i n l e t conditions and transmit p s i t i o n si,gnals t o the mvable i n l e r systems. The w i g h t of t h i s system i s estimated a t 22.7 kg (50.0 lb) pi- inlet.

'fie engine mounts a r e the f i t t i n g s wed t o support t h e lingine mounts: 'fie w i g h t s o f these f i t t i n g s are estimated a t 1.5 per- engine in the nacelle.

ccn t of thc cng ine k? ight .

.\sis)mnctric i n l e t s . - To estimate the w i g h t s of engine nacelles with asis)mncti-ic i n l e t s , the nacelle package is divided i n t o the following c a p - ' nents; t h i s hreakdohn is similar t o the one described for a 2 - D i n l e t : ( 2 Inlet cowl (3) Spike The procedures f o r weight estimation of the engine caw1 and mcnmts are the same as those described f o r the 2-D inlet/nacelle. The methodclogies to estimate the weights of the Met caul and spike were obtained from the A i r Force Tecfrnical Report SEG-TR-67-1, Prelimilliiry Design Hethodology f o r A i r Induct ion Systems .

I n l e t Cowl: The inlet cowl is defined as the t o t a l nacelle/inlet structure forward of the engine front face, exclusive of the i n l e t spike a d its systems.

The i n l e t cowl hvight is determined by the following statistical equation.

0.?31 hT = 0.159 (N) [(A ) O m s L (P2)] kg o r C 0.731 lb 7.435 (N) [ t ~ c ) O - S L ( P ~ ) I where: N = n d x r of i n l e t s A = capture a;ea per i n l e t - sq m (sq f t ) C L = subsonic duct leigth per i n l e t - m ( f t ) P = lnaximun steady-state s t a t i c pressure a t engine face a t supersonic cruise mch - k g / q m (psia) Spike: The spike is defined t o be the center body structure, including its systems and actuation. Weight of t h e spike is estisrated with the fallawing s t a t i s t i c a l equation; K = 252.9 kg/sq m (51.8 lb/sq f t ) N = nmber of i n l e t s Ac = capture area per i n l e t = sq m fsq f t ) Estimation of Airplane Takeaff Gross Weight Weight sensitivity analysis. - I n considering possible trades of rsduced drag through design changes i n the engine envelope for sollk penalty i n engine weight a d performance, it is necessary to have visibility of the net - L of all these effects an the total a i r p l a n e system. T o evaluate these effects, the sensitivities of the airplane takeoff gross weight to variations of propulsion system par=ters were &tenaid. ntese sensitivity d a t a were obtained b y conducting design trades on the baseline airplane for v a r i a : i c m s of the follow- ing items: ( 1 ) Incremmtal nacelle drag ( 2 ) Propulsion system weight ( 3 ) Engine specific fuel oonsunption ( 4 ) E n g i n e sizixg condition thrust In each case, the parameter of interest was varied independently ad the airplane resized to the &sign mission range nf 7408 km ( 4 0 0 0 n mi) while sintsining thrust-to-weight and wingloading values equal to t h o s e for the base- line vehicle.

Incremental nacelle drag: Several variations of nacelle drag were investi- gated. These were chosen as representative of the cdined wave and friction drag variations as f m d in the -?acelle shape analysis to allcw use of the trade data for any nacelle geometry analyzed i n t ! ! i s program.

The results of this trade are shom i n figure 26, which shows relative takeoff gross weight (llw;#3 versus nacelle drag at arach 2.32 for several varia- t ions of the drag incremn t at mch 1 . 2 .

Propulsion system eight trades: Airplane TOGW has calculated for several propulsion system eight increments.

Incremental propulsion weight, i n this case, is defined as a percent of the sun of the engine, nacelle, and miscellane- ous prop~lsion systems (198 kg, (445 lb) per nacelle) weights. The results of ti~is trade are shmn in figure 27, which plots relative TOG# versus propulsion weight increment .

Engine specific fuel consumption trades : Four separate trades were performed sith SFC increments applied independently to the following mission sepnts : ) f a x i m u m power climb legs only ( 1 ) (2) Supersonic cruise legs only Subsonic cruise and loiter legs only (3) ( 4 ) The entire mission The results of this trade are presented in figure 27 as relative TOGW versus percent change i n SFC.

(0.323 lb/lb) (72.5 lb/sq ft) (4000 N) -- - -- --- 1.4 m l l e &ag e mch 1.2 - 1.3 0,006 0.003 Relative XmJ 1.2 1.1 1.0 0.9 r 0.000 0.001 0.002 Nacelle drag @ 2.32 mch Figure 26. - Nacelle drag sensitivity trade.

SFC increment - percent

Propulsion weight increment - percent

Figure 27. - Propulsion weight and SFC sensitivity trades.

Engine sizing thrust: Figure 28 presents relative TOCW versus percent In this trade, it is assued engine sizing condition.

b g e in thrust at t h a t the thrust available a t the engine sizing ccmditim varies without In ; h e change in propulsion characteristics a t other flight conditions.

current s t d y , a l l engines were sized a t takeoff.

Application of sensitivities. - To demnstrate the aethod of W&yf~ the

o lw- vehicle sensitivities, an exajiple using the VCE 112C engine is i n The VCE 11X is discussed in &tail l a t e r under 'Validatian ing paragraphs.

of the Approximate Method." Additional examples are also g2.m therein.

he - baseline airplane characteristics and semi t i v i t i e s were originally computed using a friction drag that was approximately one count too high and an ambient temperature increment that was incorrect. Thus the baseline airplane should have been sxmdut lighter. lhe baseline airplane was reconputed and resulted 3 n a takeoff gross weight of 316 783 kg (698 375 lb),

a propulsion system weight (four nacelles) of 30 882 kg (68 081 lb) , and drag

coefficients of 0.0040 and 0.0030 a t mach 1.2 and 2.32, respectively. Figure 26 1 s been revised relative to that s h m in reference 2 for t h i s reason.

A nacelle drawing (figure 29) w z s made with engine accessories located an the engine without encapsulation for cooling. Weight for the nacelle was estimated to be 8750 kg (19 298 lb), which includes 198 kg (445 lb) for

misce 1 laneous propulsion systems . The revised base1 ine nacelle weighed

7880 kg (17 020 lb) . Thus, the VCE 112C nacelle is 12 percent heavier than

t h e baseline. Fmm figure 27, the relative l W W ratio, k, for t h i s change

i; 1.059.

In order t o maintain the takeoff distance, a new engine must have t h e same effective thrust-to-weight ratio between 0.0 and 0.3 mach (approximate l i f t o f f speed) a s the baseline. The effective thrust occurs a t approximately mch 0.25. Because the VCE 112C has a significantly different t h m t lapse rate with mch n m k r than the baseline (as shown in figure 30) the effective thrust is 17 percent lower than the baseline. Extrapolating figure 28 t o a thrust increment of 17 percent yields a relative TOGIu' ratio due t o takeoff thrust, k, of 1.10.

Figures 31 and 32 show installed performance of the 100-percent size VCE 112C and VCXE 502B propulsion systems. Because the Breguet range factor, $1 x L/ D/ SFC, maximi~es near minimwn SFC, the airplane w i l l tend t o f l y at o r near m i n i m a n SFC; cruise altitude w i l l be adjusted t o achieve this.

Therefore, the S F C increment may be taken a t the minimum of each engine.

This assunption i s slightly optimistic because the lift-drag ratio w i l l also change and w i l l affect the operating point. Thus, the VCE has about 6.3- percent higher SF€ a t supersonic cruise and 4.6 percent lower SFC a t subsonic cruise than the baseline.

From figure 27, this results in a relative TOGW due t o a change i n supersonic cruise SFC, RSFC, of 1.071 and due t o a change T f i 3 . 1 6 n./kg, (0.323 l b . / l b . ) w/s 354. kg./sq,m. (72.5 l b . / s q . f t . ) Range 7 408 km. (4 000 n . m i . )

Sizing point thrust increment - percent

Figure 28. - Sizing point thrust sensitivity trade.

Nbte: Dimensions in meters (inches) .

I E j Pylon planform I 6 . 7 (264.23) Accessories Figure29.- VCE 112C nacelle.

drive 0 . 0 0 . ' 0 . 2 0 . 3 0.4 0 . 5 Mo - free stream mach nunher Figure 30. - VSCE 502B and VCE 112C takeoff thruct , PRECEDING PAGE BLANK NOT FILMED 'ti u w hl n d G 4 i n subsonic cruise SFC of 0.994.

me nacelle shape of the VCE ll2C is similar t o that of the baseline

but has a smaller nozzle area. The drags used in the mission analysis c q u t e r progrim are indicated in table 17. From figure 26, the relative MGW r a t i o ~ L E t o change i n drag, R6, is l*021.

TABLE 17. - arPARISON rY: BASELINE A N D VCE ll2C EiA&ELLE DRAG 1 - 3lission analysis conputei program values

CCU*

mach 2.32 mad 1.2 0.30031) 0.00040 VSCE 502B (baseline) 0.00048 VSCE l l Z C 0.00085

The ratios k, h, RSK, ard are then multiplied together t o

"a

obtain the t o t a l relative TOGK ratio, hAL-

The neh- T W i is obtained by multiplying 1.y the baseline TOl;k' of 316 783 kg (698 375 lb). Thus, it is estinated that a vehicle neeting the p e r f u m c e requirements using the VCE 112C engine wwld weigh 401 092 kg (884 258 I t ) .

