A PHILOSOPHY OF AEROPLANE STRENGTH FACTORS.

I C A O

C I R C U L A R 2

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^{A N / 2 w}

C I R C U L A R -

M A Y 1 9 4 8

I N T E R N A T I O N A L C I V I L A V I A T I O N O R G A N I Z A T I O N MONTREAL CANADA

A I R W O R T H I N E S S

(AIR)

A PHILOSOPHY OF AEROPLANE STRENGTH FACTORS.

Pub1 i s h e d by a u i h o r i ty of the Secretary General

This Publicatiqn i a issued in English, Wenah m d S p n i s h .

Published i n Montreal, Canada, by the Internat2 onal C i v i l Aviation O r ~ a n i e a t i o n

.

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to the In Egyptian currency

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t o the

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~ o n t r e a i , Canada. Zamalek

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ICAO Circular 2 ⁼ AN/2 _page

3

TABLE OF CONTENTS

Yage

Foreword

...O... 5

A PHILOSOPHY OF AEROPLAFJE STRENGTH FACTORS Summary

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I.. I n t r o d u c t i o n

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2.. The B a s i c A i m

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⁸

3.-

Primary Load.and S t r e n g t h S t a t i s t i c s

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⁸

4.- C o r r e l a t i o n of Load. S t r e n g t h and Accident S t a t i s t i c s

...O...

10

5..

I n f l u e n c e of Design Parameters

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¹¹

6.. Some P a s t A i r w o r t h i n e s s D i f f i c u l t i e s

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7.. Conclusion

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F O R E W O R D

The purpose of ICAO Circulars is to distribute information bearing upon the progress of ICAOrs work more widely than would be possible for the ordinary series of documents.

The present Circular is a republication of a national study on a matter of fundamental importance that has also been considered at the First and Second Sessions of the Airworthiness Division of ICAO, during the discussions on the determination of minimum

structural load factors for aeroplanes,

The report reproduced in this Circular was first issued by the Aeronautical Researgh Council of the United Kingdom as Reports and Piernoranda 130. 1906. Consequent upon recommendations made by the Airworthiness Division, the report was submitted to ICAO for publication, has been translated by the Secretariat into French and Spanish and is being published as an ICAO Circular in English, French and Spanish.

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ICAByCi;tcular 2

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A PHILOSOPHY OF AEROPLANE STRENGTH FACTORS

This report attempts, in a preliminary and elementary way, to bring aeroplane structural s t r e n g t h and l ~ a d i n g ~ s t a t i s t i c s together into a logical and praetfeal philosophy of s t m n g t h factors. By c o r r e l a t i n g such s t a t i s t i c s with structural a c c i d e n t pates, the influenee _{o f} various design parameters is demonstrated and a new view of some past d i f f i c u l t i e s obtained.

1,

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INTRODUCTION

The s p e e i f i c a t i ~ n o f s t r e n g t h f a c t o r s f o r the d e s i g n of e n g i n e e r i n g s t r u c t u r e s has f o r long p r e s e n t e d t h e o r e t i c a l d f f f i - c u l t f e s , and many e f f o r t s have been made t o f o r m u l a t 3 clear p r i n c i p l e s f o r t h e i r c h o i c e , The aim h a s always been t o a p p l y new knowledge t o reduce t h e element of ignorance and s o h e l p t o

avoid having t o r e g a r d s t r e n g t h f a c t o r s a s p u r e l y e m p i r i c a l o r a s f a c t o r s o f s a f e t y o r f a c t o r s of i g n o r a n c e , As examples o f such e f f o r t s we may n o t e t h e i n t r o d u c t i o n of allowances f o r dynamlc loads and f o r f a t i g u e e f f e c t s ,

I n a e r o n a u t i c a l work t h e g e n e r a l e n g i n e e r i n g o u t l o o k has been supplemented by a n a p p r e c i a t i o n of t h e u n u s u a l l y v a r i -

a b l e n a t u r e of t h e l o a d s coming upon t h e a e r o p l a n e s t r u c t u r e , Accelerometer r e c o r d s have been t a k e n i n f l i g h t and expressed and used a s " l o a d N f a c t o r s , The c h o i c e of s t r e n g t h f a c t o r s

