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fi le D 52.1 / 341 McCOOK FIELD REPORT, SERIAL No. 1572
AIR SERVICE INFORMATION CIRCULAR
( AVIATION )
PUBLISHED BY THE CHIEF OF AIR SERVICE, WASHINGTON, D. C.
Vol. III July 15, 1921 No. 260
THE ECONOMIC LIMIT IN ASPECT RATIO
OF SINGLE-BAY PURSUIT BIPLANES ·
( AIRPLANE SECTION, S. & A. B-RANCH)
Prepared by Engineering Division, Air Service
McCook Field, Dayton, Ohio; March 22, 192 J.
Rllph Brown Draughon
· LIBRARY
WASHINGTON
GOVERNMENT PRINTING OFFICE
1921
MAR 2 8 2013
. Non•Depoltory
Auburn University
INDEX.
Page.
Statement of the problem ... . ....................................................... .. .... .. ............ . 3
D~finition of performance factors ........... . ..... . .. . ....... . ................. .. . _ .... . . ... ...... ..... ... . 3
General specifications of designs compared ............................................... .. ..... . ... . ..... . 3-4
Method of computing relative fineness factors .. . ............... ... .......... .. . ....... . ...... . .... . ....... . . 4
Table I- Comparative speeds and performance factors ......... .......... . ..... ............................ . 4
Table II- Differences in weight and resistance at 100 m. p. h .............. . . ..... . ............ .. . ....... .. . 7
Conclusions .... . .... . . ....... .. ... ___ ... .. ... . . . ... . .... ..... . ... ... . ...... .. ....... .............. . ... .. . 7-8
Appendix I- Specimen computation ... . ..... .. .. ...... .. . .......... .. ..... . ..... . . ........... .. . .. ... .. . 9
Data common to both designs ... , .. . .......... . .. ... ........ . ........... ... ............... . . ......... . 9
Computations for one-bay design ......... .. ......... .. ... ... ... .... ... .. ..... . ........... .. . . ....... . 9
Computation for two-bay design .. .. .. . .... . .. .... . .... . . ..... . . ... . ............ _ . .... .. ........ ... ... . 11
Weight computations .............. . ........................... . ....... .. .. .... .... . . ................ . 14 J
Table of resistances .............. . . . ..... ... .. .... .. .. ... .. ........... ... .......... .. ............ . .. . 15
Comparison of performances ... . ........... . ..... .. ............ _ . . . . . . . . . . . . . . .. ................ ... .. . 15--16
Appendix II- Computation of relative fineness............ . . . . ... .... .. ........ . . . ........... ...... ...... . 17
Figures- ·
Graph for comparing service ceilings.. ......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .... . ................. . 5
Curves of high speed at altitude .......... . ..... .. ...... _ ... . ..... .. .... . .. . . ...... ... ..... . .. . ...... . 6
Line diagrams of wing trusses . . ................. .. .... . ................. .. ... ... .... . .......... . . .. . .. - 10
Line diagrams of upper drag trusses ..... ... . ...... . .......... .. ............................ -. - - - - - - - - - 12
Sections of spars used ........ .. ........................ . , .......................................... . . 13
(2)
' ---
THE ECONOMIC LIMIT IN ASPECT RATIO
PURSUIT BIPLANES.
The purpose of this investigation was to determine the
limiting aspect ratio at which a single-bay biplane of the
single-seater pursuit class will give better performance
than a two-bay biplane of identical design except in the
wing trusses. Several designs were made and their comparative
performances computed .
The ·chief performance characteristics of a pursuit airplane
are its maximum speed at different altitudes and its
service ceiling, i. e., the altitude at which its maximum
rate of climb drops to 100 feet per minute. Any increase
in weight decreases the ceiling, but within rather large
limits has no appreciable effect on the speed. Any
decrease in structural resistance increases the " cleanness"
or " fineness '.' of the design and increases both the ceiling
and the high speed at each altitude. The cleanness (JJ
different designs can be compared mathematically by finc· ness
factors , which are numbers proportional to the cub,
roots of the value of L/D for the entire airplanes at the sam!-'
value of Ky.
Knowing the load per horsepower, the load per square
foot of wing area, and the fineness, the speed at different
altitudes and the ceiling can be obtained from the airplane
performance charts in Air Service Information
Circular, Vol. II, No. 183.
In all designs except those of very low aspect ratio a
two-bay cellule of given chord and span will be lighter
than a one-bay cellule of the same chord and span, where
both designs are made for the same net loading and load
factors. The only members which will vary between
the two designs will be the lift and landing wires, the
interplane struts, and the wing spars. Of these the
wires will be of about the same weight in both designs:
the struts will be heavier on the two-bay type, while the
spars will be so much heavier on the one-bay type that
the total weight of the cellule will be much greater for
the one-bay design than for the two. For a single-seater
pursuit airplane of gross weight about 2,500 pounds this
difference will be about 40 to 50 pounds. From the point
of view of structural resistance, however, the one-bay
design will be better, owing to the smaller number of
exposed struts, wires, and fittings.
In order to compare similar designs it is necessary to
develop some criterion of excellence in performance
that will take into account the variations both i.n ceiling
and in speed, and which can be expressed numerically.
There is no standard method for doing this, so one had to
be devised for this report. Two types of performance
factors were used. The " fineness performance factor"
is the product of the fineness and the service ceiling in
thousands of feet. '!.'he "speed performance factor " is
the product of the speed of the airplane in miles per hour
at any given altitude by the service ceiling in thousands
of feet. The fineness performance factor takes into
account the speed at all altitudes and is most useful when
two designs are to be compared over the entire range.
The speed performance factor must be computed separately
for each altitude, but is the more useful when the
relative characteristics at any given altitude are of special
importance. A second advantage of the fineness performance
factor over the speed p erformance factor is that it
requires less interpolating on charts to obtain and is therefore
more reliable. The performance factors computed
in this report depend in absolute amount on the fineness
assumed for the two-bay design, but the difference in the
performance factors of a pair of designs of the same chord,
wing loading, etc., will depend very little on the fineness
assumed, but principally on the difference in performance
due to the changes in weight and fineness.
The difference in weight between two designs can be
computed very easily. In hypothetical designs, such as
were made in connection with this report, it is not worth
while to try to design fittings, but a good approximation
to their weight can be made by comparing the weights of
fittings on similar existing airplanes. On the other hand
the difference in resistance is hard to determine.