Validation of the Apploxintate Mthod Standard preliminary e s ign procedures were applied in the installation of four candidate engines in the baseline supersonic transport ajrplane.

Er'ag and weight estimates kvre made utilizing conventianal prece&..rres. The airplanzs e r e then sized t o the design mission utilizing an auttnated reiterative process. The results of this task provide a more exact evaluation of the candidate engines thar is obtainable with the more approxi- mate methods resulting fran the e a r l i e r task, and thus serve as a reference for evaluation of the applicability of the approximate methods.

slan. - Four engines were selected so +ht the semitivity aethod couid

wall ted for a "ide range of engine types: E=x-

(1) PWA VSCE 502B duct-burning turbofan (2) P U . 4 W E 11X variable-cycle engine (3) GE (;E21/J10 B1 lw bypass t d j e t (4) (;E GF21/Jll B3 double-bypass variable-cycle engine Characteristics of these engines are s m r i z e d in table 18.

l h engine and installati- are discussed in the following paragraphs- While there may be different ei&t and perf- pargins and noise a d technology assmptions for the four engines, the data were used as slrpplied by the mgine manufacturers without IPdi f ication - for these di f f e m e s . Hence, results discussed later should not be interpreted as representative of the final SCAR engine studies- (mine studies are currently still lder way.)

TABLE i 8. - li\G I hT SlfiPt W l - ---A- - - - - -

1 x ; I hi

-.-- - -- - - ! \'Xi! 5033 KIi 112C GE?l/.JIO H 1 (T.21/J11 R3 r- 1 !Design airfiori, . 408 138 3 1 8 / 3 1 h-SJsec ( I h l s c i ! * [:~I)O] i (snoj ( :oo/:sa) Bypass r:!t io 1.3 0.1 0 - 3

sen-lcvcl s t a t i c 1 2h 300 23 3 1 0

takeoff t h r i s t , 1(5!1 50C1) (41 100) ! i daS ( l b ) "

j -, :Takeoff speci f i c ' 1 55

t h r ~ s t , & S / k _ g / i-b) (56)

scc i 1 h/ 1 h / w c 1 *

(30,: h191 T280 5964 rnq- w i g h t , , hg ! l b ) 13 -iflo) ( l h 050) (13 150:

'Overall length, b. 8 :. 9 6 - 9

i m ( i n . ) ( 'bb) (;73) 2-19 2.01 ( 88) ( 37) ( 79) . -- -4 - - 1 . 4 i n s t a l l e d f o r t h i s study, standard plus 8 O C day

- - -- . - _i

V5CE 502B: Refiried perfoxmance d a t a (dated January 1976) f o r the VSCE 502B engine wers used t o c a l c u l a t e revised i n s t a l l e d propulsion performance data.

-411 performance installation e f f e c t s ~ ~ c d were t h e same as f o r t h e b a s e l i n e data. I h e noise c a l c u l a t i o n procedure tias i d e n t i c a l t o t h a t f o r t h e baseline.

Per- I n s t a l l e d performance changes were very small r e l a t i v e t o the haseline.

formance d a t a a t inportant f l i g h t conditions are s h a m i n f i g u r e s 30, 33, and 34.

The n a c e l l e was revised s l i g h t l y conpared to t h e baseline, to include engine accessories (imncapsulated) and m r e r e a l i s t i c s t r u c t u r e allakances and bounds,? layer Jil-crter, as shokn i n f i g u r e 35. This engine configuration l e n t X well-defined wist a t i t s e l f kc11 t o e s t a b l i s h i n g a n e f f i c i e n t n a c e l l e shape.

t h e conpressor s , i f rrune provided space f o r the rcqiiired accessory geartox vol- une ~ i t h o u t forcing t h e n a c e l l e masimun diamet2.- ~ l c h beyond t h e nozzle diameter 1-ocat ion o f t h e engine main mo'x~t a t t h e enginc . ront frame enabled t r a n s f e r o f the mount lads d i r e c t l y i n t o t h e pylonj~iing s t r u c t u r e .

C 1 I n s t a l led performance d a t a f o r the VCF 1 l X (108 kg/sec (900 lb/ sec 1 1 k:ere c a l c u l a t e d in t h e same manner as t h e Recause t h e super- sonic c r u i s e rtirfloh i s t h e same a5 that o f t h e YXli S32B, the s= capture a r e a was The only s i g n i f i c a n t d i f f e r e n c e in procedures ax5 t h a t only a 4 dB r d t r i t i o n in w i s e due t o the coannular e f f e c t ~ 3 s used (in.;tead o f S dB) because the cshliu_st c h a r a c t e r i s t i c s and no=:~c conf i g u r a t i e n o f t h e \-CE I 'X a r e 511ih t h a t an S J R r e J u i t ion could not hc a c h i c \ - 4 . This r e s u l t s ir? s m t h r u ~ t reduct ion a t mich 0 . 3 takeoff p ~ c r ( f i g u r e 30) h-hilc t h e a i r p l a n e is on t h e gr-oirnd in order t o 5t:iy ~i t h i n E A R -3 noise r c q i ~ i rcment.;. Thrust i s redired even fui-thcr a t t h c takeoff noise mcasut m n t point. Figures 33 m d 34 campa;-e in..;t;~llccl p c r f o m ~ n c c o f t h e YX!i -503 3rd LC!: I1,Y:.

17ie i n s t a l l a t i o n of t h i s c n g i ~ c i c t o a n;~ccllc ( f i g u r e 291 i s q u i t e s i m i l a r t o trxrt o f the \ - X I : -5033. -!'he only s i g n i f i c a n t ch;~ngcs a r c a longnr engine and a .; 1 i ,:ht ly rfiiuced no::le J inmctcr.

I l / . J l O 1 : Installeti p c r f o m a ~ ~ c c o f t h e ( l i 2 l l . l I O H I w a ~ ~ i n l c u l a t c J i n 3 m-inner s i m i l a r t o the hascline except t h a t a 2-11 m i s d compression i n l e t with a captirrc arcn o f 2.0' srl m ( - 3 208 sq in. I trsc~l. l'he (:I!ll/.J10 B: has applosi - matcly Ih-lx*rccnt lower sulwrsonic z r ~ r i s e a i r f lob relritive t o takeoff a i r f l o x than docs the Y X I i 503R. If an nxis)mnctric i n l c t had hccn used : i d s i z e d f o r r personic c n r i s e , tlw s t a t i c takeoff i n l c t rcllovct-y sotrld ha\-c k e n 4 ?crcent ~ a l t c r than the L'SCIi 502R. 1 1 . : 2-11 i n l e t tins mc~c thror;t area v a r i a t i o n capabil- i t y ;tnJ I;1rgcr au~i1ia1-y cioors tli;tn the ; ~ x i s ) m t r i c i n l c t . Thus, t h e takeoff rccol-cr-y i s ;act~r;~ 1 ly s 1 ight l y h ighctr than t h a t f o r t h e VSc:li ~ ! C R / a s i s ~ m n c t r i c i n l e t . \'el form;rr~i-c J:tt:~ a t i q m r t ; t ~ t f l ight conditions a r e presented in f igtircs 36 tlirotigh 38. The no i s c i n 1ciil;rt ion proccxiirre wrrs ident icnl t o t h a t for tlic h:rscl ine. .\n esh;ltlst noi.;c r c d i ~ c t ion of S t l H a t ;a1 1 f l ight conditions tias useci ._lire t o tlic co:irinulia~- noi s c rCcicrzt ion cf t'n-t .

I

- - h a

n

-- -T . . - v--

WING LO\KR hIL .

Dimensions in meters (inches) Figure 35. - YSCI.: 5033 nrtccl le.

F C ; , ~ I ~ U T 2 83 STANDARE + 8 O C DAY Figure 36. - m:: /JIO B i and C;E21'.Jll 83 takeoff t h r u s t .

PRJXCDLG PAGE BLANK NQT The near-cylindrical configuration of t h i s engine penalized t h e nacelle shape when the required volume f o r the encapsulated cngine accessories package was added (figure 39). The package was shaped t o minimize t h e added cross section. Location of t h e main mount a t the turbine frame forced t h e engine cowl t o be designed a s a s t r u c t u r a l element and added more t o t h e required cross section.

GE21/.J11 €33: Relative t o the GE21/.11@ 91, the CE?l/.Jll 93 has even higher takcoff a i r f l o h and the same su~personic cl-t~isd airflow, thus creating a g r e a t e r takeoff airflow/inlet matching problem. Therefore, the 2 - D i n l e t was used.

Recause t h e engine operates without augmentation a t takeoff and the exhaust velo- c i t i e s a r c low, the s i d e l i n e noise is q u i t e lo\; while the airplane is on the

ground (approximately h dR beloii E A R 56 requirements ) . Hoiieve:-, t h i s signif i -

cantly reduces takeoff thrust : f i g u r e 36) and increases engine s i z e t o meet takcoff distance requirements. Some thrust cutbach is : t i l l required a t the takcoff noise measurement point. Installed performance is compared t o the G E Z l / J l @ R1 in ftgures 37 and 38.

This engine i s s irnilar. i n conf igurat ion t o the (;II21/.J10 H I c:.cept t h a t the This enabled t h e cowl imin engine mount was located r?t the conlpressor niidiramr.

t~ Ilc made nonst l-trctt:rc1 1 and reduced so~!le\ii~a t the nacelle mas irnum cross s e c t ion.