has indeed been more i n f l u e n c e d hy t h e l o a d a s p e c t of t h e m a t t e r t h a n by c o n s i d e r a t i o n of t h e p r a p e ~ t f e s of t h e s t r u c t u r e used, The two q u e s t i o n s h a v e g e n e r a l l y been t r e a t e d a s s e p a r a t e ones, and S t i s o n l y r e c e n t l y t h a t e f f o r t s 1 9 2 have been made t o b r i n g them t o g e t h e r by r e l a t i n g both t o a c c i d e n t r a t e s , I n doing s o we have on t h e one hand t o allow f o r t h e f r e q u e n c y of o c c u r r e n c e of l o a d s of d i f f e r e n t magnitudes and on t h e o t h e r hand t o a l l o w f o r t h e v a r i a t i o n En s t r e n g t h among a e r o p l a n e s produced t o a g i v e n d e s i g n , The purpose of t h i q r e p o r t i s t o try, i n a p r e l i m i n a r y and elementary way, t o weld t h e s e v a r i o u s a s p e c t s of t h e d e s i g n of a e r o p l a n e s t r u c t u r e s i n t o a logical and c o n s i s t e n t whole

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^a p h i l o s o p h y of s t r e n g t h f a c t o r s

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^and,

by s o d o i n g , t o reduce a c c i d e n t r a t e s , t o b r i n g i n t o b e t t e r

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p e r s p e c t f v e some of our p a s t problems, t o p o i n t t o ways of f u r t h e r development, and t o p r e p a r e f o r making t h e f u l l e s t u s e of t h e speed and a c c e l e r a t i o n l o a d i n g s t a t i s t f e s now accumulat- i n g ,

2,

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^{THE BASIC A I M}

L e t u s s t a r t w i t h t h e simple assumption t h a t , i n d e c i d - i n g upon t h e s t r e n g t h of an a e r o p l a n e s t r u c % u r e , we a r e aiming p r i m a r i l y t o e n s u r e t h a t t h e a e r o p l a n e s h a l l be able t o perform i t s d u t i e s e f f i c i e n t l y w i t h o u t b r e a k i n g , I n p r a c t i c e , because of" t h e importance of mfnimfsing s t r ~ l c t u r e w e i g h t , an a e r o p l a n e cannot be made s o s t r o n g a s t o be unbreakable, and s t r s c t u r a l f a i l u r e s occasionally occur under . e x t ~ e m e conditions, such a s may a r i s e if a p i l o t a%%empts t o manoeuvre a l a r g e bomber t o o

v i o l e n t l y o r i f he makes a v e r y bad l a n d i n g , S t r u c t u r a l a c c i - d e n t s may a l s o sometimes occu'r due. t o e r r o r s of d e s i g n o r work- manship o r t o t h e u s e of f a u l t y m a t e r i a l , I t i s n a t u r a l t o c o n s i d e r a l l such a c c i d e n t s i n r e l a t i o n t o t h e hours flown, and t o e x p r e s s t h e h i s t o r y of s % r a e t u s a l f a i l u r e among a e r o p l a n e s by t h e number of s t r u c t u r a l a c c i d e n t s a r i s i n g i n a given number of f l y i n g h o u r s , l e e , by a s t r u c t u r a l a c e i d e n % % a t e w , Expressed fn more p r e c i s e terms, t h e n , our b a s i c aim is t o l e a r n how t o choose a e r o p l a n e s t r e n g % h f a c t o r s so t h a t s t r u c t u r a l a c c i d e n t r a t e s s h a l l be a s s m a l l a s p o s s i b l e c o n s i s t e n t w i t h e f f i c i e n t p r o d u c t i o n and o p e r a t i o n . To h e l p t o do t h i s , we stlldy i n t h e succeeding paragraphs t h e a c c i d e n t r a t e t h a t may be expected t o a r i s e when a e r o p l a n e s made t o a s p e c i f i e d s t r e n g t h f a c t o r a r e used f o r d u t i e s i n v o l v i n g a given range of l o a d s , c o n c e n t r a t i n g a t t e n t t o n upon wing s t r e n g t h s and f l i g h t l o a d s a s most important and t y p i c a l , We t h e n s e e how t h e a c c i d e n t r a t e would probably change were t h e s p e c i f i e d f a c t o r a l t e r e d o r t h e wings c o n s t r u c t e d more a c c u r a t e l y t o t h e s t r e n g t h d e s i r e d ,

1 ,

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^{PRIMARY LOAD AND} STRENGTH S T A T I S T I C S