The resistances of the component parts of an airplane
are none too well known, especially as regards the effect
of fittings and interference. In order to make the comparison
as fair as possible, the strut fittings were assumed
to be inclosed . as in the Vought VE-7, and the best type
of ends was assumed for the streamline wires. Theoretical
sizes of struts and wires were assumed in most cases
as they showed the tendencies most fairly. In any practical
case, however, the relative resistances of the w'ires
may differ greatly from what would be the case if theoretical
wires had been used, depending on the degree
with which the actual sizes used agreed with the theoretical.
In spite of these difficulties it is felt that the
net results will be about the same for an actual airplane
and one computed as in this report.
As the majority of single-seater pursuit airplanes have
an aspect ratio of less than 6.0, that value was chosen for
investigation. Comparative designs were made of single
and two-bay biplanes of this aspect ratio and differing
values of net wing loading and chord. The most typical
designs had the following general specifications :
Wing section, R. A. F.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Aspect ratio ............. . ....... , . . . . . . . . . . . . . . . 6. 0
Netwingloading ........ pounds per sqgare feet .. 7.5
Chord ............... . ................... inches .. 60
Gap . ..... . ......................... .. .... do . .. . 60
Weight of cellule ( assumed) .pounds per square foot. 1. 0
Load per horsepower for the 2-bay design .. pounds.. 8. 0
Fineness factor (assumed), for the 2-bay design ... 110
Center span ................ .... ....... ... inches .. 30
All spars hinged at center span.
(3)
4
Other designs were made with each of the following
variations:
Net wing loading increased to 8.5 pounds per square
foot.
Chord and gap increased to 72 inches.
60-inch
(ThiS'
Spars made continuous, the upper with
and the lower with 30-inch center span.
was done for the single-bay design only.)
The specifications of the original designs are representative
of good modern practice in the design of singleseater
pmsuit airplanes, as can be seen from a study of
Table IV, page 42, " Stress Analysis and Design of Airplanes."
Each of the other designs were mad'il with only
one variation from these specifications in order to learn
tbe effect of the single changed characteristic.
The value assumed for the fineness factor of the two-bay
designs was chosen arbitrarily. If another value had been
chosen the ceilings and speeds predicted would have been
materially changed, but in this investigation the relative
ceilings and speeds for small changes in fineness are what
are desired, and in the range considered , this depends very
little, if any, on the fineness assumed , so the results obtained
may be considered the true effect on the performance
of the change from a two-bay to a one-bay design.
Table I gives data regarding three pairs of designs. In
each case the performance of the two-bay design was predicted
on the assumption of a fineness factor of 110 and a
power loading of 8.0 pounds per horsepower. The horsepower
at 10,000 feet, 15,000 feet, and 20,000 feet was computed
on the assumption that the power varied directly as
the density of the air. From the speed and power, the
thrust at the four altitudes considered was figured by
ineans of the relation, power=velocity times thrust, from
which we obtain the formula. Thrust in pounds equals
375 times horsepower divided by velocity in m. p. h .
This value of the thrust was assumed to be equal to the drag
of the entire airplane. The difference in the resistance of
each pair of designs was computed for the speed of the twobay
-design at each altitude and subtracted from the corresponding
value of the drag of the two-bay design to obtain .
the drag of the one-bay design at the same speed and alti- ·
tude. 'l'he fineness of the one-bay design was then obtained
from the relation
F,=F,-3Y/Dn,,
where F represents the fineness factor, D the. total drag,
and the subscripts identify the design considered . From
the data used, fom· values of the fineness of each one-bay
d'ilsign were obtained, one for each altitude, and the arithmetic
mean was used in predicting performance.
The above formula for obtaining the fineness of the onebay
design from that of the two-bay design is not exact,
but where the ratios of weight and resistance of the two
designs are as nearly equal as they are in the cases considered
, the error in using it is too small to be detected on a
20-inch slide rule and the work is much simplified.
By definition the fineness factors are proportional to the
cube roots of the values of L/D of the designs compared at
the same value of Ky. If the one-bay design is the heavier
at any given value of Ky, its velocity will be greater than
that of the two-bay design. The weight and wing area of
the one-bay design being known, this velocity can be
easily computed , and so can its drag at this velocity. Let
the high speed of the two-bay design at a given altitude
be V, and the velocity of the one-bay design at the same
altitude and value of Ky be V, . The relative fineness of
the two designs can be obtained by computing the ratio of
L/D of the one-bay design at V, to L/D of the two-bay design
at V ,. L is known for both designs, being equal to
the weight of the airplane. D is known for the two-bay
design. The only quantity remaining is the value of D
of the one-bay design at V, . The drag of the two-bay design
can be assumed to vary as the square of the velocity .
This is not precise , as the wing drag varies with Kx as well
as the velocity, but this effect is entirely negligible for
small ranges of speed. The drag of the two-bay design at
V1 can be· computed and the difference in drag at V, which
is known can be subtracted to find the drag of the one-bay
design at V ,. Appendix 2 gives a computation of the rela-tive
drag of the two designs by both methods. ·
Knowing the difference in weight of the two designs, the
new wing and power loadings were computed and the per-·
formance of the one-bay designs could th en be predicted.
-On the pre<liction of performance, both the airplane performance
chart mentioned above and figs. 1 and 2 of this
report were used. Fig. 1 was obtained from the performance
chart and shows the effect of small increases above
8.5 pounds per square foot in wing loading and 8.0 pounds
per horsepower in power loading on the ceiling. Fig. 2
was plotted from points obtained from the performance
chart for the velocity of airplanes with 8.5 pounds per
square foot wing and 8.0 pounds per horsepower power
loadings an(j. varying degrees of fineness. As the speed
varies very little for a proportional increase in wing and
power loadings, it can be used for both one and two bay
designs. For a wing loading of 9 .. 5 pounds per square foot
and 8.0 pounds per horsepower figs. 1 and 2 could not be
used, but the prediction had to be made directly from the
performance chart. The value of figs. 1 and 2 lies in the
fact that by comparison of differences the readings could
be adjusted so the error in computing small differences in
performance, especially as regards service ceiling, is
much less than if the work had been done directly from the
performance chart. It is believed that the curves for
service ceiling are accurate to within 20 feet or less.
TABLE I.
Pair I. Pair 2. Pair 3.
Chord ...... ... .. .. . 60 inches. 60 inches. 72inches.
Net wing loading .... 7 .5 pow1ds per 8.5 pounds per 7.5 pounds per
square foot. square foot. .square foot.
