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File D 52.33/2 53 f cCUOK FJELD UEFUH'l', SERIAL N o. 2441
A TION CIRCULAR
CAVIATIONJ
. PUBLISHED BY THE CHIEF OF AIR SERVICE, WASHINGTON. D. C.
Vol. V February 1, 1925 No. 498
• •. t:·
. ' STUDY OF S. T. Ae. FORMULA
. .
~ . ~ FOR LOAD FACTORS
(AIRPLANE SECTION REPORT )
~ :
. ··, . "" •.;. '
.... ~ ·• .
Prepared by A. S. Niles
Engineering Division, Air Service
McCook Field, Dayton, Ohio
November 14, 1924
WASHINGTON
GOVERNMENT PRINT ING OFFICE
1925
..  :; .
. .; .· · .  '
Ralph Brown f ·LIBR11P
,, ·••ii
MAY 7 7 2013
Non·Depoitory
Auburn University
 \
/
CERTIFICATE: By direction of the Secretary of War the matter contained
herei~ is published as administrative information and is required for the proper
trani;~ct!on of the public business.
(II)
STUDY OF S. T. Ae.
OBJECT I For nonmilitary ai rplanes : Monoplanes, 9; multiplanes,
7.5.
To compare the load factors for wing desigu obtained Translating t he above formula into t he ordina ry
from t he French S. T . Ae. formula with t hose used by English units, it become~
the :United States Air Service, and to 8tudy the theoreti .
cal ·basis of the French formula in order· to determine n = 0.387 K A V3/H.P.
whether or not the French formula or one of its type provided that t he velocity be expressed in hundreds of
should be adopte::I b.'· t he Air Service. miles per hour.
CONCLUSIONS
The load factors computed from t he S. T. Ae.
formula agree fai rly well in most specific cases with
t hose used by the Air Service. Where there is much
difference between t.he French and American valu es,
it is considered that the American ,·alues a re t he more
reasonable.
The French formula is partly t heoretical and partly
empirical, whereas t he American rule8 are purely
empirical. The theoretical and empirical factors are
combined in t he French formula in such a manner
that with certain types of design it does not give
ti uita ble load factors. In one case studied t he load
factor for design obtained from the formula is less t han
that actually recorded in flight.
The proper solut ion of the problem of load factors
tu be used lies in the compilation a nd study of full
ticale acceleration tests, such as those recent!~· initiated
by the Ai1_. Service, to complete t he existing fragmentary
data available. Such study might result in t he
adoption of a formula for computing the req uired load
factor , but it i& believed that t he varia bles and the
arb itrary constants used in such a fon:nula \YOtild
differ materia lly from t hose emplo~· ed in the S. T. Ae.
formu la by t he French .
DESCRIPTION OF S. T. Ae. FORMULA
The S. T. Ae. formula for computing load fado r8 as
given in the S, T. Ae . . publication " 'Condition:; Techniques
Generales, ·· dated April 10. 1922, is as fo llows:
KS(V)•
ll = 
T 1003
where 11 is t he load factor corresponding roughly to
uur high incidence factor ~ ut f r a bad di str.iLu t ion
t hat is not quite so seyere ,1 S is t he wing area in sq uare
meter:;, T i ~ 1 he hursepo\Yer. \ ' is the high speed at
t.11e ground in kilometers per hour, a nd K is an arb i trar~·
L"Oelficieut wit h the fo llowillg Ya lues :
For militar.'· nirplanes: Purs uit rnouopla nes, 15;
other mo11opla.11es, I l ; purs uit mult iplanes, 10; ot her
mult.iμl a neti, 7.5.
1 The French use a center of pressure at 33 per cent of the chord and
have no l o~,. incidence condition with the center of pressure back.
The Air Service uses a c. p. location of from 2i to 32 per cent of th e chord,
depending on the airfoil, and in addition have a. low incidence condition
with t he center of pressure back, with a specified load fact.or usua lly about.
twot hirds that for high incidence.