To s t u d y t h e l i a b i l i t y of a wing t o f a i l i n f l i g h t we have on t h e one hand t o e s t i m a t e t h e l o a d h i s t o r y t o be

e x p e c t e d , having r e g a r d t o i t s d u t i e s , and on t h e o t h e r hand t o e s t i m a t e t h e probable e f f e c t i v e l i f e of any a e r o p l a n e s t r u c - t u r e designed t o meet such a load h i s t o r y . I n our p r e s e n t s t a t e of knowledge t h 2 s i s o b v i o u s l y a m a t t e r f o r s u @ c e s s i v e approxima- t i o n , b u t t h a t does n o t mean t h a t i t cannot be placed on a

l o g i c a l b a s i s ,

To a t t e m p t t h i s i n a p r e l i m i n a r y way, l e t u s d i s r e g a r d a s secondary such m a t t e r s a s t h e i n f l u e n c e of wing e l a s t i c i t y , of v a r i a t i o n of l o a d d i s t r i b u t i o n and o f f a t i g u e e f f e c t s , and con- c e n t r a t e upon t o t a l l o a d s on t h e one hand and wing strengthson t h e o t h e r . L e t u s assume we have continuous a c c e l e r o m e t e r

ICdO Circular 2

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r e c o r d s for a s e t of a e r o p l a n e s of comparable t y p e and d u t i e s , From t h e s e we c a n p r e p a r e a t a b l e o f t h e number of t i m e s (g)

t h e t o t a l wing l o a d p a s s e s upwards through a g i v e n v a l u e

(s)

i n a g i v e n f l y i n g t i m e ( l a r g e ) , An imaginary t a b l a of v a l u e s c o l l e c t e d i n t h i s way f o r a f i g h t e r i s g i v e n below:

TABLE 1

tiring l o a d (g)

Frequency (g) i n

lo4

f l y i n g hours

0 0 0

O Average s t r e n g t h = 13 2 Standard deviation = 1.26 12

72 2.2

2

Suppose now we d e s i g n a wing s t r u c t u r e w i t h z, s t r e n g t h c o r r e s p o n d i n g t o a b r e a k i n g load of a b o u t 13 ( o n t h e s c a l e of Table I ) , If we make a number of a e r o p l a n e s t o t h i s d e s i g n , t h e a c t u a l s t r e n g t h of t h e wfngs w f l l v a r y somewhat on a c c o u n t of s i z e t o l e r a n c e s and m a t e r i a l v a r i a t i o n s , I f we t e s t e d t h e wings of 100 such a e r o p l a n e s , we might f i n d t h e i r s t r e n g t h s t o be a s t a b u l a t e d below:

TABLE I1

- roo

l i n g s t r e n g t h ( i n i n % e r v a l s o f 2 u n i t s of l o a d )

No, of wfngs w i t h s t r e n g t h s in each

i n t e r v a l

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'fhus, a l t h o u g h t h e average s t r e n g % h of the wings i s 13, of a hundred such wings two would have a s t r e n g t h of o n l y a b o u t 9

( f o e , i n 8 t o 10 i n t e r v a l ) and two would have a s t r e n g t h of a s much a s

17

( i , e , in 16 t o 18 i n t e r v a l ) ,

4,

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CORRELATION OF LOAD, STRENGTH AND ACCIDENT STATISTICS Consider now t h e 100 a e r o p l a n e s of Table 11, and concen- t r a t e on t h o s e f a l l i n g i n a p a r t i c u l a r s t r e n g t h group, s a y t h e two a e r o p l a n e s w i t h wing s t r e n g t h s between 8 and PO

-

f e e . of mean s t r e n g t h 9 , Now t h e s e two a e r o p l a n e s will, from Table I ,

on t h e average o n l y meet a load s u f f f c f e n % t o break them ( i , e , a load g a s s i n g upward through 9 ) t e n t i m e s i n lo4 f l y i n g h o u r s , s o t h a t i f t h e 100 a e r o p l a n e s of Table I1 s t a r t e d f l y i n g t o g e t h e r , and each flew f o r

