[_
.r I
Auburn University Libraries
1111111 11111 11111 11111 1111111111 11111111111111111111 11111111111111111!1 11111111
File D52.33/217
.. . 3 1706 025 84998 O
....~ cao~,• FIELD REPORT, SERIAL No. 2090
AIR SERVICE· INF N CIRCULAR
. · . (AVIATION>
PUBLISHED BY THE CHIEF OF AIR SERVICE, WASHINGTON, D. C.
Vol. V May 1, 1923 No. 440
DESIGN OF
INTERNALLY BRACED BIPLANE WINGS
(AIRPLANE SECTION REPORT)
Prepared by A. S. Niles
Engineering Division, Air Service
McCook Field, Dayton, Ohio
October 5, 1922
WASHINGTON
GOVERNMENT PRINTING OFFICE
1923
;
"·
CERTIFICATE: By direction of the Secretary of War the matter contained herein
is published e.s administrative information and is required for the proper transaction
of the public business.
(11)
.~
;,
t
DESIGN OF INTERNALLY BRACED
INTRODUCTION.
Since the appearance and great success of the Fokker
DVII, many designs have been made of internally
braced biplanes, and several have been built. Very little
has yet been published, however, on their structural
characteristics and the special problems connected with
their design. Many of the designs proposed are unbalanced
and are either not economical or weak, owing to the
peculiar properties of this type of construction being
somewhat imperfectly understood. This report is intended
to describe the properties of internally braced
biplanes which are of interest to the structural designer,
and, by a. numerical example, to indicate a. proper method
of design. Some of the points touched on are not confined
in their application to this paticular type of construction
but apply to all other types as well.
The most important feature of internally braced biplane
construction (and one which is not yet known to many
designers) is that the influence of the stagger or incidence
bracing can be very closely computed, and utilized to
allow a. great saving in the weight of spars. The principal
effects of the incidence bracing are to decrease the stresses
in the lift trusses and increase the stresses in the drag
trusses. In low incidence, for example, the rear lift truss
is heavily, and the front lift trust lightly, loaded. As a.
result, the rear spars tend to deflect more than, the front
spars. This tendency is resisted by the incidence wire
from the lower front to the upper rear spar, which is put in
tension. The vertical component of this tension acts as a
down load on th.e rear lift truss and as an up load on the
front lift truss. The rear truss, which is limited by thill
condition of loading, is thereby relieved. The front truss
receives additional stress, but as it is limited b'y the high
incidence condition, and is lightly loaded in low incidence,
no critical stresses are caused in it by this action. The
horizontal component of stress in the incidence wire acts
as an antidrag force on ilie upper drag truss and as a drag
load on the lower. This horizontal component may be
much larger than the component of the a1r load parallel to
the chord on the whole wing. Similar effects are ca.used
in the other loading conditions. In a nose dive the front
truss tends to deflect downward and the rear truss upward.
The incidence wire in this case reduces the direct stresses
in both lift trusses but puts very heavy loads in the drag
trusses. The effect of the incidence wires is much less in
high incidence and in reversed flight.
Up to the present time the American practice has been
to neglect the effect of incidence bracing on truss .stresses.
So far as the lift trusses are concerned this practice is on
the safe side, but it is on the unsafe side as regards the web
l,Ilembers of the drag trusses. These latter members,
however, have generally been greatly over13ize, so no harm
has been done. The German practice, as described by
van Gries in Flugzeugstatik, has been to allow for the
effect of the incidence bracing. On page 80 of Flugzeugstatik,
van Gries gives a. very interesting table showing
the influence of the incidence wires on the stresses in
different members of five selected airplanes, with their
averages. These values show that the direct stresses in
the front upper spar and the front lift wires in high incidence
are usually little changed by the action of the
incidence wires.
In low incidence the direct stress in the rear upper spar
is decreased 25 per cent and in the rear lift wire 30 per
cent. In reversed flight the stresses in the front lower
spar and the front landing wire are decreased 25 per cent.
In a nose dive the stresses in the lower wing are greatly
increased . These figures would be changed a little if the
American loading assumptions were used, but not very
much, as the American assumptions are very similar to
the German except for the nose dive·.
The results of static tests on the PWl:A and the TW2
have shown that the effect of the incidence bracing can be
very closely computed for internally braced biplanes with
N struts. The chief purpose of this report is to describe
a method of computing this effect and of obtaining the
resulting saving in weight of structure.
The report falls into the following main divisions:
Part I is a general description of t,he method of design
to be used, without numerical examples.
Part II is a numerical example giving the computations
required for the design of the PWlA.
Part III is a study of the static test results on the PWIA
and the TW2, with reference to the effectiveness of the
N strut in equalizing deflections and redistributing
stresses.
Appendix I describes and illustrates the new and approved
method developed by the Forest Products Laboratory
for determining the modulus of rupture of box and I
sections of wood.
Appendix II is a study of an I strut to replace the N
·strut of the PW IA.
Where the procedure is the same as for externa!Jy braced
wi~gs or has been fully described elsewhere, it is described
very briefly or a reference is given. It is intended primarily
to describe those features of the design of internally
braced wings which differ from the methods used for eitternally
bra,ced wings.
The bulk of the methods described in this report ™'Ye
been already published in more or less complete form in
the following places:
(a) Article 173,, "Structural Analysis and Design of
Airplanes."
tb) Information Circular No. 213 (McCoqk Field Serial
No. 1462) "Deflection of Beams of Nonuniform Section."
(c) McCook Field Serial No. 1480, "Design of Internally
Braced Wings for the PW1."
(d) " Handbook for Airplane Designers," edition of
August, 1922.
(e) McCook Field Serial No. 1958, " The Computation
of Loads on Spa.rs."
( t)
PART I.
GENERAL DESCRIPTION OF METHOD.
A procedure for the computation of the curves of distributed
air load on the·spars in the different loading conditions
is outlined in McCook Field Serial No. 1958,
"The Computation of Loads on Spars." As the wings are
internally braced, the wing ,tip loss will be assumed to
act from the ends of the spars to the sections where the
chord is equal to the distance to the end of spar, regardless
of the location of the N strut.
After computing the ordinates of the curves of distributed
load, the following steps should be taken:
(a) Computation of shears and moments due to l(fistributed
lift load. (In this report the terms lift and drag loads
refer to loads perpendicular and parallel, respectively, to
the wing chord and not to the relative wind.).
(b) Tentative design of spars.
(c) Computation of deflections at the N strut due to the
distributed loads, and the unit loads at the N strut.
(d) Computation of forces in tl).e N strut.
(e) Computation of shears and momenta in the spars, due
to the combination of the distributed loads and the forces
acting in the N strut.
(f) Computation of forces in the drag trusses.
(g) Comparison of maximum computed and allowable
stresses.
(h) Redesign of spars, if necessary.
(i) Design of N strut and drag truss members.
(j) Design of center section struts.
COMPUTATION OF CURVES OF SHEAR AND
MOMENT DUE TO DISTRIBUTED LIFT LOAD.
The curves of shear and bending moment due to the
distributed lift load are computed in the usual manner
from the loading curves. It is not necessary to draw
separate curves for each spar for each condition of loading.
One curve may be drawn for eacl:.. B"j)ar, in some cases for
each wing, and the values desired from the other curves
found by proportion. At any point on a spar, the moment
and shear under different angles of incidence have the
same ratio as the running loads per inch. This is not
absolutely true, owing to the effect of the dead weight of
the wing, but is a sufficiently close approximation for
design. In selecting the shear and moment curves to be
computed, those due to the highest values of the running
load per inch should be taken.
TENTATIVE DESIGN OF SPARS.
In making the first tentative design of spars, only the
etreBBe!l in the highincidence condition should be considered.
Experience indicates that the N strut will
reduce the loads in the other flying conditions, so that a
design mad.e on this basis will be acceptable. To be on
the safe side, the front spars should have a margin of
safety of from 5 to 10 per cent. Careful study of the stresses
in the first set of spars designed. will show what changes
are needed in the revisions. In the tentative design the
drag stresses may be neglected.
Some designers wish to eliminate the N strut in order
to reduce the parasite drag of the airplane. This would
be unwise, as the saving in the structural weight, the
increased rigidity of the wing cellule, and the increased
safety during a nose dive more than compensate for the
added res:witance. It may be possible to use an I strut
similar to the one used on the V. C. P. 1 instead of an N
strut as used. on the Fokker D7, but this has not yet been
thoroughly tried out in practice. In Appendix II of this
report, a study is made of an I strut to replace the N strut
of the PWIA.
COMPUTATION OF DEFLECTIONS.
In order to compute the effect of the N strut, it is necessary
to know the deflections of the different spars at the
N strut point due to the distributed loads carried under
each of the loading conditions, and also the deflections
due to a unit load applied at the N strut point. In finding
the deflection due to the distributed load, the deflection
of each spar under its maximum load should be computed,
and the deflection in the other conditions found by proportion.
In computing the deflection due to a concentrated
load from the N strut, it will usually be more conv'enient
to use a unit load of 100 or 1,000 pounds than a
unit load of 1 pound. In.both cases the deflection desired
is the deflection of the Nstrut point above or below the
center supports. In order to obtain this value, it is necessary
to compute .the deflections of. both points with reference
to the tangent to the ela.'!tic curve at the center of the
spar, and take the difference. This can easily be seen
from Figure 1, in which the deflection of a spar is plotted
to an exaggerated scale. The · deflection desired is AB
which is equal to ACDE. CE is tangent to the spar
AD at O on the center line.
Only when the spars are of uniform section can the
deflections be found by means of the ordinary deflection
formulas. Usually the spars are tapered, in which case
use may be made of the method described in Information
Circular No. 213 (McCook Field Report No. 1462) "Deflection
of Beams of Non uniform Section.' ' This method is also
briefly described in article 173 of ".Structural Analysis
and Design of Airplanes." When the spars are metal
trusses., the deflections may be computed by the method
of work, or the Williot diagram. Both of these methods
are very tedious, but up to the present all attempts to
modify beam deflection formulas to make them applicable
to shallow trusses have been unsuccessful.
Where wooden box spars are used the moment of inertia
employed in computing the deflections, and also the fiber
stresses, should be the moment of inertia of the solid
flange pieces alone, the plywood webs being neglected.
The web undoubtedly adds to the moment of inertia,
especially the part adjacent to the flanges, but the increase
is not large, and on the other hand there are shear
(2)
1
deflections which are neglected in the computation. On
the whole, therefore, it is considered advisable to neglect
the webs in computing moment or inertia.
COMPUTATION QF STRESSES IN THE N STRUT.
In order to compute the stresses in the N strut, the
following quantities must be obtained:
(a) Deflection of each spar under distributed load in
each condition of loading.
(b) Deflection of each spar under a unit concentrated
load applied at the N strut.
(c) The concentrated load at the N strut required to
deflect the spar 1 inch. This is the reciprocal of (b).
(d) The force required to deflect each pair of spars
(front and rear) 1inch. This is the sum of forces (c) for the
two spars considered.
(e) The deflection of each pair of spars due to the unit
load acting at the N strut. This is the reciprocal of (d).
(f) The division of forces (d) between the spars of a pair.
This is the ratios of forces (c) to (d).
The force required to equalize the deflections of the spars
of each pair can be obtained by dividing the difference in
deflection by the sum of the deflections of the two spars
under unit load. The result will be the number of unit
loads required. When the force required to equalize the
deflections in any loading condition is known, the equalized
deflection can easily be found. This computation should
be made for both spars an<l the results should check.
The force required to equalize the deflections of the two
pairs of spars and the resultant deflection can be found
similarly. This force should be divided between the two
spars of each pair in t_he proportion found under (f) above.
The forces acting on each spar to equalize its deflection
with the other member of its pair and to equalize the
deflection of the two pairs should be added algebraically
to determine the net concentrated vertical load on the
spar at the Nstrut point. Two checks can be applied to
these forces. Their algebraic sum should equal zero.
The deflection of all four spars due to the distributed load
plus, alg.ebraically, that due to the concentrated load,
should be identical with the equalized deflection of the
two trusses found above.
