Statistical analysis of general aviation VG-VGH data

. I NASA CR-132531 , , T 1 09 33 t%A a ,A (flAS A -CR- I ]253 1 ) b xaYZ 5 _IC _ , NA L ¥5 q OF N75- ' GENEBAL _IiATlO., VG- V G H DAYA (Ye c hnolo g y, -2 Un c las ' _ , '3 1 05 023 b _ ,,q, Inc.) 13_ L s llC $5.75 CSCL 01_ •.ad_. STATISTICAL ANALYSIS OF GENERAL AVIATION ' " VG - VGH D A TA Larry E. Clay Raymond L. Dickey M a rtin S. Moran Kenneth W. Payauys Thomas P . S e veryn Prepared under Contr ac t No. NAS1 - 12389 by TECHNOLOGY INCORPORATED Instruments and Controls Division ' : : P.O. Box 3036, Overlook Branch Dayton, Ohio 45431 for NATIONAL AERONAUTICS AND SPACE ADMINISTRATI , _I ?

i - NASA CR- 132531 ) :i p ' t _) : STATISTICAL ANALYSIS OF C -.E N E RALAVIA T ION "' VG-VGH DATA % - r _',, Raym o nd L. Dickey _" Marti_ S. Moran i i Kenneth W. P a yauys _, Thomas P. Severyn K £ • / : 5.

• t -._ 1 _ 1 I ] 1 _ 1 ) FOR E WOR D This report, prepared by Technology Incorporated, Dayton, Ohio, documents the statistical analysis of general aviation VG-VGH data. All data contained hereia were collected from general aviation aircraft operations over the past 10 years.

The NASA Langley Research Center was the procuring agency for this program under NASA Contract No. NASI-12389. The Technical Representative for NASA was Mr. Joseph W. Jewel, Jr.

For Technology Incorporated, the principal personnel active in this program were as follows: Kenneth W. Payauys succeeded by Raymond L. Dickey, Project Engineer; Larry E.

Clay, Senior Research Engineer; Martin S. Moran, Research Engineer; Thomas P. Severyn, Jr. Research Engineer; Ruth E.

Meyers, Data Processing Specialist; James E. Kirchmer, Data Processing Specialist.

The contents of this report reflect the views of the authors who are responsible for the accuracy of the analysis presented herein. The ccntents do not necessarily reflect the official views or policies of the NASA Langley Research Center.

This repert does not constitute a standard, specification, or regulation.

I

I ii ABSTRACT In support of a NASA program to represent t,e loads spec- tra of general aviation _ircraft operating in the Continental United States, VG and VGH data collected since 1963 in eight operatio n al categories [(i) twin-engine executive, (2) single- engine executive, (3) personal, (4) instructional, (S) commer- cial survey, (6) aerial application, (7) commuter, and (8) aerobatic] were processed and analyzed to determine or prepare the following: (a) adequacy of data sample and current oper- ational categories, (b) parameter distributions required for valid data extrapolation, (c) envelopes of equal probability of exceeding the normal load factor (nz) versus airspeed for gust and maneuver loads, (d) probability of exceeding current design maneuver, gust, and landing impact nz limits, (e) fa- tigue spectra for gust, maneuver, and landing impact n z loads, and (f) relationship between design and operational airspeeds.

Significant findings included the following: (i) the data distributions were mostly log-normal, the rest being normal; (2) the Instructional and Commercial Survey categories had the highest probability of exceeding the design nz limit c for ma- neuver and gust, respectively; (3) whil_ the Aerial Appli- cation and Instructional categories required only 860 and 3393 landings, respectively, to experience landing impacts of 1.67 6nz, the other categories required more than 19,000 landings to reach this level; (4) of the 24 aircraft types, 17 had air- speeds above the cruise velocity (Vc) , but none had airspeeds above the dive velocity (VD) ; the Person a l category had tNe highest probability of exceeding VC; the Instructional and Commercial Survey categories had the highest V / V C ratios Cap- proximately 1.2); and the Twin-Engine Executive category had the high_st V / VD ratio (approximately 0.925); and (5) each of , the eight operational categories had a distinct load spec- trum which reflected the operational characteristics of the category definition, and the various aircraft types within each operational category generally had loads which conformed , closely with the average spectrum.

% ?

iii j i ' , : TABLE OF CON TE NTS Section P_..aage i.i Background of General viation V G / VGH Program i 2.2 Observed Statistical Distributions ..... l0 2.4.1 Gust and Maneuver Design Limit Loads . . 33 2.4.2 Maneuver Load-Gross Weight Relationships . 34 !i i

PREC E DINGPA GE B L ANK NOT

LIST OF II,LUSTRAT!ONS Figure 1 Plot of flours vs Sample Size ludex for Composite VGH Positive and Negative Maneuver z 2 Plot of Records vs Sample Size Index for 's i0 Composite VG n z ..............

3 Sample of VG n z Data Plotted as a Normal Distribution ................ Ii 4 Sampl e of VG n z Data Plotted as a Log-Normal Distribution ................ 1 2 5 Sample of VG n Data Plotted as an Exponen- 6 Probability-of-Exceeding-an z Curve at ll0- 7 V-N Probability Distribution for Twin-Engine Executive Category Based on 20,n00 Flight 8 V-N Probability Distribution for Single- Engine Executive Category Based on 20 , 000 9 V-N Probability Distribution for Personal . _ Category Based on 20 , 000 Flight Hours of VG I0 V-N Probability Distribution for Instruc- tional Category Based on 20,000 Flight Hours ii V-N Probability Distribution for Commercial - Survey Categ o ry Based on 20,000 Flight Hours 12 V-.N Probability Distribution for Aerial Appli- cation Category Eased on 20 , 000 Flight Hours L 13 V-N Probability Distribution for Commuter Category Based on 20,000 Flight Hours of VG i vi r ....... | " " _ _ ........ _C _ __ --- LIST OF ILLUSTRATIONS Continued Figure 14 Pr o bability- o f-Exceeding-An z Curve at 150-Knot 15 Maneuver zXn z Versus Design Gross Weight f o r 16 Ude Cumulative Frequencies f o r Three Altitude Ranges in VGH Data ............. 7 4 1 7 Gust L o ad Fact o r Cumulative Frequencies in VGH Pata ................. 7 7 18 Maneuver Load Fact o r Cumulative Frequencies in VGH D ata ................... 7 8 19 L an d ing Impact Accelerati o n Ratio Cumulative 20 Landing Impact Data for Twin-Engine Executive 21 Landing Impact Data for Single-Engine Executive 22 Landing impact Data for Personal Category . 88 23 Landing Impact Data for Instructional Category 89 24 Landing Impact Data for Commercial Survey Category ................... _ 0 25 Landing Impact Data f o r Aerial Applicati o ns ? 0 Landing Impact Data for Commuter Category 92 27 Landing Impact Data f o r Categ o ry C o mp o site . . 93 28 Landing Impact Data With and With o ut Low-Range 29 Pr o bability o f Exceedance Versus V / V c for Twin- 30 Probability o f Exceedance Versus V / V c for Single-Engine Executive Category ....... 10 0 i 31 Probability o f Exceedance Versus V / V c for Personal Ca t eg o ry i01 vii

j 1 I

1 _ f v l T _ t LIST OF ILLUSTRATIONS Continued t Figure t 32 Probability of Exceedance Versus V / V c for instructional Category ............ iu2 33 Probability of Exceedance Versus V / V c for 34 Probability of Exceedance Versus V / V c for 35 Probability of Exceedance Versus V / V c for 36 Probability of Exceedance Versus V / V D for 37 Probability of Exceedance Versus V / VD for 38 Probability of Exceedance Versus V / VD for 59 Probability of Exceedance Versus V. / V D for 40 Probability of Exceedance Versus V / V D for 41 Probability of Exceedance Versus V / V D for Commercial Survey Ca t egory ......... Iii 42 Probability of Exceedance Versus V / V D for 43 Probability of Exceedance Versus V / V D for Unusual Events VG Data ............ I13 44 Percentage of Time in Airspeed Ranges for 45 Percentage of Time in Airspeed Ranges for 46 Perce.:tage of Ti m e in Airspeed Ranges for 47 Percentage of Time i n Airspeed Ranges for viii t

t

........... _ i ,I i t

LIST OF I L LUSTRATIONS - Concluded i

L

Figure

48 Percentage o£ Time in Airspeed Ranges for

49 Percentage o£ Time in A irspeed Ranges for

Aerial Application Category ......... 11 9

50 Percenta g e o£ Time in Airspeed Ranges for

Commuter Category .............

LIST OF TABLES Table Page II Characteristics of Instrumented Aircraft . 4 III Extreme VC Values by Operational Category . 25 IV Extreme VGH Values Per Flight by Op e rational V Probabilit y of Exceeding Maneuver Design Loads in 10 , 000 Flight Hours of Extrapolated VGH VI Probability of Exceeding Maneuver D e sign Loads in 20,000 Flight Hours of Extrapolated VGH Data ..................... 4 2 VII Probability of Exceeding Gust Design Loads in 10,000 Flight Hours of Extrapolated VGH Data . 4 3 VIII Probability of Exceeding Gust Design Loads in 20,000 Flight Hours of E x trapolated VGH Data . 43 IX Maneuver Load-Design Gross Weight Relationships During 20,000 Hours of Extrapolated VGH Data . 45 X Maneuver Loads in VGH Data by Operational Category .................. 4 7 XI Gust Loads in VGH Data by Operational Category 57 XII Ude Peaks in VGH Data by Operational Category 67 XIII Summary of Operational and Checkout Landings by Operational Category and Aircraft Type . 83 XV Sample Calculations for Extr e me Landing Impact . ?

XVI Ma:imum Landing Impact Load Occurrenc e s in _n z , Bands by Operational Category ........ 95 : XVII Landings Required to Reach or Exc e ed Minimum X J q [ l 1 J i _ , , _ 1 J i. INTRODUCTION i.I Background of General Aviation VG /VGH Program _ initiated a pr o gram to c o llect an operational data sample r e pr e s e nta t ive of the United States general aviation, fleet. The following eight operational categories were defined to collec t ively represen t general-aviation-aircraft usage: (i) twin-engine execu t ive, (2) single-engine executive, (3) person a ]_ (4) ins t ructional, (5) commercial survey, (6) aerial ' 5_u , izatinn, I In 1963 ,,A_A (7_ zommuter, and (8) aerobatic. Reference 1 lis t s t_pic , _l mis- _ sions in these categories as follows; Twin- and sing!e[engine executive: Charter flights - cargo and personnel.

I Business flights compan y a nd individual.

Instrumen t check flights - training for instrumen t card.

Instruc t ional flights check-out for larger aircr a f t .

Personal : , Flying club owned - aircraf t flown by club with 3 t o , 21 members: used for pleasure, ins t ruction, or business _ flights.

Individually owned - used for pleasure and business.

_ 2 Company owned - airplane rented t o indi v idual for busi- ness or pleasure flying; also aircraft used as check- ou t for heavier airplane, Instructional : Training flights all instrumented airplanes owned by flying schools; used as basic trainers for pri- v a te license; a lso used by s t udent af%er solo for cross-coun t ry flight.

_< ., Commer cial survey: -' Pipeline-patrol flights patrols flown flom 76 to _ , 91 meters (250 to 3 0 0 feet) above terrain to check for leaks or breaks in the pipeline.

Fores t -patrol fligh t s patrols flown 457 meters (1500 feet) abov6 terrain for fire detection. When fire is spotted, descents are made to 61 to 91 , meters (200 to 300 f^ot) to check condi t ion of ter-

I

f,m_ rain around t he fire.

i

Pathfinder flights - flies to fire perimeter and

marks drop area. Descents are made to 15 to 46

meters (50 to 150 feet) abo v e terrain to insure

turbulence is not too severe for chemical bomber

durin g dropping ru n . Chemical bomber drops are

observed, and effects on fire are noted.

F_sh-spotting flights patrols flown 457 to 610

meters (1500 to 2000 feet) abo v e water. Occa s -

ional descents are made t o 91 to 152 meters (300

t o 500 fee t ) .

Aerobatic: ; N o n co mp et i t ive flights - aircraft fl ow n b y amateurs.

Occasional a er obatics are performed, usually as in-

dividual maneu v ers.

Competitive flights - aircraf_ flow n in airsho w s, in national and inter n ational aerobatic competition,

and i n practice sessiens. Obligator y mane uv ers, o n e

immediatel y after another, are performed i n a re-

stricted c u be of air.

berial application:

Crop dusti n g and / or spraying fli g hts aircraft flown

at hei g hts rangin g from 0.9 to 5.5 met e rs (3 to 18

feet) abo v e crops. Spreading runs are characterized

b y sharp p u sho v er at start and hard pull- u p at end of

spreadin g runs.

Commuter:

Operational flights - normally s c heduled passenger

c arrying operations.

Crew flights - c rew training, or flights on whi c h

stru c tural or mechanica] tests are made on the

air c raft.

: These operational categories do not generally correspond

to the Reference 2 aircraft categories ( n ormal, utility, acro-

batic_ because, except for the aerobatic and aerial application

operational categories, the operators select aircraft -n the

basis of p e rformance and / or cost instead of design maneuver

capability.

The analysis will examine about 12,000 hours of VGH and

7 0, 000 hours of VG data. To obtain the data sample, three

types of aircraft were generally selected as representati v e

of e ach o pera t i o nal categor y . The type of operation , the .

number of basic types of airc r a f t, the num be r of air c raft,

and the hours of data used i n the analysis are listed in

i I I p I ' I

r

Table I. The basic VC-VGH data were collected from aircraft selected nationwide to avoid a geo g raphical bias. All in- strumented aircraft were owned by indivlduals or companies who participated on a voluntary basis. The data collection object z ve for each instrumented aircraft was 1000 hours of in-flight data during each of the four calendar quarters.

TABLE I . SU MM ARY O F R F CORDE D DATA Operational 'Iype of No. of Aircraft No. of Ilours of , Category Data T_es Aircraft _ _l ) _t _ L - 1_, in- engine V(; 3 18 14,722 e\ccut ive VGIt S 9 3,377 Single-engine V C , 3 15 8,430 cx o cut ive VGIt 3 8 1,366 Persona t V(; 3 15 5 , 4 56 In._ , :r_ , ct ional VC 4 1 7 1 0 ,357 VGH 5 6 2 , 843 Commcrc _al VG 2 14 26,089 t V(;ll 3 _. 724 :urve)' VGII , 1 4 2,291 \erial VG 3 7 1,857 appl i cat ion VGtt 2 2 4 8 4 (;ommut e r V(; 3 5 4,0o0 vGll 2 _ 1,510 \ c robati c VG 3 5 382 VGII 0 0 0 Two types of NASA re c orders , the VGH and the VG recorder , were u ed to collect the data. The VGH recorder is an oscil- lograph which records a time history of indicated airspeed, pressure altitude , and e.g. normal acceleration at a rate of approximatety one minute of elapsed time per 1 . 27 cm (0.5 inch) along a 70-mm-wide film. The VG recorder records an envelope of maximum e.g. normal accelerations and their corresponding airspeeds for the period of operation (a one-flight duration . ; to several hundred hours) while the recording medi_,m is in- ' stalled. References 3 and 4 detail the VG and VGH recorders , ,' . respe c tively.

• i The VGH os c illegraph data was reduced to digi_.al samples of indicated airspeed and pressure altitude at one-minute intervals during the recolded flights and digital samples of e.g. normal acceleration, indicated airspeed, and pressure altitude at each acceleration peak and trough outside the prescribed thresholds (±0 . 4 g for general aviation aircraft and ±0.2g for airli n e air- ' c raft). The VG da t a w a s redu c ed t o the maximum and minimum

i 3

c . g . normal accel e ra t ion in e ac h l O -kn o t in d ic ate d airsp ee d

in te rval, t he m aximum indi : ;a te d airsp ee d a tt ain e d, a nd th e nu m -

ber of flight hours during th e period t ha t e ach zecording slid e

was ins t alled.

Table II summarizes t h e p e r t in e n t da t a for th e instrum e n te d

: aircraft. With a bre a kdown by aircraft op e rational cat e gor y ,

t his t a ble lis t s t h e t ype and numb e r of installations, t he

amoun t of recorded da t a, and the per t in e n t aircraf t confi g ur a -

t ion and opera t ional ch a rac t eristics.

TA B LE II. C H ARACTER I STICS OF I NST R U M E N TEDA I RCRAFT

V G h r : 14 , 722, VGH h r: 5 , 5 7 7

Twi rl- e ngin e exe c u t i ve L y pe % - G *nstall a t 1 o n_ .... 0 £ 8 4 3 I 1 %- C h o urs ........ 0 0 7191 50 t 5 275 0 145 4 116 11_5 _ , _ 1 t n_ti l l a t t on s .... 4 1 : 1 0 0 0 0 % C tt hou : s ....... 8 2 4 6 93 _ ;. % " 3 5 0 l lS5 O 0 0 0

, oo I : 5, , 5 ' 11 58 5 c 6 ' 5 o

q_ x sm u _ _ros5 we tg ht k % .... 11". " 5 5 .6 4 0 . , _ 2 1. 4 21.5 I 22 .7 Z2 . Z 3 0. 2 23 . 1 lb ...... : : : 1 6 ¢ 55 12 5 00 _ 000 4 _ 00 4850 51 00 49 9 0 6800 SZO0 _* ng span: m .......... 1 6 . 3 11. 5 1 4 , 0 11.3 1 1,0 11 . 2 11 , 2 12 . 1 ll, Z f t ....... 53 ._ _' . 6 4 5 . 9 3 " .o 56 . 0 56.9 36. 9 3 q . A 5 6.9 ki n g .t ea : ' ft : .......... _ 4'. : 51 . 8 2 " 9, " I 0 _ I75 1 7 5 17 5 2 0 0 I _ 5 _' C 3 t s e a leve l , knot _ . 5e 8 3 53 20 5 17Z 1 8_ 1 8 2 I _2 1 0 0 ISZ Tvpe pro p uls ton ..... Turho _e_ Turbo je t T n rho p , up P isto n P , stun Piston Pis t o n P _ sto n P i ston ", ' '_%[ a t se a l e v e l, knot - . a 4 _ " a:5[4 : _ 4 2 1 _ 2 15 2 2 3 2lq 25 6 2|q n" . ...... 4 1. 0 ._1. 5 ?n . O 19. 2 16 . 3 16.3 1 6,3 1 1 18. 6 16.3 i %D at _ e a leve l , k no t s . 4 65 400 26 0 1 40 239 2 4B 2 4 3 2 62 Z 4. , " n m a _ % £ ........ _ c" lI 5 . 4 0 1 . 7 0 1 .8 0 2 .80 Z ,8 0 2 .80 Z. 6 O 2,g[ l : n£ a t %% . L 4 0 I 2 . 44 2 I 0 Z.IO 1 .97 1. 8 4 1 . 9 1 l . q 5 J 2. 5 3 : .n m a t _C ...... _ o n i _ . _ 6 2 .6 _ _ .5 1 2.S ." 2.52 2.52 2,44 _ 2 . _ 2 ' 1 %la_ l mtI P, op cr _t lnK _p e e d

VG hr: 8430, V G H i , r" 13 6 6

[-- Sl ns le-e _ g|ne e x ecut i ve _ y p e V -C * n s tallat * ons ..... 2 I 2 l 0 1 l 2 } 0 % - G hours ....... I16_ 13 7 I 0 89 8 231 1 3 9 2 2 _7 0 I 1 202 I 78 5 I 1 1 70 ] 0 13 8i , c_ in s t, U n t ........ .i o ° 1 4 _ 0 0, 0 1 , I 1 { l ) 01 , ,O , h ............ : i : _ " o o, o _ 9 16 . 5 '2'I °I 1 5 , o M IX , lOll _r oss w e Is h t' k.N ........... [ 1 2 . 9 12.9 I li . 8 1 2 .5 12. 5 1 15.1 1 3 . 9 1 4 . 7 1 I S.l I II . 3 [ 1 1 . 8 1 11 . 8 1 2.5 W_ n8 span: ' 1

.......... , ° o o , . oo I I I ,oo i , oo

m .......... I 11.0 II. O[ IO. O 10 . o I0 . 0] I O.0 I0 .2 1o.2 1 0 . 2[ ll .O ll . 0 11.o I S .0

.,n_" ..... .......... i56 o 5° ° I _ 8 5 : 8 58 , _ , , 5_ 5 , 5 i_55 _° ° I _oo ,6 o 5o_

ft : ....... 17 8 _ 17 " . 6 177.6 17 7 .6 177 . 6 181 18 1 { 1 8 1 I 17 4 I 17 4 1 1 7 4 174 " ....... i ii 1 : : , 1 o5_ i °5 1 65 1 6_ , ,5 1 6 , 1 o , _ , o 8 _ , o_ 1 o , _ 16_ 1 o_ Typ e pro p u lsi on .... , Piston P ,s tun I Pisto n Pist or Piston P i s t o n P i sto n Pi st o n P tston Pi st o n Pt _ to n Pi s t on P * ston s V(. st sea leve l, knots . .i 1 5 6 IS 6 I 1 3 q 1 5 2 152 I 17 4 16 1 1t _5 1 65 13 9 1 59 [ 159 1 59 ,_ nt s e s l. . - l . k no t _ _I_ , j : 1 , ,, _ o1 _I ' i "' I _I " I_l '] ':' I l' _l " ° 18o ^_ . t v_ ........i _ .80 _ .8o I _ .8o 5 8 0 5 ., 0 _ .,, _" °[ 5 ' °I _"° I _ '8°I 1 " 8 °I , . 8 0 . ' .,o ,,, . t so . l e .l. kno, : 19,1 9 ,, l , _ l, . 18 , 1 I . ,9 _ I 195 1 l .ls o ul l o -I 1 6_so , _°*""......... :': _ ': l _ '° _ " _ 8 8 _ ,5 _ ,,[ _5 1 _ ,, ! , 5o!_ ,5| _ , , : 5 o ........ .... . . ....................

, _ .P RO I) UCIB I LIT_ OF TI_

I I I _ I : 1 . 1 I_ , • : ..... . . _ . J ... , !

1.2 Program Objective The program objective was to provide the following: l) A check on the adequac y of the sample size for statistical analysis .

2) The statistical distributions of the parameters required for extrapolation.

3] Envelopes of equal probabilit y of e xceeding n z "_ versus airspeed for gust and maneuver loads.

4) 7he probability of exceeding current design ma- nt , uver and gust limit loads for th e aircraft categories, namely, normal, utilit y , and acrobatic.

S) A revi e w o f th e a d e quacy o f d e sign c at egories to account for opera t ional experi e nc e s.

6) F a t igue s pe c t ra for gu s t, maneu v e r, and landing impact lo a ds.

7) Th e probability of exce e ding the d e sign landing gear lo a d fac t or.

8) Airspe e d prac t ic e s in r e lation to design airsp e eds.

9) Recommendations for future _ata collection and presen t ation.