lo4

hours, t h e n t h e two a e r o p l a n e s concerned would p r o b a b l y have f a i l e d i n t h e e a r l y s t a g e s of t h e f l i g h t , Before we c a n e s t i m a t e t h e a c c i d e n t r a t e t o be expected under t h e c o n d i t f o n s of Tables I and 11, vie have t o d e c i d e over what times t h e a e r o p l a n e s do t h e i r flying, and when and why new aero- p l a n e s a r e brought i n t o s e r v i c e , Thus a l l t h e a e r o p l a n e s could be produced t o g e t h e r and s t a r t f l y i n g a t t h e same time; o r some could s t a r t t o g e t h e r and o t h e r s j o i n them l a t e r , To make t h e problem a t once amenable t o simple p r o b a b i l i t y t h e o r y and a l s o approximate t o p r a c t i c a l s e r v i c e c o n d f t i o n s , l e t u s assume t h a t t h e o r i g i n a l 100 a e r o p l a n e s a r e c o n t i n u o u s l y r e p l e n i s h e d a s s t r u c t u r a l nd o t h e r f a i l u r e s * occur, s o t h a t a t any moment i n

8

t h e ' l o n g 10 h o u r s f l y i n g time t h e c o n s t i t u t i o n of t h e 100 i s

a c c o r d i n g t o Table 11, Then we can s a y t h a t t h e chance of an aeroplane having a s t r e n g t h i n t h e c l a s s 8 t o 1 0 i s 2 i n

ioo

³

and t h e chance of t h a t a e r o p l a n e being broken i s 1 0 i n 1 0 hours.

T r e a t i n g t h e s e two chances a s q u i t e independent, t h e chance of a f a i l u r e - o f an a e r o p l a n e of t h e - s p e c i f i e d - c l a s s i s

x

1 0

-

^{i k e e}

100

"Ilfo"t'

20 i n 106 f l y i n g h o u r s , We may r e g a r d t h i s a s meaning t h a t , if a l a r g e number of a e r o p l a n e s of t h e d e s i g n and d u t i e s r e p r e s e n t e d by Tables I and I1 were f l y i n g i n s e r v i c e , s t r u c t u r a l f a i l u r e s would occur t o t h o s e i n t h e 8 t o 1 0 s t r e n g t h group a t t h e r a t e

of 20 i n 106 h o u r s , Applying t h e same argument t o each s t r e n g t h group, we o b t a i n Table 111,

- - -- - - - - - - - - - -

*

^In practice few structural f a i l u r e s occur and replen%shment i s largely necessary f o r quite othep reasons, This replenishment pmb em has interest- fng common features with other such problems i n s t a t f s t f e s ,

%

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TABLE I11

Thus t h e r e would be 32 s t r u c t u r a l . f a i l u r e s e v e r y 1 0 6 f l y i n g h o u r s , of which f a i l u r e s 20 would be found t o have occur- r e d t o a e r o p l a n e s w i t h wing s t r e n g t h s of 8 t o 1 0 and 1 2 t o t h o s e w i t h s t r e n g t h s of 10-12, This s t r u c t u r a l a c c i d e n t r a t e i s

a c t u a l l y a l i t t l e above t h e average f o r modern a e r o p l a n e s

-

t h e f i g u r e s i n T a b l e s I and I1 have been chosen t o produce such a r a t e , We have t h u s a r r i v e d , upon c e r t a i n s i m p l f f y i n g assump- t i o n s , a t an e a s y way

- -

of roughly e s t i m a t i n g s t r u c t u r a l a c c i d e n t r a t e s ,

With t h e a i d of Tables such a s I , I1 and 111, we can examine t h e i n f l u e n c e upon t h e a c c i d e n t r a t e of v a r i o u s broad d e s i g n p a r a m e t e r s and s o understand b e % t e r t h e p a r t played by them i n p r e v e n t i n g a c c i d e n t s , Suppose, for example, t h e s t r u c -

% u r e was such t h a t t h e mean s t r e n g t h of t h e wings was 11 i n s t e a d of 139 t h e d i s t r i b u t i o n about t h e mean being k e p t much t h e same, and t h e d u t i e s being u n a l t e r e d , Then i n s t e a d of Table 111 we might have Table I V , %bus:

S t r e n g t h group

0-2 2 -4 4-6 6-8 8-10 10-12 12-14 14-16 16-18

Load f r e q u e n c y from Table I

--

30,000

5 ,

OQQ

$00 10

1 0 O O No, of wings

from Table I1

0 0 O O 2 1 2 72 1 2 2

-

100

-

Acci

g

e n t s

i n

10 h o u r s (=, p r o d u c t )