.\I! other d e t a i l s of the cngine and i n l e t l i n e s development for the trio engines a r c idcnt i c a l , as sho\n in figure 40.

?la5 s properties.- \$eight estimates \\ere nlarlc for the four candidate engine - instal l a t ions. The cnginc w i g h t s , including n~z:le.; and thrust reversers, were 1))- t hc cng inc r r i : t n i ~ f a t r e ~ s . height i ncrcments for residual f l u i d s and i i i i .;cc I 1;ineuiis cng ine/;i i rf ~ i n i intcrfitc ing provisions \;ere added t o the manufac- :til.ct-'s clt~otccl licights t o ohtain the instal led engiile w i g h t . The weight sum- The n a c e l l e / i n l e t rn;i~-ics of tile engines a r e ~ ) r e s e ~ i t e ~ I in tahles 19 and 20.

w i g h t s for tltcsc engine instal lntions \<ere cnlcul:itcd from t h e i r respective naccl lc I incs tlcvclol~mcnt layout d r a ~ i n g s figures 29, 35, 39, and 40. Summar- .

its of ttic nacel l c / i n I e t rteights a r c shoim i n tahlcs 2 1 m d 2 2 . The d i f f e r - ence I n nacel lc weigbts hetween the P 1 q . A VSQ: 502R, and 1'UE 1 1 2 C engine i n s t a l - 1:tt ions is primari l y clue t o the longer engine cowl length of the VCE 112C i n s t a l - lation. For a given i ~ ~ l c t capture area, an asis)mnctric i n l c t would weigh l e s s th:~ii ;I :-I) inlet. Ilo\;cvcr, the 2-1) inlct/nacclles for the (3: (;1:21/.J10 R 1 and (:1:21/.111 83 :ire of similar ~ e i g l l t ;is the axisymletric PWA engine nacelles.

[ h i s r c s t ~ l t s from the .;ma1 l c r inlct capture are;is ;tnd cnginc dinlensions cf the ( ; I cngircs.

\el-odyn;irnics.- ho~mi~lized cross-set:tioniil area shapes of the four candidate --- rl:iccl les of t h i s study a r c presentctl in figures 41 and 42. The e s t imatcd naccllc incrernc~ltal h k i n f r i c t i o n , rk;lvc tlrag, ;~ncl t o t a l clrag c h a r a c i e r i s t i c s ~ E C E V I N G PAGE BLANK NOT FCLDOUT Figure 40. - GEZI /J11 B3 nacel ie. , TABLE 19. - ENGINE WEICHE, INIERNATIONAL WITS ;\ilogra~ls/Enginc P r a t t & Whitney General Electric Engines VSC'E 502B VCE l l Z C GE21/J11 B3 G E Z l / J l O B 1 Bare engine (including 6077 6191 7280 5964 nozzle & thrust reverser) Residua 1 fluids 2 3 2 3 2 3 23 M i s c e l l ~ ~ provisions 23 23 23 23 Engine as installed 6123 6237 7326 6010 TABLE 26. - ENGINE k'EICHTS, BKLISH UNITS Pounds/engine Pratt & Whitney General Electric Engines L5CE 502B VCE 11X GE21/310 01 GE21/JIl 03 Bare engine (including 13 400 13 650 16 050 13 150 nozzle & thrust reverser) Residual fluids 50 50 50 S O Miscellaneous provisions 50 50 50 50 Engine as installed 13 500 13 750 1 6 150 13 250 PRECLDLVG PAGE BLLYK NOT TABLE 21. - SXELLC/ IXLET WEIGHTS , IhiRY4TICWU UNITS Ei lograms/nacelle - h i s ~ n m e t r i c Tw-d imefi:sional .Ucel l e / i n l e t Y X E 5028 VCE llh' GEZl/Jll B 3 Gf21/J10 B1 Engine cwl 816 : 124 T26 760 I n l e t cowl 3'0 36 5 566 598 Sp i kc -10 -33 R v l l p s 51' 517 *.\ir i d u c t ion feati:rt*.; R!pass 4g 49 .Illxi l i a q - i c l e t 30 30 ScconJaq- a i 1- pl-ovi > - 1011s '

I

I n l e t c o n t r o l s 45 15 Engine mounts 82 90 93 110 'rot31 n a c e l l e / i n l e t 201s 2315 203': "Inzludcd tcith spike \<eight i n asis)nnnetric i n l e t s .

a Pounds/nacel le .Lxis)mmetric T ' w o - d imens iona 1 V X 5 I 1 GE2I/.Jl0 B 1 GE21/J11 B 3 Saccl l e / i n l e t I finsine c o t ~ l lT98 1557 24?7 1673 I n l e t corbl 516 1247 804 1319 Sp i k c 1632 1616 1140 1140 Ramps *:\i r induct ion features 107 107 Hlpas 5 Xusi 1 iat? i n l e t 67 67 a i r pro\- i s ions 53 53 Seconda I n l e t contr-01:: 100 100 f:nginc mounts 203 24 2 Z O h 199 -- Total nacel l e / i n l e t 4449 5103 *Included with spike weight in a x i s ) m e t r i c inlet:; 2 . 9 3 ( 3 1 . 5 ) capture area, =I m (W ft)

Leqgh, rn tft) 1 0 . 1 3 ( 3 3 . 2 5 )

6 7 . 2 6 ( 7 2 4 . 0 ) Surface area, sq r (sq ft) 2 . 9 3 ( 3 1 . 5 ) capture area, ul m (sq ft) Wth, (ft) 1 1 . 2 5 ( 3 6 . 9 ) , - a c e area, sq m (sq ft) 7 4 . 2 2 (798.9) Figure 41. - VSCE 502B and VCE 112C nacelle cross-sectional area variation.

Capturearea, s q a ( s q f t ) 2.06 (22.2) Length, (ft) 10.63 (34.9) M x e m, sqm (sq f t ) 55.7 (599.7) GEZl/J11 B3 Capture area, sqr fsq f t ) 2 . 0 6 (22.2) Length, (ft) 10.21 (33.5) 59.30 (638.5) Sdrface 2 . 2 , sq m (sq ft) Figure 42.- GE 21/J10 01 and CE 21/511 03 nacelle cross-sectional area variation.

for all of the nacelles are presented in table 2 3 . InclucEed in the table are the increamtal drags obtained f r o a n the carputer table look-y, progr;ta of the parmetric drag analysis results. The differences between t h e estimated drags and the parametric results are attributed to the following considerations: ( 1 ) The praaetric study, which is the basis of data for t h e table look-up program, was made with a resized wing with the nacelles relocated further inboani and forward i n accordance w i t h the ground mles of the study.

( 2 ) The current nacelles deviate fran a linear radius connection of the inlet face, ~ l l a x h m i area, and nozzle stations.

In snae cases, the ratio of the distance to the maximat area to the (3) total length (XAMAX/L) falls outside of the parametric study envelope, thereby requiring extrapolation.

( 4 ) Drag coefficients for intediate lsach nmbers are obtained by using a cubic curve fit based on the total drag (CDO) increments at mach 1 . 2 and 2 . 3 2 . However, since wave drag does not follow such a simplified solution, interpolated or extrapolated drags will deviate from an estimated value by In the case of the reference nacelle, the deviation was varying amounts.

-0.00017 at nach 1 . 4 .

Performance and sizing. - Perfonuance calculated for the aircraft having the four selected propulsion systems installed includes all items as described earlier under "Baseline Airplane Definition." In addition, performance has been calculated for an "ecomic" mission as described in the following paragraphs.

-4s on the design mission, the economic mission is calculated for a standard- plus-8O C (14.46 F) day.

A profile of the ecommic mission is shown in figure 43. This mission consists mainly of a mch 2.32 cruise as in the design mission; however, it is preceded b y a subsonic climb and cruise totaling 741 Ian (400 n m i ) . Fuel reserves are calculated just a s in the design mission for an alternate airport located 463 kn (250 n mi) beyond the destination airport. The ecomnic mission is an off-designmission i n that the airplane, as sized to 7408 b n (4000 R m i ) range on the design mission, carries a reduced payload equal to 55 percent of the design payload and fuel is then off-loaded to yield a total economic mission range of 4630 Ian (2500 n mi) plus fuel reserves.

The economic mission consists of the following legs:

( 1 ) W a - and takeoff - 10 minutes at idle power plus 1 mii~ute at

maximum power TABLE 23. - DRAG m A R I S O N .W UWC at1323id Reference Configuration J f E s t imtd Panmrtric A C AC' A ( : A c t ) "r V Do

bl "B "P "=DM

1.2 O.UOCITI 0.00031 -tt.O#t41 0 . W M O.IWO31 -0.000% 1 . d O.O(Wii1 0:00035 -Il.OUU17 li.lWMt52 o.IW)Utv5 1.3 0.00010 -0.IHICI2 (1.tM)UJi 2.52 0.tHMO 0.00013 -0.@0018 O.lHwS7 U.Wbd2 -O.WNld 2 . 7 1). lWW)5b O.Oimd -il.WOlj Q.0(#)41 Hrictpo~nt W 3 StllH t2.t t a r t t d 1 t k a w t r ~ c I A t AC AC A t ; Ill, l ' , ?