Knowing the vertical component of the force applied to
each spar and the dimensions of the N strut, it is a simple
matter to compute the forces in each Nsirut member.
If, as is usually the case, the center member of the N
joins the front lower to the rear upper spar, the following
conditions will hold: The vertical component. in the front
and rear members of the N will be the net equalizing
forces on the front upper and rear lower spars, respectively.
The vertical component in the center member will be
the force required to equalize the deflections of the two
trusses. The drag components and direct stresses can
then be found froin the slopes of the members. The drag
components of streBB in the N strut are carried by the
drag trUBBes, and in low incidence and nose dives may be
the greatest loads acting on these trusses. It is possible,
in computing the Nstrut stresses and the equalization of
deflections, to allow for the deflections of the drag trusses
und~r these Nstrut loads, but the increased accuracy of
the results do not warrant the extra work involved.
In practice it has been found that the N strut does not
wholly equalize the deflection of the spars. No attempt
3
has been made in the static tests to find the difference in
deflection of the upper and lower spars of a pair, but it is
believed that it is very small, being equal to the change
in length of an Nstrut member. The difference in deflection
of the front and rear trusses has been measured on
both the PWlA and the TW2, and has been found to
be approximately proportional to the computed difference
in deflection, aBBuming the stress in the center Nstrut
member at 90 per cent of the stress required for complete
equalization. To allow for this partial failure of the
N strut to equalize deflections, two sets oi stresses should
be computed: First, the stresses that would result if the
deflections were fully equalized, and, second, the stresses
that would result if the stress in the center member of the
N strut were only 80 per cent of its value in the first case.
The stresses in all members should be computed for both
cases, and the design made for the.greatest stress in each
member. In case the stress in the center member of the
N strut is very small, the second case may be omitted, as
is done in the highincidence condition in the example
in Part II of this report.
COMPUTATION OF NET SHEARS AND MOMENTS IN THF. SPARS.
After the vertical forces acting on the spars from the
N strut have been found, the shears and bending momenta
in the spars can be computed. These shears and bending
moments are added algebraically to the shears and moments
due to the distributed lift load to find the net stresses in
the spars.
COMPUTATION OF "'FORCES IN THE DRAG TRUSSES.
The component of the distributed air load on the wing
parallel to the chord is computed as for any other wing, and
divided into concentrated loads acting at the panel points
of the drag trusses. The drag components of stresses in the
Nstrut members are applied at the Nstrut point in the
same manner as the drag compoltents of the stresses in the
struts and wires of an externally braced cellule. The
forces in the dragtruss members due to these loads are
computed in the usual manner.
CHECKING TENTATIVE DESIGN OF SPARS.
The unit i,treB8es in the spara due to the lift and · drag
loads are added in the usual manner and compared to the
allowable unit streBBes. If any of the spars have computed
stresses above the allowable, a redesign must be
made. If any spar is very highly stressed in all conditions
of loading, a redesign is desirable. In making a
redesign the fact must always be borne in mind that a
change in the size of any one spar will affect the stresses
in all of the spars. This opens a number of poBBibilities.
If one spar is weak and the others are strong enough, it
may be that the most economical method of obtaining
a safe design is not to increase the size of the weak spar
but to decrease it, causing it to throw more of its load
on the stiffer spars. On the other hand, a spar may have
its stresses jncreased by increasing its size as the added
stiffneBB may cause it to carry load from the other spars
in larger proportion than its increase in section modulus.
These are rare cases, but the possibility of such effects
must always be considered when revising the spar sizes.
DESIGN OF N STRUT AND DRAG TRUSSES.
The N strut and drag trussing can be designed after the
completion of a satisfactory design for a set of spars,
The forces in these members are computed in determining
the size of spar required. There .are no particular featureR
in this design which need explanation.
DESIGN OF CENTER SECTION STRUTS.
4
It has been customary.in the design of internally braced
biplanes to follow the lead o·f Fokker in the disposition of
the center section struts. The arrangement in general
use is a single strut from the fuselage. to the rear spar and
a tripod from the fuselage to the front spar. The stresses
in such a design may be computed as follows: First
compute the forces in the rear strut and the compression
rib that are required to support the rear upper spar.
There will be a sideways component of stress in the rear
strut which will be carried by the center section of the
rear spar and may be neglected. At the front spar there
are the three tripod members with unknown stresses,
and the front spar, compression rib, and possibly internal
drag wires, carrying known loads. The forces in the
tripod members required to neutralize the resultant of
the known loads on the point can be computed by statics.
The stress in some of the tripod members will be tension
and in some compression, and will seem unduly large.
If the front spar be assumed to act as a strut between
the 1ight and left hand tripods, the stresses in the tripod
will be much less but the structure becomes indeterminate.
Extensometer readings on the PWlA gave little
indication as to the actual division of load. In any case
the tripods are only a little heavier if designed to act
independently than if they are assumed to be braced
by the front spar; so it is recommended that the more
conservative method of design be followed. This is
especially dE>sirable if the airplane is likely to be subjected
to severe unsymmetrical loads ru, in rolling. Strong
center section bracing also gives a desirable degree of
added safety in case the airplane rolls over in a· bad landing.
When Lieutenant Mosely crashed in the MB6, the
center · section struts held and he escaped practically
uninjured, but in the case of Major Kirby's accident in a
VE7, the center section struts failed and he was badly
hurt, although the impact was probably not as great.
PART II.
NUMERICAL EXAMPLE COMPUTATIONS FOR
PWIA.
This numerical example is given to illustrate the methods
outlined in Part I. The PWlA was chosen because it
was pOBBible to compare design figures with static test
results. 'Fhis comparison is made in Part III.
The computations given below are not those used in the
design of the PWlA, but are computations made to aid
in interpreting the static test results. The computations
used in the actual design are those outlined in McCook
Field Report No. 1480. The computations below are
intended to represent the static test conditions as nearly
as possible. For this reru,on, the actual values of the
strength properties of the spars in the tes.t are used ~ather
than the standard values which would be used in a new
design. In some pther cases, deviations are made from
the practice that should be followed in a new design in
order to approximate the static test condition more closely.
Such deviations, however, are noted and the proper
design procedure indicated, so that no difficulty should
arise on this account. The justification for this method
of procedure is that a single set of computations serve the
double purpose of illustrating the method to be used in
design and forming the basis of the study of the static test
results in Part III.
General data on the PWlA airplane is given in Table I
and Figure 2.
TABLE I.Oeneral data .
A,erofoil section ................... Modified Fokker D7.
GrOBB weight of airplane . .. .............. pounds . . 3,046
Weight of wings . ......... ....... ... . ....... do.... 466
Net weight of airplane ...... ...... .. ......... ilo .... 2,580
Span ................ ..... . ..... . ......... in.ches.. 348
Chord, both wings ......................... do.... 65
Gap! ................... . ..... . .. .. .... . .. do.. . . 55
Stagger ........ .. ..... .................... do .... 20.5
Area 6f upper wing . . ................ square feet.. 150
TABLE ILAerodynamic data.
Flight condition. I Angle of
attallk
(degrees).
L/D.
C.J?.
location
(per
cent).
Load
factor.
 !
High jncidence. . .... .. . . .... . 14
Low incidence. .... ... ..... . . 2
Reversed flight ... .... . ......•. .... .... .
9.05
7.07
4. 00
30
60
25
7.5
5.5
3.5
The load factor used in high incidence was 7 .5 instead
of 8.5 because that was the heaviest load carried in static
test without failure. No computations are given here for
the nosedive condition, ·as that condition was not investigated
by static test and the procedure is the same, once
the loading curves have been determined, as in the cases
given.
COMPUTATION OF LOADS ON SPARS.
Assu,me 1;ifliciency of lower wing as 0.85 as was done in
the static test. For new designs the recommendations in
the 1922 edition of the Handbook for Airplane Designers
should be followed.
Effective area of wings=l50+0.85Xl38=267.3 square
. feet.
Load on upper wing=l50X2,580+267.3=1,450 pounds
per load factor.
Load on lower wing=l38X0.85X2,580+267 .3=1,130
pounds per load factor.
Average load per inch run on upper wing, w=l,450+
348=4.l 7 pounds per load factor.
Average load per inch run on lower wing, w=l, 130+314=
3.60 pounds per load factor.
TABLE III.Average running loads on spars.
Spar.
High incidence. Low incidence. Reversed flight.
h~ h~ h~ h~ h~ h~
=1.0. =7.5. = 1.0. =5.5. =1.0. =3.5.
Area of lower wing ....................... . . do.... 138 •++++++
Location of spars in per cent of chord.
Front upper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Front lower.: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . }3
:::~:::.·..·~::::::::::::::::::::::::::::::::::: :
Items 2, 3, and 4 are the actual weights of the airplane
subjected to static test, and the values are much larger
than thooe used in the original design. The other items are
dimeruiions and are the !lRIIle as were used in the origipal
design.
Table II gives th.e principal aerodynamic da.ta and the
load factol"!! used in this investigation.
Front upper .. .. .. .. .
3.131
23.42 0 0 3.65 12. 75
Front lower .... ..... 2.38 17. 81 .216 1.186 2.74 9.58
Rear upl)(lr ..•... .... 1. 04 7.82 4.17 22.90 .521 1.82
Rearlower . ... .... .. '1.22 9.18 3.38 18. 60 .864 3. 02
The values in Table III were computed in the usual
manner from the spar locations given in Table I, the c. p.
locations in Table II, a:i;id the average loads above. The
c. p. locations in Table II are those of the actual sand load
and are used without correctfon for the difference in
location of the c. p. of net and gross loads.
COMPUTATION OF SHEARS AND MOl(ENTS,
No shear and bending moment curves were C<>mputed
directly for any of the average loads given in Table III.
(5)
The values desired were obtained by proportion from the
shear and moment curves computed in the original design
and given in McCook Field Report No. 1480. A small
error is introduced by this procedure, but it is negligible.
The average running loads on which the shear and moment
curves used for these proportions are based are as follows:
Front upper spar, 21.92 pounds per inch.
Front lower spar, _17.26 pounds per inch.
Rear upper spar, 24.25 pounds per inch.
Rear lower spar, 19.7,;l pounds per inch.
The shear and moment curves derived from these loads
are plotted in Figures 3 to 6, inclusive, the values being
taken from Report No. 1480.
In all spars the critical section is at the supports. Table
IV gives the values of the average running load and the
bending moment at the supports from the basic curves of
Figures 3 to 6 and the three flight conditions considered
in this report.
Table IV. Bending mmnents in spars at supports.
[w is given in pounds per inch run and Min inchpounds.]
Spar. Front Front Rear
upper. lower. upper.
Rear
lower
From curves in figures 3 to 6.
6
w...... . .. . . . . . . . . . . . . . . . . . . . 21. 92 17. 26 '.l4. 25 19. 74
M.. .. . .. ...... . ..... ...... . .. 169,210 202,480 185, 700 231,200
High incidence.
w... . .. . . . .. .. . . . . . . . . . . .. .. . 23. 42 17. 81 7. 82
M . . . . . ...· .... .. . .... .. . . .... . 179, 800 209,000 59,900
w .. .•. .. . . ... . . ... . . .. .. . .. ..
M ... . . .. . . .. .. .. .. . .... ... . . .
0
0
Low incidence.
1 .. 186 22. 90
13, 900 175, 400
Reversed flight.
w... . .... ............. ... . ... 12. 75 9. 58 1. 82
M.. . . . . .... .. . ... . . . . ..... .... 98, 400 ll2,300 14,000
TENTATIVE DESIGN 0~' SPARS.
9. 18
107, 500
18. 60
218, 000
3.02
35,400
Although the load on the rear spars is far greater in the ·
lowincidence condition than in high incidence, the
design of all four spars is based on the stresses in high incidence.
Experience has shown that in the lowincidence
condition, the N stru.t transfers a large part of the load
from the rear to the front truss, so that very often the net
stresses in the rear spa.rs at the critical section are lowE:r
in low incidence than in high incidence.
