= ..6.

-%II - 4“* “:. ,

...

.

. . .

.W =:...

{

. . 3

:ZCENICAL NOTES

.s ,

----———

No ● 557

,

w- -

,

-—.-——

..

https://ntrs.nasa.gov/search.jsp?R=19930081374 2018-06-10T12:44:25+00:00Z

.—

SUMMARY

.-—

“.-

-.

.

Up to the present the (?omti~ttee has ma&e no stat”ic-thrust measurene.nts , part~y b“ecause of the difficulty ofobtaining zero, T/nil .conditions in wind tunnels and part-ly because af the fact that the short e“xtrapulati’~ns afthe 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.grossW& ight .. Th&’ exceis thrust> the difK&ren&e between thepropeller t’hr:astand tk’e thrtist requ”ired to overcome airand ground resistance accelerates the.”atrplan.e~ !i!t~.eac-celeration at any vel&city may be “calculated ~rom the re-

.

-“*..,

17jA.-.Cl.l.Technical” tiote No. 557 3

.

=* .

.

.

.. :.1

.-G.

. .;i.

.,

.:

,.

,i.,

.—. . .- —

4

.,.’

s ..

..!

.

:

,,,

,

. .- ---- —- -.

“)

+’

● ✎

● ✌

N.A. C.A, Technical .Note No, 55’7..

EQUATION ITOR MINIMUM AIR ANil GROUND RESISTANCE

5

DURING TAKE-OFF

When making take-off calculations by the method usedin figures 1 and 3, the -problem of computing the air andground resistance immediately arises and it is necessaryto know the attitude of the airplane during the take-off.The angle of attack that will give the minimum air andground resistance is of considerable interest and may bedetermined as a problem in r,axima and ‘minima. The generalequation of the resistance of an airplane during take-offmay 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 persquare foot

S, the wing area in square feet

A, the effective aspect ratio including grofindeffect

.

f, the equivalent parasite area in square feetdefined by:

parasite drag = qf

If the first partial derivati-re with respect toCL ‘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 duringtake-off and defines a particular attitude for any givenairplane 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

?Lfor 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 thep510t should take off with tail low, a conclusion agreeingwith common experience-

.

If this optimum value o.fCL

is substituted in the

general resistance equation, the equation for the minimumresistance 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 effectin 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 1000f = ——— --- —.—

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 thatthe induced drag is one-tenth the total drag at top speed.

●

✌☛

.

.●

●

,

,*

.

,*

i,/ \

,/ ‘..- “

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 curvesalways come tangent to the-drag curve of the airplane inflight which is, of course, ”a.ninimum in the flight condi-tion.

Values of the coefficient of ground friction ~, asgiven iil reference 3, are as follows:

.,

Smooth deck or hard surface , . . . . 0.02

Good field, hard turf,. , . . ~ .,. , ●O4

Average field, short grass . . . ,. .“. . .05

Average field, long grass . . . , . .. . ●1O

Soft ground, grave”i or sand . . . . . .10 to 0.30

A SHORT MJZ!THODOl? COMPUTING THE TAKE-Ol?I’ DISTANCE

● J,

.,.

., OF LANIPLAW!S

The foregoing sections have described the method ofcomputing the take-off of landplanes as illustrated infigures 1 and 3. The steps are as follows:

1. Obtain the propeller thrust from reference 1 orany other source.

2. Compute the ground and air resistance from theminimum-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 thetake-off dista,nce.

This method is not very long and is the most accurateavailable. 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, inbrief, 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 ,,

,

/

8 N,A. C.A, T6chnical Note Xo.. 557

!l!kesuccess of the short me’thod depends on the factthat this velocity is, for all airplanes, exceedinglyclose 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/2acurves given in figure 6 are proportional to the take-offdistances and the deviation of these curves from straightlines 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

● *——--= ~;-= 64Te

.●

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‘iis ———-—— -..__.-..__.,___= 64 (Te & ~ Sin ~)

where a is the angle of inclination and the sign dependson 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 ws --—-————...— ——

= 64 (ge * W sin a).

and ‘e must be calculated for a different air speet than Min 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 typesof airplane the take-off distances calculated by the ~hortmethod averaged 98 percent of the distances calculated bythe long method with one extreme example giving 96 -percent.The short method is evidently on the nonconservative sideby 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 resistancefor the one representative air speed from the minimum re-sistance equation given in the preceding section,

3. Substitute the difference of,.these two values inthe equations for .Te and solve for distances

The propeller thrust “is best obtained from reference1; for convenience, however, the general thrust-horsepowercurves in figure 7 may be used with some loss in accuracy.The use of these curves should give fairly accurate resultsfor 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 beconsiderably in error.

,Inasmuch as them aximum speed is known, the ratio ofv/7m for the representative air speed may be computed andthe ratio of the thrust horse~owers may he obtained fromfigure 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——..- ~v

in 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 thetake-off performance of two propellers on a particularairplane shows that the propeller of R.A,F, 6 section givesa shorter take-off than the propeller of equal diameterhaving a Clark Y section.

3. The attitude of an airplane that will give theshortest 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 reciprocalof the acccSeration is very nearly a linear function ofthe 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,

bDiehl, 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

+“

Fig. 1

4800b~,4,- -Eff ctive pr pen er t]lrust—../ —.