T ype of design .. .. .. 2-hay . 1-bay . 2-bay. 1-bay. 2-bay. 1-bay.
--- - -----------
R ela tive weight . . .. _ 1.000 1.018 1.000 1. 017 1.000 1. 017
Fineness . . . . ........ no no. 9 no no. 95 110 no. 5
Service ceiliu g'. feet . . 21, 000 20,990 20, 650 20, 700 21, 000 20,935
Fineness perform-ance
factor ....... . 2310 2326 2271 2297 2310 2315
Speed at ground ..... 138. 4 139. 6 144. 3 145.6 138. 4 139. 2
10,000 feet ....... 134. 5 135. 5 139. 2 140.6 134. 5 135. 0
15,000 feet . . . ... . 127. 3 128.6 131. 6 133. 2 127. 3 128. 1
20,000 feet .. . ... . 114. 2 n5. 8 117.1 li8. 0 114. 2 115. 2
Speed performance
factor:
At grou nd ..... ·1 2906 2930 2980 3016 2906 2917
At 10, 000 feet .. . 2825 2843 2875 2911 2825 2828
At 15,000 feet ... . 2672 2700 2720 2759 2672 2683
At 20,000 feet ... . 2400 2430 2420 2442 2400 2412
Weight of structure ' 113.6 156. 6 128. 1 174.2 186. 2 246.4
Resistance a t 100
m.p.h.• .......... 31. 74 19. 86 33. 45 21.16 42. 67 30. 08
Advantage in weight 43. 1 ··-·--- - 46. 1 -----··· 60.2 -·-····· Advantage in resist-ance
. . ....... . ... . ··------ 11. 88 ··-····· 12. 29 ··-·-··· 12. 59
1 Includes only spa rs, wires, struts, and fittin gs. ·
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In addition to the designs for which data are given in l weight and resistance at the g1ounci at 100 m. p. h. Table
Table I, several other designs were made but were carried II gives the essential data concerning these designs.
through only far enough to determine the advantage in .
TABLE II.
2 3 4 5 6 7 8 9
Advan- Advan- 6 R
Spars. Aspect Wires and struts. Chord. Net wing tagein Weight tagein w ratio . loading. weight. ratio. resist- ance.
- -------'------ ---- ---~ ,-------- -,----------------- - -
Pounds
Inches.
per square
foot.
Hinfig_ ~~ ~~~~'.~!~:::::::::::::::::::::: ~:::.::: 6. O Theoretical sizes ..... . 60 7.5 43. 1 1.018 11. 88 0. 0049
6.0 ..... do . . .. .. ......... . 60 8.5 46.1 1. 017 12.29 .0045
Do- ............. . ... . ... . ........ .. . ...... . 6.0 ... .. do ............... . 72 7.5 60.2 1.017 12.59 . 0036
Do···-··-··········· · ·· ·· ·-······· ····· · · ··
DO· - ·············· · ········· · ········ ······
6. o Standard sizes ....... . 60 7. 5 39.1 1. 016 15.40 .0063
6.0 ..... do .... . .......... . 60 8. 5 42. 7 1. 016 15. 59 .0057
Do ............... . ........................ . 6.0 ..... do ........ . ... .. . . 72 7.5 68.6 1.019 11.40 .0032
Hinged at fuselage .................... . .. ..... . }
Front and rear trusses different ........... . .. . . . 6.0 ..... do .... . ...... .. .. . 60 7.5 43.2 1. 017 13. 98 .0057
1-bay~thcontinnous spars . .... . .............. }
2-bay with hinged spars ............. . ......... . 6. O Theoretica' sizes ..... . 60 7.5 12.1 1. 005 11. 85 .0049
Hinged a tfus,lage .... . . . ........ . ..... . ....... . 6. O Theoretical cables .... . 60 7. 5 10. 72 '13. 0
1-bay with continuous spars ... . ...... . .. ....... }
2-bay with hinged spars .... . .................. . 6.0 .. ... do ............... . 60 7.5 I 0. 32 1 13.2
Hinged at fuselage •...... .. .......... . ... ..... .. 4. O The:.retical sizes ..... . 60 7. 5 ' 12. 5 0. 992 8.86 . 0071
'Wires only, struts and spars not included.
• Advantage in weight in favor of 1-bay design.
Column 1 gives the type of spar used, The one-bay designs with continuous spars was compared to two-bay designs with hinged spars as the
two-bay design would not be helped much by making the spars continuous. At best the weight could not be cut down more than 3 or 4 pounds
an'.l the resistance would hardly be affected. The decreased vertical components in the wires would be counteracted by their greater length and
flatter slope. ·
Column 6 gives the difference in dead weight between the two designs compared.
Column 7 gives the dead weight of the one.bay design in terms of the dead weight of the corresponding two-bay design.
Column 8 gives the difference in resistance at 100 m. p. h . at the ground of the struts and wires entering the comparison.
Column 9 gives the ratio of the value in column 8 to the dead weight of the two-bay design and is an approximate measure of the change in
fineness. ·
CONCLUSIONS.
As the aspect ratio increases the one-bay design becomes
less and less economical. For low aspect ratios it
has an advantage over the two-bay design in both weight
and resistance. As the aspect ratio increases the weight
advantage drops off more quickly than the resistance advantage,
since it becomes no longer necessary to use the
minimum allowable size of spar ·for the two-bay design
and, with a thin wing section the spars of the one-hay
design must be made with very uneconomical sections
owing to the limitation on the center height. With a thin
wing section like the R. A. F. 15, at an aspect ratio of about
6.0 the advantage in weight is decidedly in favor of the
two-bay design , but the advantage in fineness of the onebay
design is still sufficient to more than counteract it in
airplanes of the type specially considered. For a thicker
section, such as the U.S. A. 27, the two-bay design would
have to use the minimum size spar, and the one-bay design
could use an economical shape of spar for much higher
aspect ratios. The effect on finene·ss would probably be
about the same. The question of the effect of the wing
section used, however, has been left to a future report.
In any particular design standard sizes of struts and wires
must be used. The relative weights are little influenced
by this fact as the chief difference in weight is between
the spars. The change in resistance is considerably affected
since the the resistance of the struts and wires are
the only ones considered. 1.'he difference in relative fineness
will be appreciably affected if the standard sizes in one
design involve a much more efficient use of material than
in the other, fo most qf the cases considered iIJ. this report
the change may be enough to change the relationships of
the performance factors of the designs considered. In
this connection, however, it should be remembered that
in these designs the aspect ratio was near the upper limit
for the single bay even with theoretical strut and wire
sizes. This is a much more important factor than either
the chord or the wing loading, and in a doubtful case it
would be necessary to compare the two designs on the
basis of the actual wires and struts to be used in each
design.
