Many technical papers on the various phases of airplane take-off have been published. Frequently, however, there appear new ideas which affect only particular scattered phases of the subject and which do not receive individual publication. It is the purpose of this paper to present several ideas of this nature which may be of considerable aid in calculating take-off performance and one idea which should correct what appears to be a popular misconception of the importance of static propeller thrust. Although these considerations all concern the general problem of take-off, they are not directly related and therefore will be treated in individual sections

Hartman, Edwin P

English

NASA Technical Reports Server

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SUMMARY
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Up to the present the (?omti~ttee has ma&e no stat”ic-
thrust measurene.nts , part~y b“ecause of the difficulty of
obtaining zero, T/nil .conditions in wind tunnels and part-
ly because af the fact that the short e“xtrapulati’~ns af
the curves from th6 regrilar propeller tests have been can-
siderett qai%e sati.s-fac-tary., If, however, the static pro-
peller fih”rust2s an-”imfiartant factor--in take-off calcula-
tzaas,, as it is-so freque~tly” considered to be, tests for
~ts accurate” &6teim_ihat ion ‘should be made.
Yigures T and 2 are intended tm s-how the true import-
ance of’ the initial take-aff thrust “in take.~off calcula-
tions Figure 1 shows take-off calculations for a bino -
t.ored transuort airplane Qf about 17,.500 .potirids.gross
W& ight .. Th&’ exceis thrust> the difK&ren&e between the
propeller t’hr:astand tk’e thrtist requ”ired to overcome air
and ground resistance accelerates the.”atrplan.e~ !i!t~.eac-
celeration at any vel&city may be “calculated ~rom the re-
.
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17jA.-.Cl.l.Technical” tiote No. 557 3
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N.A. C.A, Technical .Note No, 55’7
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EQUATION ITOR MINIMUM AIR ANil GROUND RESISTANCE
5
DURING TAKE-OFF
When making take-off calculations by the method used
in figures 1 and 3, the -problem of computing the air and
ground resistance immediately arises and it is necessary
to know the attitude of the airplane during the take-off.
The angle of attack that will give the minimum air and
ground resistance is of considerable interest and may be
determined as a problem in r,axima and ‘minima. The general
equation of the resistance of an airplane during take-off
may he written
R= ~w- vCLqS+q.f+CL2qS/n A
where ~ is the coefficient of ground friction
W, the weight of the airplane in pounds
CL ‘ the lift coefficient defined by c~,= ~&
q, the dynamic pressure bP~2 in pounds per
square foot
S, the wing area in square feet
A, the effective aspect ratio including grofind
effect
.
f, the equivalent parasite area in square feet
defined by:
parasite drag = qf
If the first partial derivati-re with respect to CL ‘s
equated to zero,
~Fi=-
?3CL wqs+2cLqs/~A=o
.
we obtain, after transposition, CL = +PITA. This value
Ofb CL gives the minimum air and ground resistance during
take-off and defines a particular attitude for any given
airplane and field. It should be noticed that the value
/’(\
~ N*A. C.A. Technical Note Ko. 557
of c!~ for pinimum resistance does not vary with the ve-
locity; it is constant throughout the run. A chart giving:
the optimum value of
?L
for a cotisiderable range of the
variables K and A 1s shown in figure 4* It appears ,:
from figure 4 that in a sticky field where v iS high the
p510t should take off with tail low, a conclusion agreeing
with common experience-
.
If this optimum value o.f
CL
is substituted in the
general resistance equation, the equation for the minimum
resistance during take-off will be ,obtained,
-.
.
IT
%in = ~w+vy+. ~Pv2~2 )
,
Rrein’= ~w + V2 (o.ool19f - 0,000934 VW)
whit’n for any given airplane and field. ‘becomes
‘rein =K+K1V2
where E and K1 are the o%vio’us constants
V, velocity in feet per second
b, effective span including ground effect
in feet
f, equivalent parasite area in square feet
The factor f may be obtained accurately enough for any/ take-off calculations from the a~proiimate relation
(-b,hp. )o x qmax x 1000
f = ——— --- —.—
f)Vm3
where (b,hp. )o is the rated engine power
n the maximum propeller efficiencymax’
Vm 5 the top air s~eed in feet per second,
This approximation of f is based on the assumption that
the induced drag is one-tenth the total drag at top speed.
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N.A, C.A, Technical Note No, .557 7
Figure 5 shows how ,the minimum groundand air resist-
ance curves for a pa~ticular example vary with the ground-
fri.ction coefficient y. It will be noted that the curves
