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File D 52.15 / 140 McCOOK FI ELD R EPORT SERIAL No. 1458
AIR SERVICE INFORMATION CIRCULAR

(AVIATION}
PUBLISHED BY THE CHIEF OF AIR SERVICE, WASHINGTON, D. C.
Vol. III May 1, 1921 No. 210
NOTES ON AIRPLANE FLIGHT
'
'
ENDURANCE (I)
(AIRPLANE SECTION, S. & A. BRANCH REPORT)
Prepared by Engineering Division, Air Service
McCook Field, December 2, 1920
Ralph Brown Draughon
LIBRARY
WASHINGTON
GOVERNMENT PRINTING OFFICE
1921
MAR 28 2013
Non•Depoirnrv
Auburn University
.,.
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I
NOTES ON AIRPLANE FLIGHT ENDURANCE {I).
PURPOSE.
It fa the purpose of this report to describe a chart which
will serve as a ready means of determining for any airplane
the minimum horsepower required or the maximum
horsepower available at any altitude which it is possible
for the airplane to reach. The construction of the present
chart is based on the method of McCook Field Serial No.
1380 (Air Service Information Circular, Vol. II , No. 183),
"Airplane Performance and Design Charts," and consists
in combining several of the fundamental relations
which are plotted in figttres 2 and 5 o·f that report, to
which reference should be made.
The chart should be useful in calculations of airplaneflight
endurance for determining (a) the maximum time
in the air with a given fuel supply at the altitude of minimum
horsepower required; (h) the corresponding speed;
(c) the fuel supply necessary for a given duration at any
altitude, either at full power or with throttled engines.
In addition the curves of horsepower at altitude as presented
may be used to indicate absolute ceiling, and in
the case of supercharged engines will provide a means
for determining rate and time of climb in function of altitude,
as well as service and absolute ceilings.
In duration flight problems it is necessary to know the
unit fuel consumption as well as the horsepower. This
report deals only with the latter and lays a foundation
for flight tests conducted with the object in view of determining
the variation of unit fuel consumption with throttle
opening and altitude .
· I. MINIMUM HORSEPOWER REQUIRED.
If the horsepower available from an airplane's engine
were reduced until a condition was reached , such that the
airplape could no longer climb from the ground, i. e., so
that its absolute ceiling was at the ground, then that horsepower
would be equal to the minimum horsepower required
to sustain the airplane. The corresponding value
of #/H. P. would be at its maximum within the range of
flying ability t We can easily determine for any airplane
this value o[ l!/.H. P.m (minimum required), study its
variation with altitude and then convert it into the corresponding
actual horsepower. The solution is entirely
graphical.
In fig. 5, Air Service Information Circular, Vol. II,
No. 183, is plotted absolute ceiling and corresponding
speed in function of lbs./sq. ft. and #/H. P. corrected for
"fineness." To find #/H. P.m, it is only necessary to find
on the absolute ceiling chart the intersection of the particular
#/sq. ft. line with the zero absolute ceiling line,
draw a horizontal to the particular "fin eness," and drop a
vertical to the #/H. P . at the ground scale. In Chart I of
figure 1 this report is plotted the variation of #/H. P.m with
#/sq. ft. for "fineness" 100, taken from the " Airplane
Performance and Design Chart" as indicated above.
Superposed on Chart I are various lines of "fineness," so
that if we start with #/sq. ft., go horizontally to the #/sq.ft.#/
H. P.m curve, and if instead of reading #/H. P.m for
"fineness" 100 as abscissae, we go next vertical] y to the
"fineness" marked on the straight lines, thence horizontally
to the right, we will find there the !!/H. P.m corrected
due to the particular " fineness." Since H. P .
required varies' inversely with (fineness) 3 (by definition),
#/H. P .m varies directly with this factor and the straight
linl)S of Chart I effect this multiplication .