0 0 O O 20 1 2

0 O 0

-

32

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Thus the _broad r e s u l t of a decrease of mean strength from 13 ^to 11 would e a serious Increase of the a c c i d e n t r a t e from 32 to

g

392 in 10 f l y i n g hours,

Alternatively, we might leave the mean strength of the wings unaltered, but choose the materials and size tolerances to reduce the scatter of strengths Pn Table 11, A s r m i n g we can thus roughly h a l v e this s c a t t e r ( a s measured by. standard deviatton), we would then _{have Table} V in p l a c e of _Table 111,

TABLE V

Strength group

No, of wings

Load f requeney _in Aeei ₁₀

8

ents _hours

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Thus by h a l v i n g t h e v a r i a t i o n of s t r e n g t h about %he e a n of 13

h o u r s ,

z

we have reduced t h e a c c i d e n t r a t e from 32 t o

5

i n 1 0 f l y i n g The f o r e g o i n g examples of %he u s e of a @ o r r e l a t i o n t a b l e of t h e form of T a b l e s 111, I V and V could be extended i n vapious ways, We m i g h t , f o r example, examine t h e e f f e c t of v a r i a t i o n s of t h e l o a d frequency % a b l e . Such v a r i a t i o n s might r e s u l t from a change of d u t i e s , an a l t e r a t i o n of t h e f l y i n g c o n t r o l s

-

^{a s}

by a n i n e r t i a d e v i c e

-,

o r from a change of p i l o t s ,

6 ,

-

^{SOBE PAST} AIRWORTHINESS DIFFICULTIES

-

When s p e c i f y i n g s % r e n g t h f a c t o r s f a r a p a r t i c u l a r d e s i g n i t h a s been customary t o a l l o w f o r v a r i a t i o n of t h e s t r e n g t h of

%he f i n i s h e d s t r a z c t u ~ e i n p r o d u c t i o n by s a y i n g t h a t a c e r t a i n f a c t o r must be achieved by a s t a n d a r d t e s t specimen; and t h i s s t a n d a r d specimen h a s been d e f i n e d a s one c o n s t r u c t e d of mem- b e r s having t h e s p e c i f i e d lower l % m % t s bf b o t h s i z e and m a t e r i a l p r o p e r t i e s , U n f o r t u n a t e l y , w h i l e such l i m i t s could be embodied i n s t r e n g t h c a l c u l a t i o n s , f t was never p r a c t i c a b l e t o make such a s t a n d a r d specimen f o r t e s t , S t r e n g t h t e s t s have t h e r e f o r e been made on specimens s e l e c t e d a % random and t h e s p e c i f i e d

s t a n d a r d specimens have t h e n been assumed t o have s t r e n g t h s 20 p e r c e n t . l e s s t h a n t h e t e s t v a l u e s ,

I f we approach t h i s problem i n t h e l i g h t of r h e f o r e - going p a r a g r a p h s , we may d e c i d e f i r s t t h a t f o r convenience we wish t o r e p r e s e n t t h e s t r e n g t h s of t h e wings of Table I1 by a

s i n g l e s t r e n g t h v a l u e ; and may t h e n proceed t o choose t h i s v a l u e s o t h a t , coupled w f t h t h e load f r e q u e n c i e s of Table I , we d e r i v e t h e same a c c i d e n t r a t e a s t h e @ r e a l n one g i v e n by Table 111.

I n o t h e r words, l e t u s aim a % a s t r e n g t h v a l u e such t h a t , i f a p p l i e d t o a l l t h e a e r o p l a n e s concerned, 1% would l e a d t o t h e r e a l s t r u c t u r a l a c c i d e n t r a t e , To do tkls, we have t o c o n s i d e r t h e numbers i n t h e second column of Table PI1 r e p l a c e d by a s i n g l e number of 100 and f i n d i t s l e v e l i n r e l a t i o n t o t h e s t r e n g t h groups s o t h a t , when muPtiplieCS by t h e number (or i n t e r p o l a t e d number) in t h e load frequency c Pumn a n t h e same l e v e l , i t g i v e s a n a c c i d e n t r a t e o f 32 i n ¹⁰⁸ f l y i n g hours.