There a.re two general methods used for the design oi the
flanges of box spa.rs subjected to bending. The method
recommended by the Forest Products Laboratory is .to treat
the spar as a bee.in and compute the maximum fiber stress
from/= My/I. This value off should be less than the
modulus of rupture as determined by the Forest Products
Laboratory method described in Appendix I of this report.
A good approximate method for trial designs consists in
treating the spar as a truss and dividing the bending moment
by the center to center distance between flanges to
obtain the total flange stress. Dividing the total flange
stress by the flange area gives the average flange fiber
stress, which should not exceed the compressive strength
of the material in the compression flange nor the tellllile
strength in the tension flange. The first method is more
accurate and should always be used for a final check. Both
methods are used in computing the values for Table V, in
order to give a clear comparison. In addition the allowable
stresses are computed both for standard spruce and
from the strength properties of the spars ~sed in the static
test. These strength properties are given in Table XXXII
of Part III. The value of the modulus of rupture of a
rectangular section used in computing allowable maximum
fiber stress, f = My/I , is the mean of the values obtained
for the two flanges. The value of the allowable
average flange stress, f = M/hA, is the ultimate compressive
strength parallel to the grain of the compression flange.
Figure 7 shows the cross sections of the spars at the center
line of the airplane and 165 inches from the center line.
The slope of the top and bottom fac.es is not indicated, the
flange being shown as the equivalent rectangle. This
equivalent rectangle is the same for all spars. The center
heights at the center line are given in Table V. The spar
sections are constant between supports and taper uniformly
from supports to wing tips.
Figures 8, 9, and 10 give the dimensions used in computing
the moment of inertia. Figure 8 gives the center
height, h; Figure 9 the clear distance between flanges, h';
and Figure 10 the width of flange, b. The moment of
inertia is found from the formula I= b (h3h'3)/12. The
effect of the webs is neglected for the reasons given in
Part I of this report. The distance y to the most strel'JBed
fiber is assumed equal to onehalf of the center height.
Table V gives the computation of stresses in the spars
due to the bending ca.used by the distributed lift load in
high incidence. The stresses due to drag loads a.re omitted,
as they are small and only a trial design is) eing made.
TABLE V.Stresses due to distributed lift load in high incidence.
Computed stress. Allowable stress.
Spar. hCeeingthetr. Edffeepctthiv. e I. A. Standard wood. Test results.
My/I. M/hA..
.Wy/I. M/hA.. My/I. M /hA. .
i~:i ii=::::::::::::::::::::::::::::: 8. 57 6.~ 135.1 5.69 5,700 4,640 6,620 5,500 6,020 8, 560
8.00 6. 26 114.2 5. 69 7,32Q 5,700 6,730 5,500 7,200 7,515
Rear upper . . .. . ... . .... . .. . . ~ . .... .. .. . . fl.04 4.29 55.3 5.69 3,270 2,MO 7,300 5, 500 8, 100 6,015
Rearlower . .... .. .. ......... . ..•.• •.. ... 5. 63 3.~ 45. 7 5.69 6,600 4, 870 7,380 5,500 5,840 5, .550
•
I •
1
7
The lower spars look weak, especially the front · 1ower, I under other loadings found by · proportion. Tables VI .
bnt the upper spars have a good margin of strength and VII, VIII, and IX give the computations from the valuPs
will relieve the lower spars of part of this load.
COMPCJTATION OF DEFLECTIONS.
The deflections were computed in the manner outlined in
article 173 of' 'Structural Analysis and Design of Airplanes,''
and more fully explained in Information Circular No. 213.
The computations of the values of M/I are not given, as
they are done by familiar methods and the basic data are
given in Figures 3 to 10, inclusive. I t should be noted
that in this report the values of M/ I are based on the values
of w, taken from Figures 3 to 6. Values of the deflection
under these loads are computed directly and deflections
of M/I to the values of Ea for distributed loads. Tables
X, XI, XII, and XIII give the same computations for a
concentrated load at the N strut. The only values of
Ea given are those for the supporting and Nstrut points,
as they are the only ones needed. The N strut is at
station 140 on each spar. The Sllpports are at station 44
on the upper spars and station 16 on the lower. Table
XIV gives the values of E in thousands of pounds per
square inch for each spar, and the values of w and the
deflection of the Nstrut point for each loading condition.
The value of E used is the average of the values obtained
by tests on the material in the two flanges.
TABLE VI.  Deflection of front upper spar.
[Avera;(e uniform load, w 21.92 pounds per inch run.]
Sta I M ML • tion . 111/ ! . Sum. t:.L. 7 !:.L. x• . j t:. X. T, 1{t:.L. (T,!ft:.L) t:.I,. Eli.
0 1,084 0 0
2,174 JO 10,870 5.00 54, 350 0
10 1,090 10,870
2,208 10 11,040 4.98 55,000 108,700
20 1,118 21.,910
2, 278 10 11,390 4. 97 56,600 219, 100
30 1,160 33,300
2,394 10 11,920 4. 96 59,200 333,000
40 1,224 45,2'20
2, 476 4 4,950 1. 99 9,860 180,880
44 1,252 50,170 1, 076,690
2, 500 6 7; 500 3. 00 22,500 301,020
50 1, 248 57,670
2,470 10 12,350 5. 02 62, 000 576,700
60 1,222 70, 020
2, 402 II) 12;010 5.03 60,400 700,200
70 1,180 82,030
2,314 10 11, 570 5. 03 58,200 820,300
80 1, 134 93,600
2, 202 10 11, 010 5.05 55,600 936,ooo·
90 1, 068 104,610
2,050 10 10,250 5.07 52, 000 1,046,100
100 982 114,860
1,888 9 8,496 4.56 38,750 1, 033,740
109 906 123,356
1,594 17 13, 549 8.90 120,500 2,097,050
126 688 136,905
1,194 14 8,358 7. 36 61,500 I, 916,670
140 506 145,263 11,035,920
145,263 766,460 10, 269, 460.
Deflection of Nstrut pQint (station 14)) with respect to support (station 44): li= I /E (ll,035,9201,076,690)~ 9,959,230/E.
55311 0312
·,
Station.
Mil. Sum.
   
0 1,774
16 1,774
3,548
20 1,768
3,542
30 1,726
3,494
40 1;678
3,404
50 1,620
3,298
60 1,548
3,168
70 1,470
3,018
80 1,360
2,830
90 1,266
2,626
100 1,114
2,380
109 986
2,100
126 696
1,682
140 456
1,152

19,236 3 ,242
8
TABLE VII.Deflection of front lower spar.
[Average uniform load, w=l7.26 pounds per inch run.]
M t:.L. yt:.L. I T~. yMt: .L Xo. I '.<.',!I!. _t:.L . (~ft:.L)t:.L.
I 0
16 28,384 8. 00 m,100 0
28,384
4 7,084 2.00 14,200 113,500
35,468
10 17, 470 5.02 87, 700 354,700
52,938
10 17,020 5.02 85,400 529,400
69,958
10 16,490 5.03 82,900 699,600
86,448
10 15,840 5.04 79,800 864,500
102,288
10 15,090 5. 04 76,000 1,022,900
117,378
10 14,150 5.06 71,600 1,173,800
131,528
10 13,130 5.06 66,400 1,315,300
144,658
10 11,900 5. 11 60,800 1, 446,600
156, 5.58
9 9,450 4.60 43,500 1,400,000
166,008
17 14,297 8. 98 128, 300 2, 822,100
lR0,305
14 8,064 7.48 60,300 2,524,300
188,369
I 188,369 1, 084,000 14,275, 700
E4.
0
m,100
15,359,700
Checks: 2:X 19,2364561, 774=36,242.
1,084,000+ 14,275, 700=15,359, 700.
Deflection of Nstrut point tstatlon 140) with respect to support (station 16): a~JJ E (15,359,700'lZT,100)=15,132,600/ E.
Station.
M/l. Sum.
 
0 2,900
10 2,922
5,822
20 2,996
5,918
30 3,112
6,108
40 3,280
6,392
44 3;360
6,640
50 3,332
6,692
60 3,268
6, 600
70 3,184
6,452
80 3,082
6, 266
90 3,004
6,086
100 2,698
5,702
109 2,472
5,170
126 1, 888
4,360
140 1,3$6
3,274
I
TABLE VIII.Deflection of rear lower spa'r.
[Average uniform load, w=24.25 pounds per inch run.]
M 11{
t:.L. 7t:.L. Xo. yt:.Lxo. ~:t:.L. (~ft:.L)t:.L.

0
10 29,110 4.99 145, 200 0
29,110
10 29,590 4.98 147;, 200 291,100
58,700
10 30,540 4. 97 151,800 587,000
89,240
10 31,960 4.96 158,500 892,400
121,.200
4 13,280 1. 99 26, 400 484,800
134,480
6 20,080 3. 01 60,400 $06,900
154,560
10 33,000 5.02 1!15, 600 1,545,600
I
187,560
10 32, 260 5.02 161,900 1,875,600
219,820
10 31,330 5.03 157,600 2,198,200
251,150
10 I 30,430 5. 03 152,900 2,511,500
281,580
10 28,510 5. 09 145,100 2,815,800
310,090
9 23,260 4.56 106,009 2,790,800
333,350
17 37, 060 8. 88 329,000 5,667,000
370,410
14 22,9?0 7.36 168,700 5,185,700
39!1, 3:10
393,330 2,076, 300 27,652, 400
Eo.
0
2,884,400
29, 728,700
Denection of Nstrut point (station 140) with respect to support.(statlon 44): o=l/ E (29,728,7002,884,400)=26,844,300/ E.
I
.I.
I
I
Station.
M/I. Sum.
    
0 5,060
10,120
16 5, 060
10,130
20 5,070
10,070
30 5,000
9, 896
40 4,896
9,648
50 4,752
9,332
60 4,580
8,916
70 4, 366
8,460
I 80 4,094
7,904
90 3,810
7,240
100 3,430
6, 500
109 3,070
5,288
126
I
2,218
3,702
140 1,484
9
TAm,i,: IX.  DPjtection of rear lower spar.
[A vcmge uniform !pad, w = 19.i4 pounds per inch ruu.J
I
I M
I
M M l'!.L. yl'!.L. x•. 7l'!.Lx0
• ~zl'!.L.
I
I
0
I
16 80, 960 8.00 647 ,700
80,960
4 20,260 2.00 t0,500
101, 220
10 50,350 5. 01 252, JOO
I 151, 570
10 49, 480 5.02 248, 100
201, 050
10 48,240 5. 02 242,000
249,290
10 46,660 5. 03
I
234,700
295,950
10 44,730 5.04 225,500
340,680
10 42,300 5. 05 213,600
382,9~0
10 39,520 5.06 200;000
422, 500
10 36,200 5. 09 184, 20D
458,700
9 29,250 4.58 134,000
487,950
17 41,950 8.96 402,800
532,900
14 25,910 7.46 193,200
I
558, 810
558, 810 3,218,400
c~:dL )/'J.L./ Eo.
0
323, SOO
674,700
1, 012,200
1, 515, 700
2,010, 500
2,492,900
2, 959,500
3,406,800
3,829, 800
1,225,000
4,128, 300
8,295,200
7,460,600
44, 878,700
41,660,300
Deflection of Nstrut point (s tation 140) with respect to support (Etat1bn 16): o= l /E (44,878,700 647,700)=44,:231 ,0CO/E.
0
44
50
60
70
80
90
100
109
126
140
710
710
734
764
786
804
802
772
723
461
0
1, 420
1,444
1, 498
1,~
1,590
1,606
1,574
1,495
1,184
461
TABLE JC  Deflection of front upper spar.
[Concentrated load of 1,000 pouI\dS at station 140.]
14
6
10
10
10
10
10
9
17
14
31 , 240 22. 0
4,332 2.98
7,490 4.97
7,750 4. 98
7, 950 4. 98
8,030 5.00
7,870 5. 03
6,727 4. 55
10,064 9. 13
3, 227 9. 34
94, 680
687,280
12, 900
37, 210
38, 600
39,600
40,150
39,600
30,610
91 , 940
30, 120
1,048, 010
0
31,240
35, 572
43, 062
50, 812
58, 762
66, 792
74,662
81, 389
91, 453
94,680
0
192,840
355,720
430,620
508,120
587,620
667,920
671,958
1,383,613
1, 280, 342
6,078, 753
Eo.