Very little change in relative performance is caused by
an increase in wing loading with no corresponding change
in power loading. What little change was found was in
favor of the one-bay design, but it was much less than
would be caused by a change from theoretical to practical ·
size of struts and wires.
With an increase in chord the relative weights remained
very nearly the same, but the difference in relative fineness
decreased. This indicates that the limiting aspect ratio
for the one-bay design decreases with an increase in chord.
One probable reason for this is the fact that the interplane
struts being very slender, their strength varies directly
with the moment of inertia. This being the case their
small diameter and hence their resistance does not increase
as quickly as the load they must carry.
If cables are used instead of wires the difference in
weight will hardly be changed, but the difference in resistance
due to wires will be about doubled. The total resistances
will be very greatly increased, but the difference
will be nowhere near as great as the total resistances would
seem to indicate. This is due to the fact that at an aspect
ratio of 6.0 the resistances of the wires proper of the two
designs are about equal and the advantage of the one-bay
design lies mainly in the smaller number of wire ends.
When cables are used the resistance of the ends is a much
smaller proportion of the whole than is the case for streamlined
wires.
As st.ated above, the strut fittings are assumed to be
in closed . If they were exposed, the resistance of the
two-bay de8igns would be increased more than that. of the
one-bay design, owing to the greater number of fittings.
The relative fineness of the one-bay design would therefore
he perceptibly increased.
In nearly all of the designs the web members of the
rear truss have been made the same size as those of the
,front truss. Very little change would be made in the
results if the theoretical sizes had been used in both
trusses.
8
In general it may bo stated that for a single-seater pursui t
airplane wi th an aspect ratio of 6.0 or less and with the
R. A. F. 15 wing section, a one-bay design will be more
efficient than a two-bay design otherwise similar, though
the spars of the former are apparently much too heavy.
The effect of the extra struts and wires of the two-bay
designs on the performance is considerably greater than
has generally been believed.
For airplanes of other types and wing sections this conclusion
may have to be modified and fur ther reports on
this question are being planned.
In order to show exactly how the comparisons were
made, the complete computations for the designs with an
aspect ratio of 6.0, a chord of 60 inches, a net wing loading
of 7.5 pounds per square foot, and spars hinged at the
fu selage is given in the Appendj.x, togethet· 'with figures
showing the spar sizes used drawn to full scale:
APPENDIX I.
COMPUTATIONS FOR THE BASIC PAIR OF DESIGNS.
TABLE III.
GENERAL DATA.
Ai1foil section . . . . .. .. .... .. .. . . . .. ...... . . R. A. F . 15
Aspect ratio....... . .......... . . . . ... ....... .. . .. 6. 0
Chord . ...... .. ........ . .. . . . ..... .. .. .. . inches. . 60
·Gap .... . . ... . . .. .. . .. . . . . ........ ... .. . .. do .. .. 60
Stagger . ..... . ... . . .. .. .. ..... .. ...... . . . . do. . . . 15
Average gross loading .... . pounds per square foot .. 8. 5
Efficiency of lower ,~ing . . .............. per cent... 90
Location of front spar in per cent of chord. . ...... . 13
Location of rear spar in per cent of chord. . ..... ... 67
Lift wires in inner bay as shown in fig. -5.
Angle
of incidence.
L/D.
Location
of
c. p.
Load
factor.
- --------- ---- ---- --- - ----
Per cent.
High incidence .... .. ... .. .. . . 12°
O'
10. 7 29 8. 5
Low incidence . .. .... ..... . . . 8.1 45 5. 5
TABLE IV.
Load on each spar at the design load factor in terms of
the load on the wing at a load factor of 1.0:
F ront
spar.
Rear
spar.
High incidence........ ... ..... ... . . .. . . .... . ... ... 5. 98W
Low incidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 24 W
2.52W
3.26W
DRAG LOADS.
High incidence ... .. .
Low incidence . .... .
i.
12°
O'
i is the angle of incidence.
L/D.
10. 7
8. 1
cot-'
L/D.
Design
tan <f,. drag
load .
5. 3° 6. 7° 0.1175 1. oow
7. O' -7. 0° .1228 . 675W
<f> is the angle between the resultant force on the wing and a line normal
to the chord.
LENGTH OF STRUTS.
Vertical component (gap
minus wing thickness).
Drag component . ........ .
Length -.,/V•+D• . ..... . . .
Length used in computa-tion
of weights.
Front. Rear.
60-3.75- 56.25 inches . . 60-3-57.00 inches.
15.00 . • ...... .. ........ 15.00.
58.21 inches ........... 58.94 inches.
55 inches. .... ...... ... 56 inches.
COMPUTATION OF WING AND SPAR LOADINGS.
Area of upper wing 5X 6 X-5=150.0 square feet.
Area of lower wing 5X5.5X5=137.5 square feet.
Total wing area ......... .. .. =287 .5 square feet.
Gross weigh t of airplane, 237.5 X8.5=2,444 pounds.
Let x be the gross load per square foot on t he upper wing.
150x+l:{7.5X0.9x=2,4·14.
x=9.93 pounds per square foot gross load on upper
,ving.
0. 9x=8.04 pounds per square foot gross load on lower
,ving.
SINGLE BAY DESIGN.
Inches.
Length of cantilever. ... .. ... . .... ..... .. ...... .. 63
Length of bay.. . . .. . .... . . . . . . . . . . . . . . . . . . . . . . . . . 102
Length of cen ter section. ..... . . ... . .... ..... .. . . . . 30
(See fig. 3.)
RUNNING LOADS PER INCH OF WING.
D ea d we1.g h to f w.m g=-l.-O-O-yXz-5 = 0 .4 1 pound per m. eh run.
Upper wing, 60X0.7w+60X0.9w+240w= 8.93Xl 50.
w= 3.99-0.41=3.58 pounds per inch run net load on
center portion.
0. 9w=3.59-0.41= 3.18 pounds per inch run.
0. 7w=2.78-0.41=2.37 pounds per inch run net load at
wing tips.
Lower wing, 60X0.7w+60X0.9w+210w= 8.04 Xl37.5.
w=3.6l -0.41= 3.20 pounds per inch run net load on
center section .