N A% "b 1.2 11.0(1053 U.tMlO(tU 0.OOU57 0.UUUSS -O.(U#IUi O.UOOQ?

il-tMWll 1 .4 0-lWUb9 O.OM158 I - 8 n.tn~1so o.wnls4 o . ~ t w b -O.IMMH)$ 2 a.OflOJ2 0.01UIS0 U.OOW2 0.00049 -0.~UH10.9 -0.00007 , - . , Q.WIS u.cnw; -ct.tnntn!, I I I Rase1 lnr V ! X L 9 ) t B

-

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(2) Cligab - Maxhm power climb t o cruise a l t i t u d e a d mach &r

(3) Cnrise - Subsonic cruise a t ntach nunber and a 1 ti- for best range

(4) Climb - Maximu power climb and accelerate t o cruise a l t i t u d e and mach n d x x

(5) Cruise - Supersonic cruise a t mach 2.32 at a l t i t u d e f u r best c r u i s e

range

( 6 ) Descend - Descend and decelerate t o 457 m (1500 feet) a l t i t u d e

using i d l e p e r

(7) Approach and land - Descend t o sea level using i d l e power

Taxi - 5 minutes a t i d l e power (8) (9) Reserve - Fuel reserves f o r an alternate a i r p o r t located 463 Ian (250 n mi) from destination airport For each of the four selected propulsion systems, a *'basepoint" airplane was developed. This basepoint is similar t o the basepoint described e a r l i e r , i n that it i s the N A S A reference airplane but with the selected propulsion sys- tem installed. This airplane is then scaled using the Vehicle Sizing and Per- formance Evaluation Program FSPEP) t o yield a baseline airplane. Again, this baseline is similar t o the baseline described earlier, i n t h a t it is the mini- mum gross weight airplane that meets a l l specified performance requirements.

To gain some insight as t o what could be expected f o r each of the 'four re- sized airplanes, an engine scale trade was performed on each. The results of these trades are presented in figures 44 and 45 which show design mission range and balanced f i e l d length versus engine airflow a t sea level s t a t i c conditions, The gross wing area was maintained constant a t 1022 sq m (10 996 sq f t ) and airplane gross weigt:t was maintained a t t h a t for the basepoint with the f i r s t selected propulsion system installed o r 377 632 kg (744 350 lb) .

Results of these trades indicate that the airplanes having the GE21 engines could be ex- pected t o r e s u l t i n a higher gross weight t o meet the design requirements. In addition the VCE 112C and the GE21/J11 engined airplanes can be expected t o pay an engine size penalty t o meet the balanced f i e l d length requirement thereby increasing t h e gross weight of those vehicles.

In the case of the f i r s t selected propulsion system, which uses a revised VSCE 502B engine installation, sizing was performed maintaining takeoff thrust- to-weight (based on sea- level s t a t i c installed thrust) a t 3.13 n/kg (0.32 lb/lb) .

Wingloading was then varied and the VSPEP program allowed t o search f o r the Iw;w = 337 640 kg (744 350 lb) SREF = 969 sq m (9969 sq ft) Sea level static airflow - Kg/sec (lb/sec) Figure 44. - Design mission range versus engine size.

TO(W = 337 640 kg (744 350 lb) % F = 969 sq m (9969 sq ft)

Sea level static airflow - kg/sec (lb/sec)

Figure 45. - Balanced field length versus enpine size.

gross weight yielding 7408 km ((r000 n ai) on * & design dssim. 1he resuftr sere then cross-plotted to obtain the wingloading for a sin- gross weight baseline airplarre. Plots of gross weight and balanced field length versus wingloading (based cwr gross w i n g area) Tor a family of airplanes having a design mge of 7408 h f 4 M O n m i ) are sham in figure 46. A l l ozkr perfomaxe requix-eawkts e r e easily ret .

For the last three selected propulsion s y s t e r l r j , it was originally intended to mintain thrust-to-weightat 3 . 1 3 n/kg (0.32 lb/lb) and winglading at that talw obtained for the 5028 baseline, which is 345 kg/sq m ( 7 0 . 7 lb/sq ft), and simply scale gross ueight to yield the w i r e d design range. However, k- to considerable differcnces i n thrust lapse rate at takeoff for each engine, this method m l d not suffice to maintain balanced f=eld length near t h e required distance. For this reason, the thrust-to-w-ight was varied in each of the last three cases while maintaining wingloading cmstant at 345 kg/sq m . Plots of gross weight and balanced field length versus thxust-to-weight ratio are presented i n figures 47 ttmmgh 49 for families of airplanes having a design mission range of 7408 ~ R I (4000 n m i . ) .

Airplane characteristics for both the basepoint and the resized baseline k-chicles are presented in tables 24 t h ? q h 27 for each of the fwlr selected propulsion systems. Design mission s l r r m r a r i e s are s h for each baseline air- plane in tables 28 through 3 5 .

Performance for each baseline airplane kas also calculated for the e c m c mission. Payload for this mission was 55 percent of that carried on the design

mission or IS 256 kg (33 565 lb) - Fml bas then off-loaded from the baseline

ro yield 46% iCI ((2500 n m i .) on the econoreic mission. Characteristics of each of the four baseline airplanes on the economic mission are shown in tables 3 6 through 39.

The results of the cconotaic mission we= used to coffpute direct operatin): cost (ROI) for the VSCE 5025 and the VCr: 112C.

(m) and return on i n v e s . ; l t l e n t

T?R IlOC and ROT calculations were supplied by Pratt and hhitney Aircraft and are presented in table 40. Input to the DOC and RUJ calculations included the following airplane and mission data supplied b y Rockwell: airframe weight, engine wight, mission fuel, W, block time, and engine design thrust.

These data are i n c t u c i p d for each of the four airplanes in tables 3 6 through 3 9 .

Econanic ... issim sumaries for each baseline airplane are presented in tables

4 1 through 48.

Sensitivity nethod verification. - To verify that the sensitivity method

of deternining aircraft takeoff gross weights i s valid for preliminary studies, takeoff gross weights were estimated using the sensitivities for the four engines. These results were then carpared with the results of the detailed 300 310 320 330 340 350 3 6 0 370 wing loading kg/% a n (lblsq ft) Figure 46. - Sizing with V S G 502B engines.

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TABLE 30. -

WEIGHT ALTITUDE MACH NO. FUEL use0 KG METf.RS KC.

402611).3 398212.2 0.0 Om299 4406.2 396092. 0 b57.2 0.500 2120.1 370960.b 18363.5 2.320 25131.6 301835.9 19678.5 2.920 69124.1 4 CRUISE 2U642m 1 21267.6 2.320 57193.9 5 CRUISE 6 M S C E N O 242332 0 6 657.2 0.500 2309.4 7 OES-LAND 241 980 e 9 0.3 0.300 351.7 240996.6 0.0 0.0 984.3 9 W C t ALL 232915 a6 0.0 Om0 8 0 8 1 1 232263.8 157.2 0.500 651 0 7 10 CLTO 1% 226368.2 12684.3 Om930 5095.6 22270803 12798eb 0.900 3660.0 221396.2 3040.0 9.442 1312.0 2124W.7 3068.0 0.432 8937.6 21169C.4 0.0 0.300 760.3 70th L FUEL usem 19092t.s TABLE 32. - GE21/J10 ' ' "YLINE DESIGN M I S S I ~ SUMWRY, INTEWTIONAL UNITS k'LIbHf AL71tUf.k MACH Nb. FLWL USEb T I H t TOTAL T I R E R M G E TOTAL KG METERS KG M I N O M I No M. KM.

--... - --- . . . - ---. ------ -----

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UI 0, 2' E h -. m u i C1 h h h m - 1 m Baseline 2Sll 141 (m 2M)

m, (a)

-1 weight, kg (lb) 95 229 (to9 913) 4630 ( 2sm) h i @ range, h (b) Far 36 T . O . dist i (ft) 1753 ( 5750) 5 1 f i e l d length, i (ft) - 1 a%] Airfrare weight, kg (lb) 112 768 (248 611) Engine ueight, kg [lb) 23 128 ( 9 -1 Missiar fuel weight, kg (Ib) 76 501 (16% 655) Block t k , min (rin) ( 167)

hgine thnst , n (lb) 251 160 ( sd 4453)

TABLE 37, - BO[NWIC MISSICA CIWWXNSTICS

YIIH VCE 112C ENGINES

Baseline I

=, kg (lb)

Fuel weight, kg (lb) Range, b ( m i ) Far, 36 T . O . d i s t m (ft) Bal f i e l d length, m (it.]

Airframe weight, kg (lb) Engine e i g h t , kg (lb) Missim fuel weight, kg (lb) Block the, rain (ittin) Engine thntst , n (lb) Baseline I 117 (r09 (920 670)

w* k (lb)

i n 070 (3n 1111 eight, kg (lb)

bisn ranse, h (a) 4630 ( 2500)

Far 3 6 1 . 0 . &st r (ft) 1816 f 5959) Bal field length, r (ft) 2159 ( 7m3) 166 931 (368 020) Air- weight, kg (lb) 56 360 (124 253) E~gine might, kg (lb)

U i c m fuel weight, kg (lbf 130 675 ( 2 a m)

Block time, rin (Pin) ( 169) 126 300 ( 95 836) Engine thmst, n (lb) *

TABLE 39. - BCQYUIC #ISION CHARKERISIICS

WITH Q21/Jll B3 ENGIBE Baseline 519 218 (1 144 680)

m s k (lb)

Fuel weight, kg (lb) 214 709 (473 353) .