0
687,280
7,126, 763
De:lection of Nstrut point (station 140) with respect to support (station 44): o=l/ E (7,126,760687,280)=6,439,480/ E.
I
10
~BLE XJ.J)ejlection nf front lower spar.
(Concenl.rut.r.d load of 1,000 pot111<ls at sl.at.iou l10.}
Sta · M M ~Af (~¥c,.L),ilL. tion. J,f/l. Sum. t,.L. 7ilL. Xo. 7ilLxo. Tc,.£. E6.
0 1,086 0 0
2,172 16 17,376 8. 00 139,000 0
16 1,086 17,376 139,000
2,192 4 4, 384 2.00 8,800 69,500
20 1, 106 21,_76~
2,250 IO 11,250 4. 97 56,000 217,600
30 1, J.14 33,0IO
2,324 IO 11,620 4.97 57,800 330,100.
40 1,180 44,630
2,392 10 11,960 4.88 59, 600 446,300
5~ 1,212 56,500
2,444 IO 12,220 4.99 6l,OOO 565,900
60 1,232 68,810
2,482 10 12,410 4.99 62,000 688,100
70 1, 250 81,220
2,48! 10 12,420 5. 01 62,200 812,200
80 1,231 93,640
2,451 10 12,270 5. 01 61,500 936,400
90 1,220 105,910
2,350 IO 11,750 5.06 59,400 1,059,100
100 1,130 117,660
2, 151 9 9,693 4.58 44,400 1,058,900
109 1,024 127,35.3
1,644 17 13,974 9. 20 128,500 2,165,000
126 620 Hl,327
620 14 4,310 9.34 40,500 1,978,600
140 0 145,667 11,168,400
145,667 8~0. 700 10,327,700
D,flection at Nstrut paint (station 14~) with respe~t to support (station 16): 6=1/E (11,168,400139,000)=11,00U,400/E.
Station.
Mi l. Sum.

0 1,736
3,472
44 1,736
3,526
50 1,790
3,658
60 l,868
3,8IO
70 1,942
3,946
80 2,00t
4,000
90 1,996
3,956
100 1,960
3,800
109 1,840
3,050
126 1,210
1, 210
140 0
TABLE XJ.I.Dejlection of rear upper spa:r.
[Concentrated load of 1,000 pounds at station 140.]
M M . M
ilL. TilL. Xo. 7 ilLxo. ~It,.L.
0
44 76,380 22.0 1,680,400.
76,380
6 10,580 2.98 31,500
86,960
IO 18,290 4.96 90,700
105,250
IO 19, 050 4.97 94,700
124,300
IO 19, 730 4.98 98,200
144,030
IO 20,000 5.00 100,000
164,030
IO 19,780 5. 02 99,300
183,810
9 17,100 4.5! 77,600
200,910
17 25,930 9.08 235,400
226,840
14 8,470 9.34 79,100
235,310
235,310 2,586,900
(~!fc,.L)ilL . E6.
0
0
1,680,400
458,300
869,600
1,052, 500
1,243,000
1,440,300
1,640,300
1,65i,300
3,415,500
3,175,800
17,535,500
14,949,600
Deflection at Nstrut paint (station 11 )) with respa~t to support (station 44): 6= 1/E (17,535,5001,680,400)= 15,8:;f, 100/ E.
:
Sta tion. M/1. Sum.
0 2,712
5,424
16 2,712
20 2,780
5,492
5,678
30 2,898
5;908
40 3, 010
6,116
50 3, 106
6,286
60 3,180
6;430
70 3, 2.50
80 3,248
6,498
6,460
90 3,212
6,260
100 3,048
5,838
109 2,790
4,526
126 1,736
1,736
140 0
11
TABLE XIII.Deflection of rear lower spar.
[Concentrated Load of 1,000 lbs. at station 140.)
M . M 2;Jf dL. ydL. x.,. ·1 6L x.,. 1 6L.
0
16 43,300 8.00 347,100
43,390
4 10,980 1. 99 21,900
54,370
10 28,390 4.97 141,000
82,760
10 29,540 4.97 146,800
112,300
10 30,580 4.98 152,200
142,880
10 31,430 4.98· 156,500
174,310
10 32,150 4.98 160,000
206,460
10 32,490 5.00 162,400
238,950
10 32,300 5.01 161,800
271,250
10 31,300 5.04 157,700
302,550
9 26,270 4.56 119,600
328,320
17 38,470 9.16 352,100
367,290
14 12; 150 9.34 113,500
379,440
379,440 2,192,600
( 2;!}l>L) t,L. E6.
0
0
173,600
347,100
543;700
·827, 600
1,123,000
1,428,800
1,743,100
2,064,600
2,389,500
2,712,500
2,723,000
5,589,900
5,142,100
28,654,000
26,461,400
Deflection of Nstrut point (station 140} with respect to support (station 16): 61/ E (28,654,000347,100)=28,306,900/E.
TABLE XIV.  Deflection of spars under distributed loads.
Base .. High incidence. Low incidence. Reversed flight.
Spar. E.
1642. 5
1843.5
1922. 5
1490.5
w.
21.92
17.26
24.25
19. 74
6.063
8.209
13. 963
29. 675
w.
23.42
17.81
7.82
9.18
6.478
8.470
4.503
13.800
w. w. cl
12.75 3.527
t186 / 9.58 4.556
0
.564
1.82 1.048
3.02 4.540
22. 90/ 13. 186
18. 66 27. 962
In a new design the value of E would be assumed at I Table XV gives the remainder of the deflection quanti
1,600,000 pounds per square inch. ties called for in Part I.
TABLE XV.Defiection of spars under concentrated loads.
Deflection due to 1,000 Load required for ~
pounds. 1 inch. Per cent of
Spar.
On 1 spar. On 2 spars. On 1 spar. On 2 spars.
Quantity . . . .. ...   . ......... ..... .  .. ..........   .... ... .. · . .  .. .. . b. e. c. d.
"d" on
each spar.
f.
12
COMPUTATION OF FORCES IN THE N STRUT.
It is assmued that the vertical components of the forces
in the N strut are the forc:;:es required to equalize the spar
deflections. The vertical components are computed on
this basis and the drag components and direct stresses
determined from the vertical components and the slopes
of the members.
HIGHINCIDENCE CONDITION.
The force required to equalize the deflections of two
spars is equal to the difference in their deflections, under
distributed load, divided by the sum of the deflections of
each spar under a concentrated load of unity.
Force required to equalize deflections of front spars:
!= 1,000 (8.4706.478) =1992 =201 O d
3.921+5.983 9.904 · poun s.
Equalized deflection of front pair of spars:
oF=6.478+0.2010X3.921=7.267 inches.
=8.4700.2010X5.983=7.267 inches.
Force required to equalize deflections of rear spars:
1,000 (13.8004.503) 9297
f= 8.248+18.992 =21.240=341.o pounds.
Spar.
Equalized deflection of rear pair of spars:
oR=4.i>03+0.3410X8.248=7.318 inches.
=13.8000.3410Xl8.992=7.318 inches.
Force required to equalize deflections of the pairs of
spars:
1,000 (7.3187.267) 51
f 2.369+5.750 =3_119=5.3 pounds.
Equalized deflection of the two pairs of spars:
o=7.267+0.0063X2.369=7.282 inches.
=7.3180.0063X5.750=7.282 inches.
If the force required to equalize the deflections of the
pairs of spars had been larger, the deflections would have
been computed for the case of 80 per cent equalization;
i.e., when the center member of the N strut carries a load
of only 80 per cent of that required for complete equalization.
In low incidence and reversed flight, this computation
is made.
The computation of the net equalizing force on each
spar at the N strut and a check computation of the net
deflection are given below.
Net equalizing force. Net defle.ction.
Front upper ............... . . . ........................... . ....... . ........ . +201. o+o. 604X6. 3=+204. 8 lbs .. · 6. 478+0. 2048X3. 921= 7. 282 in.
Front lower ............. . ........ . . ... .. ..... ....... ... ... . ... . . . ..... . ... 201. o+o. 396X6.3=  198. 5 lbs.. 8. 4700.1985X5. 983=7. 282 in. t: r.ri::_· :: :::::: :: :: :::: :: :: :: :: :: :: :: :::::: ::::::::: ::::::: :: :: :: ::::: :~!f: 8=8: ~:~t t::fJ:~ m~:: it ~:g: f~~is~~.2':,~~i°hl.
+ denotes an upward arld  a downward force.
LOW INCIDENCE.
Force required to equalize deflections of front spars:
f=(l,OOOX0.564)/(3.921+5.983)'=564/9.904=57.0 pounds.
oF=0+0.0570X3.921=0.223 inches.
=0.5640.0570X5.983=0.223
Force required to equalize deflections of rear spars:
f =1,000 (27 .96213.186)/(8.248+ 18.992)=14, 776/27 .240=
542.2 pounds.
;R=l3.186+0.5422X8.248=17.660 inches.
=27.962~0.5422Xl8.992=17.660
Force , required to equalize deflections of the pairs of
spars:
f =1,000 (17 .6600.223)/(2.369+5. 75ll)=l 7,437 /8.119=
2,147.5 pounds.
o=0.223+2.1475X2.369=5.312 inches.
=17 .660;;2.1475 X 5. 750=5.312
0.8X2,147.5=1,718.0 pounds vertical component of
stress in center member of N strut for case of 80 per cent
equalization of deflections.
The computation of the equalizing forces on the spars
are given in Table XVI and computations of the net
deflections in Table XVII. Table XVIII gives the values
of the equalizing forces and the net deflections for the
condition of reversed flight.
TABLE XVI.Erp,w.lizing forces applied to sparsLow incidence.
Spar. Complete equalization. 80 per cent equalization.
tr~~\r.rJ:r·.·........::::::::::::::::::::::.:::::::::::::::::::::::::: ~rgtz:~~~i!tc.ti.~tti\t!: ~rgtg:~~mi·.t:.t1·~:~1i~:
Rear upper . ... . .. . . . ... . ......... . ..... . .... . ,.. .. ... . .. . . . ... . .... .. . 542.20.697X2147.5= 954:8 lbs. 542.20.697X1718.0= 655.2 lbs.
Rear lower .. .. . . ... ..... . . . . ....... .. ... . .. ... ..... . ...... . .......•. 542.20.303X2147.5=1,192.7 lbs. 542.20.303X1718.0=  1,062.8 lbs.
TABLE XVII.  Net deflectionsLow incidence.
Spar. Complete equalization. 80 per eent eq nalization.
 · ·  · ~ 1~+ 
Front upper.... .. ... . ..... . . . ... . . .. .... . ........... . . ......... . .......... 0 +1.3540X 3.921=5.312 in... 0 +1.0946X 3.9214.292 in.
Front lower.. . .. . . .. . . .. ... . . .. ... . ... . .. . . ...... . ...................... . . 0.564+0.7935X 5.9835.312 in. . . . 0.564+0.62MX 5.983=4.292 in.
Rear upper .... . ... . . ... ....... .. .. . . . ......... .. . . . .... . . . . . . .. ..... . .... . 13.1860.9548X 8.248=5.312 in .. .. 13.l860.6552X 8.248=7.788 ln.
Rear lower ......... . . . . . . . .. . ....... . .... . ......... . ... . ...... . ........... 27.9621.1927X18.992=5.312 ln ... . 27.9621.0628X18.9927.788 in.
I
13
TABLE XVJII.Equalizing forces and.net deflectionsReversed flight.
Kpar.
Front upper ........................................ •... ...... ... .... . . .. ........ . . .. ......... ..
Front lower ..... · .......••........ .. ...... . .................................... . ............ . ...
Rearupper ........... . .... ... ...... .. ......... ..... .. ............ ... .... .... . .............. ... .
Rear lower ................................................. . ... . ... . ........................... .
Eq nalizing .f orcc. Net deflection .