always come tangent to the-drag curve of the airplane in
flight which is, of course, ”a.ninimum in the flight condi-
tion.
Values of the coefficient of ground friction ~, as
given iil reference 3, are as follows:
.,
Smooth deck or hard surface , . . . . 0.02
Good field, hard turf,. , . . ~ .,. , lO4
Average field, short grass . . . ,. .“. . .05
Average field, long grass . . . , . .. . l1O
Soft ground, grave”i or sand . . . . . .10 to 0.30
A SHORT MJZ!THODOl? COMPUTING THE TAKE-Ol?I’ DISTANCE
l J
,
.,
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., OF LANIPLAW!S
The foregoing sections have described the method of
computing the take-off of landplanes as illustrated in
figures 1 and 3. The steps are as follows:
1. Obtain the propeller thrust from reference 1 or
any other source.
2. Compute the ground and air resistance from the
minimum-resistance equatiop given in the preceding section.
3. Cqmpute the acceleration from the excess thrust, ‘
plot ~/a ,aga.inst V and measure the area to obtain the
take-off dista,nce.
This method is not very long and is the most accurate
available. A study of the variables involved reveals,
however, a much shorter rlethod very nearly as accurate.
In exfilanation of the short method. it may be said, in
brief, that for any airplane there is one particular veloc-
ity in its take-off run at which the acceleration, “if cal-
culated and substituted in the standard V2 = 2as formula,
will give t-ne exact take-off distance.
.9
,,
,
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8 N,A. C.A, T6chnical Note Xo.. 557
!l!kesuccess of the short me’thod depends on the fact
that this velocity is, for all airplanes, exceedingly
close to the same percentage of the take-off velocity.
The reason for this agreemen% is that in all cases the re-
ciprocal of the acceleration is very i~early a linear func-
tion of the velocity squared. The areas under the l/2a
curves given in figure 6 are proportional to the take-off
distances and the deviation of these curves from straight
lines indicates the degree of inadequacy of the short meth-
od. The acceleration at a velocity corresponding to
v~2/2, where % is the air speed at take-off in feet per
second, will therqforq be the value representing the en-
tire take-off run, This ~elocity is ~~ VT which may
%e called 0.7 VT. ,
The short-method equation may then he written,
.,,. VT2 v~z1?
s
l *
——--
= ~;-= 64Te
. l
where s is the “distance in feet, W the weight in pounds,
and Te the excess thrust talc-uI.ated for only one air
speed which is, for take-off with”no wind, Jo.5v~ or : “
0.7 VTO
The effect of an inclined runway may easily be in-
cluded,
v~2‘ii
s ———-—— -..__.-..__.,___
= 64 (Te & ~ Sin ~)
where a is the angle of inclination and the sign depends
on whether the airplane is taking off down the slope (+)
or up the slope (-).
The effect of w~nd may also be included without trou-
tle. In this case Vm must be reduced by the value of
A
wind velocity Vw,
(VT - V.J2 w
s --—-————...— ——
= 64 (ge * W sin a)
.
and
‘e must be calculated for a different air speet than M
in the case of no wind. The air speed is b
#m.
N.A.C.A. Technical Note NO. 557 9
.,
In six examples representing widely different types
of airplane the take-off distances calculated by the ~hort
method averaged 98 percent of the distances calculated by
the long method with one extreme example giving 96 -percent.
The short method is evidently on the nonconservative side
by alout 2 percent; if better accuracy is desired, a,inulti-
plying factor of 1.02 or 1.03 should be applied to the dis-
%ance as calculated by the short method.
It has been found that. a close approximation to the
# take-off time for landplanes may be obtained from the relat-
ion
t . ME--E.
VT
where t is tl~e time in seconds.
The short r,ethod may ,thusbe summarized:
8“ 1, Calculate the propeller thrust for the one repre-
sentative air speed.
.~, 2: Calculate the minimum, ground and air resistance
for the one representative air speed from the minimum re-
sistance equation given in the preceding section,
3. Substitute the difference of,.these two values in
the equations for .Te and solve for distances
The propeller thrust “is best obtained from reference
1; for convenience, however, the general thrust-horsepower
curves in figure 7 may be used with some loss in accuracy.
The use of these curves should give fairly accurate results
for present-day air~lanes but, since controllable propel-
lers offer such a broad range of selection, the controlla-
ble propeller curve in figure 7 may in certain cases be
considerably in error.
,Inasmuch as them aximum speed is known, the ratio of
v/7m for the representative air speed may be computed and
the ratio of the thrust horse~owers may he obtained from
figure 7. Since the maximum efficiency may be easily ob-