0. 9w= 3.24-0.41=2.83 pounds per inch run.
0. 7w=2.51-0.41= 2.10 pounds per inch run net load at
wing tips.
TABLE V.
UPPER WING STRESSES AT DESIGN LOAD
FACTORS.
L . F.
- 1.0
Front Rear
spar, high spar, low
incidence. incidence.
--------------,----------- -
M1 .•..........••.. •..... . . inch-pounds.. · 5,146
M1. 2 ••• ••• ••• • ••• • ••• •• • •••••••••• do .... -2, 417
S.1 .. ... .... ..... ... ... ........ pounds.. 174. 8
8 ,1 . .. .• . ... .. . . ... .. ...... .. .. . .. do.... 233.0
V strut . .. .. . .. . ........ . ........ do.... 365. 5
V1- 2 ..•. • .•••• •• •••••• • •• • ••...•.• do. ... 773. 3
01~2 (no drag) .. . ............ .. . . . do.... 1,314.6
0 +1 (with drag) . .... ...... . ... . . . do . ...... . ... .. . c_, (with drag) . .. . . .. . ..... . .... do .. . .. .... .. .. .
W 1. 2 ••• • •••..•••••••• poun,!s per inch. . 3. 58
30,800
-14,440
1,045
1, 392
2,186
4,624
7,860
9,073
11, 585
21. 40
-716,,8m00
762
1,192
2,521
4,290
4,390
4,030
11.68
This reduction in length was assumed to allow for the Figs. 6 and 7 show the loads and chord stresses in the
upper drag truss in the high and low incidence conditions.
(9)
decrease in sectional area near the fi ttings. -
53048-21-2
10
LIFT TRU:5.5 ~ ONE /3,qy DE,5!6N
F163
r 40"---- - -75'1
---------- ..so" ,1.,1· ,<5'
Hi/?51e
LIFT TRU.5.:J-:-T/1/0 !J,,qy fJE.516A.l
F!u.4
60
LOCATION OF J11!RE..5/JNO .5TRLITS IN INNER 811Y
F!a . .5
!t,fhe ovler bovof fhe two hew design all wires are
in t/ze Dione.$ off!Je .slrvf,i.
'
f1CJ(/R£.5-~-4-S
t
11
-DESIGN OF MEMBERS.
FRONT SPAR.
The dimensions of the front spar are shown in fig. 10.
Area=3.375X2.50-l.375Xl.25=8.44- l. 72=6. 72 square
inches.
1=3.204X2.50-0.217Xl.25=8.02-0.27=7.75 inches. 4
1 =6.72X3.204 639 1
C 3.375 · • •
All.o wab l e b end 1"n g s t ress= l.12Xl07,3_7050 X6.39 91500
pounds per square inch.
I / - 7·75-4 30· h 3 /
7-75 10 . h y-1.80- . me es. p=v 6.72= . 7 rnc es.
At outer strut point.
/ 0 =9073/6.72 =1350=P/A
7160
Jb=30,800/4.30 = 8510=My/I
Allowable stress=(9,500-5,500) 7,160/8,510+5,500=
8,860 pounds per square inch.
In the bay at point of zero shear.
7.75 E ii= -65X37 [15,400-232Xl67+
2~·:o (652+6fi
x102+1022
) ]
whence
ii=0.85 inch.
Mii=ll,585X0.85=9,850 inch-poundR.
Total moment at point of zero shear, 9,850+ 14,440=
24,290inch-pounds.
Slenderness ratio 102/1.07=96, allowable compressive
stress 1,850 pounds per square inch.
/ 0 =11,585/6. 72 =1725
/b=24,290/4.30
5650
7375
Allowable stress =(9,500-1,850) 5,650/7,375+ 1,850=
7,700 pounds per square inch.
REAR SPAR.
The dimensions of the rear spar as shown in fig. 11:
Area=5.91-l.69=4.22 square inches. 1=3.21 inches'.
l/y=2.31 inches 3 p=0.873 inch.
Allowable bending stress 8,700 pounds per square inch.
At outer strut point.
fc=l,040. /b=7,270. /,=8,310. Allowable f,=8,300
pounds per square inch.
1 See page 279, "St11:1ctm-al Analysis and Design of Airplanes."
At point of zero shear.
ii=0.85X11.68 7.75 115 . . h 21.40x 3_21 = . me es.
Mii=l.15 X 4,030=4,650inch-pounds. L/p=ll7.
/c=955. /b=5430. /,=6,385. Allowable f,=7 ,590
pounds per square inch.
STRUTS.
Both front and rear struts were made the same size.
The front strut carries the heavier load and was the one
designed.
Load carried by strut=2,186 X 58.21/56.25 = 2,260
pounds.
Required l=PL2/r.J2E=0.485. Strut selected, 1.29
inches by 5.16 inches.
DESIGN OF WIRES.
Load on front wires
773.3X5.98X-v'
10
~/
60
" 9,130 pounds.
From Table XXXV, page 294, " Structural Analysis
and Design of Airplanes," which gives the properties of
standard stream-line wires, the following deductions were
made and used in the design of theoretical sizes:
Tensile strength=l50,000 pounds per square inch.
Major axis of section=4 times minor axis.
Area=O. 773 are of circumscribed rectangle.
R . d f 1 . 9•130 0 0304 eqmre area o Wire 2X150,000 . square
inch.
Area of circumscribed rectangle=
00~;7°3
4
=0.0393 square
inch.
Dimensions of wire=0.098X0.396 inch.
INCIDENCE WIRES.
The incidence wires of the one-bay design and of the
inner bay of the two-bay design were assumed to be identical
and were not computed.
FITTINGS.
Each strut fitting was assumed to weigh 2 pounds,
which is comparable to the weight of the Thomas-Morse
MB-3 fittings.
TWO-BAY DESIGN.
This design was computed by the same methods as the
one-bay design.
Inches.
Length of cantilever. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Length of outer bay................................. 75
Length of inner bay...... . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Length of center section............................. 30
(See fig. 4.)
TABLE VI.
NET RUNNING LOADS PER INCH OF WING.
Between outer strut points .................. : •....
Intermediate section .......................... . .. .
30-inch section at each wing tip .................. .
Upper Lower
wing. wing.
3. 53
3.14
2.34
3. 15
2._79
2.07
12
1se.z.#
+776.Cf#
ae.4'
-,37?6#' l
/Z/.~#
UPPER 0R/l6 T,eu.5.5 -ONE fj;:;y 0E.5!6N
H10H /YC!DENCE L0"'1DIN6
Fi66
6'0Zo:.