2 . RES ULTS AND DISCUSSION 2. 1 Recorded Da ta Sample Size Table I lists the number of hours of VG and VGH data, the number of aircraf t t}'pes, and the number of ins t rument e d air- craf t in each operational category.

The number of recorded VGH hours and VG records in each operation is a significant parame t er in estimating the design probabilities. The minimum required sample size for the VG and VGH data was established by constructing a two- w a y conting e ncy table and applying the chi-squared goodness- of-fit tes t . Accordin g ly, the minimum sample sizes for the ! VG and VGH data were found to be 125 records and 150 hours, respec t ivel y . Therefore, the sample size for the Aeroba t ic categor y in both the VG and VGH da t a was inadequ a te, and the s a mple sizes for t he Aerial Applica t ion and C ommuter cate- gories in the VG data were inadequate. However, all the VG}I ' ! ' f _ 1 I T } ' da t a fo r t he C omm u te r ca tegor y w ere re co rded o n o n l y t wo in- s tru m ented ai r c ra f t w h ic h i s n o t suffici en t l y representat i v e o f c omm ut er - t y pe a i r c ra f t.

ate c onforms t o som e par t i c ular dis t ribu t ion. I t is t hen d e - sirabl e t o d et ermine the si t e of da t a sample re q uired t o ade- i In p ract i ce it is o ft u n a ssumed that a n o bs erve d var i- qua t el y d e scri b e t he dis tr ibu t i o n of the paren t popul a t i o n.

I On e widel y u s e d t e chnique i s t o test the ind e p e ndenc e o f tw o

!

randoml y chosen da t a samples by t he construction of a two-wa y par t icular valu e of t he varia t e is indepen d en t of t he random sample t h a t it is taken from, then t h e r a ndom sa m ple dis t ri- bu t ion is assumed t o adequately de s c r ibe t h e paren t dis t ri- bu t ion.

i con t in ge nc y t abl e. If t he p r ob a bilit y of o ccurrence _f a Suppos e ,:ha t n individuals or i te m s are classified ac- cording t o two cri t e r ia A an d B, t h at t here are r classifi- ca t ions AI, A2, ..., A r in A and s classifica t ions BI, B2, ..., B s in B, and t ha t t he nu mb er of individu a l s belon g in g t o A i and B i i s Nii. We hav e t h e n a r x s con t in g ency ta - ble wi t h cell freqbencies Nij an d Z Nij = n: : BI B 2 B 3 . . - B s I _ l N21 N2 2 N23 " '" N 2s _ I N i l NI 2 NI 3 " ' " Nl s i _ 3 N3* N32 N_ 3 " ' " X3 s . . - % Nr2 . .

" A r N r l Nr3 • Nrs As a fur t her no tat i o n we s h a ll deno t e the row t o ta ls by N i and t h e c o lumn tota ls by Nj; t ha t is , " i Ni = j [ Nij and Nj = [ i Nij

Of course, [ N i = [ Nj = n

i j

The n individuals will be regarded a s a sample of siz e n f ro m a mul t inomin a l po p ula t ion wi t h pr o babili t ies p_ j (i = l, 2, ..., r; j=l,2, ..., s). Let the null hypothesis, Ho , be tha t th e A and B classifica t i o ns ar e ind epe nden t , i.e . , t hat the prob a b i li t y th a t an individu a l falls in Bi is n o t a f - fecte d by the A class in which t he individ u al ' belongs. _hen < the null h y p ot h e sis is not tr u e, there is said to be an in- teraction between the two classification criteria. Two . statistical events A i and Bj ar e said t o be independent if P{A i ( _ Bj} = P{A i} P{Bj} Thus the null hypothesis is H o : P i j = pi pj whe r e _ Pi = 1 ; Z p j = 1 N o w c o nst r uct the statistic Q = [ [Ni j ' - n(Ni /n )(N J / n)]2 i,j n(Ni / n) (Nj / n) where Nij - n(Ni / n )(Nj / n) is the difference between the actual number of occurrences of a particular value of the variate N..

1 ) and the predicted number if Ho is true. Of course, Ni / n = P i ; Nj / n = p j It c an then be sh o wn tha t the statistic Q has approxima t ely t he c hi-square dis t ribution wi t h (r-l)(s-l) degrees of free- g dom. The t est c riterion is to reJec t H o for large Q. Thus, Q will tend to be small for Ho true and large for Ho false.

The value of the chi-squ a red s t atistic Q is t hen comp a red i with th e c r i tical v a lue wi t h (r-l)(s-l) degrees o f fre e dom and the desired significan c e level.

C o n t ing enc y tab l es were constructed and the chi-squared g oodness-of-fit test was applied in t he V G H sample size in- vesti g ation. Figures l(a) throu g h l(d] present the resul t s.

The point at which the r a tio of q to X29 s exceeds 1.0 is the point at which the data sample distribution no lon g er a de- quately desclibes the pare'_t distribution. Posi t ive and neg- ative mane u ver and gus t accelerations were investiga t ed. The 4 p o si t ive maneuv e r sample e xhibi t ed the la r gest am o un t o f VGH h o u r s re quir e d f or a n ad e qua te sampl e s ize. The sam e t est was applied to th e VG data. The results are shown in Figure 2.

l

' 8

: i .,_

:f\

' ,4

,> : _

l_ SO 0 1 0 00 1 5 00 2.000 Z , _ O n II O URS

a. C o m posi t e Po s it iv e nz' S i n V G H Man e uv e r s

1.

q t x ". :_ ,

.I

0! $ 0 0 ZO O0 150 0 Z O O 0 2SO0 I I OUR S

b. C ompos i t e Negativ e nz' S in V GH M aneuver s

: ! • 1 . L ) " _#& I q l \" , 0 5 00 1 0 0 o 1 50 0 1 0 0 0 2 500 IIOURS

c. Co m po sit e Po s i t i v e nz 'S i n V G H G u s t s

d / \i,, ; .

.[i

SO l) |01 ) 0 151} 0 . _ 00 0 1 5 00 IlOllll.k

d. C o m posi t e Neg ati ve nz ' S i n V G H G us t s

F i g ure 1 . P l o t o f H ours v s . Sam p l e Si ze I ndex f o r Co m pos it e

V GH P o s i t ive an d N eg at iv e M ane u v er and Gu st nz'S

!............. ] ! ] ! I _ 1 !

I.{

o _ o _ o _ o ' _o _o

_UMBER OF RECOR D S Figure 2 . Plot of R ec ord s v s . S ampl e S iz e Ind e x for Compo s i t e V G nz' S 2.2 Observed Statistical Distributions In extrapola t ing the load factor distributions t o dete T - mine the p_obabilities of exceeding t he design limits, it was necessary to fi t a distributional form to the recorded da ta .

Three utandard distribu t ions, normal, log-normal, and exponen- t ial (a special case of th e Weibull distribu t ion), were consid- ered. A widely used proced u re to establish t he d a t a dis t rib u - t ion is the chi-square tes t . However, since this me t hod re- quires a great deal of da t a, its applica t ion is limited. An al t ernative m ethod is t o plot t he data on various types of probabili t y paper (normal, log-normal, and Weibull). Then t he plot which most closely approxima t es a s t raight line indicates t he distribution type and consequen t ly t he co r responding paper t ype best suited to display t he da t a. Figures 3 t hrough 5 are samples of plots on ea c h paper type. Since, as apFarent , t he plot on the log-normal paper most closely approximates a straight line and therefore best represen t s t he da t a distribution, the data for each airspeed level in each of the opera t ional cate- gories were plotted on log-nor m al paper. Most of the recorded data conformed to the log-nor m al distribu t ion, wi t h the res t of t he data resembling a normal dis t ribu t ion. None of the recorded data rese m bled an exponential distributio n .

Except in a few flights where t he instrumen t ed aircraft within an operational category flew obviously different mis- sions or where a single instrumented aircraft flew two dis- tinct missions, t here wa_ no evidence to indicate t hat a load fac t or frequency dis t ribu t ion contained t wo or more sets of unrelated even t s. Fligh t s where t he instrumen t ed aircraf t , wi t hin an operational ca t egory flew differen t missions were , eviden t in t he C ommercial Survey and Aerial Applica t ion VGH !

da t a presented in Table IV (ex t reme v_lues per flight). The dis t ribu t ion f o r a ircr a ft t y pe 25 in zhe Aerial Applica t ion category in Table I V a lso shows a d_D a t a & n z value of +0.Tg.

Those fligh t s wi t h maximum accelera t :ons below a &nz of +0.8g were m o stly cr o ss-c ou n tr y flights and not the aircraft's pri- mary crop-dus t ing mission which generally had maximum An z values above +l.0g. T i0 _

i : i " _ I

i : ' I T ....

. 99S V G D a ta •99 Co . _m u t er .9 8 A / S 110 knots A Positive An z .9S ,gq _" . 02 .01 .OOS .002 .001 .0005 [ .0001 -. 6 - . 4 -.2 0 .2 .4 .6 log An z F i gure 4 . S a mple o£ VG n z D a t a Plotted a s a Log-Norm a l Distribution 1 2 ...... I ! I : j ..... ] ........ ] i

i

., .99 o i : : ::: V G Data 'I d i, Commut e r A / S 11 0 k n ot s I ;;, , , : . , o ] i ......

...... A Pos i tiv e _. n z . 7 J _ lJl _ r. . o . 5 ; II _,

II111

K-I .3 _ ; :::::

* I l l l l

X . 2 ! .....

: I ,l l il i

O .1 J : : ::: li, , , _ ' 1 III .( = I ..... l llll, < I I I III . 01 : :::; ! III11 !

i llll

.0 05 _ : : :-.:

" I l l l l ]

002 , ::::: IIIIII ' ill ', . 001 _ . .... II[ll; : 0 . 1 U ,; . 0.3 0.4 0.5 0 . 6 0 . 8 1.0 2.0 3 . 0 4 , 0 ,5 . 0 6.0 8 . 0 10.0 An: ,.

Figu re S . Sam p l e o f V G n z D a t a Plott e d a s an E xpo ne ntial Dis t ribu t ion 2.3 V-N Probabilit 7 Distributions Three V - N cons t an t probabili t y envelopes were cons t ructed for each opera t i o nal cate g ory from the VG dat a . The three en- velopes represent 50%, 90%, and 95% probability levels and are based on an expec t ed service life of 20,000 fli g h t hours. This means that an aircraft flying 20,000 hours in a g iven opera t ional category has a cons t an t probability of not excee d in g t he An z- airspeed combina t ions which define the envelope boundary. The , three envelopes can also be interpreted as a 50%, 10%, or 5% probabilit y t hat an aircraf t will exceed t he envelope boundary at l e ast once during 2 0 ,0 0 0 flight h o urs. T o c o n struct the V- - N , , envelopes for each operational categor y required firs t plot t ing • the log of t he An z nccurrences for e a c h airspeed rang e on lo g- , normal probability paper [se e Figure 6 ) . (In all tables and t ex t discussions, the parameters are g ener a lly denote d by sin g le values whi¢, represent the lower limits of the respective pa- rame t er r_ n g es.) Theqe "probability-of-exceedin g -Anz" cur v es : y ield a line a r r elatio n ship be t w ee n the lo g Anz values an d the probabili ty of a single Anz occurrence exceeding a An z value.

From t hese plo t s, and b y consideri n g each An z occurrence as a si ng l e st a t i st ical tr ial, i t is po ssi b l e to d ete r m in e th e p ro D - abili t y of a s ingl e t ri a l exce e ding any An z value. Dividing the t ot a l number of fligh t hours by t he t o t al number of Anz oc- curren ce s a t a given airspeed in a p a r t icular op e r at ional ca t e- g ory gi v es t h e expression f o r a statistical t rial in te rms of f fligh t hours. Wi t h a sin g le t rial e xpressed in fli g h t hours, t h e numbe r of s tat is t ical t ri a ls occurring at e a c h airsp ee d in 20,000 fligh t hours for a p a r t icular opera t ional ca t e g ory c a n be calcula t ed. It is. as s umed t h at t he s t a t i st i c al t rials (Anz o c curr e nc e s e xpress e d in fligh t hours) for th e 20,000 fligh t hours s a t isfy t he requir e m e n ts for B e rnoulli t ri a ls. Tha t is, e ach tr i a l ha s bu t t wo po s si b le ou t co m e s . Ei t her th e t ri a l e xceeds a p art icular An z value or it does no t . Se c ond, e a ch t rial is ind e p e nden t of all o t h er t rials. F in a lly, t he p roba- bili t y of exc e eding a par t i c ul a r An z valu e is cons t an t from t rial t o tr ial. Wi t h t h e above ass um p t ion, t h e A n z values for t he cons t an t pro b abili t y e :,v e lopes may be c alcula t ed as follows: {P( NE ) }n = PE P(N E ) = {P E }I / n f P( E ) = 1 - P(NE) wh ere P ( NE) = p r obabili t y of n ot exceedin g a par t icular An z value xn a sin g le t ri a l P(E) = probabili t y of exce e ding a p a r t icular An z value in a s in g le t ri a l PE = c o ns ta n t p r o babLli t y en v elope v a lue ( 0.5, 0°9, 0 . 95) I, = number of '_rials a t a given airspeed in 20 , 000 fli g h t hours for a p a rticular operational categ o ry {P(NE)} n = probabili t y of no t exc e edin g a p a r t icular &n z v alu e du r in g n cons e cu t ive t ri a ls Once P(E) is calculated at a g iven P E value for a particular operational category and airspeed, the co rr esponding probability- ' of-exceeding-n z curv e can be us e d t o dete rm in e the An z value.

These An z values are pl o tted versus airspeed for each operati o nal category to form the t h r ee constant probability envelopes.

In the construction of th e se envelopes, the VG, rather than th e VGH, data w e r e us ed since th e VG data provi d ed the larger : d a t a sa mp le.

i J + i i ] _' ' i " 1 1 ,' 15 i t _ l " , i i i !

Figures 7 t hrough 13 show the constant probability e n v e -

i! lopes for all the operatio n al categories except Aerobatic

which did not have e nough Anz occurr e nces to construct valid

'_ probability-of-exceeding-Anz curves for each airspeed.

Figure 7 shows the constant probability envelopes for

: the Twin - Engine Executive category. The e nvelope data com-

pare fa v orably with the operational usag e data presented in

Table III . Figure 8 shows the constant probability envelopes

for the Single-En g ine Executive category. Again , the envelope

da t a closely res em ble t hose of t he o pe r a t i o , _al u sage da t a p r e -

- ' sented in Table III.

• Figure 9 shows the constant probability en v elopes for t_e

Personal category. The extreme values at 150 knots in each set

of envelopes do not ha v e corresponding values in the operation-

al usage data presented in Table III. The probability-of-

exceeding-Anz curve for the 150-knot airspeed was constructed

from only 20 Anz occurrences and not all of the data points

fall on any one of the three statistical distributions. How-

ever , since the probability-of-excee(_ing-An z curves for all

other airspeeds in the Per_vnal category were found to be iog-

normal distributions, the 150-knot distribution was also ana-

ly z ed as log-normal. The tendency of the data points, as shown

in Figure 14 , to curve downward suggests that a linear extrapo-

lation would yield h_gher than actual Anz values.

Figure 10 shows the constant probability envelopes for the

Instructional category. The envelope data conform well with

the operational data presented in Table III. Figure 11 sho_s

the constant probability envelopes for the Commercial Survey

category. The envelope data are the same as the operational

data presented in Table III. The Commercial Sur v ey and Aerial

Application were the only two categories whose probability-of-

exceeding-An z curves were constructed as normal, rather than

log-normal, distributions. None of the categories had curves

with a n exponential distribution.

Figure 12 shows the constant probability envelopes for the

Aerial Application category. The extreme values at 90 knots

in the positi v e Anz envelopes do not ha v e corresponding values

in the operational usage data presented in Table llI. The

probability-of-exceeding-An z curve was analyzed as a log-normal

_' distribution for the 90-knot airspeed and as a normal distribu-

: tion for all other airspeeds. Any error in the linear extrapo- '

, lation will of cours e be larger on a log scale than on a linear

scale. An extreme Anz at low airspeed could also be due to a

flap operation and a low-altitude approach.

Figure 13 shows the constant probability envelopes for the

Commuter category. The extreme values at 190 knots in the neg-

ative An_ envel o pes d o not have corresponding " , alues in the op-

erational usage data presented in Table III. The probability-

, I ! } I i _

[ i of-exceeding = Anz curves were constructed from only 17 An z oc- currences. Again, an, " sm a ll erro_ in the e x t rapolation wo u ld be compounded on t he log scale.

. V G Da ta Twi n - e n g ine Execut i ve 4 095% envelo p e 0 90% envelo p e ": _50% envelo p e • 3

' l

• , N 2 ! , ? 0 i | l i I 50 i00 1S0 200 250 : Airspeed (k n ) +, t t -3 - l - 4 , i I J i I 50 10 0 1 SO 2 0 0 25 0 ' A i r s p ee d (k n ) _ F i g u re 7 . V-N P ro b a bility Dis tr ibution f or Twin-Engine E xe cu t iv e C a t e g or y B a s e d on 2 0,000 Flight Hours of VG D ata S VG D ata _ 9SI envel o pe I Sin g le -e n g in e Ex e cutive 0 901 envelope sub envelop_

I

3 - r- 2 - 1 - 0 I I I I i S0 100 1S O 200 250 Airspeed (kn) -1 -3 - 4 ' m S0 10 0 1 5 0 200 25 0 A ir s peed ( k n )

Fi gure 8 . V -N Pr obabil it y Di stribution for Sin g le - En g ine

Exec u tive Catego r y Ba se d o n 20,0 0 0 Fli g h t

H ou rs o f V G Dat a

VG Data Persona l 9 5 t envelope _ 50t enve l o pe 6 _ 0 9 0 t envelope 5 - N 4 t 2 - ! | 1 1,. !

0 SO 1 00 1 50 200 2 _0 -2-- i < Airspeed (kn) 5- _ - 3 - -4 - 5 ; : | ,. i I --i , • , - 6 50 100 150 200 250 Airspeed (kn)

Figu re 9. V-N P ro b a b ilit y D i s tr ib ut ion f or P e rso n a l C a t egory

Ba s ed o n 20 , 0 0 0 F li g h t Hours o f VG Data

i

I n st r uctio nal

it vc D a_

I _ 9S I e n velope -I I_ 0 90 | envelope E _ _ . 501 envel o pe

¢ -

2 _ I I i I i 0 S O 100 1 S O _. 00 25 0 • _ Airspeed ( kn ) -2 "

i

f ,I - 3 i i i i _ . A -- ,j ;' , - S - i I ,, ,I .... I I I -6 SO 1 0 0 1S 0 200 2 S 0 Airspeed ( kn) Figu re 1 0 . V - N Prob a bility D ist ri bu ti on f o r I nstruc t ion al C a t e gory B a s e d on 2 0,000 F li ght Hours of VG Da t a 2O V G Data Com m e rc i a l Surve y 4 - _ 9S t en v e lo pe 0 9 0t envelope t X 5 0 1 envelope 0 I SO 100 1 50 2 0 0 250 Airspee d (k n ) -1 -2 -3 -4 . I .] .... i l I 50 100 1 50 200 250 A ir spe ed (k n )

Figure ii . V- N P ro b a bil it y Dis tr ibu t ion f or C om me r ci al

Surv e y C a t e gory B a sed on 2 0, 0 00 F light Hours

o f VG D ata

¢ 5 ¥G Data J Aerial Application 9 5t envelope 4 _ 5 0 t envelop e 0 90t envelope

Z

0 J. l l I J 50 100 150 200 250 Airspe e d ( kn) _ - 2 - 5 -4 I . . I I I I 50 100 150 200 250 A i rsp ee d (k n )

Figur e 12. V- N P ro b a b ili ty D ist r ibut i on fo r A e r i al A pp li ca tio n

Cate gory Ba s e d on 20,00 0 F lig ht Hou r s of V G Data

2 2

'1 1 I I . _ . _ _ - ,,--. ........

V G Data Comm ute r 7 _ gs I envelope ' ! _ 0 9 0 t e n velope 6 _ 5 0 1 env e lop e [ .

_ S !

• 4 ! I l h I 9 SO lO 0 1S O 2 00 ZS O Airspeed (k n _ _ N } - 6 i.

; , ' _ 1 | ,i • 50 i0 0 1 5 0 200 25 0 Ai r sp eed (kn) . B a s e d o n 20, 0 00 F li gh t H ou r s o£ V G D a t a

i Figu re 13. V -N P ro b abi l i ty Di s tri but io n fo r Commuter C a teg o ry

i I 2 3 I " _ t I : F l ' I J J ,Z 1 J ? ,

T ABL E Ill. EX T RE M E VG VALUES BY OPE RATIO NAL C A T EGOR Y

VG hr: 14,72 2

OPE R ATION: "b i n ENG IN E [X _ CUTIV[ INOIC A TED AI RSP[ED CK N ) • _ L 60 ? _ 80 90 t O0 I l O | 20 I}O 1 40 l_ O 160 170 180 1 90 2 00 210 220 210 2 40 2 _ 0 TOIAL O. O 2 I 2 2 2 Q O,I l | I 6 T 1 5 R 2 2 1 I 4 _ 0.2 ? 7 S q T 4 • ! $ 14 |Z 1| 15 3 1 10 0.3 9 24 23 I• JR IO 4 6 6 1 4 | 6 16 6 16q 0._ 26 28 35 79 23 34 2 9 13 21 23 27 Zl 9 2 32 0 O,S 26 46 37 34 30 30 13 25 28 30 28 14 1 3 355 0.6 33 32 32 31 2q 23 1 4 25 36 32 It 4 t 3 7 1 O. Y 16 ?3 21 26 21 11 13 2 1 12 1 • 16 5 1 1 ! 2 1 5 008 ?l 16 2 2 16 1 4 2 3 19 22 22 15 3 , 19 4 0, 9 14 1 3 2 1 1 3 14 17 15 25 i ' 1 3 10 2 176 h O 11 IT 13 2 1 30 3 2 39 36 25 |5 S 3 t 171 I.l I0 6 I I 12 9 1 2 18 |0 8 9 3 tO0 1, 1 S S 2 9 t O 1 3 8 I1 1 1 3 I 3 I P?

v t*5 9 | I 2 9 S • • ) 6 4 | 5 5 i._ 9 ? 3 4 2 9 11 i 2 2 2 ? q3 los t i 2 2 3 3 6 3 3 2 6 I.6 4 I Z 1 4 1 3 I 17 1 .7 A 2 1 Z 1 1 0 | e| | I | Z 1 2 1 | l O • 1.9 1 3 I I 1 T 2 .0 I I 1 I 2 6 1.1 l 1 2 .1 t 2 *3 i 2 ,6 1 1 2._ t t 2 1.?

?. J 2. q 3, 0 3,1 3.6 3.?