Complete 80 per cent Complete ! 80 per cent
equal. equal. equal. ! equal.
Pounds.
+32.1
+193.1
 285.1
+59.9
Pounds.
+4.8
+175.2
253.5
+73.5
I
Inches. I
· ui1 .
1
3.401
3.401
Inches.
3.508
3.508
3. 141
3.141
In reversed flight the vertical compo.Q.ent of stress in the
center member of the N strut is 225.2 pounds for complete
and 180.0 pounds for 80 per cent equalization.
Table XIX gives the vertical and drag components and
the direct stresses in the N .strut members under the various
loading conditions. + indicates tension and  compression.
The d.mensions of the N strut are shown in
figure 11.
TABLE XIX.Stresses in N strut.
Equali Front member. Center member. Rear member.
Loading. zatlon
(per
D.C. I s. I
cent). v.c. ~1~ s. v.c. ~ 1s_._ 1 
High incidence .... ... .. ..... . .... ....... 100 204.8 69. 8 . 216 6. 3 1. 3 +6 342.9 156.2 377
Low incidence ..........•................ 100 1,354.0
461. 0 I 1,430 2,147.5 457. 0 +2,192 1,192.7 543.8 1,310
80 1,094.6 31e,s  1, 155 1,718.0 365. 7 +1, 755 1,062.8 484.1 Reversed flight ... . .... .. .. . ....... . ... .. 100 32. l 10,9  34 I 225.2 47.9 +230 59.9 27.3 1~:
.80 4.8 1. 6 5 1 180.0 38.3 +184 73.5 33.5 +81
TABLE XX. Design of N strut.
Member. Max. '1'. I Max. C. Length. / Size. Ult. T. I Ult. C.

s;~:::: ::: ::: : : : : : :::::::: ::::::: : :::: : :: :: ::: : : : : : : : . .. · 2; it~ 1 ... .. ;;;:.I 49.61 liX0.035
6,600 I 2,030
48.0 I X0.035 5,800 1,500
54.3 liX0. 049 9,100 2,250
The margin of strength in this design seems unnecessarily
large, and the sizes of members might have been
smaller. In the original design figures the front and rear
members were determined by the nosedive condition,
which gave heavier stresses than low mcidence, and the
margin of strength was much smaller. The center member
was ma.de much larger than is theoretically necessary so
that it would more .nearly equal the other two struts in
size and to gain increased rigidity.
COMPUTATION OF NET BENDING MOMENTS IN SPARS.
After the equalizing forces on the spa.rs have been found
it is easy to compute the net bending moments on the spars
due to vertical loads, and the fiber stresses due to these
moments. Table XXI gives the computations of the net
bending moments and Table XXII the computations of
fiber stress. Two values of fiber stress, f= My/I and
f= M/hA, are computed for the same reasons that applied ·
in the tentative design.
TABLE XXL
Spar. Flight condition.
Front upper .. ..... .. .. ................. . f~e' ~c1:fe"::: _::: ::: : :::::: :::::::::::::
Reversed flight . ........... . ..... . ..... ... .
Front lower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . High incidence .............. . ............ .
Low incidence ... .. ...................... .
Reversed_ flight ................. . ......... .
Rear upper. ... . . ............ . . .......... High incidence .. . .. . .. . ...... .. . ......... .
Low incidence •... ... . .... ................
Reversed flight .... . .. . ................... .
Rear lower •. ... . .....• .• ......... 0
•• • • • • • High incidence .•.. ... ... •... . . .. . .... .....
Low incidence .... . .... •.. •... .. ..........
Reversed night ........ . ....... ... .. ..... . .
1 Critical bending moment.
Equali 1
zation
(per
cent) .
100
100
80
100
80
100
100
80
100
80
100
100
80
100
80
100
100
80
100
80
179, :,00
0
0
98,400
98,400
209,000
13,900
13,900
112,300
112,300
59,900
175,400
175,400
14,000
14,000
107,500
218,000
218,000
35.400
35,400
w_. M.
+204.8 +19, 700 1 +199,500
+l,354.0 +129,900 +129,900
+l,094.6 +105,000 +105,000
+32.1 +3,100 95,300
+4.8 +500
198. 5 ···24,600 '+l~r:~
+793. 5 +98,400 +112,300
+623.4 +77,400 +91,300
+193.1 +24,000 88,300
+175.2 +21, 700 90,600
+336.6 +32,300 +92,200
954.8 91,600 +83,800
 ·655.2 62,900 l +112,500
285. 1 27,400 41,400
253.5 24,300 . 38,300
342.9 42.500 +65,000
1,192. 7 147,800 +70,200
1,062.8 131,800 '+86,200
+59.9 +7,400 28,000
+73.5 +9, 100 26,300
14
TABLE XXII:Unit stresses in spars.
Spar. Flight condition.
Front upper. . . . . . . . . . . . . . . . . High incidenCf\ ........ .
Low incidence . . _ .......... .
Reversed flight ..... . . . . . ... .
Front lower. ............ . High incidence . . ........... .
Low incidence . . ___ ... _ ... ~.
Reversed flight .. . .. ... ..... .
Rear upper. _ . . . . . . . . . . . . . . . . High incidence ............ . .
Low incidence. ____ .. _ . _ .. __
Reversed flight .. _ ... .. . _. __ .
Rear lower. ____ . __ _ . . _. __ . _._ High incidence ......... .
Low incidence._. ___ ______ ..
Reversed flight . ....... .
Eoualization
(percent).
100
100
80
100
80
100
100
80
100
&O
100
100
80
100
80
100
100
80
100
80
COMPUTATION OF DRAG TRUSS FORCES.
HIGH INCIDENCE.
L/D at 14°=9.05=cot 6° 18'.
Angle between resultant force and major axis of spars=
6° 181 14° 00'=7° 42'.
In the static test the angle used was7° 30', and this
value will be used m the following computations, although
7° 42' would be used in a new design.
Drag=L tan (7° 30')=0.1316 L ( indicates
antidrag).
LOW INCIDENCE.
L/D at 2°=7.07=cot 8° 03'.
Angle between resultant force and major axis of spars=
8° 03' (2° 00')=10° 03'.
In the static test the angle used was 10° 30' and this
value will be used in the following computations.
Drag=L tan 10° 30'=0.1853 L.
REV1':RSED FLIUH'l'.
By specification it is assumed that drag=0.25 L.
The moments on the drag trusses can be found by proportion,
as the curve of moment due to an average drag of
1 pound per inch is practically the same as that for an
a verage lift of 1 pound per inch. The error due to the
slight difference in the effect of tip correction may be
disregarded.
Average gross lift 011 .upper wing equals 4.17X3046/2580
= 4.92 pounds per inch run.
Average gross lift on lower wing equals 3.60X3046/2580
=4,25 pounds ;pt,r inch run.
Table XXIII gives the average gross lift load on the
"'ing in po~ .per inch run, the average drag load, the
moment at the supports due to the lift load, and the moment
due to the drag load.
M.
199,500
129,900
105,000
93, 300
97, 900
184, 400
112,300
91.300
88,300
 90,600
92,200
83,800
112,500 =jk~
65,000
70,200
86,200
 28, 000
 26, 300
Center Effective
height: depth.
8. 57 6.82
8. 00 6. 25
6.04 4.29
5.63 3.88
l.
135.1
ll4. 2
55. 3
45. 7
.4.
.5. 69
5.69
5. 69
5.69
6,320
4,120
3,330
2, 960
3,100
tl,460
3, 930
3,200
3, 090
3,170
5,040
4,580
6, IW
2,260
2,090
4, 000
4, 320
5, 310
J, 725
1, 620
5,140
3, 350
2. 710
2, 400
2, ;;20
5.180
3. 16n
2, 570
2,4~0
2, 5,'.)0
3 780
3'. 430
4, 610
I, 700
1, 570
2,940
3, lRO
,3, 90(1
1,270
l , 190
TABLE XXIII.Moments on draq irusses due to distributed
air load.
Flight condition. Truss. Lift. Drag
kL. "fL Mn
 ~  
High incidence . . ...... Upper ... 36.90 4.862 283,000 37,300
Lower ... 31.88 4.·200 373, 800 49,250
Low incidence ....... ·1 Upper. . . 27.05 5. 016 207,100 38, 400
Lower ... 23. 38 4.331 274,000 50, 800
Reversed flight ... . .. . . Upper . .. 17. 22 4.309 132,000 33,000
Lower ... 14.87 3. 719 174,200 43,550
I
The drag truss stresses in the spars are computed by
dividing the net moment' on the drag truss (i. e., the
moment due to the distributed drag load added algebraically
to the moment due to the horizontal load from the
N strut) by the distance between spars and. the sectional
area of the spars. This gives the proper value for the compression
chord, but too high a value for the tension chord,
as part of the tension is carried by the internal drag wires.
As a rough approximation the stress in the tension chord
will be assumed equal to twothirds that in the compression.
In the final design it would be necessary to divide· the drag
component of the air load into panel loads and find the
stresses in each member of the drag truss. Until a trial
design has been arrived at which is believed to be satisfactory,
however, the approximate method used here for
allowing for the effect of the drag truss stresses may be
employed.
Table XXIV gives the computations for the drag truss
stresses in the spars.
MD is the moment on the drag truss due to the distributed
load.
Wns is the concentrated load applied at the N strut.
M ns is the moment caused by Wn,·
Mis the net moment and equals MD+ M ns· A +moment
is one caused by drag and amoment one caused by
antidragtforces.
h is the distance between spars.
f, is the unit stress in the front spar andf, the unit stress
in the rear spar.
/i= M/hA where A i13 the area of both flanges of the spar.
/ I J
. .
15
Table XXIV.Drag truss stresses in spars.
Flight condition. Truss. Mn Wo, lrfns M h A /r f,
High incidence ..... ... ........ . .......... .. Upper. ....  36,600  '227.3 21,800 58,400 26. 0 11.38  197 + 197
100 per cent equalization ....... . . . .. . . ..... Lower . .... 41,800 +227.3 +28, 200 13,600 32.'5 11. 38 37 +17
Low incidence ................... . ......... Upper .. ... 32;500  146].8  140,200  107, 700 26.0 Jl.38 364 +364
100 per cent equalization .... ..... .... . ..... Lower . . . .. 42,900 +146[. 8 + 181,300 + 224,200 32.5 11.38 +606 606
Low incidence ................ . . . .. ..... .. . Upper .... .. 32,500  1'222. 6  117,600 85.100 26. 0 11. 38  288 + 288
80 per cent eq ualization . .... . .... .. . ....... Lower .... _ 42,900 +12'!2 6 + 152, 100 + 195,000 32. 5 IJ. 38 +528  528
Reversed flight ..... ...... ............. .. . .. Upper ... . . . 27,900  31.5  3, 000 +24,900 26.0 11. 38 +84  84
100 per cent equalization: ....... . ..... . .. . . . Lower .... . 36,900 + 3!. 5 + 3, 900 +40,,800 32.5 11. 38 + llO  llO
Reversed flight .................. . .......... Upper ..... 27,900  6. 4  600 +27, 300 26. 0 11. 38 + 92  92
80 per cent eq ualization .... ..... . . . ........ Lower ..... 36,900 + G. 4 +800 +37, 700 32. ,5 11. 38 + 102  102
COMPARlSON OF MAXIMUM COMPUTED AND ALLOWABLE picked out of Table XXII by inspection. Table XXV
STRESSES. gives the computations of the maximum stress in each
The total stress in a flange is the sum of the stresses due spar and the allowable stress. Both the Forest Products
to the lift and the drag loads. As is seen from Table Laboratory and approximate methods are used. The
XXIV, the drag stresses are all very small so that the load0 allowable stresses are based on the tests on specimens from
ing conditions which may cause limiting streBBes can be the spars used and are taken from Table V.
Table XXV. Maximum stresses in spars.
Spar. Flight condition.
Front upper ..... . . . . ......... High incidence .. . . .... ..... ...
Front lower . . .... .. . •. •. .... . High incidence ......... ...... .
Rear upper . ... ..........•.... High incidence .... . ...........