At altitude, horsepower required, and hence its mini.
mum value increases as the square root of the reciprocal
of the relative density. Expressed in terms of loading
per horsepower we have
#/H. P .m at altitude=(<r)! #/H. P .m at ground,
where a is the density at altitude relative to the density
at the ground. Values are taken from Table I, which
defines the standard atmosphere adopted by the engineerinir
division. The altitude curves of Chart II, figure 1,
effect this multiplication, so that if a horizontal from the
#/IL P.m scale of Chart I were drawn to a particular altitude
line, a vertical dropped from the intersection would
indicate the #/H . P ·m at that altitude. However, an additional
curve has been introduced in Chart IL which performs
a transformation from #/H. P.m to H . P.m per 1,000
pounds weight of the airplane, so that if frqm the point on
the altitude line a vertical line is drawn to the new curve,
a horizontal drawn from this intersection will indicate on
the righthand 8cale H. P.m per J ,000 pounds weight at the
particular altitude.
Now in Chart III, figure 1, altitude is marked off as
abscissae, so that we can plot the variation of H. P ·rn per ,
1,000 pounds weight in function of altitude, as we com_e
from Chart II, having used various altitudes. Suppose
that it is proposed to set up a record of endurance, considering
maximum time in the air without landing.
The weight empty of the airplane to be used is known,
as well as the area and horsepower of the engine at the
ground. "Fin eness," if not known, is selected by comparison
with the airplanes listed in Table II. Several
weights fully loaded may be assumed and performances
determined in each case by the method of Serial No.
1380, Air Service Information Circular, Vol. II, No. 183.
In general the total weight will be limited by considera·
'tions of getting off; that is to say, rate of climb at ground,
or by a minimum service or absolute ceiling defined by
the topographical conditions of the vicinity in which the
flight is to be made. The maximum total weight havi.ng
th'us bee~ decided on, the weight of fuel it is possible to
carry is known, due allowance having been made for
possible additional tanks. Now to fly for the maximum
time n ecessitates flying at minimum horsepower required
at the particular minimum altitude, and the present
chart, figure J, will indicate th~s horsepower quantitatively.
Now, if at that altitude an\f power the unit fuel
consumption were known it would be possible to make an
estimate of the possible endurance. Furthermore, reductions
in total weight due to consumption of fuel can be
taken into account, new H. P.n, may be found as time in
the air elapses, and by summation very close result'! may
be obtained.
4146321 (3)
it might be an aid to the piiot to know at what spee~ to
fly throughout the flight, in which case it can be found
from Chart VI, the development of which is described in
the following. Referring again to the absolute ceiling
· chart of figure l, Air Service Information Circular, Vol. fl,
No. 183, we have in the zero ceiling line a curve of speed
at zero absolute ceiling, hence speed at ground level at the
altitiide of minimum power required, with values of
#fscr ft. marked on the curve. This can be replotted
with #/sq. ft. as ordinate and speed as abscissae with
altitude as parameter according to the fundamental relation:
4
Vat altitude=(l/o)i Vat ground ( constant incidence)
In Chart VI, figure 1, the relation has been expressed
in such a manner that if a vertical is drawn from the
lf/sq. ft. scale to the conversion curve x, and a horizontal
constructed through the intersection, then a vertical
dropped from the altitude scale of Chart III, will intersect
the horizontal, and indicate the speed at minimum power
at the particular altitude. It is pointed out that although
the above relations between speed and lbs. /sq. ft., as well
as between lbs. /sq. ft. and #/H. P. in the foregoing, are
taken from the Liberty engine chart, the same relations
obtain for any engine, since at zero altitude.no consideration
of power dropoff with altitude, peculiar to any
engine, enters into the discussion.
II. MAXIMUM HORSEPOWER AVAILABLE.
A variation of the method for determining engine
horsepower with altitude has been given in Air Service 1
Information Circular Vol. II, No. 183, with results plott~d
as shown 1n Curves VI, figure 2, of that circular. The
characteristic dropoffs found by the empiricaltheoretical
method, have been replotted in Chart IV of figure 1, with
a cur ve of the Liberty " 12" engine with G. E . Co. ·supercharger
added. Charts IV and V are so arranged that if
we .start at .any altitude ·as abscissae on Chart IV, draw a
vertical to the particular engine curve, then a horizontal
to the lbs. /H. P. at the ground, a vertical from there
,vould cut the top scale of Chart V, giving ;i/H. P. maximum
available at the particular altitude. The lbs. /H. P.
curves, Chart V, simply multiply the lbs. /H. P. at the
ground by the reciprocal of the ratio of the engine pro'peller
factor at altitude to the one at the ground, since,
if H. P . decreases, then ;i/H. P. increases with altitude.