3.8 3,e 4 .| TOT 2 23 2 2 5 _ 2 5 225 225 ? _ S 2 _5 2 25 2 1 5 209 150 JOB 48 1 2 3 1 1 I 2564 J j i _

: 1_ ] ] , .. , - ............. 1 1 i ] _ . '

TAB LE I II .- Co nt i n u ed

: VG hr: 94 30

e O P ERAT I O N : S I N GLE ENG IN E INDI C A T E D A I R SPE ED (Kql } _NZ 60 70 80 90 100 II 0 1 2 0 l]O 14.0 150 160 17 0 180 19 0 ZOO ? IO 22 0 2 10 2 4 0 Z SO T O T AL O,O 1 I 2 _ . 0.! 1 5 3 4 13 ._ 0 , 2 l 3 I 2 2 1 _ t q 4 _ . 2 2 35 0*3 9 14 20 8 6 4 4 4 } IN |3 8 4 I lit O*A I_ 23 24 Iq I I 2 3 4 10 q 5 5 13 0 O*S I T |8 20 17 2 0 |5 S II 19 17 16 8 3 182 , 0 .6 16 2 0 26 30 24 14 16 1T 2 0 |3 7 q 208 f O,7 q 1 2 14 15 1ii 23 2S IS J8 10 3 ? |4 4 o. n I0 L 2 IO 14 14 1 4 1 3 15 20 II 7 | 141 O,q 6 8 B 12 I I 14 12 I ' l 9 4 2 1 0 1 , IsO 10 8 lO lO 12 Iq 16 I_ 15 8 l | 2 4 1,1 4 3 | 7 6 8 8 S ? II 4 61 1,2 T l 2 7 6 $ II 6 4 I I SI • ", 3 6 q 3 1 3 T 9 10 5 2 I 5 2 1. 4 S 4 1 2 _ 4 5 3 2 2 0 1 .5 2 2 2 l 2 _ 1 1 I 17 1 , 6 _ I 2 2 2 3 2 IS 1,7 1 I i 2 1 1 ? I I.g 4 2 4 I il 1 .9 I 3 2 I ?

2 , 0 1 2 1 4 2.1 I I I 2 *2 I 1 2 2*3 4 4 2, 4 1 l 2° S 2.7 a " 2,q | 1 _ ol 3,2 3.3 3,_ : _ .6 3,7 3,it 3.9 4.0 4 ,1 T O T 1 31 13q ]38 1t8 13q 1 3q | 3q 13q 13q 1 19 6q 4 1 I0 3 1482 0 O EI _ AT I O N : S |N 6L[ E N G INE I N DICATED AI R S P E ED (K N) : _ . N Z 60 TO 8 0 90 100 110 12 0 130 1 4 0 1 _ 0 160 ITO 160 IqO ZOO _ lO ?20 230 240 2 _ 0 T O TAL - O,O 2 Z 2 t 1 2 I 1 1 -O*l 3 1 1 IJ 2 1 1 2 ¿q -0.2 1 _ 3 1 q 8 l O 2 37 - 0,3 5 1 2 I I 1 2 8 6 4 3 7 It 8 8 4 qq - 0, 4 ZI 2q 2* 21 1 3 2 5 '5 10 l ? 6 1 1 I SO -Oa q 21 1 4 3 3 25 2 'J 11 1 1 10 8 | q q 7 I 1 9 " , -0,6 1 0 2 4 23 33 26 22 q 13 22 10 5 3 2 00 -O,? 12 6 1 6 20 24 27 20 1 8 20 13 8 2 1 86 -O,a 1 4 T 9 13 tq 22 19 1 8 2 1 T 5 S I 1 60 -0,9 tO T S ? 8 21 2 4 21 |1 7 8 12q - 1 .0 5 I 1 5 4 7 14 I O 2 4 I? 8 / ' 3 118 -1 ,1 S 2 I 3 5 T 11 8 4 2 4A -I* _ ' *) 3 1 2 I 4 8 3 A _ t l -I .3 3 6 I 3 T 3 7 4 34 - I ,4 2 4 1 5 I 3 1 1 7 - I ,S 4 _ ' 1 1 1 2 11 - 1.6 3 I 1 2 3 I I1 - I,T 2 1 I 2 6 • - 1,8 1 2 1 _ ' - I.q S I I I I q - 2.0 1 I 1 1 4 - ?, I 1 I -2 , 2 I I -2,4 -2, _ 2 2 - 2,6 _ , -2.?

o2.8 -2,9 - 3 . 1 - 3 ,2 - _ l,, 3 - | , 4 -3,6 - 3 ,q *4 , 0 - 4 , I TO1 I)l 1 18 1 3 8 t30 13q I 3q 13q 13q 139 II q 6q 4 1 I0 ) 1 482 f

: 26 i

........

; I I I _ i " i I

; '1 ] 1 t 1 l ........ 1 I

T A BL_ I I I . - Co nt i nue d

V G h r : 5 45 6

04:'E R ATI O _ : PE RS ONAL |NO|CA l' FO A IR S P EEN t K N ) _ Z 6 0 ?0 |0 90 100 L t0 t20 I _ 10 140 1 5 0 160 |7 0 | ll0 1 9 0 200 2|0 2 2 0 21 0 2 40 250 TOTAL 0.0 Z Z 0 ,! t 1 1 1 4 0 . 2 1 1 t 4 4 2 2 Z I?

0,3 2 2 * 6 2 2 1 2 1 2 2 0.4 1 2 _ , 3 I ' J 1 2 | S 1 1 5 2 0 ,5 12 8 S 4 b 9 ? 4 2 4 1 6 7 O*b 17 ' 13 8 S 10 li q 4 I 3 Ill 0.7 | 9 R 1 4 t4 b 5 2 | 6T O. ll 9 ).IS I? 1 7 I S tO 9 1 1 97 0,9 9 1 6 20 1 4 q 6 b | 2 1 a O 1 . 0 1 5 I S 2 3 19 12 tq 6 3 2 1 14 1 . ! I b 10 13 1 3 I S 4 4 4 3 76 1. 2 q 10 q t6 t • g 4 2 I 1 77 I*S 2 II 5 S S 1' 4 I ) 7 L *4 t 3 5 3 6 _ 5 I i i 3| t*S | 2 2 6 1 2 1 3 1| 1 .6 2 l 5 4 4 Z I 1 1 2| 1.7 I 1 3 1 l I | I, B 2 2 2 I 1 Q I* q I I I 1 4 2 .0 ! 1 l I 1 S 2. 1 1 I | ) 2 , 2 l I 2.3 2 ,4 I | 2 ,5 1 1 1 3 2,6 2,8 2 , 9 3.0 3. 1 1. 2 1*3 $.4 3.6 - .8 l os 4.0 4. 1 T O T I Ill 12 S t2 7 12 6 126 i ts 79 31 2 O t3 " f I 809 O P ERA T IO N: PERS O NAL I N OI C ATfD AIR S P£[D (KN; AN Z b0 70 6 0 90 1 00 I I 0 12 0 1 30 1 40 ) 50 1 6 0 1 70 t|O 190 2 00 210 2 2 0 2 1 0 2 40 250 TOTkk - 0°0 -0,1 t 3 2 2 8 -0.2 1 2 _ II 4 1 2 2 6 -0,1 5 l l 2 5 4 2 i 2 2 2 S -_ .4 8 4 1 3 8 I S q ) 2 2 1 I S _ - 0 , S 14 14 ! 1 3 8 t4 4 7 1 _ 80 -0 ,6 1 1 15 12 9 12 1 2 O ] 1 i 1 87 - 0.7 t t* 1 9 le 1• q S q Z 9 _ -0.8 1 ? Z l 22 2 4 t• It t O I 3 1 12 7 -0.9 1 3 1 3 1 9 2 0 2 U t• $ 3 2 II2 -1 *0 I* 2 0 )5 1 9 l | tl 9 6 3 2 117 - 1. 1 • 5 • 8 I I 0 ) 1 I 50 - 1 o 2 l 2 ? 8 ? 3 I I 30 - 1 . 3 2 6 4 6 10 I 1 1 3 1 -1 ,4 4 4 1 I 3 2 3 IA • l ,q 2 2 2 2 I 1 t tl - I, 6 2 I 1 t -I,7 1 I i 3 -I . a ! 1 i 3 -i ,q I I ?

_ , - 2 ,0 I I • 2 ,1 I I I ) -2 0 2 - 2 ,) - 2 ,4 i - 2 ,S I I - 2 .b - 2 ,? I I - Z ,I * 2 .q

.,.o., ., RE P RODUCIBIL I TY OF T H ]_

. , . ,'_ ' 2 O R IGINAL PAG B I S POOR

- 3, S -),?

°),| - 3 , 9 -4,0 -4,1 YO T I i ll 1 2 9 12 7 126 I | b 1 1 5 T9 5| 2 0 1 3 ? I il _ l

2 7

TAB LE III. - C on t inu ed VG hr: 10 , 35 7 O P ER A TION: INSTRUCTIONAL IND I CATED AIR SR EEI _ (K N I A NZ 60 " t O 80 qo 100 110 12'0 130 I40 150 160 1?0 180 190 200 210 2 20 230 240 Z50 T O TAL 0.0 t 1 Z 0.1 3 I I 5 O,Z 4 5 4 6 I T 0.3 I 2 2 7 _ 3 2 20 0. 4 Z I I T q 2 4 2 20 0.5 4 4 6 1 4 7 2 3 2 a,2 0,6 tO 6 S 6 '$ } 4 1 40 0*? I T T 13 13 l O 4 ! I _ 5 8 0.8 l 6 6 I| 7 6 4 1 42 o.q 2 10 q 10 II 4 2 2 1 48 l ,O 3 IS 17 13 17 Iq S 3 I | 86 1.1 t I0 12 10 4 5 3 Z 1 2 52 1 ,2 3 1 3 l Z 12 1 6 7 2 3 I 6q 1 ,3 6 16 21 I I 9 1 0 1 1 75 1 .4 _ 18 16 16 7 3 5 1 1 70 l * q I ? I1 13 8 ? _ 1 50 1.6 Z 4 II 1 3 6 I 2 I 40 1 , 7 5 5 7 9 3 _ 3 1 1 .8 2 6 1 3 I 13 I,q 2 1 2 I 3 I _ 1 2 2.0 2 2 4 2 1 1 1 13 2,1 • 3 | l 6 2.2 1 2 2 2 1 I q 2 .3 2 1 1 I 5 2. 4 I I 2 I 2 ?

2 ,5 2.6 1 I 2 2.7 I I 2 ,fl 2 2 2 . q 3. 0 3. 1 I I 3* 2 3.3 3, 4 1 I 3._ I I 2 3.5 4 .0 I I 4,1 TO T 2 9 139 157 |5 7 IS2 106 5 2 33 | b 4 3 2 BS0 O PERATION: INSTR U CTIONAL I N DI CA T E D A IRSPEEO (KNI AN2 60 70 80 90 100 llO 1 2 0 130 140 150 1 6 0 1 70 180 I90 200 2 10 2 20 _ 3 0 2 40 2 50 T O T AL - n ,O 5 1 6 6 4 3 2 | 37 - O .I ! 5 A 4 3 21 *0. 2 ! I0 7 2 I 2 I 24 -0.3 11 1 7 7 6 2 I 44 -0.4 | 4 I 5 I0 T 6 6 I _I -0,5 6 6 T 1 8 II 5 4 2 I I 61 -0 _ 6 1 3 $ 18 19 10 5 2 I 76 -0, 7 3 1 6 !2 2 0 16 1 2 3 2 I 8 5 -O,S 2 20 3 2 20 22 3 3 I 10 3 -0.9 6 lq 2 6 34 10 7 2 I | Oq -I .0 8 2 _ 32 24 20 4 1 I I t O -l.l 3 ? 14 T 2 2 I I 37 -1,2 5 6 9 2 1 1 2 4 i -1,3 3 q 10 S 3 30 -I . 4 | 2 5 5 ? I 16 , -I,5 1 3 5 I 3 I 3 -1,6 3 I 1 5 -I. 7 1 2 P 2 7 l - l ,n -1.q I 2 I 4 -2 . 0 I I - 2 , 1 - 2 . 2 - 2 .3 1 1 2 - 2 . 4 - 2 , S - 2 ,6 -2 ,T I - 2 *q * 3 ,0 - 3, I t I -3 , 2 -3.1 - } . 4 - } . 5 -3,A -l.T -3*a -}.V - 4 . 0 - 4 .!

T0T 2 q 139 155 15 5 1 5 4 tO6 52 33 16 4 3 2 S _ 6 f ....... _.............

.......... j i J ! ............. ! ............. ) .....

TA B L E II I. - Cont i nue d

VG hr : 26 , 089

n P E_AT t O N: ¢ OMM FRC [AL 5U_V[¥ ] NnI C A TF N A IPS P [ E n ( _ N) _ N Z 60 T O A O q O |0 0 11 0 1 2_ |30 1 40 1 5 0 | 60 |70 |80 |q O 200 2| 0 2 2 0 2 3 0 26 0 _50 T O TA L n , n 6 | 2 2 II O,t 6 | 0 4 _ 2 | ! Zq 0 , _ [ _ 3 6 12 4 5 ! | ! 36 0,3 7 l 6 tO 1 3 ? 8 1 _ 1 I _8 0. 4 15 1 3 II ? B 16 ? q I 5 2 94 0 ,5 IS 14 :l l O 13 I _ | 0 6 6 ? 4 [ [ 1 0. 6 I T q 8 I0 1 2 1 5 11 8 q 5 3 1 |0 4 0. ? 14 t 3 1 6 5 I? q 6 A 10 6 | tO3 0 ,8 14 18 7 12 23 q 5 6 3 4 1 10 2 O,q 16 I M 14 1 2 2 3 1 2 l| 6 ? 8 127 1.0 4 8 25 3 _ 3 5 30 21 2_ 8 9 4 ] 2 35 I*1 22 2 9 21 2 4 20 l! 14 8 9 2 16 0 1.2 21 3 9 24 33 22 1 2 ? 9 6 173 1 .3 lg 3 0 34 25 |7 lq 13 I 4 | | 170 1 , 4 I 0 I q 24 _2 15 q |0 IO 3 12l I.q 14 2 3 22 _ 15 18 % IQ 2 123 1 ,6 |1 15 2 3 17 l? 9 I0 4 _ 1 0 8 I,? 4 1 5 Iq 1 7 3 14 _ I 3 83 I*M 5 1 4 8 9 13 6 1 3 1 60 I.q l I M 1 6 12 2 5 2 4 q 2 , 0 1 _ 1 7 II Iq II 2 1 | c S 2 *t 4 I O 1 3 6 6 4 | 4_ 2 . 2 I q I! IO 3 2 I I 5 8 2,_ 2 2 6 7 3 6 2 l 79 2,4 2 l ? 4 l 2 1 7 2 .q 2 _ _ 3 1 1 13 2 . 6 l l 2 I l I I 8 2.7 I I 2. A 1 l l 3 2,q ! 1 2 3,1 3,2 I I 2 _ .5 l l %6 I l 3.?

_ ,q 4,0 4.1 TOT 2 _ 32 6 3 2R 3 2 A 32 8 2 6 5 175 130 29 4 9 18 2 22 g1 O PER A TI O N: CO MMERCI A L S UR VEY |NDICATFD AIRSPEE D ( K N) _ NZ 60 ?0 8 0 9 0 I00 11 0 | 2 0 150 14 0 1 S0 160 |TO 180 1 90 2 00 210 220 2 50 2 40 25 0 T O TA L -O,O 1 8 3 1 I 1 I _ -- : -0 .1 2 2 2 4 I 1 16 8 4 1 2 _2 -0,2 8 l O 8 8 6 8 4 8 4 3 67 *0.3 1 0 ? 8 6 6 |_ ? I O ] 4 2 2 76 - _ .4 22 q 6 7 6 1 4 ]l lO 2 4 5 94 ! -O,S 2 9 I _ 8 5 II 2 0 2 0 1 2 3 6 4 |32 : -0,6 53 3 8 15 tO 13 1 3 7 3 10 4 2 16_ 3 -0,7 43 5 6 22 15 2 6 2 7 1 0 7 1 1 3 220 2 15 _ ; * 0 , _ 3 4 4 2 4 0 3 0 2 8 1 6 I I 5 2 ?

-0 .9 2 1 5 2 4 6 39 3 8 23 6 7 | 1 3 24_ -I,O II 4 0 75 52 5A 2 0 lq 12 8 S 29 6 --_ -l*! q 6 32 3 5 2 9 I 0 ? 6 q 2 14 1 - 1 .2 l g 1 6 30 14 9 7 4 3 I 9 3 -1.4 ' 6 ' Iq 21 ' ? 3 I ;_ - | . 5 6 e 11 I 0 5 ? 6 l -1.6 2 2 ? S 5 5 • 2 2 3 4 -l *? I 4 2 5 _ 5 5 25 -I,A 8 2 5 _ 7 3 3 2 _ q -1,9 2 2 3 6 _. 2 3 1 _ -2,1 2 2 l 2 2 l . _0 - 2 * 2 l l | 3 I 2 2 I 1 2 -1,3 4 4 1 6 31 2 8 16 7 II 3 1 l 11_ = _ . 3 l 1 2 2 2 l I IO -2 ,4 l 2 I l I l 7 -2,5 l 2 I 2 I ?

-2, 6 1 5 l 3 -2,7 I l l 3 - 2 ,0 2 I -2.9 I I 1 1 4 , -3,0 I l 2 2 6 -3,t l I - 3 . 2 I l 2 =3, 3 -3, 4

. 3. 5 REP_.OI'_TCP?IT TTY OF T H_

-3. 6 l

"3" ' t)t_IG I _A L _ P A GE I _ P OOR

-3, 8 _ I -3,9 t - 4 . 0 - 4 ,1 -4, 2 - 4 , 4 l l - 4 ,5 I I I 3 T OT 25 5 52 6 _ 2 8 3 2 8 32 7 2 6 3 17 4 1 29 7 8 4 9 18 _ 2_ ?v

TAB L E I I I . - C o n ti n ued

V G hr: 18 5 7

OI_ ERAT IO * d : AERI AL A PP L ICAT IO N | N DIC4TED A |RSP[[ i ' ) (K N I _NZ 60 70 I0 qo 1 00 11 0 120 | 3 0 16 0 1SO 1 60 170 1SO 190 Z OO 2 10 2 2 0 23 0 2 40 2SO TN TAL 0.0 1 I 0ol 0. 2 0. 3 ! I I 3 0.4 0.5 ! l 1 1 0.6 I I I " _ l ?

O.7 [ I 2 0.8 l 1 2 O.9 2 7 1.0 2 I l I 5 1.1 1 l 1 1. 2 I 4 2 Z q 1.3 .' 3 2 2 I 1 I0 1.4 3 l 3 2 q |.S l 2 I 2 I I l 9 1.6 9 l 2 1 2 9 1.7 2 1 " J 2 R I. P 3 Z 2 2 2 II I.O 1 2 2 _' 7 2.0 I 9 i 1 6 2.1 l 2 2 l 6 2.2 2 .9 2 2 2.4 l l l 9 2,S I 1 2.6 l I 2 2 .7 2,8 2.q 3.0 2 1 3 3.1 l l 2 3,2 9 , 9 9 .4 _o 5 3 ,6 3.7 3 , | 3 .q 4. 0 TO_ 21 ZI 21 2 1 19 1 7 6 126 OPERA TION: A ERIA L A PPLI C ATION IN DICATED A IR SPE E D {KN) N Z 6 0 70 80 qO lO0 IlO IZO 130 140 150 160 170 I R O 1 9 0 Z OO 2 10 220 2 _ 0 240 2 _ 0 T O T A L -0.0 1 l l -0.1 l 3 -O. Z 2 1 I -0.9 l 2 I l 3 *0,4 2 k _ q -O,S 1 I l 6 -0.6 2 1 l 3 3 -0.7 I 7 7 -0.8 _ _ 2 3 -0.9 2 3 4 2 6 -1.0 Z 3 3 6 9 I II -I,i I 4 2 2 2 I 18 -1o3 _ 3 2 l 1 17 "1 °4 2 9 t 3 2 10 -I*_ l I i IZ -1.6 3 I 2 9 -I.? 6 -I .B - |, q -Z,O - 2 . 1 _ 2,4 - 2. 9 - 2. ?

- ? . R - 2. q -3.0 - 3 ,1 -3,?

* 3 . 1 - 3 ,4 * ) .q -1.6 - 3 , ?

- 3.A o 3 ,q -4. 0 -4,1 Tq T 2 1 2 1 2 1 2 1 |q |? 6 | ? 6

3 O

, l j ] 1 i

TA B LE III. C ont i nued

[_ V G hr : 4 0 6 0

O P E_a_ I C,;_. CO,W_U T FI_ I"I D I C A T {D AIPSPECD (K_, AN I a0 70 B V l 90 100 ||0 1 2 f_ 130 1 4 0 1 5 0 1 6 0 170 180 Iq0 2 00 2 10 22 0 230 24 0 2 e_ O TOTA L 0 , 0 0.1 1 ! I 3 0,2 I I I 4 I Z 1 0 0. 3 ? 1 1 3 2 1 1 I 1 I _ O . G I 3 ,I, 3 3 I I 2 I Z Z 23 0 ,_ ? I _J I I I Z 2 Z I 1 6 0, 6 I '4 5 4 $ Z I I I 2 I 3 I 30 ( 1 . ? l Z 3 3 6 ? 3 1 _ 2 itA 0 , 1 l 3 A 3 I I 1 1 ,i 1 1 22 O, q I ? I it 3 7 1 Z 4 , 1 i t 34 1,0 I 1 3 5 6 4 1 1 it I it 5 1 , 1 I I 1 3 Z 1 2 2 | _l, 1 , 7 I 1 | 2' 2 3 2 l _ l, _J ? $ I I 2 ! I 0 1.4 2 it 1,5 I 1 2 1 . 6 1 1 it 1 . ?

I. Pl 1,_ 1 I • 2, O I I I 1 _, ? , . I I 1 2 ?, 2 1 1 2.3 • 2, 7 2 . #, it . A l , 2, 0 _ 3 , 0 3 ,?

} 3.3 3, 4 3 , A i t .A it I 1 7 5?

i Ir) T 1 A ? 0 it O ZI ?1 it l it l 21 Zl itl I q 1 7 lit 5 1 : _" OPERA T IO N : CO I_W UTfR INDICATED AI RSPEE O ( K N ) ANZ 6 0 70 80 qO 100 I10 IZ0 130 140 1 5 0 1 60 I?0 180 lqO itO0 ? 10 7 20 Z 3d Z_ 0 it'_ O T I_ TA L *0 , 0 1 I -0.1 1 1 1 3 -0, ? 1 1 I 2 1 _' - n ,_ | 1 1 I I 2 ' 1 I 2 1 l_ - 0,5 I 7 ' 3 Z 2 ! 1 ? 3 I Z '_ , -0 , _, 2 3 3 6 _ _ , I l 2 l I * . I " . t -0.7 _ , _ , _ 6 3 2 3 I it 2 1_ -0.i l 1 2 '_ 6 2 6 3 4 3 _ n - 0. 9 1 ' ) I _ 4 _ ? 2 73 -I .0 Z 2 3 5 7 it it ' _ I, _ J ?