Design range, la (mi) 4630 ( 2500) Far 36 T.O. dist, m (ft) 1855 ( 607) 831 f i c l d length, n (ft) 2232 ( 7323) Airfrane weight, kg (lb) 207 300 (457 018) mine weight, kg (13) 73 812 (162 728) Hission fuel weight, kg (ib) 162 334 (357 886) Bloik time, etin ( u h ) ( 166) sine thrust, n ( I t ) 524 557 (117 325) k .

b

TABLE 40. - DOC, Ioc, AND R O I

VS(=E 5028 V%F, 1 1 X Direct aperating cost, cents/seat statute mile 2.17 2.73 Indirect operating cost , cents/seat statute mile 0.91 0 -98 Return on investment, t 20.2 1 1 . 0 i Assurptions : 1 . 1974 dollars 2 . 1967 ATA DOC d e l updated to 1974 3. b c k k e d California Co. IOC model 4. 4000 hours annual utilization 5 . 15-year life 6 . Fuel cost of 35 cents per gallon 7 . Revenue of 8 . S cents per passenger statute mile 8 . 55 percent load factor 9. 2500 n.mi. trip distance !m a

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TABLE 4 2 . - VSCE 5028 BASELINE ECOMMIC MISSION M Y , ENGLISH UNITS

LE6 ' OPERbT!Oh( WEIGHT ALTlYUDE IrbCW kca F U E L USE0 TtWF T O T A L T I M @ RANG): TOTAL PA)(CC NO. POUNDS F E E T POUNDS Pika M I N a N o m a . N a Ma

-

- .--- 6 CRUIS-E 7 DESCEND 8 DES/LIN[r

- -.--.- - -

9 T A X I 10 59 OES.

11 C L l 1 9 0 0 -------.

12 C L ~ A C C E L 13 C R U I S E 1+ DLSCliNO ---.

1% ~ a i f ~ a 16 OLS/LANO

-

-

z (I)

* i a (I) W % A TABLE 45. - GEZl/JlO B1 HASE1,INI:. l ~ C ~ 1 I C MISSION SIJ~VMARY, IN'IERNATIONAL UNITS LEG O P E R I T I O N WEIGHT ALTITUDE YACM hC. C C t L US%D KG. HQTERS KG.

NO.

I N l T IbL bE I G b T 4 l l a c s . c 1 NU c TO 4 ~ 2 8 ~ 1 . A C O O 0.299 4801.0 4 1CC240 7 457.2 0.500 1882.4 2 C L I 1 5 0 0 3 C L I P 0 399921.5 10351.3 0.900 10997.3 0.900 225360T 4 CRUISE 31739C.T 101 t1.7 31t615.6 15079.6 2.320 20775.2 5 CLIACCLL 6 CAUISE 25C890.4 2C244.4 2.320 65725.2 i8635i. 2 457.2 0.500 25380 1 T OESCENO 8 DES/LINC 5 t 1551. 5 0.0 0.300 394.7 6.0 0.0 1023.2 9 T A X I 286934.3 280 100.6 C O O 0.0 6533.7 10 5s PES.

11 CL/1500 279357. 5 457.2 0.100 1013.1 17285.0 0.950 12440.8 12 CLlbCCEL L t t 9 1 t . l 13 CRUISE 2t45F7.7 17291.9 0.950 1919.0 14 OESCENC 263318.3 3C4O.O 0.354 167904 247290.6 3C46.0 0.333 16019.7 15 L O I T E P 16 DESILANC 4.0 0.300 767.5 24t!31.1 t c t h i ruu USIC- l t l o t t . 6 analyses discussed previously. 'Ihe calculations and results are sulslarized i n table 49. The nacelle drag increments are those used in the detailed analysis a r x l are shawn in table 49. Specific fuel cmiapticm immaents were obtained from plots of installed perforrance (figures 31 through 34, 37, and 38).

Takeoff thrust increnmts were obtained fmm figures 30 and 36. Propulsion weight increarents wer~ obtained by adding 198 kg (445 lb) per engine for miscellanecn~~ propulsim s y s + s to the nacelle and engine weights of tables 19 throqh 22. Included in the table 49 is a colum for the "revised" base- line.

Table 49 indicates good agmenmt of the sensitivity nethod relative to the detailed analysis for engines with d l changes relative t o the baseline [YSCE 502B and V(=E 112C).

Ihe error increases as the total takeoff gross weight ratio, hAL, bxeases.

Reasons for error inc1t.de the follaring: (1) Reading and extrapolating the sensitivity curves m a y produce sarpe errors.

(2) Sensitivities for changes ir, transonic acceleration thrust were not incl~rded. Tables 24 through 27 indicate a wide range in thrust-drag ratio at ma& 1.2. Thus, acceleration times and fuel used may vary widely fmrn the baseline.

(3) The assunption that the aircraft w i l l cruise at mininan SFC is optimistic; the lift-drag ratio characteristics my tend to drive the operating point to a high SFC.

Scaling factors of the detailed analysis are determined for small (4) changes and are therefore of questionable accuracy for large changes in air- craft daracteristics.

mile the differences i n takeoff gross weight using the two methods are large for the large aircraft, the accuracy of the sensitivity method .is suffi- cient to indicate when changes may be of interest and when they are definitely not advantageow. Thus, the sezsitivity method allows the user to easiiy iden- ',wn table 49, the largest contributor to t i f y problem areas. For e x q l e , vehicle weight increase of the VCE 112C i s effective takeoff thrust (& i s 1-10) while the largest contributor of the GE21/J10 B1 is prapul- sion system weight ((a is 1.16) .

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b -- J Engine shape, airflar-lapse rate w i t h llladr m&er, thrust-lapse rate w i t h radr auber, SIX, and mise characteristics hatre Large effects on aircrdft take- off gross wight. r r ~ an exaple of engine shape effects, a caparison o f cross- sectid area variation of nacelles w i t h W.Z S O B and VCE 112C engines i s sham in figure 3. Ihe only si-snificant difference i n shape is that the WE ll2C has a smaller nozzle exit area. lhis r e s u l t s i n drag ard takeoff gross weight changes as sham in table 4. 'Ilrrs, a nozzle -that i s 0.013 (1.7 i n . ) d l e r i n dieter results in takeuff gmss weight inrrarent of 3 ZOO kg (7 000 l b ) just & t o the l l a c e l l e drag change. As s b m i n figure 25, a a?-drag-cant change results in about a 1-percent change in takeoff gross wight.

Engine airflow lapse rate with radr m d e r directly affects inlet capture area. For exarl;le, the C;Ul/JlO 61 has appmximtely 16-percent 1 - r slper- sonic cmise airflow relative to takeoff airflar than does the V S E 502B. l k slgller capture area results i n approximately 4-percent lower inlet m r y at static conditions and therefore r a k e d takeoff thntst. In addition, the smaller capture area results i n a mre w i d increase o f nacelle cross-sectiw area with nacelle length, and therefore higher drag.

mine takeoff thntst and thnrst lapse rate with mch lluber has a signifi- For cant effect on engine size required t o meet takeoff distance r e q u i m t s .

exanple, the VCE 112C has 6-percent l a k i e r takeoff thnst at static diticns and 20-percent 1 - r thrust at ma& 0.3 ( a t redwed v r to aeet mise re- This quirenmts) than the V!XE 5028 for a given static takeoff airflcw.

resulted i n a considerable increase i n engine size to aeet balanced field length requirements . A s indicated in figure 27, a change of 1 percent in SFC at supersonic cruise results i n a 1-percent change i n aircraft takeoff gross weight or about 3 200 kg ( 7 000 1b)- F~~gine e-xhaust noise characteristics have a significant irpact on aircraft All four engines were a s s d to enploy thrust cutback takeoff gross weight.

W v e r , all the engines did not take a t the takeoff noise neasurernent point.

full advantage of the extra g n w d attenuation while the aircraft uas still on the grormd. For exafsple, the GUl/J11 B3 has 20-percent lower thrust-per-mit airflow than the bSCE 502B. Thus, the C;EZl/Jll B3 yields approximately 6 db lower sideline noise a t takeoff on the gtuund, but it iust be sized larger to meet t h e takeoff distance requi rement .

'Ihe sensitivity method has been shown to be a valid sethod for preliminary assessment of p - i o n system modifications, and it is therefore recamamded t o be used for this purpose. Continued airframe/propulsion integration studies arxi coordination effort between engine and airframe manufacturers i n the afore- mentioned high-sensitivityareas are also recaaaremled.

l h i s r g p a d i x d e s c r i b e s r ~ r p r q g r a d e w e l q d t o & t e ~ m c e l l e ~ t a l drags for the NllSA onowring srprrsanic transport ocafisurrtirm.

~ i n p d s i n c l * f n e s t r e r ~ ~ r a d ~ ~ ~ ~ d e f i n i R g a w e l l e m I c r r ) r . I h t a p o i n t s o r e s t o r s d i n t m i a l t o t h c ~ t o n p n s a ~ t u r r l c rd fricticm drag vrlucs w i t h rp to six idqmwknt variables. Given a set o f ~ ~ t e r 5 , t h e p r o g r r s e t s ~ o r r r y s s o r s t o ~ s a i n ~ search. Ibar, a ahic i s fit to t k e data points, rd tOre drag - t s sre & t e * .

'Ihe w e p m requires 4OK bytes of mmry, d e d case, arrsisting of faa e v a l u s t i ~ ~ ~ of nacelle drag, requires rbart -1 seands of execution tire an a IW 370/168.

lhis appendix relies heavily an references 1 and 2; thars, the resder s h d d have a q y of those rekmnces as he reads the follawing.