Now if we ·proceed from the first points on the lbs. /H. P
lines of Chart V, vertically up to the conversion curve ot
Chart II, thence horizontally, we will find on the righthand
scale, H. P. m per 1,000 pounds weight, which can in
turn be plotted against altitude. in Chart III. Here is a
means, then, of determining the actual horsepower of the
engine for flight at full throttle at any altitude, and if the
unit fuel consumption were known in function of altitude
and horsepower or r. p . m., it would be possible to determine
just how much fuel had to be carried for a certain
flight endurance at high speed at any altitude. Such an
endurance figure is generally specified for Army airplanes,
and one of the purposes of this report is to provide a basis
for a series of flight tests with the object in view of determining
unit consumptions.
ill. CRUISING FLIGHT.
Instead of flying·at high speed or full throttle and corresponding
high unit consumption, it may be desired to fly
with reduced throttle and at lower speed, but with a unit
.•
consumption so much iower that iess fuei wouid be consumed
in flying a certain distance. The latter condition
of flight is more economical, though slower, and is called
flight at cruising speed. Suppose we have set up the
fundamental curves of Chart III for an airplane which is
our example. At 10,000 feet, the maximum horsepower
available is 66.5 per 1,000 pounds weight. Now suppose
the engine is throttled to 50 H.P. /1,000 lbs., what will be
the speed in horizontal flight? Draw a horizontal from
50 on the righthand scale of Chart II, from intersection
with conversion scale drop a vertical through CJ:iart V.
Now draw a vertical from 10,000 feet, Chart IV, to the
engine curve, thence a horizontal through Chart V, and
the intersection with the previous vertical will indicate
the corresponding j:i/H. P . at the ground. Using this
value on the Performance Chart of Air Service Information
,Circular Vol. II, No. 183, figure 5, we can find the horizontal
speed at 10,000 feet. Repeating this procedure fo.r
various throttle openings and altitudes, it will be possible
to determine the best altitude and speed at which to fly,
most economically for a given distance.
IV. SUPERCHARGING. 1
In Air Service Information Circular Vol. II, m;. 195 is
described a method for finding the rate and time of climb,
service ceiling and absolute ceiling of an airplane equipped
with a supercharger. Rate of climb was first expressed in
function of the ratio ;i/H. P. m / lf/H. P. a for the airplane
without supercharger, and then determined from this law
for the airplane with supercharger and new values of the
ratio. The solution was wholly analytical, whereas it can
be made mostly graphical. In figure 1 we have set up
the curves of H. P. a and H. P. m with altitude. The ratio
H.P. 0 /H. P. m can be used for expressing rate of climb,
since it is equal to the ratio #/H. P. m/#/H. P. ,. Rate of
climb depends on excess horsepower, so that the greater
the horsepower available and the smaller the horsepower
required, the greater the excess, the ratio, and the rate.
The intersection of the curves in Chart III, in any case,
indicates absolute ceiling, since horsepower available
just equals minimum horsepower required. When the
rate of climb curve has been established for a supercharged
job as outlined above, and in Air S~rvice Information Circular
Vol. II, No. 195, then service ceiling can be found
when rate of climb equals JOO ft. /min. Time of climb is
obtained by integrating the rate curve.
V. CONCLUSION.
The present chart provides a method upon which may
be based a flight test program for definitely determining
the unit fuel consumptions of engines in function of altitude
and throttle opening or r. p. m. The importance of
. such data can not be disregarded, and once it is obtained
by the method herein outlined, it can he used in conjunction
with figure 1 to solve practically any problem of
flight endurance. In the case of supercharged engines,
figure 1 provides a basis for determining rate of climb,
service, and absolute ceilings. Some interesting results
may be found with regard to endurance at altitude of
airplanes equipped with superchargers.
1 An analysis of the Eff~ct of Supercharging .
•
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FIG. !.Horsepower altitude chart.
TABLE !.Standard atmosphere.1
Standard Tempera ture Percentage Percentage J; altitude. • centigrade. pressure. density.