-I. I I I I I I I I I I I I 0 -1 ,2 I 2 ' 1 it I I A -I . _ 1 1 3 2 ?

= -I , _, 1 1 ?

- I,' _ I 3 -I, 6 1 it I I - I ,8 - l ,q - it ,l -2, 7 . - _ ,3 _i - _ ,0 -it,6 -2,?

R ROD U eIB rI'g OP

.,., ORIGIN A L PA G E I S POOB. .

*] .I t - l ° V - l ,q -t,,O T0T I I A _' n ? ( } itl ;t _I itl Z I it l ; _I l q l ? l it 5 ? l I I i__I ]i TA BLE III . - Conc lu ded V G hr : 382 A'_ . . _ ' _ ?_ _ r _ _, i r , m _1 _ l? t _ I ) F, I I . 1 5 0 lb P I? 1_ I mn I CJ n ? ¢ 1 n _ I N ? _0 21 q 24 t l I %0 T')T _ L P ° _ Z 1.0 " 7 1.2 I 1 I 0 1 , . I l l 1 I ? - " • 7 : 'o _ Z I ** I I ) , " I q 'I,_ I 1 i ... _ • _ 1 In _, . _ l I I ) 1 ? 1 I , ... : I , I 2 _' 2 t .

' I •. I ? : I _ I l -. I 1 I I l I 1 I _, " . _ 1 , | 1 t , _ , . ? I I • _ .* ! I l I I i I _ . I ? I 2 I l I m _ . I I I I ! " , • ._ I I I l I • " _ : I I I l 2 I _ ' ° ? I I I l I I I Z . " I I I ° - A.( : _ _ p t , _ I00 I __ 1 2 n I)0 I _.0 l q0 1 6 0 ) 7 0 I t lCl 1 9 'I 2 0 0 2 1 n 7 7 o 2 3 " I _. r , ? _ . _ 1.1 _ 1 I -_. 2 I - 0 . _ I 1 | . i. _ ! I I ! I I . I . : I I I I - I . _ ! I I ° | . _ I ° ? o , . I 1 = ? . _ ! : - I ° _. 2 ? _" I 1 t !

._° p | I 2 ) I I . _ . e I I 2 I ._ .,. I I I I I I I I I _' . . _ . c ?

- 5 . ,.

" q '_ I I I I _ " . ¢. q 2 ) I . _ .. r , i I | _ t " . _ ., . 2 I I ) t I ?

; =),i) . ' t ,( .p l . ¢) =I I, 7 IO % 2 , ) _) I I i I,', | _ "! , I !

t

J

I The data in the constant probabilit y envelopes conform I quite well wi_h the operational us a g e data for a ll s e v e n c ate - L gories having sufficient An z occ u rrences for each airspeed.

In the 90% and 95% envelopes_ the An z values were usu a ll y con- i [ siderabiy higher than the corresponding values in the operational data. This was expected since the An z occurrences can be con- sidered random events that would have a statistical distribution only within some r a nge of An z. The limits on this range a re } determined somewhat by the s t ructural limitations of t he aircraft sys t em, mos t ly by pil o t i and the effectiveness o f the c ontrol b u t actions, l_hile t he Anz occ a rrences may conform to a s t andard I distribution within this ran g e, t he standard distribution will i show a finite probability for a & n z occurrence be y ond the limits of this range. Because of its larger data s a mple, the ! V G d a t a w a s u se d t o c o ns t ruc t t he cons t an t pr o babili t y envelopes.

' If V G H d a t a h a d bee n u se d, the gust loads could have b ee n se p- i arated fr o m the maneuver loads. The gust loa d s coul d be treated f as t rue rand o m occurrences since t hey a re an exponen t ial func t ion t ! of altitude and are randomly g e nera t ed by an external ener g y source. Maneuver loads would h a ve to be treated as a condi- [ tional distribu t ion which would be trunca t ed a t the limits of } the An z range 2.4 Design Limit Probability Levels [ 2.4.1 Gust and Maneuver Design Limit Loads ! The probabilit y levels for current gust and maneuver , design limit loads and ultimate (1.5 x design) limit loads were calculated from the V G H data presented in Table IV The prob- !

ability levels were based on 10,000 and 20,000 flight hours and were calculated for all operati o nal categories except Aerobatic.

i Each probability level represents the probability of exceeding , a particular limit l oa d ,t least once in either 10,000 or 20,000 necessary flight hours. Again it was to first construct the i probability-of-exceeding-An z curves f o r both gust and maneuver loads for each operati o nal category. These curves sh o w the probability o f ex c eeding a given An z in a single flight. Each were assumed to satisfy the requirements for Berno u lli trials.

i flight was considered to be a statistical trial, and these trials The number of trials (flights) in i0,000 and 20,000 hours was calculated for each operational ca t egory. The probability P(E) of exceeding a particular limit load at least once in either , i0,00_ or 20 000 flight hours was calculated as follows: PNE = ] - PE _ : P(NE) n = PNE % P(E) = 1 - P(NE) i t j j

whe r e PE = p r ob a bili t y o f exceedin g a g iven . An_z in a .sing l e

trial (as read from probabillty-of-exceedlng-An z

cu rv es)

= probability o f n o t e xc ee ding a gi v en A n_ in a

PNE single t rial

P(NE) = probability of n o t exceedin g a given _n z in n

consecutive trials

Q

n = number of trials in either 10,000 or 20,000 flight

hours

Tab l es V through VIII p r esent the r esu l ts of the

abo v e calculatio n s. A s indicated in these tables, the opera-

tiona l categ o ries have the following trends: Instructio n al

has the highest probab i l i ty of exceed i ng the design and ul-

timate n z limits dur i ng maneuv er ; A erial A pplication has a

h i gh probability of exceedin g the des i gn n z limits but a l ow

p ro bability o f exc e eding t he ulti m ate n z limi t _ d u ring m a n eu-

v er; Commercial Surve y has the highes t probability of exceed-

ing t he design and ul t ima t e n z li m its du e to gust; and Aerial

Application has almos t a z ero probability of exceedin g t he

design n z limits due to gus t s.

2 . 4.2 Maneu ver L oad - Gross Weight Relationships

Rela t ionships between recorded maneuver loads and

design g ross w e ights were determined over the ran g e of aircraft

g ross weigh t s in t h e normal aircraft category. The t hree Anz

values a t each gross wei g ht represent 50%, 90%, and 95% proba-

bility levels and are based on 20,000 flight hours. An aircraft

flying 20,000 hours a t a gi v en g ros s weight has a 50%, 90%, or

95% probability of ne v er exceeding the corresponding An z value.

The technique for compu t ing t hese Anz v alues is t he same as t hat

discus s ed in S e cti o n 2.3, V -N Probability Distributi o ns. Since

the actual wei g ht c o nditi o ns correspondin g to t he recorded n z

v alu e s w e r e not av ailable , F ig u r e 15 is a p l ot o f A nz ve r s u s

d esign g ross wei g ht for e ach of t he thre e probabili t y le v el s .

" Also sho wn i n Figur e 15 is a cur v e of th e m i n i mum d e s i gn l o a d

f ac tor a s stated i n FAR P a rt 2 3, Se c t i on 2 3.337 for the norm a l

' ai r c r aft c a t egory. Table IX p r es e n t s the design gross w e i ghts,

number of recorded flight hours, nu m ber of recorded fligh t s, and

Anz values for e ach probab i lity level.

' 1 1 : ! i ]

!

TA BL E I V. E X TRE M E VGH VA LUE S PER F L IGHT BY OPERATIO N AL CAT E GORY

VGH hr : 337 7

POSI T I V E _ S A NU _ VF. Q _ P [_A T IO N gql -- T W |N ENG|N F [k_ 'CUTIV £ A / C T y O F ,a ,% ,6 ,7 , a ,O i,0 l , l 1,2 1,3 l . a I , 5 l,b I,T 1 ,8 1,9 7 .n 2 . 7 " f r) T A k 53 17 I t b % I I 2 I q' - ? 2 qc I 3q _ 6 3 _ ) ? _ , 15 _ 5 4 I 1 2 ! 2 I 5 q _ 3 20 7 4 2 3 1 I 1 1 I I s , 7 _A 13 2 60 46 74 1 6 7 "/ I0 3 Z 1 _ _ 1 _ I "46 ?6 9 1 3 7 6 ? 3 2 4 1 I i10 TO TA l _ 31 2 4q 1 36 R6 5 2 ' _ ( _ 13 21 i0 T 3 2 S 2 2 ] 1 1149 NE ' & A' ( I v r ' 4a '_ uEvEn _ P E O A T|( _ N 9 q| - - ra i n Ee, IC, INF F X i r C UT|vF" A_Z -% A / C TVP . r .& ,% ,6 .7 ° 8 * q 1.0 I*! I, 2 1 ,3 1.4 1 . 5 1 ,6 to? I,8 1,9 T _ [ A L 2 4 4 2 _ ' _l 2 2 2 1 _ 6 _ _ 2 7 R 3 _R 5 2 l f ,' _ _ 3 28 I0 * 3 I l lq I _ 6 2 l I _ TO T A L 3b _ ;O_ J 47 I ? 13 1 '53 _ °

VCH hr : 1 3 66

POSITIVE MA NUEVE P O P En AT i n N qq _ -- $ 1N 6 LE F* _6 1NE EXFCUTIV F /X _I ' A / C T _ 'P[ ,4 , 5 ,6 ,7 , g .g I,0 l,l 1 , 2 | ,3 1 ,4 1,5 1 ,6 1.7 l , _ l |,9 T O TAL ?A |Z 2 | 2 1 7 9& 5 4 2R 1 4 14 ? 7 i 2 Z 3 _ I _ ?

g 6 41 2 6 1 9 3 l! 1 5 I I 2 l _ 201 TO ' rA I. , 152 7 1 41 _ 5 10 18 4 • 3 4 7 1 2 355 _ [G A TIVF M A NUE V ER OPE RA TI O N qq2 -- _I NGLE FNGIN [ rXF C UTIV F An t A / C TYD[ . A ° 5 °b ,7 °8 *q I, _ I , l 1*2 l *3 | ,4 1, 5 |,6 1,7 1 , 8 |,q 7 . " _ ° 2 TOTAL ?A 4 4 _ ? 1 5 q I I I I e n TO TAL q4 ] _ _ | R |2 q 6 |qO |

i k_o_JCiBILITY OF i

i r , 1 1 I ! T 1 I ' ! _ I , I I

TAB LE I V. - Cont i nued

VGH h r : 724

POSITIVE MA NUEVE R OPERATIOH 9q3 * - PE R SONA L _ N 7 A I C TYPE .4 .5 .6 *? .8 .9 !. 0 | * 1 | . 2 1.3 1 .4 |,5 |,6 1.7 1.8 1.9 2.0 2 . ? TOTA L 12B 3 8 IT IS !1 S 4 S 3 2 1 I 1 1 n 3 IOA 21 8 4 5 _' 1 1 il Z6 T 4 2 3 i 43 TOTAL 85 32 23 18 _ , T 6 4 2 | 1 | I 190 _ FGATIVE M AN UEVE R O P EPAT 1O N ; q3 -- P ER SONA L A _ Z A / C TYPE ,4 .5 .6 .T .8 oq 1.0 l*! 1 ,2 1.3 io4 l* _ 1. 6 |.7 1 _ 8 1.9 TOTAL 12B 1 8 T q 1 2 I ! 1 4n 2n tO A 7 4 2 3 4 11 T I I 1 l_ YO TOTAL 32 1 2 il 4 ? 2 ! I

V GH h r: 2 84 3

PO ! .;T lYE N ANUEVER OPERAT I ON q94 -- INSTRUCTIONA L A _Z A I C TYPE .4 .S . 6 . T .8 .9 1 . 0 I.1 1 , 2 1,3 1,4 I.S !, 6 1.7 I. 8 l . q 2. 0 2.1 2,3 2.4 3.1 3. ? TOTAL 14 56 44 30 Z 9 I R I O 1 5 | t 4 4 1 1 3 I 1 | 1 _ t 7 16 llS T7 SO 54 45 32 21 14 IT 14 6 I1 9 2 2 4 ! 1 47 5 I T 84 36 33 26 13 1 4 8 2 2 4 | I 1 1 226 IS S? 38 24 3,, 19 14 2 0 6 5 i 3 I 1 1 i i 1 2 I 22 4 13 183 121 8 0 58 46 43 3 5 2 3 ?0 17 10 9 5 3 2 I 6 57 TOTAl 490 t16 21 1 2 01 141 113 99 58 48 40 24 24 1 8 4 5 8 ? S I 1 2 1 1 8C 9 : N EGATIVE MANUEVER OPERATION 99 4 - - TNST R UCTIO NA L _ NZ A I C TYPE .4 ,5 ,6 e7 .fl *g 1.3 l* I !.2 1.3 1.4 I* S 1.6 I e7 |.B l*g 2 * _ ? *1 TOTAL 14 51 ?_ 9 8 3 I00 1 6 g2 40 30 9 6 4 3 1 185 t I T Y_ 30 25 9 4 2 I 149 I_ 38 3 5 11 5 4 1 3 99 13 l_ O IIR 7 _ 2 3 7 2 I l 386 T O TAL 4I T 2_2 1 5 1 $4 2 1 14 8 I 1 g|g

TABLE I V . - Continu e d

VGH h r: 2291

PO_ I TIV F N ANtJ F VE R OP E QAT I O N qq 5 - - (ON N ER CI AL SURVEY AN ?

A / C TYP_ 44 ,5 - '_ , T ,8 *q I°0 |* I 1.2 1.3 1,4 Io5 106 1,7 1 .8 1,9 I q 5 6 5 3 2 1 2 # * 3 3 I I I_ . A 17 1 4 q I R 22 33 t, 6 77 T T 5 7 2 4 13 1 0 g 9 I qq 4 2 1 9 1 8 [4 1 1 R 6 5 1 4 1 I 4 9 14 1 6 22 1 6 22 20 14 1 9 2 5 2 1 @ 7 3 TO TAL 78 5 'i 54 5 1 5 5 63 6 7 1 01 10 5 82 37 20 1 6 1 4 II 3 OPFQ AT IOq 9 q 5 -0 C, ' ) ' _NFQ C IAL SU RVF. Y (CONTINU ED ) i _ 0¢, i T 1 VF . u . AN_ tJVF Q A / C TYPF 2,0 ? el 2.2 2 . ,3 2* #+ 2* 6 2.7 Z*8 209 3 . 1 3 . t 3o I , 3.5 "4 e6 TOTAL l q 6 _ 2 Z _ 2 3 3 2 I 2 1 1 69 I b A I _s 13 o 21 2 L # .q I • T O TAL T l 3 2 2 S 2 3 3 2 | 2 1 I R4T { P N EG A TIVE MANU FV ER O PEle ATTO N 9 9 5 -- CONNERCIAL SUR V EY I _ N Z ; _ 4 1 C TYPF ,4 . _ .6 o 7 ,R .9 l , n I * I 1 .2 1.3 10 4 I, S 1 ,6 1 . 7 1 ,8 1 09 T O TAL l q 20 12 9 3 1 1 46 16A 26 l O I I 2 | 41 q _ 2 ! I_ # * 2 I 41 4 q 5 3 _1 9 _ 4 I I02 _ T f_T_L 12 f) 66 2 _ 7 6 3 3 I I 23 n

. p RoD v cmmrr v or

37 '

; 1 i f ' '

TABLE I V. Cont i n u ed

V GH hr: 484

PO SITI V E MA NUEVER O PERAII ON q q6 -- AERIAL A P PLICAT I O N A N .7 A / C T Y R E ,4 ,, = 5 ,6 .7 .8 . 9 1.0 I * I 1.2 1.3 1.4 I,S 1,6 1,7 1,8 1,9 7 . 0 2 .1 2, ? ? ,3 Z, e , ? . _ T O TAt 2 4 71 127 1 2 6 119 86 6T 4q 39 14 12 2 3 _ 2 7 20 2 3 16 l = J 13 6 18 I R 4? 7 5 lOl 164 16 7 1 9 0 178 144 I l l 6 5 41 2 0 In 6 t I 140 q TOTAL R? 142 1 .' 49 1 2 5 1 0 4 8 5 96 11.4 115 ] ,T6 169 193 Ifll 146 111 6 5 41 2 0 I 0 6 3 1 21 2Q NEGATIVE NAN U E V E R O PE R ATION qq6 -- AERIAL A P PLI C AT IO N A l E TY P E .4 . 5 .6 .7 *B , q 1 ,0 |- | 1.2 1.3 1* 4 1 , 5 | ,6 1.7 |.8 1.9 T O TAL Z 4 174 qfl 45 14 b 73 63 5 5 107 1 67 31 5 317 195 q8 Zl 1 I l 1341 TOT AL 2 37 IS _ 152 1Bl 321 317 19 5 q6 2 1 I I 1 1678

VGH h r : 1 5 10

P O SITIVE MA NUEVER OPERATION qqT -- C OMMUTER ANZ A / C TYP E ,_, . 5 , b , 7 .8 .9 1,0 l, | 1 , 2 1.3 1,4 1. 5 1 . 6 | T I , R | .9 T _ TAL 21 _ 2 0 T 3 2 4 l 37 26 I O Z 21 1 1 9 2 4 I l l l 3 lS6 TO TAL 1 2 2 2 8 t4 II 6 4 I l 2 l 3 Iq3 N_ GA T IVE MANUEVER O P E R ATI O N q qT - - C0MMUTEP G NZ A / C T YPF .4 , 5 .6 ,7 , 8 ,q I.O 1.1 1 , 2 1 .3 1.4 1,5 1, 6 I , ? 1.8 T O TAL In 2 M T I ?

8 2 2 6 56 13 4 6 2 l 9 2 TOT A L 6 _ 1 4 6 6 2 | " ! ' ' l

TAB L E IV. - C o n t inued

VGH hr: 3 377

POSI TIV E GUST OP E R A TI O N q9 1 -- TW IN EN GIN E _ XE C UTIVE A / C TYPF ,4 . 5 .6 ,7 .8 *9 1 *0 l* l 1 * 2 1 .3 1 , 4 1, 5 1 .6 1 ,7 1 .8 ! ,9 2,1 T O TAL 4 60 34 2 3 q 14 4 4 1 2 I I 1 5t 2 17 8 qR 36 2 4 13 4 1 I I 3 _ , 6 3 83 41 16 4 4 2 2 2 IS 4 SA 2 34 1 6 S 8 2 43 2 1 l O 3 2 I I 2 I 565 1 ST 1 6 8 4 2 ! n q I TOTAL 612 354 1 _ , 5 84 54 20 1 | 1 6 2 I 2 2 I I _ 16

Z

_ ' N E G A T IVE GUST _N Z A / C TYP E , 4 . 5 **6 ,? *.8 .9 1 .0 l *l 1,,2 1.3 1 ,4 i*. 5 !*.6 let 1,6 1 .9 TOTAL I O P ERATI O N 99 1 -* TMIN ENG I NE EXE C UTIVE I 4 S O 34 21 1 2 6 2 7 4 | 1 3 7 ? 1 63 9 7 44 21 2 6 I 334 3 Iq2 42 15 ? 8 2 1 I S T 5 k 2 43 155 63 4 1 I? 8 5 4 1 1 538 1 $4 16 7 2 1 1 gl " TO TAL $ 9 2 344 15 0 83 3 4 19 13 4 " 5 1 1 1 1247

VGH nr: 1 3 66

PO SITIVE GUST O PERATI O N q9 2 - - SINGL E ENGINE EXF C UT I VF " A N z A l e T Y DF ,4 ,5 , 6 ,7 , 8 ,9 I*0 I*I I, 2 1..3 1, 4 I ,§ 1 , 6 1, 7 | , 8 1,9 TO TAL TA 3 9 5 "q _4 2 4 13 T 3 2 1 1 7 6 9A 118 q' _ gl 69 3 8 I g 3 S 3 I 2 1 43 2 8 Tfi 7 3 81 T2 5? 34 2 4 13 8 S 3 I I ' c,50 T OT AL 235 219 196 167 t_ g $ 9 I 0 2 0 1 2 6 5 2 I 1 0 5 8 N F G ATIVE GUST OPER A T IO N 99 2 - - S I NG L E E NG INE FXFCUTIV E AN Z t A I C TY P F , 4 . 5 , 6 *. 7 ,8 ,9 1,0 1 , I 1.2 1,3 1.4 1 , 5 1,6 i.T l.g 1.9 2,2 _ . _ VOTAL TA 45 41 31 2 7 1 2 3 4 [ 166 q A 116 I OS gO 4 2 37 1 2 ? 4 2 2 3 I 411 8 118 95 s T 5 1 41 qO 17 I0 3 4 [ I 44 8 T n TAL 27 9 2 4 _ 178 1 2 0 90 55 ? R 14 S 6 3 1 1 I I 10 2 5 - r

TA B L E I V . - C ont i n u ed

VG H hr : 7 24

POS I T I V E G US T O P E P A 'rl O N q 93 -- P E RSONAL AN Z A / C r V PF , . ,5 ,6 .7 ,a . R l,O t,| 1,2 1 , 3 1,4 1,5 l ,b 1 , 7 [.8 | . 9 T O TAL 1 2B 92 52 21 I N l 2 ! 1 79 loa 4 9 4 0 1 8 _ 4 l I lib l I 49 40 IS 1 6 9 S 1 34 TO TAL 190 1 3 2 5_ 3 1 14 7 1 1 l 4 3 1 NE GATIVE GUST O PERATI O N 9 9t - - PERS O NAL _N 7 A / C TYP E .4 ,5 .6 ,7 .8 ,9 1 . 0 1,1 1 ,2 1,3 1 ,4 1 . 5 1,6 1.7 1.8 l , q T O T A L 1 28 R 6 42 23 12 5 1 l ITO IOA 42 33 17 6 I I ] 1 102 II 62 2 _ IR 7 4 | I 1 |l q T OT AL 190 I00 58 25 IO 2 2 I I 2 39 1