Low incjdence .... .... .... ....
Rear lower . ....... . ....... . .. High incidence ........ .... ....
Low.incidence ...... .. . .. .....
Equalization
(per·
cent).
100
100
100
80
100
80
P/A is the direct stress in the spar due to drag loads and
equals / 1 or/, from Table XXIV and given a + sign if
compression. It is equal to 2/3 / 1 or 2/3 f, and given a 
sign if tension.
My/I and M/hA are taken from Table XXII.
fb and f, are the computed maximum stresses,
fb=p/A+My/I, whilef,=P/A+M/hA.
Fb and F~ are the allowable values corresponding to
/band/,.
CONSIDERATIONS FOR REDESIGN.
Study of Table XXV discloses several interesting facts.
According to the approximate method, all spars have a
good margin of safety and might be cut down in size.
This can be seen by a comparison .9f f, and F,. If the
standard value of F, had been used (5,500) the margin
would be greatly decreased and the front spars would be
considered well proportioned and only the rear spars
overweight. It is of interest to note that the front lower
spar, which was stressed 200 pounds per square inch
above the standard value in the trial figures of Table V,
has 280 pounds per square inch margin of safety according
to Table XXV.
The true basis for a revision of design, however, is the
comparison of /b and Fb. Here we find the front upper
spar is stressed above the allowable, the front lower has a
fairly reasonable margin and the rear upper a large margin,
and the ·rear lower is just on the point of failure. If the
values of Fb for standard wood had been used, however,
all spars would have a margin of safety.
The explanation of the test results is probably as follows:
In low incidence the rear lower spar would have been
stressed to the breaking point if only 80 per cent equalization
had been attained. As a matter of fact the equalization
was greater, so the spars were able to hold the test
55311 0313
P /A. My/I . Af /hA . [b /, . Fb F,
+200 6,320 5,140 6,520 5,340 6, 020 8,560
+40 6,460 5,180 6,500 5, 220 7,200 7,515
130 5,040 3,780 4,910 3,650 8,100 6,015
 190 6, 150 4,610 5,960 4, 420 8,100 6, 015
20 4,000 2,940 3, 980 2 920 ' 5,840 5,550
+530 5,310 3,900 5,840 4;430 5,840 5,550
load. In high incidence the front upper spar would have
broken under a load of 7.5 if the deflection had continued
proportional to the loads. That spar, however, was first
to pass the ela6tic limit and deflected excessively and
either refused to take on load from the other spars or threw
off load onto them. These other spars had a sufficient
margin of strength to take care of this extra load and the
structure held. Under a load of 8.0, however, this action
was not poBBible, as the strength margin of the front lower
spar had been wiped out and the structure failed. The
front upper spar failed first and the others failed in quick
succeBSion. For this study of what happened in the
static test the values of Fb from the results of tests of specimens
are valuable.
For purposes of design revision, it is more useful to use
the values of Fb computed for standard wood and given in
Table V. Using these values we find the front spars are
very closely designed, while the rear spars show a considerable
margin of safety. If, however, the rear spars
are lightened, more load will be thrown on the front spars
and they will probably be overloaded. Therefore, the
only possible revision is a decrease· in the size of the rear
spars and a simultaneous increase in the size of the front
spars. Owing to the greater height of the front spars this
could probably be done with a net saving in weight.
DESIGN OF DRAG TRUSS MEMBERS •
As the drag truss 6tresses depend mainly on the equalizing
forces in the N strut, neither the N strut nor the drag
truss should be designed until a satisfactory spar design
has been developed. The N strut design is given in
Table XX. The design of the drag truBB members follows
custom;i,ry practice, and will not be considered here in
detail,
16
DESIGN OF cE:.TER SEcno:s: STRUTS. 'I A unit upward load at the rear spar causes a ten$ion of
1.237 in member D and compression of 0.272 in E.
There are a nu~ber of possibilities for t?e ar~angemen~ , These forces are obtained by applying the equations of
of the center sect10n struts, but t~e bafilc pnnc1ple~ o equilibrium at the points of application of the load. At
design are .the same. This report grves the computat10ns each spar support three members are assumed to carry the
for the design o.f _ce1'.ter sect10n_ struts m 'the arr~n!em~nt load. At the rear support the members are D, E, and the
adopted by Fokker 1.n ~he D \ II and b} the Air ~ervice center section of the rear spar. At the front support the
m the PW lA. This 1s the usual arrangement and has members are A · B and c. Under symmetrical wing loads
so~e r. nterestm. g f eatures. The rear s~ar i.s supported bY the direct stres's in' the center section of the· rear spar due
a srngle strut and the fron.t spar by~ tnp.od. The 110men to the forces acting at one support is equal and opposite
c~ature. of the '.:.~mbernr·s 18 sho~·i: ~nI Figure 12 and the to that due to the. force~ at the ~ther suppo~t. In the case
dimenswns are .,iven Table XX\ · of an unsymmetrical wmg loadrng there will be an unbal
TABLE XXVI.Dimensions of center section stmts. anced side load which will be carried by the drag trussing
Member. L. v. D. S. V/L . D/L. · S/L.
to the tripods. The magnitude of such a load is not computed,
but care should be taken to see that there are members
so located as to be able to carry it. If the center sec
A ........ .
13.
c ..
D ........ .
E .. ...... .
43.M
53. 62
43.42
52. 95
26. 00
28. 00
42. 75
18. 75
42. 75
0
14. 625
14. 375
 25. 750
11. 625
26. 000
30.0
29.0
29.5
29.0
0
0. 643
. 79i
. 432
. sos
.0
o. 336
. 268
. 593
.220
l.000
0: ~i tion of the front spar were considered in action, the stresses
. 6SO \ in the tripod members would be greatly reduced, but this
j 48 effect is neglected for the reason stated in Part I.
E is the compression rib.
L is the length in inches.
Vis the vertical comuonent.
D is the drag component. .
S is the side component perpendicnlar to the other two.
TABLE XXVII.Stresses in tripod due to unit loads.
Member A. MemberB. MemberC.
Stress due to unit upward load .. . 0.528 +2.423 1.395
Stress due to unit drag load . . : ... . +1.i74 .532  .766
+ indicates tension and  compression.
The computation of the net loads at the center section
supports follows. The vertical loads are the total net loads
on each spar. The drag load at the front support equals
the total drag on the upper truss plus the load in the compression
rib due to the drag component of member D.
The distributed vertical loads are found by multiplying
the load per inch run by the loaded length of spar. To
this is added algebraically the equalizing load to obtain
the net vertical load. The drag_loads are found in a similar
manner. The computations are given in Table XJ...'VIII.
TABLE XXVIII.Computation of loads at supports.
Equaliza
Flight condition. tion (per
cent).
Support. Wt. lWt'• L.,..
High incidence . ............. . .... . .. 100 Front .. . .... 23.42 +4080 +205
Rear ........ 7.82 +1360 +337
Low incidence . ..... . ............... 100 Front .. . .... 0 0 +1354
Rear .... . .. . 22.90 + 3987 955
80 Front ....... 0 0 +Hl95
Rear ... . .... 22.90 +3987  655
Reversed flight .. . . ... ... ... ...... . .. 100 Front . ... . . . 12. 75 2220 +32
Rear ........ 1.82 317 285
80 Front ....... 12. 75  2220 +5
Rear . .. . . ... 1.82 317 25.3
I is equal to 174 inches, the half span.
wL is the average lift load per inch run and is taken from Table rn.
L.,. is the vertical load on the spar at the N strut and is taken from Table XXI.
wd is the average drag load per mch run on the wing and is taken from Table XXIII. n •. is the drag load at N strut and is taken from Table XXIV.
L.
+4285
+ 1697
+1354
+3032
+1095
+3332
2188
602
2215
570
D.
+ 5. 016 +872 1222 350
··+.i.":ioo· ····+1so· ·:.:a2· ···+1iii
.. +.i::ioo· · · · ·+1so· ······:.:ii· · · · · · + ,.i2
Table XXIX gives the computations of the stresses in the rear supports in the various loading conditions and the
resultant forces on the ftont supports.
TABLE XXIX.Stresses in roor supports ·and net loads on front supports.
Flight condition .
High incidence .... .. . ... .... ... .............. ... ........... .
Low incidence ......... . ........... . ...... . ............ . . . .. .
Reversed flight . .... .... . . . .. . .•.......... . .. ... .............
Equalization
(per
cent).
100
100
80
100
80
L, is the lift load at the rear support from Table XXVIII.
So and S. are the stresses in D and E due to L,.
Dis the drag on the wing from Table XXVIII.
The net drag is the algebraic sum of s .. and D.
Lr is the !Ht load at the front support from Table XXVIII.
L,.
+1,697
+3,032
+ 3,332
602
570
So, s ... D.
+2,100  462 ~rJ +3, 752 826
+4, 125 907 350
745 +164 +718
706 +155 + .742
Net drag. Lr.
1, 535 +4,285
1,416 +1,354
1, 257 +1,095
+882 =grs +897
_,
j
17
The loads in the last two columns of Table XXIX a.re I net stresses in the tripod under the various conditions of
multiplied by the streeses due to unit loads given in loading. The results of these calculations are tabulated
Table XXVII and added algebraically to determine the in Table XXX.
TABLE XXX.StreBSes in tripod8.
Equali Stress in A.
Flight condition. zation
(per
cent). L. D.
High incidence . . . ... . . . . . ... . .. . ... .. . . . 100 ~m 1,801
Low incidence ... . ... . . . .... . . ... 100  1,662
80  578 1. 475
Reversed flight ... .. . . . . . . . . . .. .. . . . . . .. . 100 +l, 155 + 1;035
80 + 1, 169 +1,052
L is the stress in the given member due to the lift load on the tripod.
D is the stress due to the drag load.
Stressm B.
T. L . D.
4, 062 + 10, 385 +817.
 2, 376 +3,280 +754
 2, 053 + 2, 653 +668
+2, 100· =i:~~  469"
+ 2,221  477
T . L .
+11; 202  5, 980
+4;034 1, 889
+3,321 1, 527
5, 771 + 3, 050
 5,847 +3, 090
TJ.s the total stress m the member and is the algebraic sum of Land D .
It should be noted that L and D are direct 'stresses due to lift and drag loads and not llrt and drag components of a load.
Stress in C.
D. T.
+1, 175  4, 805
+l, 085 80!
+963 564
676 +2,374
687 +2, 303
The computations for the design of the center section struts are given in Table XXXI. The maximum loads
are taken from Tables XXIX and XXX.
TABLE XXXI.Design of cenw section struts.
Member.
A • . . .. . . .. . .. . . . . . ... . . •. . . •.•. . .. . . . . . . . ...... . . .. ... . . .. . ... . • . . ..
B _ .. .•• ••• . . •• .• .•.. .• •• •. •. ••• • •• .• •• . • •• . • .• •• . .• •• • . .• •• . •• • . .••
c ........... ..... ..... ......... .. .... .. ..... .... ........ .... ..... .. .
D •. ... . . . .. . . . . . . .. . .... . . .. .... .. .. . . . . .. ... .. . . ... . .. . .. . .. . .. . ••
Maxi.mum Maximum
tension. co::~ Length. Size.
2, 221
11, 202
2, 374
4,125
4,062
5,847
4, 805
745
43. 6 1. 25 by 0. 049
53.6 1.50 by .049
43. 4 1.25 by . 049
53.0 . 875 by • 035
Ultimate I Ultimate
tension. c~~~
10,170
12, 300
10, 170
5, 000
4, 500
5,200
4, 500
830
From the figures above, all members are safe ih tension, I occurred in static test was probably due to the action of
but Band C are unsafe in compression. In a new design the center section of the front spar.
they would have to be revised. The fa.ct that no failure
PART III.
STUDY OF STATIC TEST RESULTS.
Two internally braced biplanes hav,e been static tested
at McCook Field with very interesting results. These two
airplanes are the PWlA, designed and built at McCook
Field, and the TW2, designed and built by the CoxKlemin
Aircraft Go.. A study of these tests has been made
to determine what indication they give regarding the
validity of the method of stress analysis recommended in
Part I of this report. The results of this. study ~e given
below.