Crptun! arer, sq. f t .

w--* sq-

Input value of AC saved, sq. a . (sq. f t . ) mirr area sq. f t .

,'kiaarP arca sq. l a .

,Nozzle area sq. f t .

Nozzle area sq. m .

!@ice1 le drag i n c m a e n Z at E W I 1 . 2 Nacelle drag incl.ement at k c h 2 . 3 2 bile drag increernt at input Madr ;umber Friction drag incresmznt at Mack 1.2 Friction drag haxsent at t?adi 2.32 W a v e drag incraaent at Mach 1.2 W a v e drag im:rwmt at f- 2.32 D i e t e r of capture area, BX ( f t . ) Straig!\t line slope for curve defining ?.kach mmbr effect on totdl drag Conversion factor fran sq. ft. t o , q . m .

Conversicn factar from feet to Hleters Set t c ~ f for use in equation definin;! (=Wlil ;-tach n m k r Conversion factor fnrra sq. m . to sq. it.

Gonversion factor frola meter to feet Total nacelle length, 3 . (ft.)

Set to 2 for use in equation &finig Cik2-i Total naceile length, m.

d

Set to 029 sq. m . (lOOOO sq. fi.) for basepoint wing area

Slope at point where !tach is 1.2 Slope at point &-ere !-tacJi i s 2.32 bference wkg area, sq. ft.

Reference wing area, sq. r n .

Length to m a x k area, ft.

Length to maximrn area, m .

Refer to the di~cussion of subroutine NL%At: for definitions of the s?-a;bols associated - 4 t h data statements in that subroutine.

Roblest Description W a v e and frictim drag inc-ts *re detexmined for a range of para- retric nrcelle shapes i n reference 2. I n order t o deteraiae drag increarnts for rary nacelle shope of interest, values w t be interpolated and/or extra- polated. A mjor part of the program is involved with the deteminatim of t k data points to use whcn calculating the drag associated with a given set of values of the W e p e d s t variables. Once these data pohts are find, a cubic equation (reduces to a linear fit for tm points) is fit, and the desired &pedcnt variable is calculated. This sorting process and l3e resulting ahic fit occurs i n a definite order and i s repeated many tines before the final amaer i s detennhed.

Ihe writ method for fitting a cubic is s i m i l a r to Hemite interpolation in that the coefficients of the cubic are detewined by tm points and the derivatives of t h i s d i c also satisfy tfre slopes evaluated at these two points.

lhe derivatives are defined by passing parabolas through those points using a total of faw.. points for the derivative evaluation. (A arbic is also &- fined using a total of three points with a modified definition for the two s l o p e s ) . These points are chosen so that the desired independent variable is in the middle interval.

EIethod of Solution There are four possible situations that mst be handled b y the program: 1 . Given four points w i t h the value of the independent variable in the middle interval, 2 . When t h e desired value is i n the last or first interval, 3 . Wen there are only two values, and 4 . Hhen the value i s outside the range of data.

Given four points with the desired value of the given h d c p x h t

variable in the middle interval, as shown in fm A-1, assme the equatian

will go thmugh thc points P2 d P3. Also, the derivative is evaluated at P using the points P1, P2 and P for the caldatim of the coefficients A ~ , h and cl. It is also evaluatf at P3 using t h poilts P2, P3 and Pq so that equation ( 1 ) passes thm@ points Pt and P3 and the der5vatian equation (Z), also satisfies the slope at these t w points. * r e - fore, four equations result t o d e t e - A, B, C, and D, in mpation ( 1 ) .

lhis is the basic m r i c m e t W used by the! program to determine t h e de- pendent variable Z given Q. ' I h e detailed equations are contained in a following sect ion.

is in the last interval, the cubic is defined Wen the desired value

by points P3 and P4, and the k rivative at P3 is &temhd by passing a

quadratic thrash P2, P3, and Pq while the derivative at P q is defined b y passing a straight line through points P3 and P4. Similarly, wfaen

9 is

the first iqterval, the cubic is defined at points P1 and P2. The s ape at P2 is derived by fitting a quadratic through P1, P2 rmd P 3 . Ihe slope at P i i s the slope of the straight line passing through points P1 a n d P2. In both cases, only three points are used. In the event that only tm, points are defined, then linear interpolation is used. H k n umstraints are ~iolated,

t h e p m s s deternines points as if the value of + is in t h e first or last

interval.

Then, a linear or cubic ax-ve fit results i n the calculatia~ of an extrapolated value for 2 .

Prognm Description OPERATLIG EN\qROSENT. - This program was written using stadad Fort? a n statements using a Ibl SYS370 l r a o d e l 168 cqmter w i t h the operating system os/vsz.

P - i SPECIFICATION5. - Source listings of the mail program, NDRAG, and subroutine WIAE are at the end of t h e appendix; memory requirements are: NDRAG - 9874 decimal bytes NDTLAE - 3806 decimal bytes T h e program uses 40K bytes including system subroutines, and no comnon is used.

PRKRNl k O W DEFINITIONS. - The m a i n program calls subroutine MIIZAE

t o initiate the interpolation for the total drag given values for the inde- pendent variables. Four calls are made in order to calculate the necessary quantities a t each of two lnach nunbers.

Wn Program ! W e (NURAG]: The main program performs thc follading f u r c t i m : (1) Setup of data for subrautine MIIZAE, (2) Cmersian of units, (3) Calculatian of the effect of )i$ch nunber on drag incremmts, (4) Input and output and checks on independent pameter values, (5) Setup of data in data stateaents, A large portion of this mdule is involved in setting up the input d a t a in the correct fonnat for subroutine WlUE. The input variables required for this subroutine are 'ku , % , h X L +and).!. Here,

-

L F x'q'

=((% and these are set up and used in the English s y s t a

of inits. (Refer to figure A-2).

The main program also includes the conversion of data from hrglish to International units (and vice-versa for input -output convenience.

The calculations for the f b c ! ! nunber influence on total drag increment start a t statement number 83. DER, the slope, i s determined fmn the equation

Ihe slope at fkrch i . 2 then has a value of 2.0 * DER, and the slope a t

bfach 2.32 is 0. 3SfDER. (These values for the end derivatives are estimated fmm a study of the basic shapes or trerrds inherent in c u m s such as Figure 61 on paze 87 of reference 2). Using these two points and the two derivatives, a cubic is f i t , and the total drag increment at any M b r h number is determined.

Additional functions include the input and output of data and the necessary calculations t o &tennine i f a constraint has been violated. If this i s the case, the value of the variable i s printed cwit and the program extrapolates.

?he ranges are: Indep. var. I1 .4 3 k c 1.

-

L con ICI.2

1 - 4 7 ]

Figure A-2 - NDRAG FILW CWW

Indep. var. 13 1.25 5 - k 5 2 . 0

Ac

Indep. var. 14 Indep. var. t 5 2 0 . 5 A~ 5 40.

h k p . var. 16 1 . 2 5 M 2 . 3 2 independent variables 3, 4, 5 , and 6 are required for the calculation of friction drag.

Included i n the first part of the module are several data statements.

These contain values of the inkpendent and depdent variables as d e t e * e d f m m Figure 24 through 59 for wave drag and f m a Table XI11 for friction drag of reference 2 . Each array has a special definition and the order of the variables is specified by the interpolation methad frum subroutine MJIZAE.

Values of the independr2t variables are: Indep. var. ti, %AX = .4, .5, .6, .7, .75, -8, .85, .90, 95, 1 . 0

t

Indep-var. t2, - %l = 1.0,1.2S,l.SO,2.0

Ac

Indep. var. 13, = 1.25, 1.50, 2.0

-

Ac

Indep. var. 14, - L = 5.5, 7 . 0

Indep. var. 85, AC = 2 0 . , 3 0 . , 40.

Indep. var. %6, El = 1.2 and 2.32 Each data statement array is defined b e l ~ w .

NX is the array of the nunber of values for each independent variable i n the order as specified above.

X is the array of individual values of the independent variables i n the order as specified a b o l r e .

2 1 1 is the array of values of the dependent variables for friction. drag fram reference 2, Table XIII.

The order of these variables i n the Z 1 array w i l l be described by using notation defining the independent variables used for the calailation of friction drag. Ihw, variable X3 has three. values %(I) , X3 (2) and X3 (3) ; variable X4 has two values Xq (1) and X4(2) ; variable Xs (I), Xs (2) and X s (3) ; and the last variable Xg has two values Xg (1) and Xg (2). The f i r s t variable in the 2 1 1 array corresponds to the following order for the indepedemt vari- ables : Then, for the second element, Then, for Z1(4), 21(5), and 21 (6) repeat the f i r s t three lines with X4(l) replaced by X4 (2). Nrrw a total of s i x 21 values are defined for 21(1) through 21(6). Values for Zl(7) through Zl(12) are obtained when these f i r s t In the f i r s t 6 lines six lines are repeated with X5 (1) replaced by X5 (2).

replace X5(1) by X5(3) then Zl(13) through Zl(18) are detennined. So f a r , If these 18 1.ines 18 lines or values for Z 1 have been defined using %(l).

are repeated with replaced by % (2) then 21(19) through 21 (36) are

Y 1 ) specified. These 3 lines represent the 21 matrix for the friction drag.

This is the definition of the data sequence required for the 2 matrix as used i n subroutine NIYlUE.