27919 25+
COMPARISON 0.1!' FRENCH AND AMERICAN
REQUIREMENTS
The S. T. Ae. formula was applied to 28 a irplanes of
various types with the res ults tabulated belO\Y. In
most cases t he figures a re based upon t he results of a
flight test. In a few cases estimated performances
were used. In gene.ral t he use of estimated performances
will result in higher load fa ctors as t he high speed
and the quantities of " ·hich it is a fun ction are usually
estimated optimisticall.v .
Load factors required for various A mer ican airplane;;
.1 I 2 I :; I ~ ' 5  l1  ~··
Load factor
. .\ irplanc K .\ \' H. P.
  _~ __ 1 __ : _ _ _ ____ F rencl'__l li . S .. ·\rn1y
PW L __ ___ __ __ 10 I 2(.3. 8 1.46 370 8. 9 i 12.0 (S. 5)
NB3A " """ 10 I 209 I I. 40 '.JOO i 8. 4 1 12. 0 18. ii)
PS~. l ~ ·    15 l ~l
1
, J.45 2'.0 I l~. 0 12.0 (~ . ~ l
P\\  1 .......... 10 250.~ l. 515 454 •. 4o 12.0 ( ~ . . >)
PW8 ______ ___ 10 28i 1.68 438 ll. U 12.0
PW9 __ ________ 10 2;5:l 1. 63 448 9.4 12.0
TP L  ·  lO ~4.; l. ;\li 400 7.6 I ~.5 ( 7.~)
DH4R .... .... 7.5 3i~ l. 18 400 4.o (5.0) 8. 5 (6.0)
G AL .. .  · 7.5 89!• l. O!i 800 3.8 (5.0) I (7.0)
X~·ct\~~~,~~~:. i.5 3E3.6 1 1.25 282 7.12 8.5 ((i. 5\
XB lA (Bis • I pa1.10) __ __ __ __ i. 5 353. G 1. 33 '.JOO 8. q4 I 8. ,; (6 .. 5)
§8=L :::::::: 1 ~ 5 g~ u~ :~ . ~:J~ ~: ~ 16
·
5
>
C05 _____ ~  ./. 5 ;345 1. 33 400 5.89 I 8.5
DB ID. ...... 11 686 1. 16.5 700 ; 6.6 I 5. 5
N R SL _______ · / 7. 5 1191 0.995 800 ' 3.~ (~.0) 4.5
t;f!91__ ~:: :: :: u 3, ~~~ 5 I n~ ' 2, t~ Uii (aO) u (4.0)
TA3 __ ________ 7. 5 203 0.987 llO 5. 15 1 8. 0
TA5 __ __ __ ____ 7. 5 255 1.038 210 '.l.95 (5.0) 8.0
TA6  7. 5 202 1.152 210 4.2i (5.0) 8.0
TW: 3. ........ 7. 5 280 1.03 180 4.92(.;.o) 8.0
Messen ger_ _ .. _ 7. 5 142.< 0. 96i fi4 5. 8:l 7. 5
JLf> ______ ___ __ ll 353 1.112 243 8.54 5 .. ;
T 2 ___ _________ ll 924 L OOS 400 lO. 1 5. 5
VCPR _________ 10 205.8 1.85 600 8.:Ji\ ., (li. 5'1)
R3(\TcrYi!le) __ L5 143.6 2.25 430 24.2 (7.5)
R 6 (Cun.is>) .. 10 136 2. 25 430 13. U (8. 5) I
In t he above t a ble column 2 gives t he value of K
specifi ed for use with t he S. T. A.e . formula.
Column 3 gives t he wing a rea in sq ua re feet.
Column 4 gives the high speed at t he ground iu hundreds
of miles per hour.
Column 5 gives t he horsepower observed in t he
flight test or the rated power of the motors used. ·
Column 6 gives t he load factor for use in design as
obtained from the S. T. Ae. formula. As the French
(1)
2
, ... \ i \).
'(\ ~'
specify that 5.0 is the minimum allowable value, whet ~nq similar that will not be subjected to that
the formula gives a smaller value, it is followed by 5. mane1t~e The chief weaknesses of the formula are
in parentheses. tfia a least one quantity that slwuld be considered as
Coluinn 7· gives the load factor now required in the a variable is made a part of the a1'bitrary constan.t, and
High Incidence condition by the United States Air doubts are entertained as to the validity of the assumpService.