VGH hr: 2843

POSITIVE GUST O PERATI O N 996 -- I N S TRU C TION AL A NZ A I C T YPF .4 .5 .6 .7 .8 .9 1 ,0 I. I 1 .2 1 ,3 1.4 1.5 1.6 1.7 I,e 1,9 2. I "_. _ T OTAL 1 4 I R4 8_ 26 l_J 2 1 _ ' " _ ' 1 6 A I _0 145 R 2 38 20 I0 I 2 2 I I I _ 1 '7 77 58 1 8 q 2 1 6 4 I_ 113 6T 35 14 6 2 I I 23 <I • 13 584 252 5 q 23 8 7 2 1 I 1 9_ 7 T OTAL l l t I R _In 21 q 9 ? 3 R 19 4 _ I 3 I 2 I I 2 1nr NEGAT I VE GUST OP ERA T IO N 9 9 4 -- IN S TRU C TIONAL AN Z a / ¢ T_ P F , 6 . _ .6 .7 .8 , g I .O I.I 1.2 1.3 1,6 1. 5 1 .6 1 .7 1.8 1.9 T O TA L 16 1 66 n n 2 1 5 I 2 I 28_ 1 6A 166 1 2L 73 3R 15 5 _ 6 1 2 | 428 t 1 7 q5 6 4 19 9 I I 169 15 1 2 2 T3 27 5 ? 5 I 24 0 13 5 29 IR O 4R 2 _ 7 2 I 790 T OT AL | 07 6 5 _ 7 IRR RO _0 | 5 4 5 2 2 1 l tql l

4O

TA B L E I V. - C onclu de d V GH h r : 229 1 ' , _osxTIv r _UST O PF R ATI _ N qq r _ _. ¢OMM FR C I A L SU R VEY _' _z "r _ / C TY P E , 4 " 5 " 6 . 7 " 8 " 9 I* O I 0 1 1"2 1 *3 104 1" 5 1 " 6 1°7 1°8 1 ' 9 2"2 T OTAL i 19 8 q 14 1 3 7 6 5 I 2 2 6 7 | 6 A 13 4 9 84 120 86 9 0 31 16 3 5 2 I I _0 1 g 8 15 _ 4 6 7 55 2 8 27 12 5 2 4 2 3 I 275 4 9 g 3 5 17 { TOTAL 45 1 1 5 170 1 8 8 1 21 12 3 4 8 22 5 1 1 6 3 I I I R6n N EG A TIVE GUS T OP ER# T I ON 995 -- C OMMERCIAL S U R V E Y _; A NZ _ ' A I ( TY PF °4 ,5 ,6 ,7 ,8 ° q 1,0 I,I I °2 I°3 I°4 I ° 5 1. 6 1.7 I,8 I° 9 2o | 2 $ 4 T _ TA L _ ; 19 9 14 I I 7 15 5 2 2 1 2 1 I 70 16A 15 47 4 9 6 6 10 3 71 54 33 2 3 22 7 5 3 I I 4 9 7 q _ 9 3 0 57 64 4 4 26 27 9 5 2 1 I ! 27 6 4 q II I 2 I _ T O TAL 44 q l 1 _ 8 13 g 1 5 9 1 0 2 83 44 29 26 q 5 4 2 1 I 8 5 7 V GH hr : 484 P OSITIVF _ UST ! - Op F _TI_'_ t_ q6 - - t _r P IA L AP PL ICA TI ON ZS4Z A , 'C T Y_F . 4 . _ °6 . 7 .R . 9 1° 0 1. 1 1.2 1,3 1 .4 1 . 5 1. 6 1 ° 7 1 .8 lo 9 T O TAL 24 3 4 IR 4 1 57 2 3 16 5 2 2 _ TO T & [. 50 23 6 1 80 N[ ( 1 AT I V E _ UST OPER AT I ON 99 6 -- AE_!A L A PPL IC AT IO N L_N Z A / C T YPF °4 , 5 , 6 .7 ° 8 *q I °0 1. I 1.2 I°3 |.4 1. 5 1,6 I°7 I° 8 1 . 9 T O T AL 24 4 3 13 4 ] 6 1 23 _ ? I 1 2 TO TA L 4 7 2 0 4 I I 7 _ VGH hr : 151 0 PO S I T IV F GUST OP E OAIION 9 9T -- CO MNu T E # Z_ N / A / C T y p e ,4 °_ ,6 ,7 o8 , 9 I .O I* I I o 2 t , 3 I ° _ I ° 5 1 , 6 |,T I °8 1 .9 TOT AL [: ? R 16 4 l_b 6 8 4 0 2 8 9 I0 2 I 2 45 0 _ 56 q 2 6 3 20 120 67 45 6 6 2 I | I T_ TAL _ g _ 2 66 1t5 _ 3 _ 15 1_ 4 2 2 I I lOl9 N E W,r i V E GU S T _. OP E RA T ION 9_ ! -- CON N UTF _ AN 7 A / C TYP F . _ , 5 , 6 , 7 °8 ,g I .O I°l 1. 2 1.3 1,4 1_5 1 ,6 1.7 1 . 8 1 ° 9 T OT A L 2_ 14 9 1 05 T2 50 2 5 20 R 2 5 I 2 I _ 4 0 !- , _ 2 6 3 44 I10 ,9 21 15 8 2 I 1 5 T I T O T al . _93 2 1 5 14 1 T I _ 0 Z_ I 0 _ 6 1 2 1 lO l l I. 41 q t ! 1 1 1 _ 1

TABLE V . PROBABILITY OF EXCEEDING MANEUVERDESIGN LOADS IN

10,000 F LIGHT HOURS O F EXTRAPOLATED V G H DATA r

Design Limi t Design Ul t ima t e Operational Axrcraft Category Category nz Probabillt_ nz Probab t lit.. )2 I_ tn- e ng t ne normal "3.8 . 485 * S . 7 .01 " I xecu t l y e - 1.52 . 000 -2 . 28 .tt llI_ qtngle-en!.'l ne normal +3 . 8 .717 *5 . 7 . 031 I xe c ut _ v o -1.5 2 . 515 - 2 . 2 8 . 0 17 Perqonal normal *3.8 . 32t .5.7 . 907 - 1 .5 2 .tll_ - 2.28 . 004 Instr u ct lonal u til _t)' *4 .4 . 877 .6. 6 052 -1.7 0 .514 -2, 6 t .084 C ommercial ut l 1 i ty * 4 ,4 . 0 0 0 Survey -1 . 7 6 .013 -2. 0 4 00 4 \erlal normal *3 . 8 .850 +5 ." 0o0 Appli c at2 on " I. 52 .000 - 2 .28 .Ill)() C o mmuter hormal * 3 .8 . 372 *5 . 7 . 020 -1.52 .003 - ? .28 .000

TABLE VI . PROBABILITY OF EXCEEDING MANEUVERDESIGN LOADS IN

2 0,000 F LIGHT HOURb O F EXTRAPOLATED V GH DATA

Design I A ma t Design Ult imate Operational Axrcraft C a t e_L q __ _ Ca t e ..._ 2L _ __nz Probab i 1 i ty n : P r o bab t i it ) 2 h, : n- eng t ne nor w a 1 *5.7 .033 1 xecut 1ve - 1 . 52 .001 -2 . 28 . 0 0 0 qlngle - engine normal .5.7 ,061 l,xecut Ive -1.5 2 .531 -2.2 8 . 0 9 2 Perso al nozmal + ] . 8 i 5 _ 8 + 5 I _ , (1 1 , _ 1 . 52 . 08 9 - 2 . 2 8 . O0 _ ', Ins t ruct l onal at _ 1 i t y *4. 4 ,9 8 5 * b . 6 . l O1 -l, 76 . 7 0 4 2.6,1 . lo1 Commerc ta I u t I IIt) ' + 4.4 ,(10(1 + 0 (_ . (1 0 1 1 Survey - 1 . 70 . 020 -2 t _4 .Od _ Aerial normal *3 . 8 .9 7 8 +5 7 .0(10 A ppl lcat ion -1 .5 2 . O 00 -2 2 8 ,(lO0 I Commuter normal + 3 . 8 . 606 *5 7 .114 1 1 - 1 . 52 . 005 - = 28 .qO0 i i (

TABLE VII. PROBABILITY OF EXCEEDING GUST DESIGN LOADS IN

i0,000 FLIGHT HOURS OF EXTRAPOLATED VGH DATA

i Deslgn Limit Desi_ U__Itlmate Aircraft Operat l o i_al i . Ca t e , o K £_rZ_ C a t e .o K __Z an z Pr o bab i 1 it>" An z Probab i 1 i t_z _' 'I_, i r l- Cllg t n _ ' no rma L 42.4 .106 45• 0 .002 -2.4 .ObS 3.6 • C)()i i I \k ' _.l J[ I _,t' I xecut tvc _ _ Ingle- cog tne normal +2.4 .271 * 3.0 . O01 " -2.4 •188 3.0 .000 l'e,'sonal normal + 2.4 .002 * 3.6 .OOO '- - _. 4 .004 3.0 .000 Instructional utility . 2.5 . 00 7 -2.5 .009 3.7S .000 Co ilmerc i al at i I It y • 510 4 3.75 .005 " Survey -_ q . 729 3.75 . 014 i ker ial normal +2,4 .Or)o +3.6 .000 -. lppl i_at Ion - 2,4 .00 0 3• 0 .000 Commute r norma I + 2.4 • 209 4 3.0 . OOO - 2.4 .390 3.e. .009

TABLE Vlll. PROBABILITY OF EXCEEDING GUST DESIGN LOADS IN

20,000 FLIGHT HOURS O F EXTRAPOLATED VGH DATA

D e sign Limit Design U ltimate Operational Aircr a ft _n Prob ability Ca t eOg__)_ Cateo_,_[ Z _nz P r obabxlit__ _.z Twln - engtnc normal -2.4 .201 4_.6 . 005 ] X O CUt IVC -2.4 .126 -3.0 .001 q)nglc-eng_ne normal 42.4 .468 43. 6 . GOI ' l,xecut ive -2.4 .343 -3 . 6 , (lOl l)e r_onal normal * 2.4 .005 43. b .t)O0 -2.4 .007 -3,6 .0()(3 l n_ t ruct ) onal ut ll ity +2.5 .015 +3.75 • 000 : - 2 . 5 .0 18 -3 . 75 •000 ( o w _,erc ta I ut i I i t) ' + 2. S .765 * _. 75 .0 I 0 _,u rye) ' , - 2.5 .92o - 3 . 7 e) 029 ?

\or lal n o rmal +2, , I ,000 4 _.b OI)o _, _PI) l)_ at ion - 2 . 4 .001 -_ . 0 0 011 i I_ ( 0 m1111 ! t c r n o r ma I 4 :. 4 . 3 ? 4 + _ • (_ (l l 2 r k - ; :•4 . 628 -3.9 . 0}7

!

, 43

[ t ....... -_

.. _ I I , I i ] ) •

TABLE IX. MANEUVER LOAD-DESIGN GROSS WEIGHT RELATIONSHIPS DURING 20 , 000 HOURS OF EXTRAPOLATED VGH DATA Probability of l ) esign Never l.xceedlng , ' ,nz ¢;ross VGIt Data l}_$_%_ht(lb} llourb tllghts t _ o __.

I , 131) 1{}{)7.1 3117 3 . 10 3 0_ " .9 , 1 1 qSII 31(I . 6 " -' , 5.. 4.66 4 38 3.(,1 2 "(}0 569.1 502 5.37 4 71 3.73 I II(I0 34t_.8 582 2 99 2 74 2.2- 1 3u( ) 115 2 .s 1578 2 38 2 29 2 .0- ' 9 ' q9 _ . 8(_ 5 -_ n 30 . (1 14i7 3 03 . . .

1(I 2Sl_ 914." 3277 5 2 4 4 89 3.82 11 t)tl(_ 093. t l 830 4 56 4 12 3 . 30 l 2 4 S00 8 2 4 . 1 731 2 47 2 35 3,12 2.5 Review of Categories As previously noted, the eight operational categories do not correspond to the FAA aircraft categories, normal, utility, and acrobatic. Although the eight operational categories more closely identify the operational load experiences of the vari- ous aircraft, the following analysis indicates the need for their further refinement.

Figures 16-a, 16-b, and 16-c show that both the magnitude and the frequency of the Ude'S for the Twin-Engine 2xecutive category are greater in the 1829 to 6096 meters (6,000 to 20,0_0 ft) altitude range than in the 6,096 to 15,240 meters (20,000 c o 50,000 ft) altitude range. Since aircraft flying in these two altitude ranges experience different gust and maneuver loads, the Twin-Engine Executive category should be separated into two catc.- gories, one for the higher flying turbojets and the other for the turboprop and piston aircraft.

.- The examination of the VG data by aircraft type shows that when aircraft in the Single-Engine Executive and Personal cate- , gories fly at common airspeeds, their Anz'S vary little. A l- though the single-engine executive aircraft can operate at higher airspeeds , the data analysis would not be affected by combining the two catego.'ies. Figure i0 shows that the constant proba- bility envelopes for the Personal category are considerably higher than the FAR minimum maneuver load limits for aircraft in the normal aircraft category.

1 ! ........

The examination of the VGH data for the Commercial Survey categor? shows that three of the four aircraft types in this category had very different maneuver load experiences. This sug g ests further breakdown of the Comar,ercial Survey category by , mission type.

2.6 Fatigue S pectra From the ¢!stribution of repeated acceleration peaks re- corded in the VGH data , fatigue spectra were derived for three types of load conditions: gust , maneuver , and landing impact.

The s a st accelerations were converted to derived gust velocity , Ud-. The gust and maneuver n z peak distributions are presented ineTables X and XI. The landing impact accelerations were normalized by dividing the load factor n z b y 2 .67 , the minimum design i n ertia load factor.

2.6.1 Derived Gust Velocity (Ude) 2.6.1.1 Ude Computations A derived gust velocity Ude was computed for each gust acceleration peak in the VGH data by using the following equation" Kg Ude Vea n z 1 + 498 (W / S) where Kg subsonic gust alleviation factor 0 88 _g 5.3 + pg

2(W l S )

_g airplan e ma ss rati o - p c ag Ude = derived gust velocity (fps) p = atmospheric density (slugs / ft 3) W / S = _ing loading (psf) = mean aerodynamic chord (ft) = gravitational constant (ft / sec 2) V = equi v alert airspeed (knots) e _ a = slope of normal force coefficient (1 / rad)

TABLE X. MANEUVER LOADS IN VGH PATA BY OPERATIONAL CATEGORY

VGH hr: 33_ ,,

TABLE X. Continued

VGH hr: 1366

[ "_ A n _ P FI D I_IO N: %l_16Lf f N GINF F X fC UIIV _ " V F L • P 0 5 1 T l V f I, CC IrL[RA? I "_ N 11[ _A r _ ) . 2 * 1 * k .5 * b ,? .i _ , _1 1 .0 1. 1 1. 2 1 . 1 1. 4 1.5 | .6 1, ? T_T_ ' LF S S 6 t ) I 31 I I, 10 ?

7 _ h ? 7 _ ino 17 q _,_, _3 11 I ¢_ 3 ' ; 3 | 2 ; 11 2 I I n s o 6 _ 11 lr, ? q r, 2 I ? "_ I _n I_O a _ 20 1 1 ? 6 Z I 2 2 , " I 0 7 I_ 1 _ 4 2 ? I i l I / 2 |7 _ I I ?

I ¢ 0 _nO ? tn 2_ 0 -- I Z I'O ? q O l flO V f _ I I P _ I _ 'r l k _,I I ? ? _tr 7 1 6 Ifl ? $ , ' , ;'4 t2 I I II _ ' _ ? I

4 8

TABLE X. - Continued T ABI, E X . - Continued L V GH hr: 724 , r_ a _ , o Z o _ o o _ . " * " o _ . _ _ . _ l. ; 1 . 2 !.1 I. _ l o _ I . _ 1 . 7 1 . _ ! . _ . f_,S °a L 1 A , l_ 1 l ' " J 1 _ • I 1 l 1 m_ " ' _ l. _ ' 1 _ ? ?

I_ ^ "" = 2 ? _ 3 ? I I l, r 22 r 2_f ' n n P V _ ATI 0_ : O F_$O_al.

v_. P OSI T I V _ A CC E L E R ATI O N I_l_l 7 . _ 2.1 _ . ? 7 .3 2. _ 2. _ 2. 6 2. 7 _ . A 2. 9 _ . O _ . 1 _ .2 _._ 3. _ _ o _ YO T AL LF_ IC _n 2_ _n 1 3 7 1 1 0 _ 12n I 1 7 I_ l0 2In 7pn 2 _ N 5O I TABLE X. Continued _l° %F qA" I ' _F ad[FtrC_ T T_N im i_,_ - ° ? - . I -. - -.9 ° ._ -._ -- P . .o - 1 .n -i. l - I. ? -l°_ - I . ' . -I.' _ -I._. - l . _ I% T AL tr q_ _* tO I * " ! 97 qr I " in _ I! _ l I ? _ 1 1 t _ P 1 2 ) I "r I Qn • _ Z_ r 2i n VGH hr: 28 4 3 n *f{ . PO_] TIV F A C( f L[_ T I _N ?

? ?

_ *, ln ' '_ _ t l 2 _ , 1 _,2 1 22 60 _, ¢, I 1 22 I I _ _ l r a _q _ 7 6 " _ l a ; - _ 2 0 l_ lo _ 6 _* S l ,_ I l ? o ? " I l_O 1 I I , _ n _. ? ,' n 7_ n 2 _n , ._ _ ' __ _ nc OR IC P ' M, P A( I P , 1S POOR TABLE X. - Continued OP EI _ A T I h i l l : | h. 5 T@UC T I O N AL A h V [ L. P O S I TIVE k CCE L [_ AT IO N _IA S) 2.0 2. 1 2* 2 2.3 2 ._ 2. '; 2.6 2,7 2 .t l 2°_ _ . O 3 . 1 _. 2 3 . 3 _ o _ ' _ -' _ r qTAL c _ d , , , P O 22 2 _ ZlO ! 2 I ! I 1 ,n_ 1 2 0 2 17 1" _0 l' rO 21 0 2 2 0 2" , O 2 60 2 eO 32 _ 3 _ ,0 & R O VIr !

; , 1 _ J i , " ! v I l "" I !

TABLE X . C o ntinu e d

V GH hr: 2291

r' I P t"_ 'AT]ONt COMMf' a C IA I. SUqVFV VEL o POSil IVF A CCFL_A T I ' _N _ [ ASI 2 _(_ 2 . _ 2. ? 2 . _ ? _' ? o _ ' 2 ° _ 2°T ?° _ ? °_ 1o _ _1 _° ? 3. 3 3 _ _° ' _ _ °6 _'O TAL _ O 2 e , I _- ? P , | la 2 1 _0 I I _ ' _ _' Iq( _ 1 _ 0 |p A _ ? 2 I 1 _ I 1 ?5 0 [ _(_ 2 1 l| q' / | ?O 1 1 QO I 1 _0 I 1 ?3 _ , ? Ir _ I I e , , , P4_ ?AB t ? qO _ 0 0 l _ ( ')V r

TABLE X. - Continued

VGH hr : 484

An z O _p_ATTn_: AtrIAL &PP[ [C_T I ,"I_ V F L. PD S I T I V F A C C[LF_ AT ID N I_IA_I o2 . 3 ., , 5 .6 o ? . R . 9 1,0 lol I°Z 1. 3 I o_ ! .5 I o5 1 . 7 I . R I. Q L E S_ _n 7 _ 5 _ - _ 5 _1 2 _ 13 q _ _01 3 26B4 2 34 _ 1 9q l 1 3 _0 AT_ 56 1 _ 3 2 2 07 q_ * _ lq A O f_ 2 l ln ? 1 2 7 7 14 7 _ 16 5 n 1 837 ! 73 "_ I_15 1 4 _0 122 1 l Ol q t _ _ , _7 %_I 2 1 q 13 1 7 _ 1 1 _ _ I 1 I 2 1 2 l _l l 7 1 ? 0 _rlO 2_,0 i ?_n T T O

5 4

TABLE X. - Continued

L n z VFL. Nf C , A_ " IV(" A CC E L F _AT I_ ' ; _K_S_ °._ - .'_ - .4 - .5 - , _ -o ? -, _ -, q - I*(_ - _ . I -1 , 2 °_°_ -l °_ -I o5 -L o _ - t o ? -t._ - _(_ _OTAL _ LF . S % 1 1 i rr } r) I' _ I_ q _ ¢_ 6 1 9 7 II r 1 l_P 1 1 2 1P t _ r ,, q r i I i !

..........

.r

TABLE X , - Concluded

VGH hr: 1510

_ pE _A TI r N: CO@_U T _ p ,_ n VFL. P O S] TI V[ ACCFLE PA TI O N (K |JS ) ,? ._ . 4 ._ . _ . 7 , 0 ._ l * O l * l | . ? 1 ,3 I* 4 1 . _ 1,6 1 . 7 T _ T a [ 7 n _ l 11 _r q I I ?p qn 2 1 7 6 I 2 o _ d _ 110 1 4 4 ? ? I 1 _ 1 4 0 t 7 t2 _ 4 ? ? I I ! _n 16 o I O 1 I 1 I lgO _ ?

£ 2 00 I 1 1 ?1 0 ?

??0 1 ? *n 1 ?? o 3 I n j 3? 0 An OOF r _ A T I r N C O_,_NTr n V F _, Nfg_Tl ' * t _ r ( ¢L V n_ T I_ N ¢I¢ | A t , I - , ? -._ .._ -._ -° ¢ _ -, ? -,_ -, _ .I,0 -I,1 -I° ? -I*_ -I. _, -l°*i - I° 6 -I° ? Tq T A L L_S_ 7 _n 1 1 11n I _ 1 7 i ) _ _ o I_ _ I 2 nr ? In 1 ? , r, t ? _" _ r _ r ., , , r , • n r ? 1 _ n _ I I , _ I " , , j

i

1 : & TABLE XI. GUST LOADS IN VGH DATA BY OPERATIONAL CATEGORY VGH hr : 3377 ?

V F_ . PO51TT V E A CC E L ERATION _k I_ , l . 2 o _ . _ . _ ° _ . 7 . 8 og l * O _ , . I 1.2 l*} 1 o 4 1.5 L . 6 1.7 T _ T _ L _ 0 l I 1 3 70 l _ I I I _0 1 1_ I v 2 0 _n I 1 51, _ 2 62 II_CP " 4 1 _n 18 _ '1 2 7 0 II_ I q 2 I TM '.6 2 r I , I Z ? 9 l_, O 9_ 14 _ q - a ll 7 _ 2& 1 0 3 3 2 I q? 8 1,' , n I1 7 2 1 ll_" _, 151 5 0 2 8 12 4 I I 1 9 2 6 1 7_ I_I _ 2 t _ l 2A_ 122 3 " _ 7 3 I I 13 5 _ 20 0 I ? '_ 4_ l n9 3 8 _ 5 2 1 I 3 80 ? 1 0 l q 2 "_I _ I I ' 5 5 31 # * ? 2 0 _21 _ ¢' 2 1_ 6 1 I 3Dg 2 t n 2_ ,5 7 n _ I i t 6 a _ , 53 2_r_ Z91 "_A I _7 _ 1 _ 7 I _ 5 0 ? 3 0 2_ 7 _ , I1 2 35 B 1 l 2 _ 62 26_ 2 1 _ , _ I 8 7 20 I0 10 I t _ * I 0 2"_0 l q 8 2 _ ? _ 3 9 7 ' _ I I I 35 1 L q O 21_. "_7 _ , 7 I¢ , _" 1 317 _ l l O |O A 7 7 3 6 19 _ Z 2 2 0 U 3 2r _ 5 _ 2 3 _ , _ 5 a 1 1 28 t_n S I _ 2 I 16 _ t _O _ 2 I0 37 _ 2 ?