/ \*\/ \ \

,4000 /\.’ .

~ ‘] <’t~j NorIIl;l// 12) 25 percent loss in st?tic thrust

/.,-.

a0

/4- --(3) 66 percent loss in static”thrust

~ 3“200- / t

.$m —. )a)b /

dg 24OO /““ .%

I w-P o

~“I

s’ I i= 160C

t

I II\ i

,Air plus ground ~esistance& I

I I~ ~

800 .— — .— .—

I

V/nD=O.2

0 _&..-lL/—

Ti

1 l-tTake-off distance I

. 40 - Feet Percent(1) 1200 .100

:rn .{2) 1200+ 100+ . .(3) 126@

$105

2 29

q- “/ Y ~ ‘ “’

—

.,

-*J W~ ~

,---_ + +

*o 20 40 60 80 100 120

v, f,p.s.

Figure 1..-Effect of variation of initial take-off thrust on thetake-off distance of a transport airplane.

**N.A.C.A,Technical Note No. 55’7

A

+-l$f-l

.

d

>

800

0

ho

20

0

,.-.

,?ig. 2

I,-

Ii!

I

771//

I.—..

I

/ i,.—.

I

i i1, 1! I I .4S+–-

o 20 40 50 80 100 120

● 50

.40

.30

.20

.10

.0

v, f.p s.

Takeoff di~t~nce, s Take-oflftime, t.,.-——___ ———Feet Percent Seconds Percent

(1) 1480 100 (1) 24 120(2) 1600 109 (2) 30 125

l’i=~re2.- Effect of variation of initial take-off thrust onthe take-off distance a]idtake-off time of a flyingbest.

.. ,\..%

N.A.C.A, Technical Note No, 55’7 Fig. 3

\.,

12C0- / r ~

/ ~%% .%ffective propeller thrust

\R,,A.F,6 section propeller

‘~~. ._;

—— —-. I

—. ——- - ——..— — I —-. I

s“ ‘— ‘— \t-l ‘J Ef~ective propeller thrust.800 -–~’-~Clark Y section propellera)8 I ‘$ 1m

~ ~l!” -.Ii

: 600’kdGd I

I; 400- i

5 l!!,— I—, I

Air plus ground r~sis~a.nce-~ “200 —— -+-- —— —. — .

II

“~I!

0-P-

I’ I

+ -

t I—. ..—. —J

; 2G- +._ .Tdm- cf!fdistance.

a -1- Yeeti i ??hti~565

}~ercentm t

788 139

/ -“- ——

7“I1

i2 1

l-t--T-.L. . Jb . * . w

Clark Y

“p-tt--&=L-

0 20 40 60 80 100 12P I(?Cv, f.p.b’,

Figure 3.- Compari son of the take-off of a pursuit plane whenequipped with fixed-pitch pro~ellers having different

blade sectims.

,)

f’.

*

N.A.C.A, Technical Note No. 557 Fig. 4

.

t’

* t

2,/

2,L

2*(

.

.8

.4

c .08 ,12Ground-friction coefficient,“~

.20

Figure 4.- ~ for minimum take-off resistance, 1/2 wrA.

3-——..—/2

—...

--l>--I---

._J__..

-L.24

.

1200 ---- --.+-. - .–

-—.- -.——

--+-} - -{

10CIO–“-–– —-1

Ii9“i-+ i

.800——.0

Ivg-P03

.$+

ds!cd

.@

xl!3 . la

o 40 80 120 16CJ 260 240 280 320v, f.p.s.

Figure 5.- Curves of minimum resistance during take-off for different values of

%..

.

wor.u-l

ground-friction coefficient..

-.-t “4

,,

.2[3

.1(I

1z

o

.10

1z

o

.10

1z

o

.lC!

1%

o

+. b“. *

+~q-++--!-+---_“_‘_.l ~“~_!_._’——

I—— -

~ =3-.-;=+;$::..;.;~~- _“:~~~;+ ,f--’?!$::s-~--J-+-_ ---LJ=4-=.J=-‘--- ‘--.-11-=v!q++-l-J;-+---+‘-~‘--- ---++-p

--- ---- -L._]-.-!-J_., i-L-..l_ 1 {+–_,-–-,.__+..- + . ~__–.-....–+----_J~-.L._._. !_._!..__l- !..-.L...-!.- L --l--‘---- %-suit aimlane

-“II-f

=f-.-.j +--’ ------+--

- ? ;* ;~- ;+-J ‘: ~--~~-~- :.

1 1—- —’

Transport airplane I 1 \“---F-

1 I I I2,000 4,000 6,000 i?,000 lQJEXI 12,000 14:002 16.COO

V2,(f.p.s.)~

Tigure 5.- Curves showing that the reciprocal of the acceleration is v:ry nearlya linear function of velocity squared.

E-.

‘=30

.

%wm.“o-a

--$ t.

N.A.C.A.Technical Note No. 55’7

#’

“.

.9,7

.8 –—

1----I

L7—.,

%.3L

!

.2

r

,1

cE—-/.

.1 .2 .3 ●4 .5 .6 .7

Controllable\t

t.—

I

/i

I

Speed ‘ _ VMaximum speed ‘ Vm

.

,

... ,Figure 7,- General full-throttle thrust-horsepower curves.