I% i s c l e a r from Table IHI t h a t t h l s e q u i v a l e n t s t r e n g t h l e v e l i s _between EO _and 1 4 , and by rough g r a p h i c a l i n t e r p o l a t i o n i t i s found t o be about 1 2 , That is, if a P P t h e a e ~ o p l a n e s con- cerned had a s t r e n g t h of $2 and underwen t h e l o a d s of Table I., t h e n t h e a c c i d e n t r a t e would be 32 i n ¹⁸

S

f l y i n g hours. T h i s e q u i v a l e n t s t r e n g t h i s about 73 per c e n t , below %he mean s t r e n g t h s f 13, and c s ~ r e s p s n d s t o %he mean l e s s 0,8 t i m e s t h e s t a n d a r d d e v i a t i o n of Table XI, I t w i l l be noted t h a t , a s i n a random t e s t t h e r e i s a good chance t h a t t h e specfmen w i l l ap roxfmate t o t h e mean, t h e s e f i g u r e s of 1 2 , 7+ per c e n t . a n d . 0 , g may r o u g h l y be compared w i t h t h e f f g u r e s t h a t would r e s u l t from

Page 14 ^{I C A O} C i r c u l a r 2

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^AN/2

t h e p r e s e n t 20 p e r c e n t , r u l e , i , e , 10.4, 20 p e r c e n t , and 2.1 r e s p e c t i v e l y . I t should a l s o be noted t h a t t h e former s e t o f f i g u r e s a r e s t r i c t l y a f u n c t i o n of t h e l o a d i n g f r e q u e n c i e s a s well a s of t h e d e g r e e of s t r e n g t h v a r i a t i o n ,

Another ppoblem of t h e p a s t , though worked on more i n Germany t h a n elsewhere, i s how t o %$Pow f o r t h e e f f e c t s of load r e p e t i t i o n on t h e behaviour of complete a e r o p l a n e s t r u c t u ~ e s . Even i f such e f f e c t s were l a r g e and s u f f i @ f e n % d a t a were a v a i l - a b l e , 1% was always d i f f i c u l t t o s e e how any allowance c o u l d be brought i n t o a l o g i c a l system of s t r e n g t h f a c t o r s ; b u t w i t h Table 111 b e f o r e u s t h e r e seems more hope of t h i s . I t may be p r a c t i c a b l e t o scheme an e n l a r g e d v e r s i o n of Table I11 t o make f u l l p r o v i s i o n f o r r e p e t i t i o n e f f e c t s , o r a l t e r n a t i v e l y t o

d e v i s e a n approximate p r o c e s s by s u i t a b l y tlweightingw o r a d j u s t - i n g t h e f i g u r e s i n t h e second o r t h i p d columns,

No a t t e m p t h a s been made i n t h i s e x p l o r a t o r y r e p o r t t o s t a t e t h e f r e q u e n c i e s and p r o b a b i l i t i e s concerned On t h e mathe- m a t i c a l terms of s t a t i s t i c a l t h e o r y , Bu% 2% is e l e a r t h a t t h e

simple examples d i s c u s s e d i n t h e Tables c o u l d a l l be c a s t i n t o a l g e b r a i c form, u s i n g a p p r o p r i a t e g e n e r a l i z e d f requency laws, and t h e r e l a t i v e importance of d e s i g n p a r a m e t e r s d i s c u s s e d i n g e n e r a l t e r m s , Such an a n a l y s i s , whether g r a p h i c a l -r a l g e b r a i c , would have complicated t h i s f i r s % simple d i s c u s s i o n of t h e

m a t t e r b u t might form t h e b a s i s f o p a u s e f u l s e r i e s of wing s t r s n g $ h , ' l o a d frequency and a c c i d e n t r a t e c u r v e s f o r u s e i n t h e review of d e s i g n f a c t o r s , The e f f e c t s o f d f f f e r e n t systems of replenishment t o t h e simple one adopted i n #4 f o r Table 111 a r e a l r e a d y being examined.

Another p o i n t , t o which t h i s a t t e m p t t o s t a t e a p o s s i b l e p r a c t i c a l philosophy of s t r e n g t h f a c % o r s draws s p e c i a l a t t e n - t i o n , i s t h e fundamental i r n ~ o r t a n e e of c o P l e e t i n ~ , load and 9 t r e n ~ t h s t a t i s t i c q o

LIST OF REFEEZENCEq

1, BOGo Pugsley,

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Strue%u~al Researoh f n Aeronautics, June, 1939.

2, A.G. Pugsley,

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The correlatfon of Aeroplane Loading and Aeofdent Statf s t i e s . R,A.E, Report, No, S,M,Eo3207, (5922), Aprf lo 1942,

( ~ n p u b l i shed) ,

3, ^NOR, Campbell,

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Replacement of perishable members of a continuously operating system, Supplement of Journal of Royal S t a t i s t i c a l Society, Vol, VII, 2, pp, $10-130, 19Q,