I / _B OV f T n TAL _ ', .7 7 7 _2 5 _,2' s 187 N _q l _ 7 6 1 98 3 _ 12 2 7 2 1 2 2 I L _ 35 nD FI _ T T C N ' T W I N FNGIN E FxFCU TI V[ ' n / r l o N E GA T IV F 4 C CELF_ T I_ N i_ l_ , _l - .2 -° _ -o _ -.5 - . 6 ..7 -. 8 -° g - 1 .o - I . ! -1 .2 -l .: _ - l . _ - I. _, - 1 . 6 - l . ? " J ' _ [ r "_ - ¢, l lnp ? l 1 1 2 t 7 l_ I | I_ Ilri I _ l n ? _ 6 I¢ . "_ _ I t_ I _ r _ _ ? 1 ) 27 0 72 3 2 _ _ _ . | . t " _ i_ , ^ 7_ 2 8 7 1 7 _' t _ [' _ _ 19 q 6 2 I I I _ A n l_/t I _ _ ' _ _ ' _ t _ o l / _ ¢_ t 17 1_ _, l 1 I _ O ] I _ ql " _ ? 2 17 _ , 1 1 2 9 1 ;' _ ( _ I ?6 _ . 9 _ _ _2 I n _ 4 _"_ ?In Iq2 _, ? 7 t . , _ 2 q I 1 _" 21I _ I _1 2 ' _ f 2,_ _22 I ?

_r , n _1 _ _ r I_ I 18 7 ; llq o_ . 2 ? _ I R c 1 I _ r_ .

t 2" _ . 9 _l _ I n 2_ , 1 I _ _ ? I 1 _ , o l l 2 _ I', _n J _q_vF tqfAI 2_1 ' _ ? ._ . _ . _,_ I ? _ . _, ' _'_ 2q¢_ b ? _ ? l _ . _ ' I I I _ y < _ _ # , " ; 7 TABLE XI. Continued VGH hr: 1366 i

F

t

, TABLE Xl. - Continued

rl i • n _n G P P , ,_ 2 , 1-

VGH hr" 724

TABL r : XI. - Continued VG H hr " 2843 6O

i

I

!

TABLE XI. Continued i_ T _ , . ., _ ° . '. -._ -." _ . t, - ._ - *_ -° _ - |* 0 -|°I - I °_ - i °_ - _° 4 -I° S - l._ -_o ' _ -| ._ -I° q f ' I t A L Q_ _2 2_ _ _ i _ ?I _ I 9 4 I | 1 1 _ 144 11 _ : _ 6 _ . | 7_ Izr 2 !

I_ 0 _ 1 2_O : _rn _ 2 P

, I

J i ? 61 i, i TABLE XI. - Continued VGH hr: 2291 !

21 r ! - r 2 1 " 2

TABLE XI. - Continued

" - 2 . _ - ? o l - 2 . ? - 2 . _ - ' .' , - 2 ,_ - ? . 6 - 2, 7 - 2 . fi - 2. g -'(. _ -_,1 - a , ? -) . 3 - _ , _ - _ .' _ "3r_ , l , o IQ_ i , , _ l q 2;', ?

2t t , 2_e li t [I _ I toDUCL_ILI [ PO0 ] _ . . .

ORI GI NA L PA G Z l_ - -

6_

n TABLE XI. Continued VGH hr: 484 TABLE XI . - Concluded VGH h r: i S l O I b _ n i _f'_AT I _N : C_ u u tf _ = t . f t. P _ TTI v F _CCfL r etT I 'N } _ 0 I 1 I 20 I t - t _ 1 7 4 7 I i ? _ ] * ' _ 4t 3 I_ Y *_ I 0 | h 5 ] I ] ] 700 I _ ¢' )' ?? ) O ? 1 _ & _ I 9 00 _ O O |_ _ 7 _ 4 II Q 4 K I | ? q _ Z t e t? I g ? _ ? 6 _ t,- t.- ti e : . :: _ _ P ro tt |fiN: C t )uu L l _ t F O ? n _Fi • N fG t T l v r _C C _'LEPl tTI ON ( ¢I_% , -. ? -, _ *. _ , -.b -.6 -.? - , 8 - ,0 - I . 0 -I,I - I , ? -I. ] -I. _ * 1 .5 -;,8 - 1 .7 T_ T _ L • t _ Z ?

_n l t I _n 2 1 6 1 _ 0 Ie,_ _; t ? t , 6 10 _ ' 3 _ l 5 5 '_ l 2 1 qb q 21 n _ 7 # , ? I _l ? ? o • ,_ im t _ l 11 0 t ¢ 0 ' , " IAO I?n t , q r ) ¢ f 1 r" _ 6S ' The values of Ve and o were computed from the mid- calue3 of the 10-knot indicated airspeed interval and the 2000- foot pressure altitude interval containing thc recorded data at the gust acceleration peaK. The aircraft weight was assumed to be constant for each instrumented aircraft and was set equal to a normal operating weight estimated by the operator.

In the analysis of derived gust data c omputed from re- corded c.g. vertical accelerations, it is important to note that (1) the relation between Anz and Ude is inversely proportional to Ve so that the effects of inaccuracies in Anz measurements are magnified in Ude values at ver y low airspeeds , and (2) since the _nz measurements were not taken inside the digitizing thresholds (±0.4g for most aircraft), the corresponding Ude values omitted were as large as 14 to 17 feet per second for the various opera- tions so that the validit y of the presented Ude spectrum is lim- ited to the range outsid e approximatel y tl6 feet per second.

Table XII presents the calculated Ude peaks with a breakdown by operational categor y and airspeed range.

2.6.1.2 Ude Spectra The cumulative frequencies of positive and negative Ude peaks per nautical mile are presented in Figure 16 for the seven operational categories represented b y the VGH data. The low altitude spectra for 0 to 1829 meters (0 to 6000 ft) in Figure 16-a were most severe for the Commercial Survey categor y and least severe for the Aerial Application category. The mid- dle altitude spectrum for 1829 to 6096 meters (6,000 to 20,000 ft) in Figure 16-b were relativel y closely grouped with the Com- mercial Survey category having the most severe spectrum. As shown in Figure 16-c, onl y the Twin-Engine Executive category had a gust spectrum above 60 9 6 meters (20 , 000 ft).

As described above , it is likely that the Ude spectra below 16 ft / sec (5 m / sec) are biased by the acceleration digi- tizing threshold at the lower airspeeds. For this reason , the Ude curves in the region of bias are shown as dashed lines.

2.6.2 Gust Accelerations The cumulative frequencies of positive and negative gust load factors per nautical mile are presented in Figure 17.

" The largest gust acceleration of 5.3 was recorded by an air- craft in the Instructional category and the highest frequency ' of gust acceleration peaks was recorded by an aircraft in the Commercial Survey category.

2.6.3 Maneuver Normal Load Factors The cumulative frequencies of positive and negative maneuver normal load factors per hour, per flight, and nautical mile are presented in Figures 18-a, 18-b, and 18-c , respecti v ely.

/ L i T ABL E XII. Ud e PEA KS IN V G H D ATA BY OP E RA T ION A L CAT EG ORY VGH hr: 3377 a. Operation 991 - T w in Engine Executive Positive Ude Peaks T AR L F_ _Y r} P r PA TT r_ N q q l _ F D IvE r G UST tP O_ lY t V f) V5 V[ L O C I T Y + Vf'L • (` r R f r ED GUST _, 0 4 A I ? 1 6 ? n 2 4 Z _ _2 3 6 4 0 4 4 4 8 52 A BO VF T O T AL LrS S 5 n l I b e 1 2 3 ? _ 7 2 i 1 11 qO 4 10 4 1 1 2'0 9 0 ]fi ? ! _I 1 2 62 100 '_ 37 ? l I 4 I 1 ?0 _ " II0 "_ a 1 71 %ia 10 3 I ?.79 I20 120 16 _ _ .7 I0 Z I 349 13 n 2 _ 3 263 69 I _ _ • _ 85 14 0 _04 _ OO q5 16 Z I 9 7g I _ 0 _ ' _ o Q ? _4 3 ? _ 17 1 I 1 _ 0 5 1 6n 3 fl I _ 2 4 299 ql ? 3 3 I 1 926 17_ 1 02 OQ 3 J?A " 43 I 0 I 13 _ 5 190 1 _ ) Z_ n 6 4 12 2 00 1 2" _ 3 103 ?I ;' ZIO ?? I _ _ 80 I S ! 1 )14 220 _ IR ?19 6.5 IZ 3 I I 339 Z3O q7 ;'_ * ? 9 0 21 3 4_ 3 240 1t4 ? 0 4 1 13 1 4 '5 5.50 Z'_ O 1'5 1 2n 9 8 _ 6 3 4 4 62 260 163 I_ 4 4 l 1 9 2 I 4 10 27 n 1 75 Il q 49 A l I 3.5 1 20 0 167 P_ 26 .5 Z _ 6 290 2 0 ++ _ 8 1 2 2 I 317 3D 0 1"4! 6<_ 10 3 1 ZI4 3 10 11 _ 7t 12 3 1 ZOO 330 _ A 3"4 13 3 o_ "4 40 _ 1 2 _ 2 7 ?I 3.50 7 R I 16 36 0 _ * 6 I0 370 ? ?

A BO VE T (` TAL Iq_ O 7?eZ _ 7 4 R &14 1"4 _) 2 7 I++ 3 "4 3 [ 1263'5 Negative Ud e P e aks T aRLE _ _ y O PE _ T I(`N 99 1 nE n lV E D G U ST IN EGATI VF_ VS V F LOC _ TY VFL , D _I_ l V _D GUST 0 -4 -8 - I ? -16 -20 - 24 - 2 11 -3 2 -36 - 40 - 44 - 4 B -52 A _O VE" T O TAL *- TO TL LF 5 _, I I I ,_e } I 60 1 t _, ?0 4 4 1 ,5 R(` 4 9 "4 I 1 7 _ 7 9 0 3 0 | k 4 2 .54 ll6 I00 _ I01 44 9 I 164 _3 4 II0 ? 2 1 1 2 $1 6 171 4 .5 0 1 2_ $ 8 99 2 9 6 I I 19 4 $4 3 130 2n 4 199 4 1 1'5 2 I I 4 63 104 0 14 0 I 49 1 28Z 43 1 4 1 032 |file 1 _0 .5 0 949 ??| ?| 1.5 5 3 1 360 Z86S " I_0 33 1 1 9 4 ?B7 99 12 3 ' _ 15 9L "4 SI 7 1 70 66 q?O t _5 4 1 11 I 1 0 9 4 _ 449 Ill(` q _ 217 73 ? l 2 4 4)0 96 2 19 0 1 9 266 .S R _ 1 "4 Z _ 29 770 2O f) 2 I fib 9 2 2 _ 3 308 6Bfl 2 1(' 2 1 194 11 2 21 _ 1 2 _ .53 66T 2 2 0 5 9 1 95 09 7 ) _ 93 6 9 ?

230 q_ 16 4 ,a le II I 1 310 763 2 40 11 9 ? _ R 76 I _ J | I 4 1 0 960 I t 2 .5 0 14 3 l._O 46 6 _ 348 glO 260 14 1 1 7 _ 6 _ 5 381 79 1 " 270 131 _ 1 4 9 _ 3 4 3 _ ? _ 673 ?nO 1_ 6 11 5 Ig ? 77_ ',5 9 29 0 176 11 2 1 5 _ _ Oq 6 Z _ JO0 _ 10 93 1 3 I JR7 40 1 : 31 0 _ 4 T _ 16 I 1 74 _ 2 4 3 2 0 5 2 A _ n I I 1_9 2_ ?

I 3 5 0 ' _ ' _ 32 2 2 69 1'5 4 340 26 4 ? 8 l 92 1'5 3 3.5 0 5 _ ! I L ?

160 1 0 _ l_ 2.5 3T O 2 ?r;tI L 14 9 1 6,+_ q 23_ J _ q40 I19 2 3 11 _ I 2 1 019 3 23428 T A BLE X II. - C o ntinued VGH hr: 1366 b. Operation 992 - Single Engine Executive Positive Ude Peaks TA R LF 5 r iy O r _ F RAT I ON q q 2 r_E R | VF D GU S T I o( lq ITIV F] V S V r L O CITY VE t . r ) E _ [VE D G UST r ) 4 R 1 2 1 6 2 0 2k . 2 R 32 36 40 44 48 52 AB O VE TOT A L LF 55 2 " 3 1 2 8 _0 I 3 I 2 7 6O I 7 1 9 70 _ q 36 I 0 2 62 80 4"3 1 ? 1 _0 I0 5 2 48 qo A"3 4 R 2 ! 1 0 7 ] I 6 8 6 I0 0 148 6 7 8 7 9 8 I q14 110 I_0_ | 5 79 199 ? 1 I 1 I 3 00 2 120 10 _Z"3_ Z 31 3 Z4q 7 7 2 I I 5856 13 0 11 2 06q 1A 48 161 29 1 2 1 412Z 1 4 0 Z 2 1 9 2 IB 61 ? 28 ? 7 5 431_ 15 0 lq7S 1 6 47 ? 2 4 37 _ 3 891 160 634 3 7 2 49 9 1064 _ " 17 0 1 7 1 0 4 31 18 0 lqO 2 00 210 i 230 1 I 2 40 25 0 26 0 27 0 28 0 2 9 0 3 00 "310 33 0 "34 0 "35 0 3 6 0 "37 0 M B O V _ T O TAL 4"3 1 16 9 0 109 2 1 1 4 16 191 "3 2 7 4 2 2 4 21 6 Nega t ive Ude Peaks T A_ L F5 _ V DP B PA TI ON g 9 2 D F P I V E _ , r , u% r ( _F G A TIV F I VS V FL O C I T _ VF L. F)F " _ l V F 'r _ C , L IS T 0 - 4 - 8 - 1 2 - I b . ?t l - 7 4 -2_ -_ ? - "3 6 -40 -4 4 - 6 8 - 5 2 A BO VE T O TAL *-T O TL LE55 I I 9 '_r rJ I ' 60 ? 2 q 1 8 7 0 1 0 1 9 2 3 6 ! I 60 122 _0 4 2 I 1 5 64 a , 1 22 6 41'4 Q r _ qr_ 41 7 121 15 I 6 35 13 2 1 I00 2 q O _ l _ 12 R 15 I 12 9 7 2 2 11 IlO 1364 1 737 1 7r _ 19 _ . 1 329_ 6 291' 12 _ ? _ 1 51' _ II1 9 103 I0 ] I 2 8 3 6 869 2 ! I' _ 0 13 15 29 9 ¢ _9 105 I0 ? I 272 9 685 1 14 0 1 _ "31 14 18 1 86 IT _ I '_21'9 T S q4 13 0 1581' 1406 Iq9 21 ? I 32 16 1'107 160 5 7 9 30 3 32 6 81'0 1q 3 4 I T O 21' I I 38 69 1 80 I 9 O 20 0 2 1 0 2 30 I 2 _ 0 26 0 t 270 2 _ r) 2 9 0 3 0 0 32 0 "330 .3 60 35 0 ,3 6D 3 7 0 A I_r ) VF _ ' ql AL 3 0 8 714 R447 11 38 126 2 0 1 2 1 I I 18 4 ql 4 , _7 0 ?

68 _

Y _ | !

1 1 T ' ' 1 1 1 I TABL E XII. - Continu e d V GH hr: 724 c. Operation 993 - Personal Positive Ude Peak s TABLF_ _Y OP E PATInN q9 3 D F PlVED GU S T [ P O %ITIV E] V % V FLO (I T Y VF L, D E R IV ED GUST h 4 _ ]Z 16 7 0 _ 4 2 g _2 36 40 44 4B $ 2 A BO V E tOT A L L E_ S 2 4 _ l I 14 _ 0 4 6 1 11 60 1 2 I1 5 2 1 Z 33 70 TO 50 _ _ I E 5 g O 4 Z_4 B I 5 1 3g6 qO 13 _ 52 3 q o 4 T5 2 I00 97 _ 74 |3 2 | 497 11 0 q _ I qO 2_ 1 307 | 2_ _ 91 ? _ R ZO 2 5RI 130 Z43 q 7 10 350 1 An 3 _ B ! 4 3 15 0 S I 6 Iq o 2 00 22O 2 3O 2_ 0 _ 60 2 70 2 80 2 9 O 3O 0 31 0 32 O 3 4 0 35 0 37 0 ABOVE T O TAL qO _ I B3R 3 05 3 2 12 3 ? I 309 _ Negative Ud e Peaks T A f _ ti ' S qY O P E R ATI O N qq3 DE P lV r D GUST ( NF SA T IVF) VS VFLOCI T Y V E Lo DE_ Iv FO G U S T r) - 4 - R -I _ - 'o -_ 0 -24 - 2 R -3 E -36 -40 -_ -_ , # - 5_ A BOV E T O TAL +-IO T L L F SS 7 5 2 I 15 2 9 50 3 3 14 60 ? 7 2 |6 49 ?_ 4 q 5 9 6 114 23 q 90 63 _ , '_ 6 79 IC Z 5qO 1 3 4 2 ii 0 g O l b 2 Z t I 269 5 ?6 I_0 1 2 1 71 5 _ I 200 711 1 3 h 196 _ , R 1 2 6 5 615 IAn ? l q 3 0 73 150 I I 7 t 6r ) I ? o 1 8 o 1 9 o ZO O _0 23 0 25 0 2_0 3 1 0 3 2 0 i _3 0 _ 4 D 3 6 0 ABOV F TO TA L 55 R )414 _ Og 11 6 q 2 | _3_ q 5 4 _ 4 )

69 : }

f I _ , _ | 1 I TABLE XII. - Continued VGH hr: 2 84 3 d. Opera t io n 994 Instructional Positive U de Peaks T An LF 5 B Y o r ' FR A T| ON 9 q 4 f 'ER|vF D G U S T ( P OS ITIVE) V S VE L OC IT Y Vr l * O£gIV E D ' ;L'$ _ 0 ' ,, R 1 7 1 6 7 0 24 2R 3_ 3o 4 0 44 48 5 2 A B OVE TOT A L L ES S 1_ 43 q 5 5 3 2 1 86 '_ 0 46 Bl 35 q 9 I ! I 1 83 6 ri 77 8 2 74 37 I | 2 ! _ |03 70 6 243 9 4 1 4 55 6 I 29Z I 80 9 67 2 16 6 344 4 : 7 l 1 3 52 7 9 0 417 6 17 112 1 5 3 2 tl60 | 00 _ n 15 9 IO 1 220 IIO Z l 9 30 _ P l Z O 2 2 ' 4 I50 i 1 5 0 1 70 1 9 0 20 0 2 1 0 2 30 2 AO 25 0 2 6 o _ - 21q o 29o 3 0 0 _ _20 3 40 3 6 0 ARO VE TOTAL 1 46 3 6 2 16 1 2 53 22 6 4 5 [ 9 B 6 l Z I 9240 / | i _ [ - .