0 15. 00 1. 000 1. 000 1. 000
1,000 12.84 . 965 .972 .986
2. 000 10. 75 . 930 . 944 . 972
3,000 8. 71 . 897 . 917 .958
4,000 6. 73 . 864 .890 943
5,000 4.81 .832 . 863 .930
6,000 2.95 . 802 .837 . 915
7,000 •1.14 . 772 .811 .901
8,000  .61 . 744 . 786 . 887
\!,000 2. 30 . 715 . 761 . 873
10,000  3.94 .689 . 737 . 859
11,000  5.52 . 662 . 713 . 845
12,000 7. 05 .637 .690 . 831
13,000 8.53 .613 . 667 .817
14,000 9.97 .589 . 645 .804
15,000  11.35 .567 .624 . 790
16,000  12.68 . 545 .603 . 776
17,000 13. 97 . 524 . 582 . 763
18,000 15. 21 . 503 .562 . 749
19,000 16.40 .483 .543 . 736
20,000 17. 56 .465 . 524 . 723
21,000  18. 67 .446 .505 . 711
22,000 19. 74 . 429 .487 .698
23,000  20. 77 . 412 .470 .686
24,000 21. 76 .395 . 453 . 675
25,000 22. 72 .380 .437 .660
26,000 23.64 .365 .421 .649
27,000 24. 52 .350 .406 .637
28,000 25.37 .336 .391 · .625
29,000 26.19 .323 .376 .613
30,000 26.97 .310 . 362 .602
1 Engineering Division.
Gronnd: 15° centigrade.
29. 92 in. Hg.
0.07608 # per ft.•
Jf
1.000
1.015
1.030
1 043
1.060
1.075
1. 093
1.110
1.128
1. 145
1.164
1. 184
1. 205
·1.226
1,244
1.267
1. 289
1. 310
1. 335
1. 360
1. 383
1.408
1.433
1.458
1. 482
1. 516
1.541
1. 572
1.600
1.632
1.663
0
T ABLE II.
..; ~'d
Airplane. ' gj ~8
~8
Ji:: .'ii I>: bl)

Caproni Triplane .. . . 12,900 1,420 1 450
G.A.X ...... . ..... . 9,748 I,004 1;188
LePere Triplane . . .. 8,577 872 1,700
Martin Bomber ..... 10,225 1,070 1,665
Martin Bomber • .... 9, 185 1,070 1,700
Martin Transport . .. 10, 225 1,070 1,665
Martin Torpedo . . ..• 12,098 1,080 1,675
JN 4D2 .... . ..... · . 2,016 353 1,450
M::.1:~.:::::::::::: 2,639 214 1,900
4,065 490 1,580
DH4 . ....... . ...... 3,920 440 1,630
Fokker DVII .. .... 2,100 236 1,560
Sp.ad 16A ... . . . . .. . 2, 844 328 1,670
LePere Biplane .. .. . 3, 774 391 1,725
VE7 . . .... ... .. . • _: _ 2, 095 285 1,730
SE 5 .. .............. 2,060 245 1,725
Ordnance"D"· 2,432 261 1,885
Junker L6 .......... 3,605 417 1,445
U. S.XBlA ........ 2,994 406 1,730
ThomasMorseMB3 2,094 252 1,835
VCP 1. ...... .. ..... 2,669 269 1,925
ThomasMorse S6 .. 1,477 206 1,260
1 Low compression Liberty " 12s."
• Without bombs.
~,d
~8 p.;
P 0 .... Pi
III"" ..,
 
11,~ 12. 3
11.~
834 10.3"
832 12. 3
834 11.0
832 12.'3
833 14.6
90 22.6
343 7. 7
388 10.5
400 9.8
184 11.4
240 12. r
420 9.0
183 U.6.
180 11.4
341 7.1
243 14. 8
316 9.5
338 6.2
347 , 7 .. 7
85 17.4
I
i
O'
"' ..,

9.1
9. 7
9.8
9.6
8.6
9.6
11. 3
5. 7
12.3
8.3
8. 9
8. 5
8. f
9.6
7.4
8.4
. 9.3
8.6
7. 4
8. 2
10. (
5.(
as .
~""g"
a~
~~

ioo
105
112
105
106
106
105
·.73
143.5
'i.13. 5
·120
117
116.5
{fti
,121.6
147
,I, ••
Ol'•
i£;~
~ Ol
 
90
90
92.
93
93.
94
5
5
94. 
96 .•
99
99
100
104
104
107
108
108
108 mr :152 113
154 114
i 97 117
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