ARWl through mW1 are arrays of values of the dependent variable for

wave drag, for Mach 1.2. The basic metW for ordering the dependent vari -

rr-y 21, with t m additional ables is the same as for the friction d . . , independent variables.

Arrays ARW2 through FRK? are values of the dependent variables for wave drag for Mach 2.32. Again, the method for ordering is the same as for friction drag only with two additional independent variables.

Subroutine NmZAE: The main fmction of this subroutine is to determine the value of the dependent variable Z for given values of the independent variables X(1). These points are contained in the DATA statements appearing in the main program.

The calling sqmnce for this subroutine is where NN hnkr of idpncht variables (4 or 6) .Ilnay of given values of independent variables ]IG X Array of independent variables Z Array of dependent variables NX Array of nudber of values given for each w e n t variable RES Final required Z for given XG using X and Z arrays Coefficients of the cubic f i t t o the data points thus A,B,C,D defining Z values (In some cases t h i s reduces t o a linear f i t with two coefficients C and D) .

Initially, various arrays are defined for the purpose of determining the location of the f i r s t Z t o be used from the Z array. The object is t o determine which interval of input points in the X array w i l l be used t o calculate the Z array given XG. After these subscripts and indicators have been set, the evaluation - the necessary equations for the Z array can be m e ccqosition of this array, and the sequence of steps leading t o made.

the final Z value w i l l be outlined here. (Refer t o the section 'Method of Solution" for a descripticm of the n-er of intervals used given the X array and t o the section 'Equations For Curve Fitting" for the equations used for the curve fit.)

The pmcedure, for calculating the location of :he f i r s t Z (LISE) t o be used, s t a r t s with defining the ICF array where ICF(1) = N i r m b e r of values of each independent variable (I) t o be used for curve f i t (i.e. 2, 3, or 4) Next, the IGAT(1) array is s e t t o the following values, i f ICRT(1) = 1, XG(I) is in one of the middle intervals = 2, XG(I) is i n the f i r s t interval = 3, XG(I) is b the l a s t interval.

(I) array is &fined as the location in the X array A t the sanre time, the of the f i r s t value t o be used for M q x d e n t variable I. Thus, the subscripts for the X array for the polynunial curve f i t are obtained.

Thr? location of Z(I] given values of X(1) array are then determined. The equations t o do this are contained between statement nurbers 32 t o 35 in the listings a t the end of the appendix. The fonnula, Nrv-1 Z ( I ) i n d e x = I & ( l ) + M((1)*NX(2)..,*NX(k)*[~(k+l)-11 (3)

C

specifies the location (or index) of the element number in the Z(1) array associated with each sequence of values for the independent variables X(1).

(ihat is, an analytical gearing between the X and 2 array is defined.)

Statenent n m h r SO, which sets LL, thmugh statenrent nunber 2000, where the polynaninal for the curve f i t is evaluated, is described by a step by step analyses of the coding in the section "Step By Step Analysis of Subroutine NDIU."

That section also describes, by specific example, the evaluation of the LLCl'R sequence a t statement nmber 410. Thus, the location of the next Z t o use is developed. Figure A-3 describes the flaw within t h i s subroutine with emphasis cn control during the evaluation of the Z matrix. (Refer t o l i s t i n g of subrouting NM'LAF for complete swl definition.)

An example of the use of equation 3 w i l l be demonstrated w i t h the friction drag data. For conwnience, number the variables 1 through 4 (instead of 3 through 6) a s described i n the previous discussion of ind.ependent variables; therefore, Variable I1 is h with NX1 = 3,

ac

Variable #2 is - L with MC2 = 2 ,

dc

Variable #3 is AC with M(3 = 3, Variable W 4 is M with NX4 = 2.

Let subscript refer t o variable number: Z(1) is dependent variable for XI (1) X2(1) Xj(1) Xq (1)

Figure A-3 - m I A E F m r aWrr

Frcm equation ( 3 ) for Z(7) and for elarent 1121, l k n the elerrent is: k r 2 ( 2 1 ) , values i n equotian ( 1 ) for elaent 3122 give t h e elaart Because of the number of variables i n each array, the value of equation ( 3 ) would always be 1, and new Z values are spcified by LL arrays when l i f l o d i f i e d by LUTR values. lhat is, the I4X a p p a r b g i n t h i s w l e is mdified by LL anay.

PRoGWM IM;IC.- Figure A-4 h s a program flar during the calculation of the Z array. Ihe last Z calculated is the final result. Note that i n this figme the muired n - r of Z values is determined by the n m h r of values Figure A-5 shews in -re cmtained i n the next array o f independent variables.

detail the series of Z as c3lculated for the friction drag. Z(XX;1 fbllows as a result of ten previous curve fits there three are linear and seven are cubic.

INPVT-OWIW SPECIFICATI(3N.- Standard input-output functions are utilized t o input case data and to output the calculated total drag for each mach nunber.

Ec input data is printed out for identification purposes.

input: A read tape 5 is used to read 1 case of 1 card cantaining seven numbers with a E10.6 forarat- In order, Card Colurn Identification

Word I1 - % Capture area

W o r d 12 - hW Maxim area

Wad 13 - % Nozzle area

Word f 4 - $m Lengthtomxinunarea

Wcrd- - L Total length

Word 1 6 - SREF Reference wing area

Word t 7 - )f Mach n h r

Figure A94 - PWX;RAM FILM FDR Z ARRAY

Noxmal input is a s - to be in the English units with the basic 1 - masured in feet. A nina sign in colum 1 indicates the units are in the International units with the basic la@ mmsured in reters.

A write tape 6 w i t h an F format is used for printing data. The a;ltprt: above input data and the fricticm drag, wave drag and total drag for Mach 1.2 and 2.32 are printed. Also printed is the total drag for an inpn EQdr nrber.

RESTRICTIONS. - Each figure for uave drag in referena 2 caitains values

of WAC for a g i ~ n value of W A C A c Physically, v+ cmot eaced

. W A C , but in a m a t h a t i c a l sense a lluerical valm for the drrg l a t be

- - - - - In t h i s case, &en deterrined in order t o sustain the interpolation pxum?ss.

a lirit is excee&d, the extrapolation ~ s w that the limiting values of

drag are used for vallrs of q+ greater than .kuc/+. ihat is, on f i g m 24

(rekmce 2) with ho curves for v+ of 1.0 d 1.25, dizq values for the

1-50 and 2 . 0 curves are a s s 4 t o be i d w r t i d t o +hose for the 1.25 curve.

The &r of points ~4 in the curve f i t Qpends on wkre the desired value

of W A C falls relative to the index values of 1.0, 1.25, 1.50 md 2.0. I f

l . S ~ q ( k S 2 . 0 then last three points d d k used. Ylm 1 . 2 5 * ~ ~ I 1 . W , a total of four points W d be used for the curve f i t since this is the hhen extraplatian for the 9ther in&qxdent variables is middle interval.

requid,no limitbig values of the variables are substituted.

is specified by the cadition l'he terminal point for each wave Jrag value that the boattail angle does not exceed 10". In order to satisfy this require-

ment, the final drag value for each c u m (i-e. each .w& walue) is repeated

in -05 increnents for +W(/L until X T W L is 1.0. Thus, the proper drag level a s set by the maxima boattail angle w i l l be m x t .

DL4CWSI-ICS. - Wen a desired value for an independent variable does not fall within the given data range, the variable and its value w i l l be printed.

The calculations w i l l use this value for the extrapolation as described above.

Subroutine WL4E contains several tests to cietennine i f calculated i d e z values are set properly. The statement ruaaber of the test generating the diagnostic is printed out.

TEST CASES, - Cases 1 and 2 (tables A- I and A-I I are presented herein and the values of CDO have been verified by carparing with valms read directly f m table XI11 for fricticm drag (CDF) and figures 24 through 59 for wave drag (OK) in reference 2. Cases 3 and 4 are presented for the NASA LTV nacelle, described in reference 3. These cases were c h d e d by cross plot- ting the curve Qta.

The parametric study is based cm a nacelle that had straight line radius connections of the inlet fece, mcWm cross secticm and the nozzle exit. The NASA LTV nacelle deviates fran these straight line camections and, therefore, it is necessary to sisulate the nacelle with straight lines. Case 3 (table A-111) s h l a t e s the LTV nacelle using the inlet capture area, actual a u i m m area, and the nozzle exit area. A considerable difference in CDO may be noted.

I t has been detembd that the best sim- l a t i o 1 1 i s a b ~ b y u s ~ t b e ~ . r - s e c t i a n l m r t b r t o a z m at

t t w ~ o f s ~ ~ - - - lbratbtinlttrad1Bemz4e

~ ~ s ~ w l y r ~ t b s s = ~ a a ~ a ~ m t s d inQpm5. I b e . r d r u m r & u i 8 t i a a u i l l b e ~ t c l ~ 1 0 1 . Cast54 [table kIV) tsthel8tmsiru]rtiaarmdtheQ)[t*srgnewithtbecrrl- ~ . s T ~ l m o o in M i s a - 0 tbc h w mid- errticms: 1 , l'k r i was msized £ma 10,996 s q . f t . for tht rift- am- figurrtiaa to 98l9 s q . f t . fi3.r the m t r i c study.