tained, the maximum thrust horse~ower and t-ho thrust horse-
power at the representative air speed may be quickly calcu-
v
t .h~.is in feet per second or T = .—-- X 375 ~“here ~ is——..- ~vin miles per hou.rc
#
10 N,A* C!,.A ,Technical Note No ; ,55.7
CONCLUSIONS
,.
1. The ~ropeller thrust in the early stages of take-
off has but a very suall effect on take-off distance. )
2“0 A considerable error may result from using R.A,.F.
6 propeller data to compute the take-off performance of a
~ropeller with a Clark Y section. A comparison of the
take-off performance of two propellers on a particular
airplane shows that the propeller of R.A,F, 6 section gives
a shorter take-off than the propeller of equal diameter
having a Clark Y section.
3. The attitude of an airplane that will give the
shortest take-off run does not ~ary with speed and is rep-
resented by the relation ‘CL = ~.LTTA, where CL is the
lift coefficient corresponding to the optimum attitude, ~
is the coefficient of ground friction, and A is the ef-
fective aspect ratio, .
4* A short and reasonably accurate method of calcu-
lating take-off results from the fact that the reciprocal
of the acccSeration is very nearly a linear function of
the velocity squared.
Langley Memorial Aeronautical Laborator:r,
--
National Advisory Committee for Aeronautics,
Langley Field, Vs., January 27, 193.6.
1.
2.
3,
Hartrnan, Edwin P.: . Working Charts for the Determina-
tion of Propeiler Thrust at Various Air Speeds,
T*R, ~Oa 481, I;,A.C,A, , 1934.
.. ..
Freeman, Hugh E.: Comparison of Full-Scale Propellers -
Having R.A,I?,-6 and Clark Y Airfoil Sections. T.R.
~Oa 378; N.A.C.A. , 1931,
b
Diehl, Walter S.: TLe Calculation of Take-Off Run.
T,R. ~~Oa 450, ;;,AcC,.4,, 1932. -
.
8, N.A,C.A. Technical Note No. 55’7
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Fig. 1
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—../ —./ \
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,4000 / \.’
.
~ ‘] <’t~j NorIIl;l
// 12) 25 percent loss in st?tic thrust
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a0 /4- --(3) 66 percent loss in static”thrust
~ 3“200- / t
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800 .— — .— .—
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Take-off distance I
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Figure 1..-Effect of variation of initial take-off thrust on the
take-off distance of a transport airplane.
** N.A.C.A,Technical Note No. 55’7
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l’i=~re2.- Effect of variation of initial take-off thrust on
the take-off distance a]idtake-off time of a flying
best.
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N.A.C.A, Technical Note No, 55’7 Fig. 3
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12C0- / r ~
/ ~%% .%ffective propeller thrust
\R,,A.F,6 section propeller
‘~~. ._;
—— —-. I
—. ——- - ——
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— I —-. I
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t-l ‘J Ef~ective propeller thrust
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Figure 3.- Compari son of the take-off of a pursuit plane when
equipped with fixed-pitch pro~ellers having different
blade sectims.
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N.A.C.A, Technical Note No. 557 Fig. 4
.
t’
* t
2,/
2,L
2*(
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c .08 ,12
Ground-friction coefficient,“~
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Figure 4.- ~ for minimum take-off resistance, 1/2 wrA.
3-
——..
/2
—...
--l>--I---
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-—.- -.——
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o 40 80 120 16CJ 260 240 280 320
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Figure 5.- Curves of minimum resistance during take-off for different values of
%.
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or
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ground-friction coefficient. .
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Transport airplane I 1
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2,000 4,000 6,000 i?,000 lQJEXI 12,000 14:002 16.COO
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Tigure 5.- Curves showing that the reciprocal of the acceleration is v:ry nearly
a linear function of velocity squared.
E-
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%
w
m.
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--$ t
.
N.A.C.A.Technical Note No. 55’7
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Speed ‘ _ V
Maximum speed ‘ Vm
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Figure 7,- General full-throttle thrust-horsepower curves.


Considerations of the take-off problem

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