-IO{J . .3
UPPER DR.46 TRU.5S - 0NE.. fj,4y DE.5!6N
Low INC/DENCE LO/lDING
F16. 7 r 40" 37-,5 " ·r-i
3£.4"
-!~9# l
13z_3• 110.#;1 ooe~
1404.0
UPPER DR/16 TRu.55- Two fJ/IYDe516N
H!6H INCIDENCE LOllO!N6
Fla. tJ
(}9.~
UPPcJ: QR,46 TRt/SS - Two fJ,4y 0E..5!6N
Low INCIOENCE L0/70/Nu
Fl6. 9
fi6URcS-6-7-tJ-9
I
I
. I
13
'
~
"' ___.___.__ . ..___-t----___,_[
FRONT5P.4R
ONE 8-4Y 0E..5!6N
F!o. lO
'
~
":i
U_...__ __ ~ t ~ I
'
~
~
I
I
le)
~
~
•
~
_L·'-----'----+---------....__,._.---L..
RE/lR ..5P-4R
ONE f3.4y 0E5!6N
Fi6./I
F/6t1Re.5 -10-11-1e-1s
0<5. ,,
I
I ~
U11' "
I
I
I
I
ERONT .5P/lR
Two !J,4y DE.516N
66. IZ
I-- /,00"
I
I
I '
L_ ~
I ~
I
I
I
RE& ..SPAR
Two 3/lv. D£S!6N,
Fio, /.3
14
TABLE VII. INTERPLANE STRUTS.
MOUNTS, SHEARS, ETC., AT DESIGN LOAD The interplane struts were designed as for the one-bay
FACTORS. design.
Front spar, Rear spar,
L . F .-1.0 high low
incidence. incidence.
M, .. ............... inch-pounds. . 1, 912
M, ...... . ..... ....... . ..... do.... 1, 357
M,- , .. .. ..... .. ............ do.... -841. 8
M,-, .... . ............. . .... do.... - 530. 3
s+, .... ........... .. .... pounds.. 139. 6
S-!-2 ••• •• •• ••• ••• • •• •• •••.•• do.... 115. 4
C,- , (no drag) ...... ... .. ... do.... 570 c+, ....... ... ....... ....... do ........... . ... .
C-, .......... .. ....... .... do ... . ....... .... .
C,-3 (no drag) .. ... . ........ do.. .. 1, 330 c+, ....... : .... ... ......... do .... . .. .... .... .
C-3 ••••••••••••••••••••••• do .............. . .
11, 434
8, 115
-5, 034
-3, 171
8.34. 6
690.0
3, 409
3,467
3,068
7,953
8,372
9, 445
6,2-33
4, 424
-2, 744
-1 729 ·
'455.1
376.2
1 858
2;412
3,030
4,336
5,508
5,266
W ..... . ...... .. pounds per inch.. 3. 53 21.11 11. 51 X,-, ..................... inches.. 39. 5
X ,-3 •• • •••••••••••••• • • ••• • do.... 32. 7
V. C. (outer strut) ....... pounds.. 214. 5
V. C. (inner strut) . ....... . do.... 670. 5 V,-, .... .......... ... .... .. do.... 455. 7
V ,-3 • •••••••••••••••••••••• do.... 910. 7
1,283
4, 010
2, 725
5, 446
699
2,186
1, 486
2,969
COMPUTATION OF STRESSES ·IN UPPER DRAG
TRUSS.
Figs. 8 and 9 are line diagrams of the truss in high and
low incidence conditions of loading and show the external
loads and the stresses in the chord members.
T ABLE VIII.
DESIGN OF SPARS.
The dimensions of the spars are shown in figs. 12
and 13.
Sp ar. Location. A . I. I /y . L/p. o.
---- ----- - - ---
F ront . . .. Outer strut ..... 2.44 2. 93 I. 68 0 0.0
Outer bay . .. ... 2.44 2. 93 1. 68 68 . 384
Inner strut ... __ 2. 44 2. 93 I. 68 29 0
Inner bay ...... 2. 44 2. 93 1. 68 46 .106
Rear. ..... . Outer strut ..... 1. 81 1. 33 . 984 0 0
Outer bay ...... 1. 81 1. 33 .984 88 . 463
Inner strut .... . I. 81 I. 33 . 984 29 0
Inner bay ...... 1. 81 I. 33 . 984- 59 . 128
Com puted . Allowable.
Spa r. Location. [, . /1, . I /,. /,. ~ I_!:__
------
Front . . . Outer strut ..... 1, 420 6,810 8, 230 5, 500 9,130 8, 500
Onter bay ..... . 1, 420 3, 790 3, 2l0 3,200 9,130 7, 510
Inner strut ..... 3, 430 4,830 8,260 5, 200 9, 130 7,500
Inner bay ...... 3,880 2, 480 6,360 4,550 9,130 6,340
R ear .. . . Outer strut ..... 1,330 6,340 7,670 5,500 9, 040 8,420
Outer bay ...... 1, 670 4,220 5,890 2, 150 9,040 7,100
Inner strut .... _ 3, 040 4, 500 7, 540 5, 100 9, 040 7, 450
Inner bay_._ .. _ 3,040 2, 470 5, 5l0 3, 800 9,040 6, 150
These spars were adopted for the purposes of this report
in spite of the fact that the compu ted stress in some
cases is greater than the allowable stress. The object
in designing these spars was to find the weight of spars
required for an airplane of the size considered and by
changing the proportions of the bays the stresses could be
reduced so that these spars or spars only a little heavier
could be used.
v . c. Stress. I. D. L . _____ , ____ ------------ ----
Outer strut ..... . . .
Inner strut ....... .
1,283
4,150
1,330
4,150
o. 266
. 831
DESIGN OF WIRES.
1.11
I. 4S
4.44
5.92
The ,vires were also designed using the same assumptions
as in the one-bay design .
Stress in outer front wires
455. 7X5. 98X.J
752
+;t+
152
4,420 pounds.
Stress in inner front ,vires
910. 7 X n". 98 X .Jso2+60' 60 =7 ,200 pounds.
s. A. A.
0. 773
B. D .
-------!-------- ---- ------- -
Outer ........ .. . . . .
Inner ............. .