TEST 'RESULTS ON THE PW'lA.
Three sets of results of the PWlA are of interest; the
tests on the physical properties of the material in the spar
flanges, the observed ·deflections at the N strut, and the
extensometer readings on the center members of the
N struts. Table XXXII gives the physical properties of
the material used in the spars.
T.\BLE XXXII.Strength properties of material from
PW1A spars.
Spar. Flange. E. F,. Remarks.
Front up {Top .... .. l,S!i5,000 8,805 8,560 Brash material.
per. Bottom ..
Frontlow {Top ......
1,420,000
2,Cll5,000
9,950 6,610 Low specific gravity.
er. Bottom .. 1,672,000
Rear up. ~Top ...... . 1,830,000
per. Bottom .. 2,015,000
Rearlow IJTop ....• . 1,411,009
er. '[.\Bottom .. 1,570,000
Standard ...... . ...... 1,600,_000
Eis the modulus of elasticity.
Fh is the modulus or rupture.
11,840 ·7, 515
10,220 6,415 Do ..
10,875 6,015 Do .
12,020 8,475
8,995 5,550 Do.
7,100 6,550 Spiral grain I :8.
10,300 5,500
F, is the stren~h in compression parallel to the grain.
All values are m pounds per square inch.
Table XXXIII gives the valu8!! of the observed deflection
at the N struts under the greatest loading in each of
the flight conditions, obtained from McCook Field ·Report
No. 1885.
TABLE XXXIII.Observed deflections at N strut.
Loading. fLacotaodr. Front. Rear.
7.5 7.50 7. 60
f~ /:c1iJ;::..: ::: :: ::: : : :: : : :: : : : :: :: 5. 5 4.40 ti.40
Reversed flight ......... . •.............. 3.5 3.05 3.25
These deflection readings are not very precise, as the
readings were not taken directly under the N strut, and
there is insufficient data on the possible settlement of the
supports. This error is not serious, as the relative deflections
are more important than the actual deflections, and
the relative deflections are not greatly affected. Only in
the lowincidence condition was any attempt made to
correct for settlement of supports. In low incidence the
apparent deflections were 4.9 inches in front and 6.1
inches in the rear.
Four sets of readings were taken of the extension of the
center member of the N strut, in the highincidence and
lowincidence tests. In the highincidence test the
readings were erratic and no determination of the stress
could be obtained from them. Theoretically there was
very little stress in the member, and the readings made were
in agreement. In low incidence three of the sets of rea,dings
agreed very closely, giving a load in the member at
L. F .=5.5 of 1,940 pounds. The fourth set diverged from
the other three and, if accepted, would bring the average
to 2,050 pounds.
COMPARISON OF COMPUTED AND OBSERVED DEFLECTIONS.
The observed deflections and those computed in Part
II are given in Table XXXIV.
TABLE XXXIV.Deflections at N strut.
Computed.
Observed.
100 per cent 80 per cent
Loading. equalization. equalization.
ol ~ ~ ..;
C ~ ~ .t ~ ~
0 Q) 8 '" 8 Q) ... "'
is. ~ ~ is. ~ ~ is. ~ ~
High incideuce
...... 7.50 7.60 0.99 7.28 7.28 1. 00 7.28 7.28 1.00
Low in,c idence
. ..... 4. 40 5.40 .81 5.31 5.31 1. 00 4.29 7. 79 . 55
Reversed
flight .. . .. . 3.05 3.25 .94 3. 40 3.40 1. 00 3. 51 3.14 1.12
In high incidence the deflections, front and rear, are
practically identical, as was indicated by the theory.
The difference of 0.1 inch is smaller than the precision of
the. observations. The actual amount of deflection was
7.55/7.28=1.04 times that predicted, indicating that the
spars were only 96 per cent as stiff as the tests on the
flange material indicated.
In low incidence the observed deflection of the front
truss was 81 per cent of that of the rear truss. Eighty per
cent effectiveness of the N strut would haveresulted in a
deflection of the front truss only 55 per cent as great as
that of the rear truss. This indicates that the N strut
was more than 80 per cent effective. Since 01, the deflection
of the front truss, and Ii,, the deflection of the rear
truss, are in the ratio of 4.4 to 5.4, we can compute the
effectivenea.s of the N strut as follows:
5.4 01=4.4 or
or li1=0.815 or
01=0.815 or=0.223+2.369 P
lir=l7.6605.750 P
Whence P = 2,009 pounds
li,=6, 112 inches
o1=:4, 980 inches.
(18)
19
As the vertical component in the center member of the
N strut for complete equalization is 2,147.5 pounds, the
effectiveness of the N strut in low incidence is
2,009/2,147 .5=93.6 per cent.
The axial load corresponding to 2,147.5 pounds vertic.al
component is 2,192 pounds. Using the three sets of
extensometer readings which agreed, the actual load was
1,940 pounds, indicating an effectivenessof 1,940/2,192=
88.6 per; cent. If the average of all four sets of readings is
taken, the effectiveness is 2,050/2.192=93.6 per cent, the
same value as obtained above. The most probable explanation
is that part of the equalization, about 5 per cent,
is due to the ribs and the remainder to the N strut. If the
N strut were not·present, the effect of the ribs would be
much greater, but not enough to insure safety, and the
torsional effect on the wings would be much larger.
The ratio of observed deflection to computed deflection
was 4.40/4.98=5.40/6.11=0.884, indicating that the spars
W(lre 13 per cent stiffer than assumed.
The results of the reversed flight test are hard to understand,
as the computed deflection of the front truss was
greater than that of the rear, but the actual deflection was
smaller. This would indicate an effectiveness of the
N strut greater than 100 per cent, which does not seem
possible.
TEST RESULTS ON THE TW2.
The only data of interest from the test of the TW2
are the results of tests on the spar material and the deflection
readings. No extensometer readings were made in
this test. After the tests had been made the deflections
were computed by the same method as for the PW lA.
These computations are not given in full , but only the
resuits.
Table XXXV gives the properties of the spar material.
Several specimens were cut from each flange and the average
values reported. The average modulus of elasticity of
each beam was assumed as the mean of the values for the
two flanges, weighted proportionately to their volumes.
This does not give an exact value of the deflections, as the
modi'1l11s of elasticity probably varied between different
sections of a spar, hut it was the most reasonable figure that
could be obtained.
TABLE XXXV. Strcngth properties of material from TW2
spars.
Spar. Flange. I ft:n%. E of spar. [ Fh F , Remarks.
 1 · 1 \~~~~ Front μp {Top. .. .. . l, 9!4, 000 . . . . . . . .. . . 12, 220 ,, os.'i
per. . . I Bottom. . 1,705, 000 1,865,000 11, :195 5, £05
Front low {Top...... 1,866,000 . . . . .. . . . . . 11, 870 6, 530
er. Bottom . . 2,02R, OOO 1,915,000 12, l bO 6,540
Rear up {Top . . .... 1,233,000 .......... . 10, 930 5,865 Brash.
per. Bottom .. 1,679,000 1, ..... 11M1 ll,44Q 6, 360
Rear low {Top...... I, 2&l, OOU 9,580 5,310 Do.
er. Bottom .. l, Ral,000 1,470, 000 12,2!0 li,"/Hi
Fb and F, ha Ye the same meanin;: as in Table XXXU.
Table XXXVI gives the observed deflections, and the
computed deflections for both 100 per cent and 80 per cent
effectiveneBB of the N strut. In computing the deflections
care was taken to employ the loadings actually use<l in
the static test.
TABLE XXXVI. Dejlections of TW2 spars.
Observed. Cor1puted.
·  ~
Loading.
lOOpercent 80percent eqtialieqil~~~
a zation.
~ ~ .81~ ..,o~ ~ .2
_ ___________ ='.__ £ I ~ I £ l ~ ! ~ _
Righi r.cidence 6. o 5. 35 1 5. 35 1. 00 II 6. 32 6. 32 6. 36
1
6. 22 1. 02
Low inridenre. 1 5. 5 4. 20
1
5. 40 . 78 5. 88 5. 88 4. 79 8. 26 • 58
Reversrd fli~ht 3. 5 3. 00 3. 30 . 91 J 3. 71 3. 71 3. 79 3. 51 1. 08
The results of this test are very similar to those from the
PW lA. In high incidence the N strut equalizes the deflections.
In reversed flight it is apparently more than
100 per cent effective. In low incidence it is ,between
80 and 100 per cent effective. Comp~tations similar to
those made above for the PWlA give the exact value of the
equalizing effect as 91.2 per cent, and the deflections as
5.40 inches for the front spar and 6.94 inches for the rear.
In every case the observed deflection is considerably
smaller than the computed deflection.
DISCUSSION OF TEST RESULTS.
For both airplanes tested the computations showed that
only a small force was needed to equalfae deflections, and
the tests indicated that this force was developed. In
reversed flight the fact that the rear trusses deflected more
than the front trusses, although the computations showed
that the opposite should occur, is hard to understand. · It
is of minor importance, and no attempt will be made to
explain the phenomenon until more static tests have been
made.
The crucial question which determines the validity of
the proposed method of design is whether the N strut will
be at least 80 per cent effective in the lowincidence condition.
The answer to this question given by the tests is
emphatically positive. In the one case the effectiveness is
91.2 and in the other 93.6 per cent. It might even be possiule
to use a value of 90 per cent instead of 80, but only two
tests have been carried out; and itis much better to use the
more conservative figure until more airplanes have been
tested , especially when the lack of precision of some of the
computations is considered.
Several interesting questions raised by the tests will now
be considered.
RELATION OF COMPUTED TO OBSERVED DEFLECTIONS.
In most cases the observed deflections were smaller than
those computed, and there is no definite relation between
the two. Two possible ca_uses immediately suggest themselves.
The values used for the modulus of elasticity may
have been in error. This may be due to at least five
causes: (1) The modulus for the spar may not be equal to
the weighted average of the moduli of the flanges. (2) The
weighting may not have been done properly. (3) The
strength properties may have changed between the time
the airplane was tellted and the time when the specimens
from the flange were tested. (4) The test specimens may
not have given the true average for the flanges. (5) The
20
modulus may have varied along the length of the beam, in
which case the deflections would have to be computed
from a curve of M/EI, using the proper value of Eat each
sec_tion, instead of a curve of .M/EI in which a constant
value of E was used. The other main cause that suggests
itself is that the values of I used were too low. In these
computations the webs were neglected, though it is probable
that a part, at least, of the web should have been considered
effective. If the webs were to be considered in
computing I, the direction of the plies would have to be
taken into consideration as well as the web thickness. The
thickness of the web and the direction of the grain of the
plies probably have an effect on the value of E also.
EFFECT OF VARYING MODULUS OF ELASTICITY.
The modulus of elasticity may vary in two ways. It
m·ay vary from point to point or from section to section
along the spars, and it may vary between spars. The
deflection at the Nstrut points is proportional to the
moment of the area under the M/EI curve about the
Nstrut point. The values of M/EI near the center line
of the airplane, therefore, have · a greater effect on the
deflections than the values near the N strut. If the material
near the center line is of better quality than tha.t near
the tip, the actual deflection will be less than that computed
on the blk!is of a constant value of E , and vice versa.
If the moduli of elasticity of all spars were the same, the
equalizing forces would be the same, no matter what was
the actual value of E. In designing spars it is necessary
to assume E=l,600,000 pounds per square inch for all
spars. In any given airplane the values of E for the different
spars will be different. It is of interest, therefore, to
compare the equalizing forces indicated by the static test
deflections wi.th the computed values based on the designing
assumptions. This can be done for the TW 2, as
equalizing forces were computed for both the standard
value of E and the values obtained by test. The net
equalizing forces so obtained for high and low incidence
conditions arc given in Table XXXVII.
TABLE XXXVII.Net equalizing forces on.spars.
Equalization.
Loadin~. Spar.
I I Observed.
100 per SO per
cent. cent.
High incidence .. ... Front upper .... . .