Ibe Ihe above discursiaa w m s d y tbe 1 . 2 ad 2-32 WIcfi a d e r data points.

plber i s & r i d fm a cubic airwe fit a d d i t i d CXXl at any specified dcxribed m page 5. llw M a t i o n o f ( 1 1 0 q b e a s rrh as -.W02 b e - 1 . 3 Ehce md 1.5 Mach due to tbe fact that the true drag a#fficient as a functim of Mach rrder Qes mt a ~ j e s s u i l y follar a cubic.

Figure A-5 NMELLE NtNMALfZIFD CWSS-SEXXIONAL AREA VARIATION 0RK;INAL PAGE 18 OF WOR Q U -

CAP IURE A R E - . n u r n ~ . ~ c r q FT 7

MARXC1W A R f A 4 o l 8 S Q R # +5.W S9 F I B m r z z t ~ AREA 3 - 4 1 s o n 4 37-54! sc - 8 --- - --- LOCI UF MAX, -AREIF-- -6 -21 - - N ' t - - 20 I U.-- F1# TOTAL LENGTn 10.36 )I 4 33-99 F t a I U C R ~ L M ~ A L )(IICLLLE r!es cm eFrcjr ms . - - - - - - --

nrm 1.2 CbF- " I l r O O C 5 3 --- CDWm 0- WWG - COG= O m f 30*3-- -

WACW 2-32 C I b F = C.00041 a ) t @ 0-QCOO7 U C g C.*C.OO% C O W 0.06093 MACH t m 2 6

---- - -

- - - - --

C A * f t . P t i S . t C 3-72 ; ~ k t 5 SC F T I SL 6 7 ) RAY ?Pien rItl r 7:. S C Ft 4 t:.,ir N P I I L t A k t k L . C i SC: N ( c . ' . ; : SU k T ) ( V Z -46 FT 8 L C ' C r I . F Y A X e A R t b I**&+ P1 Ti t h ~ L t M . T n &>.'3 )r 4 -5, .3c. FT I 1. Slope u s * parabolic fit Gemml equatian of parabola z = g X t + b x + c (1) S l q e of parabola Z I 1 = Z a x + b (2) If given thxee independent variable values w i t h corresplrding dependeat variable v a l ~ s h: Solving equation (3) for a and b

lhen substituting in ( 2 ) above the slope at + is

2 . Derivation of coefficients for the &ic General f o x l a of cubic Z = a X 3 + b x 2 + c X + d Slape of cubic 2'- 3ax2 + 2bX + c To determine the d i c passing thmugh t m given points, (X2,Z2) and

(X3, Z3, anl having given slopes, S2 and S3, at these points, the follaring

system of equations is solved for a, b , c , -and d .

ZZ = aX23 + bx22 + cX2 + d (4)

z3 = ax33 + b ~ J 2 + + d

s 3 = 3 . x 5 2 + 2 b x 3 + c Solving for the four mbmas: '3-'2 1 b =

- 4 - (x3+23) G3-4).. 1 5

1 %-5

c = s2-n2 b - %2 a

d = Z2- aXZ3 - b ~ z - C %

3- Final calculation of &pendent variable The ckpemknt variable Z is then calculated u s i n g the coefficients

a, b, c, d and the given value of % in the equatim

SlEP BY !XEP ANALYSIS OF -INE NIKLAE The sequence of steps to calculate the friction drag w i l l be defined by reference to the program steps mtained in subroutine MIIZAE. PriBlary -is of the following discussion i s on setting values of cumters and subscripts leading t o the &tenhation of the final interpolated value for 2.

Thus, refering to the section on s u b m i n e NUl'iAE for definition of independent variables, Fnx? statements starting a t statement maher 3, Program steps ending at statement &r 23 define the I S array as: Also, for I G A T assune IGAT(1) = 3, IGAT(2) is linear, IGAT(3) = 2, Refer t o equation (3) of this appendix for the locatiaa of A, IGAT(4) = 3.

first Z to be used, i.e. ' LIsrZ = Lgc(1) = 1 'Ihe basic logic for performing the calculations, starts at statement ~ m b e r 50.

NIV = 4 L = 0, LL = 0, LLCIR (I) = 0, I = 2, 3, 4, S For J = 1, 2, 3, andM= 1, 2, 3: The derivative of X (XPR) with vaules from f i r s t X array are tiwin determined: Then, IL = IGAT(1) = 3 for XG1 in last internal for variable X I ; then go to 72.

A t statement P72, IPN = 1, IIN = L = 1, IS = 2, M = 3, I R X = 1 and go to 80 Calculate slopes S(2), S(3) and A, B, C, D and final ZPR(1) = AX + BX~+CX+D for X = XG1 (me equations for these quantities are defined in Appendix A ) Note that LLCI'R(2) = 0 here Test LLClR(2) - ICF(2) = 1-2< 0 and K-2 = 0 , go to 310 for next Z to be used from Z array Find LL = LL+LLCI'R(2) *LP where LP = U?X(l) = 3 Note that LLCl'R(3) = 0, then go to 50 Therefore, here ZGlll in ZPR(1) has been calculated and since LL = LL+LISTZ = m ( 1 ) + 3 = 4 , the next cycle w i l l calculate Z ~ 2 1 1 . (Note m ( 2 ) = 1) Reset, K = 1, L = L + l = 2 , I C = ICF(1) = 3 For ZPR, J=1, 2, 3, IiC2, 3, 4 and Again, for X array, 1XX=3 and since k=l, IX=W (1)=1 so that Again, IGAT(1)=3, go t o 72 and calculate slopes, A, Bs C, and D for f i t so ZPR(2) is defined.

Note that here Zclll and ZGZl1 in ZPR(1) and ZPR(2) have been calculated and next is a linear b ~ t e r p o l a t i ~ with respect to X2 values.

Subscripts for Z are defined in Figure 6 .

A t 55, IIX = NX(2) = 2 and since K 1, go to 49 where I=K-1=1 and IX=NX(l) + I & (2) = 3 + 1 = 4

IXP = IX + J - 1 = 4, 5 for J = 1, 2 so that

IIX=2 so go to statement number 64 for linear curve f i t for C 6 D and go to 2000 for ZPR(1) or ZGGll calculation.

K=K+l=3, LLCI'R(3) = LLCTR(3)+1+1, K'2, t o to 315 and Set KKPK-l+2, LLClX(2)=0

Find next 2 t o be used fzvm array, redefine U ere NX1=3, NXZ=2

hln I O O Q - W - L u L Q c m * > Q 3 > I L e + L 0

- 0 %

n Y- Q - e

.- a 0 3

L - 3 - a n - cP > ( o m >

-- >

U L L) c Q - m U > C L 0 0 - C U 9 - a c e a 0 m a 0 0 1 u c e u c a x

-- a u u

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Y- L .-

U L L - a.- O B

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L e u u w u The next 6 elements of the Z matrix will be processed for ZG 21 and

26221 with the same logic as for the first six elements, but now LLL+

L I S n = 7 for Z the prim values. The X values are the same as for the first six lines.

'Ihe next series of calculations ends with the calculation of 2 ~ 2 1 from 3~121 and XGZzl. Similarly, ZGlS1 and 26231 are used to determine 2 ~ ~ 3 1 . Since three values of Z for variable nunber 3 have been determined a cubic can be fit and the resulting answer is Z m 1 . Thus one value of Z has been determined corresponding to the first value for variable nwnber 4 .

Next, replace variable 4 by its second value and proceed through t l - calculations the same a s above.

This determines z C ; c & 2 and one more line interpolation produces Z m the desired value of the dependent variable given values of the independent variables.

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lnln * 9 J 4U.J 8 U 3 4 c c wed C d U ' dC(CC1 t 0 0 O O C 0 0 0 ! o o c o 1 . Bonner, E., ct 31, Influence of Propulsion System Size. Shape. and Ixation on Supersonic Aircraft Ilesign, Rockhell International, ,USA CR 13-3544, December 1974.

2.

Bonner, E . , et al, Effects of Nacelle Shape on Ilran and Weinht of a .SMer- sonic Cruising .-Iil'clraft, Rochxell International, xC.l CR- 144893, October 1975.

3.

MU CR- 132374, .Advanced k r s o n i c Technoloav Concept Studv Reference Charactcrist ics, tiampton Technical Center I : K :lerospace Corporation, 21 kcember 1g7'i.

Lockheed-California Company Report LR 26133, An Airline's View of Reserve 4.

Fuel Requir-nts for t h e W r s o n i c Transpo rt, 19 Septeniber 197f; Bushell, K . W. , Measufemrent and Prediction of Jet Noise in Flight, 5- AIAA Paper 75-461.

6. Crosthwait, E . L . , K e m n , Jr., I . G., and Roland, H . G . , et al, Frelimina

+

Design bkthodology for Air-Induction Systems, General D , d c s , Fort vlsion, Technical Report SEG-TR-67-1, January 1967.

Schoenhen, K . I V . , Resistance of Flat Plates Moving b u g h a Fluid, Trans- 7 .

actions of Society of Naval Architects and Marine Ennineers , Vol 40.

8. Sumner, 5. , and Short, B. , Free Flight Measurements of Turbulent Boundary- Skin Friction in the Presence of Severe Aerodynanic Heating at Mch Mrnbers from 2 . 8 to -- 7.0, NACA 'I?V 3391, 1955.

Lana~, H., The Wavz hag of Arbitrary Configurations i n Linearized Flow as 9.

Determined b m l i q u e - Planes, WC4 R ! 4 AS5.918, 1955.

10. Bonner, E . , Theoretical Prediction o f Supersonic Pressure hag, Rockwell International Report XA-66-862, 1966.