TABLE XII. Continued VGH hr: 2291 e. Operation 995 - Commercial Survey _ Posi t iv u Ude Peaks " i O[QIV F D %U%T (D O S I TI V f l V% VELO C I T Y T_ 3 LE_ mY OP_W_TION _ " , 0 _ A 1 2 16 20 2 4 2 8 32 36 40 44 48 52 A B OVE TO TA L V r L. D £ R [VE D G U S T L F S% 22 2 2 8 2 1 _ 50 ? ! 131 4 5 5 2 ] 2 o _ 7_ 1 6593 2 2 02 3 4 0 6 2 8 92 08 6 0 71 R 52 6 9 5 7 0 l 136 0 _- R O _.... q 51 2 _ 34 , 4 6 , 1 8 5 I ! 1 6 7_ 9 2 2 17 1 5 307_ 4 1423 R 6 1 5 2 2 t 2 54000 l l O !_ 6 13 7 5 ? 26 _ q 8 3 3 20 _0 i I00 21 1 _81 3 282 _5 1 0 2 53 6 J " 120 ? 4 q 525 6 1 | 1 2 8 4 8 |3 0 10 7 180 22 | 0 5 ! J 20 150 63 _ 4 _ 3 17 3 I 1 IP 1 6 0 31 3 0 32 1 9 8 4 3 1 1 2 5 ITO q 4 9 58 31 ? 2 1 2 1 1 6 0 lSn 2 5 1 27 4 4 3 I 02 1 4 0 11 1 175 2 6 5 3 2 27 _ 1 9 0 22 16 6 l I _ 6 20 0 _ 8 2 18 210 11 8 3 22 2? 0 4 7 2 13 230 L 2 ) 2*0 ? 2 2_0 _ 2 7 0 28 0 29 0 30O 3 I n 3 _0 31 0 ABOV F TO T Ik 3 1 E 9 9 94 856 1 _ 4 5 8 1 2 6 3 1 7 9 3 5 17 6 3 1 1 414 17 Negativ e Ud e P_ a ks TA _L F % PY O P E _ & T I ON q q S n F_ F t _ G U ST ( NFG A TIV_I VS VELOC I T Y VF L . DE R Iv fr _ GU ST - , o - 4 - 8 -12 - 1 6 - 2 0 -24 - 2 8 - 3 2 - 3 6 - 4 0 -4 _ , -4 5 5? A B_ VF TO T A L * "_O T L LFSS 1 4 I_ * 12 I I I 4 3 g O _n 6 7 8 32 9 1 | 12 7 332 60 & 2 9 3 5 4 R 2 12 2 _ 7 9 2 2 _9 70 I _ 5 _ 4 .% 16_5 308 4T ? _, T lO 0 1 6 3 06 80 64 P 8 399'_, 80 84 115l £ 48 25 8 t 1 55 5 5 0 1229 42 9 0 16_6_ 331 2 4 595 6 6 27 _ 4 9 3 " % 6 56 6 8 _ 110681 10 0 101 2 6 93 5 0 12 10 9 26 1 1 B g qO 143 _ lln 8 52 2206 '_1_ 4 9 1 2 _ 2 I 3 4 35 S .% %5 lZ_ 9 3 1 4 3 ? l 3 2 6 0 1108 1 30 153 lB_ 11 L 1 3 5 _ 6 T_ 1 4 0 1 44 101 2 2 6 2 I 5 2 8 1 35 3 : 150 5 3 4 0 5 9 15 7 6 I 181 363 | 60 22 '%0 78 _0 1 3 9 2 194 3 2 2 ' 1 7 0 4 46 _ 2 1 6 fl I 2 1 1 I 11 2 _' 72 180 2 16 8 .% 3 _ 1 25 9 2 I _9 _5 2 0 0 1 3 2 5 _ 2_ 41 210 2 5 2 _ 31 ' 220 3 ] 3 ; z o r 230 I 2 2 2 T :0 2"% 0 I 1 3 ! _ ' 2so r 3 0 0 '. . 3 10 $ 3 2 n 33n 3 4 0 3SO 36 0 _ : 3 T 0 ASOV F •- _ , T O TAL I 25 6 _ i 5 fl 83_3 176 44 2 4 f _ 0 tR A 6 i _ 2 4 5 _ 7 ? 9 13 4 6 12 2 7 60_ g ' } 71 ' s i 2 , :" T ?, _J.E XII. - Contin a ed V G H Or: 484 : f . Operation 996 - Aerial Appllcation Positi v e UJe Peaks • , T_kf' ) o_ O _ F _AfION 996 nF o I,_r£ 6U_ H ) '_SI_IV t _ V$ VEL O CITY _ _ LZ l b 7 0 2= 7 _ '_ 3_ 6 0 4_ _ 5 Z A _O VE Tg T _L LFS_ _ o 3 2 1 6 ; t O _T L _ _ 1 67 Qg 11 l 111 t _ O _ _ 1 9 I](' I 1 } :- I _ e r , _ . |£t ' I; ( ' , - 2_0 _60 ] 6 0 )T0 T_IAL _ 1 6 @ 6 ] T _ 2 Z_ N_ g ati v e Ude Peaks nF_IVF') (, A _t {Nf C , k T I Vt'_ VS V TLO CI T Y vFL, DE_ T V_% G US T 0 -_ . - '_ -12 -1 6 - ? 0 - 2 _, -Z_ -'_ ? - )6 -'WO - _._, -_, B - 5 2 A.40V lr T OTA L ,-T OT L t FSS 6 0 _ _ I 6 IZ 7 0 _ 7 h 0 l I _ 9 1 2 6 _n a ' _ 11 1 g S 206 In o 1 2 ) 1 2 ) ) n I 1 2 0 Z _D 16 0 I 7 ( I l p O + lg r _ 2 0n 2 1 0 2 _( ' } 7!10 2 4+ 0 t ? _ 0 L _ _ n lo o ] t o _4C s 4 6 0 " _ T _ ' _ flO VF T O TA L I 1_ 7 2_ I ? ] 1 I T _ _0_ ! ! t TABLE XII. Concluded VGH hr: 1510 g. Operati cn 997 - Commuter Positive Ude Peaks T AR L E_ _, Op+ F nA r ] ON _ 9 7 ' PlV F r G US T (PnSITIVrl V$ VF L O C I T Y VFL , [ I F R l V ED G'JS T 0 _ , _ I_ 1 _ ?0 2_ _R ? Z 3 _ 40 4 _ _ * q 5 7 , ' ,BOVE T_ TA _ L F S% _n 2 I 3 7 0 _ 2 8 0 2 _ _ 9 Qn R 4 _ 1 1 1 7 I On ? 6 Z i 1 _ llO 2 8 IZ "_ I I 4¢ 1 1 Z O " _ 6 flq _ 7 _ 2 3 l 1 17 6 1 3 0 Ib 4 1 3 7 48 q I 2 1 I 3 6 _ laO 4R4 1 9" _ 44 8 2 2 I 73 4 i_ 3 18 176 Zq _ 1 1 5]4 160 III 1 1 8 2 3 8 2 2 6 2 17 0 IR I 1 3 9 36 b 5 I I }69 IRO 4 1 9 2 2 1 _* 0 1 4 _ * 2 700 laO 6 ? 8 1 97 2 0 _ I 9 00 20 0 20 1 6 ° 1 4 9 I 1 _ q 5 _ l n _ 11 2 I 6 8 _ 2 C Z_O ZS O ZS O ]00 ]I 0 ]20 T O TA L_ 2 66 ¢ ) IS q } t1 _ R 1 11 14 _ I l l 449";' N e gativ e Ud e P eaks T_I E _ Q Y D t _F_ TI ON c _ c _ 7 DFPIvF_ _U ST CN F G AT IV_ ) V 5 VF L _ C l ? v Vrl * DEF _IV FD G U S T - _ , - R -1 2 *1 6 - ? 0 -24 -_ r -3 t' - _ -40 -44 -4fl -5 2 A BO VE _OT_ ( _ * T O TL L r _5 g C 6 2 Z _ 2 = I1_ 1 6 1 8 " t 4 6' _ I I _ l_O I '_ 1 51 3f t _ a.a b 6 9 9 l_n ' _ q Z 180 62 t 7 3 3 "_'7 _ 6 I 1 60 1¢_ 6 Iln 7 0 7 1 ;' _ " , 0 6 17 0 | fi _ 1 66 1_ 8 6 _ _ 74 76_ 1 R O 3t9 ? 36 % 1 1 4 b 2 . ._ 6R I _1 ,4 _ _ I R A 6 _ I h 7 7 4 7 _ _ ' Z ? l O 7 7 3 I "_ 1 '_ q ? ZO ? 2 2t_ z 2 p 6n 3 2 n t 4 t l &R O V t , ' :,_.'_TTT v OF' T_4_ 73 l i s

7S

. d_ | I ,, _ ' I I I I , 1 0 1 o.,_ - _ .......... 1 .....

_o >,o " '' l " , i i I r ........ ........ , _ . 1 e J _ . ¢ . ,_ ....... ; . ..;-._ .... , ........

Zl N I,-,_ _ iL 10 fl _" o _ _ _ u I , , ' :: ' I _' [ .... ,......... I....

< , _ o -_. _ !!!i :": : : " ........ : ....... :!: : ': _, __._ _ ..... _._ ._ ....

_, _ I ,'_ 'J U _ " T .......... [ .... ! " " " ol _ o c: _ _,_ - -T _i : _ _ L. _ . ..........

• "4 _ > , _" u _. _-_-_ L_I-"< L_ ' ' _ , ' ' I!i ' !

"= "- °i l i!; / _'' i_ _

, -_ i t ) ::'=-_- ._ . ': lk.:" ::: :: "'- . " ....... i ...... - " " " -- I , , I , , ,I-T7 I........ + ..... -- 2 _;5 10 -3 I _;_-. ._ : _, : _ . - L - .... _ - • ........

.............. ' , 2 ........ J - ....

_. "-T ................ T T ..... i.....

I0 - 4 i It ' ' : " , ' , ] i ' i _ ,' ' ''' i , I ' -_-_:-_ 1 : : __: Jc l _"2 : : ' : "_ " - .... ._:. :-i .... " -5 :- ,_., . ___ __-__--: __ _, •-_-_-*. _ . . E-:. t _:I-L:-7." 44-i ..... "-- -_ "- 7_Z : _-;-_i!t,t_, _ _4i ........ _L ] "" ' ..... +-'" - ' . -1 " 2:: .-: -, : rT- _ : _ z __ .._ , _ _ , .., .......... _ ; _.! :_: ...... ; .__.._ ....... __-__ ..... ..

i I ' i i I ' i ? , : ,_I , ' '

_o ,l,,il" _ iiiilt _ 1!I: I . I,, , Oil II

' -3.0 -2, -2.0 -I.S -1.0 - .S 0 .S i 0 I.S 2 . 0 2,S 3 . 0 3.S GU S T LOAD FA C T O R S A N z Figure 17. Gust Load Factor Cumulative F requencies in VGH Data ) t 1 I 1 1tl 3

° 1 I

° 1 1

. _

__ _ ._ .... \

l .... I " [ .... [ I ........ 1 _

"

: iii!! ':! ',':?',: I , i

i0 "4 • , : , ......

-3.5 -3.0 -2.5 -2.0 -1.5 -_.0 m• 5 0 .5 I .O 1 .5 2 , 0 2.5 3 .0 3.5 4.0 MAN E UV E R L O AD FAC T ORS Nz , a. Frequen c y per ttour Figure 18. h;: . neuver Load Fa c _3r Cumulative / requenc_es in VGh _ata I , ," I l i I i l I i ] ! • I 0 ILl

I

-4I lh -3.5 -%.0 - 2 .; -2.1) -1.5 -i.0 -.5 _ .5 1.0 1.5 2.0 2.5 3.0 3.S 4.0 MANE'JVII!_, LOAD FACTOR._ N, b. Frequency per Flight Figure 1.8. Continued -5 : : :! : I" i0"6 -4.0 -3.,5 - 3.0 -2 , S -2.0 -l.S -I.0 -.S 0 .S 1.0 l.S 2.0 2.5 3.0 3.S 4.0 MANEUVER LOAD FACTORS N z

c. Frequency per Nautical Mile

I

Figure 18. - Concluded

The Aerial Application category has the highest fre- quancy of maneuver loads with i00 peaks per hour above 0.5 nz, one peak per hour above 1.77 nz, and one peak per hundred hours above 2.38 nz. The Commercial Survey and fnstructional cate- gories have the next highest frequencies at all levels up to 2.5 n z and the highest frequencaes above 2.5 nz. The most ex- treme negative maneuver load of -1.9 n z was rec o rded by an air craft in the Instructional category.

2.6.4 Landing Impact Acceleration Ratios The cumulative frequencies of the positive impact ac- celeration ratio, nz / 2.67, per landing are presented in Figure 19. The 2.67 divisor is the minlmum ground load design inertia load factor specified in Reference 2. The largest landing im- pact acceleration was recorded by an aircraft in the Instruc- tional category but the highest frequencies at all nz / 2.67 ra- tios below 0.95 were recorded by aircraft in the Aerial Appli- cation category.

2.7 Landing Impact Probabilities The An z values in this section are the initial positive • m x landing impac_ accelerations recorded during each landing impact.

!

With the An z s grouped in 0.1g increments, the data represent the combined values from operational and checkout flights.

Since the recorded Anz'S are the initial positive values, they may not be the maximum values that occurred during landing impacts. Therefore, che small percentage of occurrences in the Ln z range from 0.0g to 0.1g were excluded to make the frequency distribution for each operation more realistic. Further inves- tigation showed that these exclusions would have had negligible effect on the analysis.

Table XIII summarizes the nur_her of operational and check- out landings for the aircraft types in each operational category.

2.7.1 Analysis The ext,Jme value theory discussed in Reference .5 was used in the analysis of the frequency distributions of landing , impact data. The theory provides a limiting form of the maximum value distribution; this form is a simple analytic function.

This section outlines the procedures used in deriving the fre- quency distributions and control curves, and presents the sta- tistical data. Table XIV lists the symbols used in the follow- ing discussion.

8!

1 1 1 l 1 1 !_._,¢.t !lit t[Jt ! :' ; if!: _ SYM OPERATION i_ iI f t i i 1 l t , i i i i t 1_1 !'11-lilt ._/.i,, :'kN_.'_ .-_', ,: .... ,',; .... ; .,':-' ,:_ _i'. O T win-engine executive ' :i_ _N_;qP_q 4 .: -_., _i_.t'.._.i_ i:.: A Single-engine executive "_ _J%-!-.. _'i_r " _ r_ i.c_irl'_, ,7 ¢ i ! _ i 1 ll d %''_i- i _.: : ! i i ' l ;_ [i iii11, , _l] lil:l !_i [_JLIJ_ n Pers o nal _: , !itl _ i_._-'_ [':il tlitl!':!ii!i _ Instructional ..' .i{_i XKK_ ':\'[ 'i_l_i,ll! :: [l!!'

' .;: .:_[_*_'_\;:._L::I.t.. {l!ii:t-;i{ 1_ Commercial sur v ey

_':!IiN:_N ' N'N_i }:; ! Commuter _t! t i i!) ' : 0 Aerial applicati o n 10-1 '1_'.,:._,"¢_ ; " " ' ' ':i : 7:1 i¢ '

' \:x\ _'x t;ii!l!::!i

'i i " I' [i}.:l i i'i.! :' l"il ! I I ''1%. it7-'ll fi'! " :" " t' , i _ " , I ! : .i , .

. r.....

:-=-" \ ; _ . _x

• " i

.... t "- +_ _ ....

" ; ; .... . • :', , ,- --

_ , ,.-7.. _ _ 7 r

• 'i i

:I . .: i ':l' : i;"l ," _ _:, , I, i _ _ _

; . _7--i- 7 : '--.- -- -.--- r. --:..,- _ --

.... _ :-1- ! .--. !_ ......._, .

1 I 1 ':" • ! !

I ..... I ...... t

10-4 t . 4 .5 . 6 . 7 . 8 . 9 1 . 0 1 . 1 LANDING INPA C T LO&D FACTOR RATIO nz / 2.67

Figure 19. Landing Impact Acceleration Ratio Cumulative

, Frequencies

I i i I lllf' 1 i i l ! ,

TABLE XIII. SUMMARY OF OPERATIONAL AND CHECKOUT LANDINGS BY

OPERATIONAL CATEGORY AND AIRCRAFT TYPE

N umber o f Landings , Operational Category / Op e rational Checkout Aircraft Tzpe Flights Flights Total Twin E ngine E xecutive Totals 2975 422 3 3 97 Air c raft Type 1 749 164 913 Aircraft Type 2 595 63 658 Aircraft Typ e 3 !67 31 198 Aircraft Type 4 504 23 527 Aircraft Type 5A 960 141 1101 Single Engine Executive Totals 784 36 820 Aircraft Type 7A 108 0 108 Aircraft Type 8E 260 10 270 Aircraft Type 9A 382 22 404 Aircraft Type 9C 34 4 38 Personal Totals 1642 0 1642 Aircraft Type 10A 260 0 260 Aircraft Type ll 256 0 256 Aircraft Type 12h 1126 0 1126 Instructional Totals 4422 0 4422 Aircraft Type ]3 1904 0 1904 Aircraft Type 14 73i 0 731 Aircraft Type 15 236 0 236 Aircraft Type 16A 1104 0 1104 Aircraft Type 17 447 0 447 Aerial Appli c ation Totals 1245 0 1245 Aircraft Type 23 921 0 921 Aircraft Type 24 324 0 324 Commercial Survey Totals 671 1 672 Aircraft Type 9B 293 1 294 Aircraft Type 16A 378 0 378 Commuter Totals 4977 15 4992 Aircraft Type 26 2621 i0 2631 Air c raft Type 28 2356 5 2361 TCTALS 16716 474 17150 • I" .

J TABLE XlV. SYMBOLS USED IN LANDING IMPACT STUDY statistical parameter of extreme value distribution u statistical parameter of extreme value distribution v reduced variable, defined by y = ,(x-u) x random variable • . F* _y) l-W* (y) i_'* ( ) ' / cumulative probability distribution of y, defined _.

as e -e-y t n number of maximum values ::: number of valuL in order from smallest to largest t" nt.mber of occurrences in a L_nZmax band (_ ' n_ reduced standard error of ruth of n values Ill Vde derived gust velocity 'l{x) return period, number of occurrences required to equal or exceed a value of x c Iiuler's number, equals 0.5772 (c / _) S m standard deviation of mtb value, equals m a , / -_n a bar over a symbol indicates the mean value of i the variable 2.7.2 Eguations and Procedures The following paragraphs present the equations and pro- cedures used in calculating the extreme value distributiens.

After the raw data in Anzmax bands of 0.1g were first summed frcm largest to smallest banS, a relative cumulative frequency was calculated. This frequency is represented by the symbols (Q) in Figures 20 through 27.

-- -- 2 The mean values Anzmax and Anzmax were then calculated by . 2.f Z Anzmax f Z Anzmax _n = and -- 2 = Zmax n 5nZmax n where the Anzmax values are the midpoints of the 5nzma x bands.

The reduced standard error was then calculated by - 2 ( _n 2 I / 2 (o ¢ _)m = [Anzmax . Zmax) ] Next the statistical parameters of the extreme value distribu- tion were computed by 1 _ ¢ _(o ¢_)m u = _nZmax - I /a (0.5772) Then the redu . :ed variable distribution was computed by y = a (anzma x u] From the foregoing computations, the cumulative probabilily and corresponding smallest value for the probability distributions were calculated by _e-Y ,_ _ ' * (y ) = e F * (y) = t W * (y) The sn, aiiest _alue for the probability distributions of the re- ' duced variable were then plotted as solld lines in Figures 20 thr o ugh 27. Table XV presents sample calculations for _rbitrary data.

I 1 ] 1 1 i0 4 - - , - *' [ , -, 10-60 [ .4 .8 1.2 1 , 6 2.0 2.4 i i LANDING IMPACT ACCELERATION, g Figure 20. La n din g I m pact Data for Twin-Engine Executi v e Cate g ory

't

i:, ;;_ * P_i:ti' t : la_,ding_Imoact Da*a " ' ' ;--{,7}-1_ OS l ngle Eng. E_,'c. 816 L--d ' gs 't

I L ' il I! I , _

i._ i:11 ' ,r i _.._] • 00 !_:_ ::i!: .. , .......................

+ _ " t ' _ - " ;;* t : " + ' : ' " * ........

/ I x, r : " ,7_i ' ,', :1 ,_/ ' /I,I _' _1!i:7/',,: , ' , ' l':i:l I :]_-T , ! _-_ _.,treme,,,_'alue. Distribution, ' '1 ..' .I , I ' ' . ,, mIll / lll'i 1 Iii I;, :1 ,: , _ I i L_ | | _ i i .... i ' ' ' i . i 10-1 i !! I', iv , ' ' t ' ' ' " * - -- -ft -_ t' + :_ '-t t * ............... ' ' *

-:T::]{:I' L.... _ r

i " _ I _ 1 _ , ] , I i ' i , ! ' '/ +-l& 2 _g_l-2- ) -.-i ....... I*_L_- - 4, .- I ....... _ 4 -, • T" T , , _ ' i I I i '

_ ..... , r , v / \ _NJII !,t ,,1_11_i l ,' , Jl , : .... ,,: , /

q + }l l t r 1 l

_ - i!v_'_ ; : = ! ] : : ; ' I : .... 4- . .'J .4

_o 2 :!! i'i] I II I I : _': _ ' :' ': -

..... :::: ..... i:._ : ::_k : _"_: : :t'tl::;: ;i::l: ; :: : :: : ,:_

i _- _221-:: " : :Z. _e,_ ! , -

< ,:l, ::, :: >' :'_!-

...... ( ii

_+-'--_ .... #.................. _7: ::- : : :::-.b_ °> - :::: A

2-2 .E._2_--_1: 7 _.27 ......:- _-_: - - -:x- r 7

" ,_ _'_K_LI. a .'_ A _ ' .... ' '

i: ,. I.i, _': i i_ ..... ' _i !, k ; I ,,i

...... IX '

" I i I I ' : : [ .._-a-4 : _- , ,I1_ - i i '. :\.

l 0 S ' _ [ ' _ ' ' Ii _ ' , _ l' _ ' ' ;, ' I [ ' [ _ I ' .... l .... ] ....... _7: '

i: I"" : , , _ '" ,] L',_!' '_ ' ' "

fill Iii ,',! ',l:! i! I/ I', I', x , : ,

6 I [!/:]L: _:I L .L_''iil , I Ill_ . , _1,,,.. ,: ..... ._

1 0 0 . 4 . 8 1.2 1.6 2 .0 2.4 ' l A NDING IMPACT ACCELERATION, g

Figure 21. Landing Impact Ilat;, _or Single-Engine F.xecutive

Category

i -S i0 1 0 " % . 4 .B 1 .2 1 .6 2.0 2 .4 ' L AND I N G I M P ACT ACCEL E RA T IO N, g Figure 2 2 . La n d ing Imp a ct D a t a for Pe r son a l C a t_gory

&. "_

| ! _ ! I | I

Figure 24. L a nding Imp a ct D at_ for Commercial Survey

C a t e gory

9O

i

I L a nding Imp ac t Dat a OA e ri_l Kppli c ations lZ 4 5 Ldgs i0o 'I 10-5 ilt ' I0"0 . 4 . 8 1.2 1._ 2. 0 2. 4 ,i LAN D ING I M PACT ACC E L E RATION, g !If , ] Figur e 25. L a n d ing Im pa c t Da ta for Aerial Ap p lic a tlons Ca t eg o ry : .

I 91 : -i I I I t

! ' !

Land ing Impact Dat a 0 C o m m ut e r 4 666 _ d gs 10 0 -6 .L0 0 . 4 . 8 1.Z 1 . 6 _ . 0 2.4 t . L A NPIN G I M P ACT A C C E LLRATI O N, g

Figur e 26. Landing I mpact Data f or C o mm u ter Category

i TAB LE IV . S A MP LE C A L C U LAT IO N S F O R EXTR E M E L AN D I N G IMP A C T P ROBA BILITY D IS T RIBUTIO NS . ,it 9 Zmax An_ An . f An " "f l{aud -max f c__f Pr (f) Z max z max ___Z_____ 0.1-0.3 0.2 53 87 1.00 10.o 2.12 -0.350 0.758 0.3-0.5 0.4 24 34 0.591 9.6 3.84 1.486 0.203 0 . S-0 . 7 0 . 6 10 10 0 115 6.0 3.60 3.321 0. 0 35 A--n z = 0 . 301 b--fi z Z = 0.110 max max z (o C n)m = 0 . 139 i /a = 0 109 u = 0.238 With a breakdown by operational category, Table XVI summarizes the maximum impact An z for each landing in the entire data sample by listiILg the number of such occurrences in the respective An z bands.

After the extreme value curves were developed, a method was needed to measure the reliabilit y of the sample es- timates. As indicated in Reference 5, the "control curve" method derived b y E. J. Gumbel provides a simple and rapid method of indicating the reliability of extreme value distr_ butions. With this method, the standard deviation for the different curves at various levels of probability is calculated by

[q / E)

n Sm - a, / 'n The extreme value curve plus or minus the standard deviation gives a 0.68 probability, and plus or minus two times the stan- : dard deviati o n gives a 0 .9 5 p r o b a bility, that a sample value lies - within the interval, For the ultimate value, the interval about the distri- : . buti o n f o r 0.68 pr o bability was found to be , 1.14 ±Sn = for 0.95 probability 2.97 ±Sn = -- The p en u l t i mate 0 .58 a n d 0 .9 5 pr o ba bi l i t i e s w ere foun d t o b e _ 0.754n 1 7 3n ±Sn_ 1 __ and ±S n_l = _--_ / _ re s pec t iv e ly.

The con t rol in t ervals were ex t ended a lon g t he ex t r a p- ola t ed por t ion of t he ex t r e me value curve sinc e t he in t erv a l around t h e m os t probable lal g est v a lue does no t depend on t h e num b er of occurrences.