2,210
3, 600
0. 0147
.0240
0. 0190
. 0312
INCIDENCE WIRES.
o. 069
.088
0. 276
. 354
Outer incidence wires, assumed standard 10- 32 S. L.
wires, which are the size used by the Thomas-Morse
MB- 3. The inner incidence wires were assumed identical
with the incidence _wires of the one-bay design.
STRUT FITTINGS.
The same strut fittings were assumed as for the singlebay
design.
COMPUTATION OF WEIGHTS.
In computing the weight of the spars it was assumed
that the routing ended 12 inches from each end of the spar,
and that there was an unrouted section 6 inches long at
each compression rib. To allow for the decrease in depth of
the spars at the tips the computed length of the spars is
10 inches less than the actu al length .
TABLE IX.
WEIGHT OF SPARS.
I-bay d esign. 2-bay design.
Front. Rea r. Front. Rear.
------ --- - -
Length of routed portion. i11ches . . 276 276 276 276
Length of unrouted p ortion
. _ . ... . ... . . .... . . . _ ... inches ._ H 74 74 74
Le11gth a t tips, not figu, ed .do .. ,. 10 10 JO 10
Total len gth of spars . . . . ... do ... . 360 360 360 360
Area of routed section, squa:-e
i nch es . ....... ....... . . . ....... 6. 72 4. 22 · 2.4-l 1. 812
Area of unroutcd section, square
inch es . ........ .. ......... . .... 8. 44 5. 91 3. 38 2. 625
Total volume of 1 sp a r, cubic
inches . . . . ..... .. . . ..... . ...... 2,480 1, 602 924 694
Weight of 1 spar .... . ... pounds .. 38. 75 25. 00 14. 42 10. 83
Weight of 2 spars .. ........ do .. .. 77. 50 50. 00 28. 84 21. 66
I
, _
15
TABLE X.
WEIGHT OF STRUTS, WIRES, AND FITTINGS.
1-bay design.
Struts . Wires . Fittings.
------------ - --- - --- - --
Size in inches ...... _. _____ ...... _._.
Area in square inches ..... ___ ..... __
Length in inches _ .......... . ....... .
Number ................. . .......... .
Total weight in pounds ........ : .... .
1. 29 X 5.16
4. 86
55. 5
4
16. 86
2-bay design.
0. 0304
119
12
12. 28
8
16. 00
Struts. ,¥ires.
J!~~~ Fit-
Outer. Inner. wi:-es. tings.
Outer. Inner.
---- - - 1- - - - ----- --- - - - --- - --
Size in inches .... 1.11 X 4.44 l.4S X 5.92
Area in square
inches... . ...... 3. 60
Length in inches.. 55. 5
Number......... 4
6.40 ). 0147 0. 0241 0. 0125
55. 5 97. 2 79. 5 66
4 12 12 4 16
Total weight in
pounds. . . . . . . . 12. 50 I 22. 20 4. 8/l 6. 52 J 0. 98 32. 00
TABLE XI.
COMPARISON OF DEAD WEIGHTS.
1-bay. 2-bay.
-------- - ----- - - - - 1---- ----
Front spars .. ____ ._ . . ... _ ... . . ... .. . . . ...... . . . .
Rear spars.. . .. _____ . ... _ ...... . .. _
Outer struts .............. . . .................... .
Inner struts .. ___ .. .. ... .. . .. .... . . . .... ........ . -.
77. 50
50. 00
16. S6
Outer wires....... . .. . . . . . . . ... . . . . . ... . .. ..... 12.28
Inner wires... ... . .... . ........ ----- .... - -. - - -- -- .
Incidence wires . ___ . . . .. . . .. . _ . _ . ............... .
Strut fittings ....... .... . . . ...... . . . . . . .. . . . .... . . 16.00
Total. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172. 64
129. 56
Advantage of 2-bay design . ... . . . . . . .... pounds .. 43.08
Aatio of weights is 1+43.08/(8.5 >(287 .5)=1.017.
COMPUTATION OF RESISTANCES.
28.84
21. 66
12. 50
22. 20
4. 86
6. 52
0. 98
32. 00
129. 56
The basic comparison of resistances was made at 100
m. p. h. at the ground. This value was modified for speed
and altitude by assuming the resistances and therefore the
difference in resistance to vary directly as the density and
as the square of the velocity. The resistance of the struts
at 100 m. p. h. at the ground was taken as 0.01416 L D,
where L is the vertical projection of the strut. Another
method would have been to use the actual length and a
correction factor for the slope of the strut.
The resistance of wires was obtained from the curves on
page 17, Appendix C, McCook Field .Report No. 1147.
These resistances were corrected for slope from the curve
on page 19, Appendix C, of the same report. Only half
the value given by the curves for the resistance of wire
ends was used. The length used in computing the resistance
of wires as well as their weights was the theoretical
_length. No allowance was made for the decrease in
resistance of two wires one directly behind the other due
to interference or shielding effect.
It is fully realized that the figures for the resistance of
wires and struts are not exact. Comparatively little is
known of the actual resistances of such members when in
the structure. The interference of the different members
have a marked effect on their resistances so that the resistance
of a structure is not equal to the sum of the resistances
of its component parts taken by themselves. On the
other hand, it is felt that the difference in resistance of the
two designs as figured is not very much in error, and that
the ded11ction from these figures while slightly in error.
quantitatively are correct qualitatively. Though we can
not be certain, it is felt that the error is in favor of the twobay
design.
The resistances computed are tabulated in Table XII.
TABLE XII .
2-bay design.
1-bay
d esign. Outer
bay.
Inner
ba y.
-------------- --- - ---- ----
\Vires and vertical plane:
Length . .. . . .. . ............. inches.. 473
Resistauce per inch at 100 m. p. h... 0. 0066
Resistance ................. ponnds.. 3.13
Wires not in vertical plane:
Length ..................... inches ..
Resistance per inch at 100 m . p. h ...
Slope correction ...... .. ..... . . . .
Rrui:;tance. _ .... ____ ____ .. pounds ..
Resistance of ends of one wire .. _. __ _
f: lope correction ____ . _ ... _ .. __ . ___ . .
Rroistance of ends in vertical
946
. 0066
. 975
6.10
1.10
. 975
plane . . ......... . ........ pounds.. 2. 20
Re3i,tance of ends not in vertical
plane ............. . ...... pounds. 4. 29
Length of incidence wires ..... _ .inche;, . .
Reshtance per inch at 100 m. p . h ...... . ......... .