+ 1F9 I +'l/27 +317
Front lo,ver ..... . 470 452 394
Rear upJ:)er . ..•... +281 +246 +140
Rear lower ....... 0 21 63
Low incidence . .... Front upper. .... . +961 +1,200
Front lower ..... . +498 +393 +516
Rear upper .... ... 7nO 550 789
required to equalize the deflections of the trusses are
greater than they would be if the material were of uniform
quality. As a result the net stresses in the front spars are
greater and in the rear spar less than they would have
been if uniform material had been used aiid the structure
acted in strict accord with the design assumptions. Even
in this case, however, which is an extreme one, the error
is not serious.
ERRORS IN DEFLECTION READINGS.
Owing to the practical requirements of the static test,
it was not possible to measure precisely the same deflections
as those computed. ThB error was small, however,
and the ratio of the deflections observed and of those desired
was practically the same.
EFFECT OF FAILURE OF N STRUT.
If the N strutshould fail or be shot away, its equalizing
effect would be lost. This would increase the stresses in
the rear spars in low incidence far beyond the allowable.
Looked at from another point of view, the factor of safety
would be decreased. As the stresses without the N strut
are in no case twice as great as the stresses with the N
strut, the ultimate load factor would still be more than
onehalf of the dE>sign factor, which is sufficient for the
partially. disabled airplane. In any given design it is a
simple matter to compute the allowable load factor with
the N strut cut, For instance, in the PW1, the unequalized
bending moment in the rear lower spar in low incidence
is 218,000 inchpounds, giving a value of My/I of
13,400 pounds per square inch and of M/hA of 9,890 pounds
per squ~re inch. The allowable values for standard wood
are 7,380 and 5,500 pounds per square inch, respectively,
and for the material in the test specimens 5,840 and 5,550.
Dividing the allowable stress by the computed and multiplying
by the load factor 5.5 the values of the ultimate
load factor become as follows:
For standard wood, 3.03 for My /I and 3.06 by M/hA.
For the wood used, 2.36 for My/I and 3.08 by M/hA .
The required load factor in low incidence for partially disabled
pursuit airplanes is 2.5, which is less than all of the
above values except one. The low value is based on the
strength values of the spar actually used, which happened
to be made of lowgrade material which should have been
rejected. In this conne.ction it is ·only the values based
on standard wood that are bf real importance.
+l, 195 1 GENERAL CONCLUSION.
Rear lower._ ... .. 'e933 80! 927 The static tests of the PWlA and the TW2 indicate
that the method of design of internally braced biplanes
Owing to the high modulus of elasticity of the front recommended in this report results in a safe and economical
spars and the low modulus of the rear spars, the forces structure.
APPENDIX I.
ALLOW ABLE UNIT STRESSES IN BENDING FOR
BOX AND ISPARS.
INTRODUCTION.
It is well known that the shape of box and I spars of
spruce has a pronounced effect on the fiber stress at elastic
limit and the modulus of ,rupture of the spar. Investigations
at McCook Field resulted in the adoption of a formula
for computing the modulus of rupture of I sections. This
formula is given in the Handbook for Designers (1921
edition) and in article 174, page 279, of" Structural Analysis
and Design of Airplanes." More extensive test.a have
recently been carried out by the Forest Product.a Laboratory
on both box and Ispars and new formuhe have been
developed for the ratio of stress at elastic limit and modulus
of rupture of box and I sections to the same quantities for
solid rectangular sections. The original data of the
McCook Field test.a check very well with the Forest Products
formulre. Owing to the more extensive range of the
forest product.a laboratory tests, both as to number of
specimens tested and variety of shapes, the formulre
given below should be used in place of the McCook Field
formula.
STATEMENT OF FORMULA;;,
The term "form factor" is used to designate the ratio
of fiber stress in a box or Ibeam to the fiber stress in a
corresponding solid rectangular section of equal width
and depth.
Let ¢.=Form factor for fiber stress at elastic limit.
4>0 =Form factor for modulus of rupture.
Fiber stress at elaEotic limit for box or I section.
Then 4>0 Fiber stress at elastic l~t for solid rectangular
section.
Modulus of rupture for box or I section
</tu Modulus of rupture for solid rectangular section·
According to the forest product.a laboratory tests
4>0=0.58+0.42 ( k bt +~}
<i>u=0.50+0.50 c \;b' +}}
Where k is a function of the ratio of depth of compression
flange to depth of beam.
If u=vers_13 (depth of compression flange) expressed in
depth of beam radians.
k=0.293 (uCOS u sin u).
b=width of beam.
b'=thickness of web.
. In box spars, b1 is the sum of the thicknesses of the plies
in which the grafo is parallel to the axis of th€ beam.
If ply wood is used in which the grain is at 45° to the axis
of the beam, use b1 equal to onehalf the total thickness
of the ply wood.
The upper half of Figure 13 is a curve with k plotted
against the ratio of depth of compression flange to depth
of beam.
The lower half of Figure 13 gives curves for finding
the modulus of rupture of spruce beams directly when
the ratios b1/b and tjh are known, where·t0 is the thickness
of the compression flange and h the center height. Figure
14 shows sections of box and I spars with the dimensions
b, b1 , tc, and h indicated.
When the flanges are not rectangular in shape, they
should be replaced by equivalent rectangles as shown in
Figure 14. In such cases in the formula My/I, y should
be taken as the distance from the centroid to the most
stressed fiber of the equivalent section, and I as the
moment of inertia of the equivalent section.
NUMERICAL EXAMPliE.
The use of this formula is illustrated by the computation
of the modulus of rupture of the front upper spar of the
PW lA at the critical section. The dimensions of the
equivalent section are given in Figure 7, except the center
height which is 8.57 inches. b=3.4375; b'=0.1875;
t. =1.75; h=8.57.
The grain of the ply wood webs is at 45° to the axis of the
beam so that only half of it.a thickness is used in computing
b and b1
• b'/b=0.0546 ; t0 /h=0.204.
From Figure 13 the modulus of rupture is 6,600 pounds
per square inch for standard wood.
To find the modulus of rupture for the adual beam,
using the strength properties from Table XXXII, the .following
computations must be made.
From Figure 13, k=0.243 for tjh=0.204.
(bb')/b=0.946
¢=0.50+0.50 (0.243X0.946+0.0546)=
0.6423
Modulus of rupture=0.6423 X 1/2 (8805 + 9950)=6,020
pounds per square inch.
RECOMMENDATIONS.
In designing box or I spars the strength of the section
in bending should always be checked by the use of the
Forest Product.a formula.
In making trial designs of I spars it may be convenient
to use the McCook Field formula for the modulus of rupture
for routed sections.
In making trial designs of box spars it will probably be
most convenient to determine the size of flange by the
formula A=M/jh, where j is the ultimate compression,
5,500 pounds per square inch for standard spruce, and h,
the centertocenter distance between flanges. Each flange
should be designed for the case in which it carries its maximum
compression, except that one flange should not have
an area greater than 2.5 times that of the other flange.
The above formulre have reference only to the strength
of beams in bending. The strength against shear must
always be investigated. At present little is known about
the rational· design of box spar webs to carry shear, but
tests ~e being made at the Forest Products Laboratory
to develop a method.
(21)
APPENDIX II.
DESIGN OF I STRUT FOR PW IA.
Figure 15 shows a line diagram of an I strut and the
main compression ribs of the PWlA and the vertical
components of the forces required to equalize the deflections
of the spars in low incidence.
Vertical component of force in
DE=l,192.7793.5=399.2 pounds.
or
DE=l,354.0 954.8=399.2 pounds.
H
on.z ontal component=399.2X9.25 55=I39.7 pounds.
Applying "'EM=O about point EPX55+
954.8X 2.05l,354.0X28.05793.5X12.05
1,192.7X20.45=0.
=55 P+l.96037,9909,560 24,390=0.
69,980
P = 55 = 1,272 pounds.
If the vertical distance from top of lower. wing to bottom
of upper wing had been used instead of the centertocenter
distance, we would have
69,980
P=48=1,457 pounds.
With the N strut we had 1,462 pounds. This shows
that the forces acting on the drag trusses due to the equalizing
member do not depend on the kind of member used.
Bending moment at
E=793.5Xl2.05+1,192.7X 20.45  l,272.0X12
=9,560+24,39015,260=18,690 inchpounds.
r/fs;. /.
Bending moment at
D=l,354X17.2+954.8X8.81,272Xl2
=23,290+8,40015,260=16,430 inchpounds.
Maximum stresses in DE, 800 pounds compression;
18,700 inchpounds bending:
My 18,700
J=r I/y=M/J= 55 000=o.34.
'
Try 2! Xhinch tube of Specification 10225 steel.
A=0.7087 square inch.
A of tubes in N strut=0.1199+0.1656+0.1061=0.3916.
Then, if steel tubing is to be used, the main member
alone haa a sectional area practically twice that of an
N strut which carries a larger load.
As for resistance, the total width of N strut tubes is only
3t inches against 2~ inches for the I, or an increase of
0. 75/2.5=30 per cent.
The compression rib would have to carry a bending of
M=l, 192. 7X16.25=19,380 inchpounds ..
19,380
I/y=55 ooo=0.35.
'
Again, a 2~Xh tube, or its equivalent, would be needed.
The weight and resistance of a wood I with wood compression
ribs would not be aa great aa for steel. But it ifl
doubtful if the I would be aa good to us(aa:the N.
"
~.u·
_348 _
!16" ea" 96" ·r a.¢"
T
_i
~4" ,u'' .. 1 .. az"•l4 /24
11 .. , .. 34,~
r/es.2.
FIGS. 1 and 2
(22)
~.
 · 
>,.I ""
"
I' "'
'"
f fr
'
I',
~ . /, " ~: ..
CJ /I ~ ... ' I'. ' (' ,, /j
~
~ '" ~~
' "'
" /,
" .....
rRO/YT VPP&,e .5p,qe C
"' I
' ,, /?v. loud= ZI. 51Z /,b~ ,;::,er. zn. rc.:n
"' " IJ
1,L I
I .' " I 
" ,, "
..... ,,
., 7
tJ ,r

0 A7 t'O J() 40 ;_so 60 70 40 ":7 100 //(} 1eo /80 /40 /60 /60 /70 180
t?/.sf'a,rce /ro;,,/ C'enterLirce o/ Flir.,m'ane (m tncil.e~) r!Ci.3
"
' ;•;
= ,. ,,
"
1 ~'"' ~ ~ ,, r,
"' .... .~ 
I' ,,., rJ.
" ...
. IJ "
"' "
I Iii " "' I
"
" ~ ,,
" I
I' ' " " ,~ ....
rffOIVT LOWERSP"9R
I...
" 11,1 ~  " i.At'_L(}AP "" /7Z6 LB. P£H IN lfVN "
" V
1"
........ .
"· ~ 1;
I,
0 /c..' eo ~ <JU
.! "
cc, t!:I ,u ~ I(, /(I(, , .. , /~'O /.:JO ,;,,
/. " /60 / I? /, '()
FIC:i. 4
)
"
" " "
"' ,~ ,~
'
I I \
I
\
,, I\
'
'
"
.
I'.
I"'
'
''
0 /() t!.O .J() ~~ ..:c; e~ /(,, 80
'
" "
'
"
,€c;,Q,e t/PPe.e ..,5p,,q,e
",: L.ood t.'?. es /.5 ,pcr /n run
"

~
9t) /<70 ' //0 /c'() /30 /4()
·
'

A>, /,'l !i.' t,
rl&,5
,,
'/
,,,
..
'/

/ <::>
...
"' c,,
,,
I ,
'
"
t
"
 "
"'
"'
,_
" ,_
"
I/ ~
' ~
" ,,_
' "'
" ,,
' r..
r..
I' " "
"
~.,,
"
"
" "'
Pene tt.owere SPRe 1.~
v. /IXN:i' "' /.9.'N ~/,.S.,P£r. i n run
'
" '  ..c
........
"
~~
~
/0 c;; ..: " 4LJ .:J[) e: .. )C, i" .; IC, /Cl!C 1/0 /CO /. >I! I ''CJ '
'() /60 /?t)
r/G. G