T ABLE X V I . MAXIMUM LA N DING IMPACT LOAD OCCURRENCES I N A n z " B ANDS BY OPERATIONAL CATEGORY Operational Category Twin Single _n_m .. x Engine Engine Aerial Commer B'_n_' lixec Exec Person Instr Ap.j_lic Survey Ccmmut 0 I-C , 2 500 71 2 53 303 50 144 1516 Ii 0 2-0 3 1117 202 463 1304 187 206 1528 • _ , 0 3- ( / 4 876 188 367 969 268 129 845 ._ 0 4-0 5 495 153 228 676 246 84 458 i: 0 5-0 b _34 89 123 375 168 47 206 i " 0 o-0 7 96 67 75 203 111 25 84 0 7-0 8 38 24 2 8 114 73 13 21 0 8-0 9 22 1S 16 99 48 5 4 i : 0 9-1 0 5 4 16 ._,,_ 37 5 3

t

i 1 O - ] 1 5 1 7 32 19 1 I-1 2 1 6 32 13 I I _ 1 3 2 1 24 14 I 4-1.5 7 4 I q-l.6 I 2 i I i 1 3-1.4 !0 6 1 h-l.7 _, 1 7-1.8 1 . . I ' OTAL- n 3389 816 1584 4407 1245 656 466b

i

2.7.3 Design Load Factor

In smoothing the irregular probability curve of the

recorded data, the extreme value theory provides a consistent

and rational basis f o r extrapolation beyond the li m its of the

recorded data. Since the frequency distributions are of the

exponential type, the numbe - of occurrences required to reach

or exceed a given Anz level can be computed by

l og e T (An z) -- _ ( x - u) (R efere n ce 6 ) o r T(Anz) = e a (X - u) = ey Using t h e s e e qu a t i on s a n d the da ta f r o m Table XVI , t he number of landings required to reach o r exceed the minimum desig n impac t load fact o r o f 2.6 7 g can be determined. Table XVII presents t hese totals f o r each opera t i o nal categ o ry.

T A BL E X V II . LAN D INGS R EQU IR ED TO R EACH O R E X CEED MINI M UM D ESIGN L OAD F ACTOR Ldgs to Re a ch or Ex ce ed • Operational Cate gor y_ Min. Design Lo ad Factor Twin Engine Executive 269,297 Single Engine Executive 19,295 Persona l 19,554 Instructiona l 3,393 Aeria l Application 860 Commercia l Survey 8 1 ,321 Commuter 1,507, J 2 1 Composite 14,739 2.7.4 Low-Range Occurrences As mentioned previously, the occurrences in the 0.0- to 0.1-An z range were excluded in the extreme value calculations.

The following discusses the effect of these exclusions on the frequency distri b utions derived.

Table XVIIt lists the number of anz occurrences omitted in the extreme value calculations and the c o rresponding percent- a g e of the total landxngs for each operational categor y .

_ On th e basis of _he p e rcentages in ra_le XVIII, the extreme value distri b utions for the Commuter category were r e - calculated with the 5nzmax occurrences in the 0.0g to 0.1g ran g e.

Figure 28 depicts the curves derived with and without the low- range imp ac ts . As apparent, t h e difference between the t w o ex- treme value curves is negligible. The contr o l curves were not derived since they would reflect the same magnitude differences.

: The high a cc eler a tion values be tw een 1. 2 g a nd 1 . S g would not be present if m o re landing data was avail a ble.

i I 4 _, I j

L

i TABL E XVIII . SUMMARY O F 0.1G TO 0.2G DAT A No . of Percentage of ' Operational Ca te gory Occurrences Landings Twin Engine Executive 8 0.23 Single Engine Executive 4 0.49 Personal 58 3.33 Instructional 1S 0.34 [.

. Aerial Applications 0 0.0 Commercial Survey 16 2.58 Commuter 326 6.53 2.8 Airspeed Practices As calculated from VGH airspeed data, the probabilities of exceeding _he design cruising speed ratio, V / V C, and the desi g n _ dive speed ratio, V / V D, are presented in Figures 29 through 35 and Figures 36 through 4 2 , respecti v ely. In each figure, each symbol set represents a particular aircraft in the operation I t y pe, and the dashed line indicates the average probability for i the ratios at incremental V / V C and V / V D levels.

_ Although 17 o f the 24 a i rcraft t ypes had airspeeds above VC, none had airspeeds above VD. The highest probability of a ! Vc exceedance is in the data for the Personal category. T he highest V / V c ratios , approximatel y 1.2 , are in the data fo r the I Instructional and Commercial Survey categories. The highest V / V D ratio, approximatel y 0.925, is in the data for the Twin- I Engine Executive category.

Based on the Unusual Events VG da t a, Figure 43 presents : i the probability of exceeding t he V / V D ratio on a log-normal scale. For each of seven of t he operational categories, the • curves are average probabilities at incremen t al V / V D levels.

The maximum V / V D point in t he curve for t he Twin-En g ine Execu- t ive category represents only one occ u rrence a t t ha t level.

The high values in the curve for t he Instructional category • are based on seven airspeeds with V / V D ratios at or above 1,0 as recorded on t wo different aircraf t t ypes• For each of the seven operational categories, Figures 44 through 50 present histograms of the percenta g e of flight time spent in airspeed ranges for each aircraft type and the air- craft composite in a cate g ory.

I I

F igu re 2 8 . L and ing Impact D_ta With a n d Without Low-R a ng e

Impa c ts £or Co_ ; ,at e r C a t e gory

._ 98

i I ! 1 ! !

I . 9999 SINGLE ENGINE ..... 1 ........ _ .... _ . l I , , / , I , ' : ' '/ ''

1 _'_ . . ill, I !?:. : , o z37.z

i :iitiiii! ; ;it N: o

. 99 .gs- " '_ " ..... -_ !:_'- ..........

................. _ " * ? Z ......... _ ., _- . +4.... ' ............ 44_ ....: LL L .: L ....

_ ; t_ t _ / ' t *_* _'T,_, _ t t } "1 " "- 7 ! t t ': _- : '. "'±t.'T'_rt't t • _._, * ....... t .... 11 t_ * t .... . ............

g . 8 o....l................... - ..................... z,_ _ :. z_ :::_.: . :tt:: .......

t...................... t .:- .:£ F':_ 5

o .S0 _+t_r ..... " ................... _ '_- "-'-'_i--_l_*"-_ .... t',:,_., _-il_*+_ : :_ :: :tl-..:._- t :::: ::::::::::::::::::::::::::: : :: : :::::::::: _:_ :::_':' ;;:_ _ ::::::::: ' ::::-.: :;:: :::: :::::::::::::::::::::::::::::::::: ::::1: ':: : ,::] .... : :::::::::::::::::::::::::: . ..a ::x:::: :::: i:' _ : :_-: / _:: !:::'.::!i:::" ::: _ : ] : : !:l:!-.. . ._ : i':ii_i'_=:-'i : : " ; . :_ :ii_ ::: " :::: :::: :: - :: :::: i::: ::::i:.::-,:L: "::: :::: :::: :L:: ::_ ::'.:L'" X_::_:: "' " : :: " 't .... i....

j i ..... : ..... :-L. a,: .,'. ,- 4 "'z.. ,.: ....... : ............ _.. ,Li __,L L/ :

.o_ _i::i_t_:!_!_;_ _:i_ _: ::_ i_:_:._::_:_.:.:_i.:,._1:_: :!i:ii!_ i : _i,i!i,!!!!

. 01 ..........

_._: |!i_ II ii /I!!! ili: i . !,_]!l', iU _]J!!! [[!

.ool _ _H!t_;_H!__i_,4{,_,:_.!__ ,, •

"0 001 . 2 . 4 .6 , 8 1.0 v / v c Figu r e 3 0. P ro bability o f E xce ed anc e Vers u s V / Vc for Si n gle- E ngine E x e c u tive C ategor y i00

Figure 31. Probability of Exc e edahce Ve r sus V / V c for

Personal Category

iOi

1 i , ' J - , { i {

Fi gur e 32 . Prob a bility o£ E xceed a nce Versus V / V c £ o r

Instructional C a tego r y

1 .02

i 1 '1 T _ 1 ' t i ! 'I ) l ! i I I , i ,, _ ! I v , | I J .... a .....

VG H Data . 99 . 9 8 R . 9S .uO01 . 4 .6 . 8 1.0 1 . 2 v / v c Figure 35. Pr o b a bility of Ex_ e edanc e Versus V / Vc for Commuter Category : .9999 •_ TWIN ENGINE l ; EXE CUTIVE '-7

]

S ymbol llr s .999 O 8

D 0

A 4

O 8

O 1 •

. 9 5 I .90 z

.80

X o .50 o _ . . 2 0 ,10 . O S .001 • . 000 1 .2 . 4 . 6 .8 1 .0

,, VlV D

Fi gu re 36. Prob a bilit) o f Exceedance Vers u s V / V D for

T win- E n g ine E xe cu t ive C a t eg ory

, : 106

!

. 999 9 PERSONAL Symbol Hrs . 9 9 9 0 2 38.7 [] 209.4 A. 275 .4 .99 723.5 . 98 o . 9 .ooi .0001 , . 2 . 4 .6 .8 1.0 V l v D Figure 38. Prob a bility of Ex c eed a n c e Versus V / V D for Person a l C a tegory I

i

• I .00 . 00 0 .2 . 4 .6 . 8 1 .0

v / v D

: Figure 39 . Probabilit y of E x c ee d ance Versus V / VD for

Instructional Category

¢ .9999 A E RIAL__ APPLICATION Hrs .99 (. O 2 : 8.7 [] 309.0 59 7 . 7 •9( . VGH Data .9 8 Lii ' .o_ .oi .o01 .0oo.1 . 2 .4 .6 . 8 1. 0 ' V / VD

F i g ure 40. Prob a bility of E xcee d a n ce Versus V / V D for

Aerial Applic a ti o n C a te go ry

ii0

i , iii I I I i ,I, i- i i ,I l . 99 9 9 COMMUTER S zmbol Hrs 0 59 4 .5 • 9' ) 9 [] 914.7 1509.2 VGH D ata .99 .98 , .95 . 02 , 01 ,001 .0001 .2 . 4 ,6 , 8 1.0 t V /V D Figure 42. Probability of Exceedance Versus V / V D for C ommuter Category ' 1 I l ] .99 9 :"' :" iT)i: " i -..:-:: _._ ::-:: ::':I'::" S y mbol '0"Rerati'o__n Hours .J: ..;':::I::::[:: .,:" .

t ' .98 "' t' "_.:I;:" l . : _ _ t_:_ : : ::::i: Q SEE 8430 • 95-- : " 0 INS 1 0 357 ° ' : : . b, CS 26034

.9o. ,i .... \_: _: :!i : - '- -- 0 _ iso3

• :-I: " : " " " .'_, : _'[::':i:::: t : " i A CO,',I 1992

z .8o , i_

i ! ^ [_!i :_x:::_: t = '-::'t :!::

o <o _: _'__--_i. :-i:l:_.:f_ : _

' i : !i

.lo . . . " '"! "

.o_, :. . .... _ :!::ii!:::!t! "

!. X_t.:q:. :!_:!!: .:..: _ :: _i _..:: -..

...... _::_ :t!:i! ............... ..-=.._-

--:'i "" :; ! .:'T;.!; : :I; L 'I;:;:I:'::I:"'I;;T:I;Y:I"t;'"I" : I

...... _.......... : .......... _ - '_ l og V /V '.......... _ A :_L,-_ ....... ___.+/ '_./,,_._.

.0001 -.IS -. i -.OS 0.0 .OS C .

.7 .7S .8 .8S .9 .95 1.0 1.05 1.1 V / _, D

Fi g ure 43. Probability of Exceedance Versus _ r/ VD for

Unusual Events VG Data

1 O 0 __ . ,-_-,..

Twin Engine Executive-Composite 75 (3375.7 hrs. ) SO[ 32,3 25 L _15 . 9 1 4 .0 0 0.2 3.7 9.4 8.1 8.4 4.7 2.4 0.3 A / C Type 1 b S0

:s 16.4._.° v ...9, 22.7 I

5.6 6 2 6 7_ 11.0 _ 3 ^ • I 0 0 . 1 . - .-.-:.-.--. - .-...._..., : .. ........ ........-'......-. .::::.:.:.:.:::::.: " " O 4 _: A / C " t ype 5A - , 75 ._a2 5 1 0 0.4 o A / C Type 3 < z 50 39.2 38.2 _a 2 1 i:::!.>: : :i .:. i:i , 8. 4 A / C Type 2 7S -

I

75 70 . 1 A / C T ype 4 , :.., ' ,'. , ;:: ' ::': 2S ( 7 5 3 " : : :' : ::: : : .::::': ) • ' ::i :::i:!::: "i:.: :' I . 4 / ' 0 LESS S 0 80 II0 140 170 200 230 2 60 290 320 350 380 ' INDICATED AIRSPEED (.KIAS) Figure 44. Pe r centage of Time in Airspeed Ranges for Twin-Engine Executive Category e W L r ._ 1 5 07 5 00 " Sing!e 4 6 E ngine. 4 (1366 E xecutive' 5 hrs . ) - C°mp°site • 0 0.I } A / C Type 8 • 75 u .l _ 50 42.6 - A / C T ype 9A c < 75 _ 65.8

iii ii::ii iii

u = _ 50 r !?!:.i!!%ii_i!i::li!_i: . ........: . .....:....:.. •• "•• " . - .-•,.•.•- --i:_:_:i:i:i:i:_:!:_:_:!:i: ' A / C Type 7A 7_ J 50 4 1.5 4 1. 4 _ : , 2 5 : ........... : ': + : +:' : ' : ':':' : ':-.-.......,.-.. . ..., . .':':':': ': ':+:':':':': , . '.'.' .' .'- '. ' . '-' .'-'. _ " == = = = ============ = ====== == ====== = = = " ' " " """'"" ..... . ...,........ . ......:::::: ::: ::: : :: : ::: : : :: ::: -. • .-. •- . ••• ............. .:': ' : == = ======= =============================== 1 I.3 "iiii!iiiiiii_:i_!iiii!! ' !i_ii!' : ::_ji_£:i:i_i!

0 , O. 2 ;..3.:.9 _ __._...__.' ] i!:.!:'::.1:.iii:.i-:.i:.i iiii."::."_':..:.ii!i!iiiii! 1.7 _, _ , LESS 50 70 90 II0 130 150 170 190 20 INDICATED AIRSPEED (KIAS) ' _ Figu r e 4 5. Percentage of Ti m e in Airspeed Ranges f_ z Single-Engine Ex e cu t ive Cat e gory w llS : ) r , ¢ A I 0 0 Pe rs on a 'i -'Compo s ite 75 (723.4 hrs.)

50 41.0 ) ..o....o..... . .-. v ....., : 2 S 2 3 .6 iiiiiiiiiiiiiiii!ii!ii! 2 3 . 8

===========================!ili_!ii!_iii_iiiiiii_)i 8.2

, 0 . ._ _..S" 1 ::::::::::::::::::::::: ::::::::::::::::::::::::::: 0. I | ] . , A / C Type II -_ $ 5 . 3 8i:::!:!:_:i:i:i:?i:!:i: SO _j , -.-.- .° ......... .. ...-.

.--- 25 :i::!:_:_i:i:_:i::_:!! 21 6

...a 15 . 0 !!ii!ii::i:iii:_i!!!:!i: ,.7.7. L _._

" 7 _. : : : 2:: : :::::: : :: : ::::2 : : ::::::: : :::: : :::::::::::: b . •.......... :--:.... : - :.:-::-:--':-:-:-:'::':-:':':-:-:-'- 1.2 l_:_::: ......... :........:.--:-:.:.:-:-:.:..:.:-:-:1 :,,1,, 0 I ::::::::::::::::::::::::::::::::::::::::::::::::::::: 5::::::: :::: _: .:::::::::::: 5 ] _ 1 I 'D _ a A / C Type 10A ; L2_ < 75 Z ; "'_ 50,3 u 50

...... ii;ii iii ii!i!i ! ii:iiiij

2 5 _ ' 5 . 8 ' n _ I . 7

i{iiiiiii{ii{{!{!ii{iii{iii

U :-:-:-:::'" ........ ' I I I A / C Type 12B 62.9

s o iiiiiiiiiiii!iiii!i!iiiii

25 27 . 2 _i] 0 0 :1_{ii_ii__ 3 i iiiii!!{iiiii:iii!iiiiiiiiiiiiiiiiiiiiiiiiiiiii!iiiiii i_....':,:i:!:! 6. 7 , , , -_ L E SS 5 0 70 90 II0 13 0 150 17 0 190 210 I ND I CAT E D A I RSP EE D (KIAS) , F igu r e 46 . Percentage of Time in Air s peed Rang es f or Pe r sonal Cate g or y a )

! •

I { ) O _ ....

In stru c ti o n a l-C o mpo s ite , S (2_42.4 hrs.)

i _o 3 8.3 2 3. 0 _ 2 4. 2 : : :: ::::::: : ::: : ::::::: . m • i) ........ Imml : A / C T y pe I3 " 7 5 SO 4 2 .4

j.L.j.!.iii!!i 2 0 . 7

27 .9 _{#ii ' ii!ii!

F I 9 4 4 :::::::>- ' :E:::::::K:::: • . ...: ...... . !_Ei!_E!E!'.'..'!_!_!!! ; :_I : :::::::::::::::::::::::: 2. S 0 . 2 j i I 11 ' ' :- _ a A / C Typ e I S _" " 511 2 9.6 17 a 2 0 .2 _ 21.7 -_ 2 5 , , _____ • ...... : ::i:!:E:i:E:E:_:I:E:!:E: W u _ 0 :' o A / C T ype 17 _ 7 5 < z 5(I 31.1 u 22 1 _? l "25 ....

u_ " 3 1 2 1 ":':':':':': ' :_':::: ":':':':':':':'::':':: 8 0 1 1 0 .............

• " :Ti:i:i:K:i:E:i:i:i:i :i:!:!:!.E:i:i!EEEE!_!EE " 0 . S A / C T ype 16 7 5 S O 38.0

2s _

,,__ _L_ o._, , , A / C T ype 14 49.0 5(I

• i!i # ,iiiiiii i',i o

=========================== .6 , , , , 0 ................... ' LESS 5 0 60 70 8 0 90 I0 0 II 0 12 0 1 30 1 4 0 • INDICA T ED AIRSPEED (KIAS) )

Figure 47 , Percentage o£ Time in Airsp eed Ranges for

Instructional Cate g o r y

' I ' I i ; I , !

I0 0 Co m me r cial S u r v ey- Co m po si t e 75 (2291. 0 hr s.)

50 3 7 .8 44.7

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7 5 A / C Type 19 , 5 0 3 2 .0 39,0 ! 2S 9.0 0.3 " 1.7 0. 3 LESS S0 70 90 ii0 130 iS0 170 190 210 230 I N D ICAT E D AIRSP EE D (KIAS)

i Figure 4 8 . Pe r cen t age of T im e in Ai r sp ee d Ranges fo r

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Com m er c ial Surve y Ca t egory

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' 118

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I 0 , _ I - :-: .: .: . ; . :.: . : . : . : . : - :-:.:/_ • v ::::::::::::::::::::::: :::::::::::::::::::::::::::::::::: 0 • 2 I t ! I LESS 50 70 90 110 130 150 170 190 INDICATED AIRSPEED (KIAS) Figure 49. Percen t age of Time in Airspeed Ranges for , Aerial Application C ategory # !

G Commuter- Compos i te 75 . (1;09.0 hrs . ) e

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L E SS 50 80 110 140 170 2 00 230 2 60 INDI C ATED AIRSPEED (KIAS)

F i g ur e 50. Percenta g e of Time i n Airspeed Ran g es f o r

Commuter Category

120 "

• 1 , T 3. CONCLUSIONS On the basis of the number of recorded flight hours, the VGH data sample was adequate for all operational categories except the Aerobatic c a tegory . On th e b a sis of th e number of records, the VG data sample was inadequa t e for the Aerobatic, Aerial Application, and Commuter c a tegories. The flight hours in the VG and VGH data could not be compared sin c e the VG recorder registers only e xtr e me v a lues and the number and frequency of c oincident p e ak valu e s are unknown.

I The observed data distributions wer e log-normal in most • c ases and approximately normal in the rest. The C o mmercial Survey category had t wo dis t inct da t a distributions, one en- route to and from the operational mission and the other during t he mission performance.

The Inst r u ct ional a n d A e ri a l Appli ca ti o n categories had the highest probability of exceeding the design positive nz limits for maneuver; the Instructional category had the high- est probability of exceeding the design negative n z limits for maneuver, and the Commercial Survey category had the highest nz I probability o f exceeding the design limits for gust .

The Aerial Application and Instructional categories had I the most sev e re landing impact data since they required 860 and 3393 l a ndings, respec t ively, t o a t tain 1.67 An z while the other categories required more than 19,000 landings to reach this level Of the 24 instrumented aircraft types, 17 had airspeeds above V c , bu t none had airspeeds above V D. The Personal category had the highest probabiiiLy u_ _^_ , ,b . u , ....

!' Instructional and Commercial Survey categories had the highes t V / V C ratios, approximately 1.2; and the Twin-Engine Executive _ category had the highest V / V D ratio, approxima t ely 0.925.

Each of the eight opera t ional c a tegories had a dis t inct ; l o ad sp ect ru m whi c h r eflected th e o p e rational chara c t e ristics _ of the category defini t ion, and t he various aircraft types k _ ' within each o perational category generally had loads which • c onformed closely with the average spectrum. The data for the • • separating the data for turbojets from the data for turboprop Twin-Engine Executive categor y could be analyzed better by .. and piston aircraft• Because of the close simil a rity in the per t urmance results, the Sin g le-Engine and Personal categories ,' co uld be c o mbined to si m plify t he analysis.

4. RECOmmENDATIONS A statistical method to substantiate the adequacy of the sample size should be de t ermined by periodic reduction and an- alysis o f th e da t a while it is being recorded. Comparison of each an a lysis to pr ev ious a nal y ses should yield information concerning the ad e quacy of da t a already recorded.

The V-N da t a for the cons t an t probabili t y envelopes, such as t hose shown in Figures 7 t hrough 1 3 , should b e refined to ass e ss the design r e quiremen t s for th e high-airspeed, high- acce le ra t ion re gim e .

I The landing imp a c t spec t ra should also b e investiga t ed by using sink ra t es ins t e a d of lo a d f a c t ors because of the co m plex dynamic t ransfer func t ion inheren t in t he landing ge a r sys t em.

i I q I t ! ' 1 ! 1 I ] _ _ " I REFERENCES I . Jewel, Joseph W., NASA Aircraft Safet y and Operation , Problenls Conference, May 4-6, 1971, NASA SP-270.

2. FEDERAL AVIATION REGULATIONS, TITLE 14, Part 23.

3. Taback, Israel, The NACA 0.l-Damped V-G Recorder, NACA TN 2194, 1950.

4 . Richardson, Norman R . , NACA VGH Recorder, NACA TN 2265, 1951.

5. Pr e ss, H., The Application of Statistical Theory of : Extreme Values to Gust-Load Problems, NACA Report 991, 1949 6. Gumbel, E.J., Applied Mathematics Series 33, National Bureau of Standards, Department of Commerce, 19S4.

7. Pratt, K.G . , and Walker, W . G., A Revised Gust-Load Formula and a Re-evaluati on of V-G Data Taken on Civil Transport Airplanes from 1933 to 1950 , NACA Report 1206, 1953.

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