Resi3tance of wires ...... _ ..... pom1ds .. __ .... . . . .
Resistance of ends .. ___ ... . .... _ .do .... . ......... .
Length of struts. . . . . . . . . . . . . . . . . . . . . . . . 226. 5
D . ...... . ... . ................. 1.29
Resi3tance ........... . . .. ...... ponnds.. 4.14
TABLE XIII.
1,164
.0050
. 965
5. 61
. 70
. 965
4. 06
172
. 0048
. 82
1. 60
226. 5
1.11
3.56
SUMMARY OF RESISTANCES.
1-bay .
316
0.0062
1. 96
632
.0062
. 955
3. 75
.97
. 955
1. 94
3. 70
226.5
1. 48
4. 74
__________________ , ---- - ---
Lift and landing ,:vires . ... ... ~ ..
Incidence wireJ.
\ \,.ire er1ds .. ..
Struts. _
Total...
Advantage of 1-1- ay de;.·:, ign. .pow1ds
9. 23
6. 49
4.1-i
19. 86
COMPARISON OF PERFORMANCE.
11. 32
. 82
11. 30
8. 30
31.86
19. 86
11. 88
The two-bay design was assumed to have a fineness of
110, and a power loading of 8 pounds per horsepower .
The wing loading was 8.5 p ounds per squ,are foot.
16
Table XIV gives the high speed, horsepower, thrust,
difference in resistance and resistance ratio of the two
designs at the ground and at altitudes. The high speed
at the ground, 10,000 feet, 15,000 feet, and the service
ceiling was obtained from the airplane performance chart.
The speed at 20,000 feet was found by drawing a smooth
curve through the points located from the chart and interpolating
on it. The values can be checked on the curve
for/=110 in fig. 2 of this report, which was obtained in the
manner indicated above. The horsepower at the ground
was determined by the wing and power loadings assumed .
At altitudes the horsepower was assumed to vary directly
as the density of the atmosphere. The difference in resistance
was computed by the formula
where i:,R is the difference in resistance at a given altitude
and a velocity equal to the high speed of the two-bay
design at that altitude. i:,R100 is the difference in resistance
at the ground at 100 m. p. h. in this case 11.88
pounds. Vis the high speed of the two-bay design at that
altitude, and ii is the density of the standard atmosphere
at the altitude considered. The resistance ratio at each
altitude is the ratio of the resistance of the two-bay design
to that of the onecbay design at that altitude. In order to
find the resistance of the two-bay design as a whole, it
was assumed equal to the thrust of the engine, which latter
was found from the relation: Thrust equals power divided
by velocity.
TABLE XIV.
At 10, 000 15, 000 20,000 Service
ground. feet. feet. feet. ceiling.
--- - -- - - - - -
Hi~h speed .. m .p .h . . 138.4 134. 5 127.3 114. 2 108. 8
Hor.3epower. _ ... . .. . 305 225 190 160 ----- ---
Thrust ... _. pounds ..
Difference in resist-
826 627 560 525 - ·-· ····
ance ...... pounds .. 23 16 12 8 -- -·- ·· · Re,; istance ratio ... __ 1. 028 1.026 1. 022 I. 015 ........
Using the formula in the body of the report, the average
value of the :fineness of the one-bay design is 110.9, an
increase over the two-bay design of 0.9 of a point, or a
little less than 1 per cent.
From figs. 1 and 2 the performance of the one-bay design
and the performance factors of ·the two designs can
be computed. These data are tabulated below.
TABLE XV.
COMPARATIVE PERFORMANCE.
--- - - - - - - - - ---,-.--------,----.------
1-bay.
Advao-
2-bay. tage of
1-bay.
- ------------ --- - -----
Service ceiling . . .................. feet..
Speed at gro1111d ... ___ . .. ___ ... m. p . h ..
10,000 feet. .. . _ .. _ ... ___ .. ___ .do ... .
15,000 feet .... _._ ... ___ ..... _ .do . . . .
20,000 feet .... _._ .. ______ .. __ .do._ ..
Fineness performance factor .. ...... _ .. .
Speed performance factor at gr0tmd .... .
10,000 feet ...... __ .. _ ..... __ ... ___ . .
15,000 feet .... __ ..... _ .... __ . .. . __ . .
20,000 feet ...... .. .... . .... ..• . __ .. .
21, 010
139. 6
135. 5
128.6
115. 8
2,330
2,933
2, 847
2,702
2,433
21,000
138. 4
134. 5
. 127. 3
114. 2
2, 310
2,906
2,825
2,673
2,398
10
1.2
1.0
1. 3
1.4
20
27
22
29
35
I
APPENDIX II.
COMPUTATION OF RELATIVE FINENESS.
In the body of the report,, reference was made to two
methods of computing the fineness factor of the one-bay
design from the data regarding the two-bay design and the
difference in resistance. In the computations below the
fineness of the one-bay design is calculated from the data
regarding the performance, etc., at the ground of the design
used in Appendix I.
APPROXIMATE METHOD.
Assumed fineness factor of 2-bay design . ____ . _ . _ . 110. 0
High speed at ground, 2-baY. design ... ___ .m. p. h. _ 138. 4
Drag at ground at 138.4 m. p. h., 2-bay design.lbs.. 826
Differance in resistance at 138.4 m. p. h. at ground
_ ... _ .. ... _ .. _ ....... ll.88X(l38.4/100)2=2~ pounds.
Drag at ground at 138.4 ID. p. h., 1-bay design.lbs._ 803
F,=110.03, /826 , - 803=110.ov11.028=111.o
Fineness factor ·of 1-bay design=lll.0
EXACT METHOD.
Total weight: One-bay design, 2,487 pounds; two-bay
design, 2,444 pounds.
High speed at ground, two-bay design, 138.4 m. p. h.
Drag at ground at 138.4 m. p. h., two-bay design, 826
pounds.
Ky=0.0004442.
Speed at ground of one-bay design when Ky=0.0004442,
139.5 ID. p . h.
Drag at ground of two-bay design at 139.5 m. p. h.,
826X(l39.5/138.4)2= 840 pounds.
Difference in resistance at 139.5 m. p. h., ll.88X
(139.5/100)2=23 pounds.
Drag at ground of one-bay design at 139.5 m. p. h.=817
pounds.
a/L1D2 · a/2487X826 , --
F1=110.0 -y D
1
L
2
=110.o -y 817x2444 11ov1.028=111.o
Fineness factor of one-bay design=lll.O.
(17)
0