Where the particular airplane is one that tions made in regard to certain factors the magnitude
was designed when a lower value was specified for its of which are not known and are therefore merely
type, the older requirement is added in parentheses. surmised.
Study of the above table shows that only in the cases As the formula stands there are three variables, the
of the DBlB, NBL1, JL6, T 2 and the racers are wing area, horsepower, and high speed at the ground,
the values required by the French greater t han those but they are so combined that there is really only one
now required by the Air Service for the type of air variable, the minimum drag coefficient of the airplane
plane considered. In the case of the NBL 1, this is as a whole. All of the other factors upon which the
due solely to the fact that the arbitran· minimum load factor depends are combined into an arbitary conallowed
by the French is greater than that allowed by stant depending on the t ype of the airplane in question ,
the Air Service. In the cases of the DBlB, JL 6. all military airplanes being divided into four, and
and T2 the values given by the French formula are 50 civilian airplanes into two t y pes. In the compl'ete
per ceht higher than they would be for biplanes of the formula, as given by M. Huguet, the more important
same performance, and it. is believed that in all three quantities are the ratio of di ving speed to speed at
cases the ,·alues given by t.he French formula are too maximum load factor, rat io of parasite drag to minihigh
, and those used by t he Air Service much more mum wing drag, rat io of propeller drag in the dive to
reasonable. the \Yeight of the airplane, and the ratio of maximum
The present Air Service requirements for racers are lift on the airfoil to minimum drag on the airplane.
admittedly too low, but it is not believed t hat the use Arbitrary values of the first three ratios and the maxiof
the French formula would put their design on a mum lift are assumed in order to justif.v t.he arbitrar:·
more rational basis. The R 6, though designed for a constant used in the formula. This would be quite
higher load factor t han the R3, failed in flight yet, satisfactory if the values assumed for these ratios were
according to the French formula, the R 3 should have corref't and the designer was allowed to use onl.1· airbeen
designed for a factor almost twice as great as foils with the maximum lift a ssumed. As it is, the
that_needed for the R 6. res ults of the tests on the PW 7 show that the values
_.\.most serious objection to the adoption of the French
formul:;i is sho1rn by the figures for t he PW7. According
to the formula a load factor of 7.45 would provide
a safety fac tor of 2.0 over the most probable load, yet
Lieut. Doolittle recorded an actual .load factor of 7.9.
BASIS OF S. T. Ae. FORMULA
The t heoretical basis of t he S. T. Ae. formula is given
in " La Construction des Avions" by L. Huguet. In
that book the maximum load is assumed to occur
during the maneuver of flattening out from a dive at
terminal Yelocity . The expression for the maximum
load factor is developed in a manner similar .to that
employed by the writer in McCook Field Serial Report
No. 2388 " Preliminary Study of Theoretical Loads on
Wings ." In fact, t he discussion of t he problem in iVL
Huguet's book great ly influenced the writing of the
report mentioned.
The theoretical basis of the French formula is considered
sound for pursuit a irplanes and other types
likely to be di ved at high speeds, bnt not for t ransports
•
assumed are not proper for present day design s.
It. might be argued that the formula could be imJll"
O\"ed by considering the maximum lift coefficient as
an additional Yariable, but that 1rnuld still. leave the
other three ratios. The final values selected by the
French for the arbitrary constant 1rnre checked bY
comparing the results of their formula. with the res ults
of accelerometer tests made by the British iu whi ch .
:L2 was t he maximum .load factor recorded. More
recent tests i11 the United States sho1\· that that Yaluc
can be, ancl proba bl:r often is, exceeded in practice.
In t his country, and also in England and German:· ,
the load factor requirements have been determined by
studying the res ults of accelerometer tests and estimating
direct ly from them wl)at should be the values
specified for t he vario)Js types. This is by far the
preferable method, as the requirements are t hen admittedly
purely empirical and t here i8 no apparent!:·
rational .formula to lead one to forget that the .load
factor used is really based primarily upon assumptions
a.; to t he magnitud e of three 11nkn o1n1 quantities.
0