1、= 6.-%II - 4“* “:. ,. . .W =:. . . 3:ZCENICAL NOTES.s ,-No a71 557,w- -,-.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.SUMMARY.-“.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.Up to the prese
2、nt the (?omtittee has mai.,.:,.,i.,. . .- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4.,.s !.:,. .- - - -.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“)+a71 a15a71 a13N.A.C.A, Technical .Note
3、 No, 557EQUATION ITOR MINIMUM AIR ANil GROUND RESISTANCE5DURING TAKE-OFFWhen 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 an
4、gle 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 writtenR= w- vCLqS+q.f+CL2qS/n Awhere is the coefficient of ground frictio
5、nW, the weight of the airplane in poundsCL the lift coefficient defined by c,= it is constant throughout the run. A chart giving:the optimum value of ?L for a cotisiderable range of thevariables K and A 1s shown in figure 4* It appears ,:from figure 4 that in a sticky field where v iS high thep510t
6、should take off with tail low, a conclusion agreeingwith common experience-.If this optimum value o.f CL is substituted in thegeneral resistance equation, the equation for the minimumresistance during take-off will be ,obtained, -IT%in = w+vy+. Pv22 ) ,Rrein= w + V2 (o.ool19f - 0,000934 VW)whitn for
7、 any given airplane and field. becomesrein =K+K1V2where E and K1 are the o%vious constantsV, velocity in feet per secondb, effective span including ground effectin feetf, equivalent parasite area in square feetThe factor f may be obtained accurately enough for any/take-off calculations from the apro
8、iimate relation(-b,hp. )o x qmax x 1000f = - .f)Vm3where (b,hp. )o is the rated engine powern the maximum propeller efficiencymaxVm5 the top air seed 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.a71a13a11. a71a71,
9、*.,*Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i,/ ,/- “N.A,C.A, Technical Note No, .557 7Figure 5 shows how ,the minimum groundand air resist-ance curves for a paticular example vary with the ground-fri.ction coefficient y. It will be noted tha
10、t 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 iilreference 3, are as follows: .,Smooth deck or hard surface , . . . . 0.02Good field, hard turf,. , . . .,. , a
11、71O4Average field, short grass . . . ,“. . .05Average field, long grass . . . , . . a711OSoft ground, grave”i or sand . . . . . .10 to 0.30A SHORT MJZ!THODOl? COMPUTING THE TAKE-Ol?IDISTANCEa71 J,.,., OF LANIPLAW!SThe foregoing sections have described the method ofcomputing the take-off of landplane
12、s 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
13、.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 ai
14、rplane 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 ,/Provided by IHS Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 N,A
15、.C.A, T6chnical Note Xo 557!l!kesuccess of the short method 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 iearly a linear fun
16、c-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 tov2/2, where % is the
17、 air speed at take-off in feet persecond, 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 vz1?s a71 *-= ;-= 64Te .a71where s is the “distance in feet, W the weight in pounds,and Te
18、 the excess thrust talc-uI.ated for only one airspeed which is, for take-off with”no wind, Jo.5v or : “0.7 VTOThe effect of an inclined runway may easily be in-cluded,v2iis - -_.-_.,_= 64 (Te if better accuracy is desired, a,inulti-plying factor of 1.02 or 1.03 should be applied to the dis-%ance as
19、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-iont . ME-E.VTwhere t is tle time in seconds.The short r,ethod may ,thusbe summarized:8“ 1, Calculate the propeller thrust for the one repre-sentative air
20、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 distancesThe propeller thrust “is best obtained
21、 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 airlanes but, since controllable propel-lers offer such a broad range of selection, the contro
22、lla-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 horseowers may he obtained fromfigure 7. Since the maximum efficiency may be easily o
23、b-tained, the maximum thrust horseower 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#Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 N,A*
24、C!,.A.,Technical Note No ; ,55.7CONCLUSIONS,.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 aropeller with a Clark Y section. A com
25、parison 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 spee
26、d and is rep-resented by the relation CL = .LTTA, where CL is thelift 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 rec
27、iprocalof 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 Vari
28、ous 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. -.Provided by IHSNot for ResaleNo reproductio
29、n or networking permitted without license from IHS-,-,-8, N.A,C.A. Technical Note No. 557+“Fig. 14800b,4,- -Eff ctive pr pen er tlrust/ ./ */ ,4000 / . . 8000ho200,.-.,?ig. 2I,- Ii!I771/I.I/ i,.Ii i1, 1! I I .4S+-o 20 40 50 80 100 120a71 50.40.30.20.10.0v, f.p s.Takeoff ditnce, s Take-oflftime, t.,.
30、-_ Feet Percent Seconds Percent(1) 1480 100 (1) 24 120(2) 1600 109 (2) 30 125li=re2.- Effect of variation of initial take-off thrust onthe take-off distance aidtake-off time of a flyingbest.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. ,%N.A.C.A,
31、 Technical Note No, 557 Fig. 3.,12C0- / r / %.%ffective propeller thrustR,A.F,6 section propeller. ._; -. I. - - I -. Is“ t-l J Efective propeller thrust.800-Clark Y section propellera)8 I $ 1m l!” -.Ii: 600kdGd II; 400- i5 l!, I, IAir plus ground rsisa.nce- “200 -+- . .II “I!0 -P- I I+ -t I. . J; 2
32、G- + ._ .Tdm-cf!fdistance.a -1- Yeeti i ?hti565 ercentm t788 139/ -“- 7“ I1i2 1 l-t-T-.L. . Jb . * . wClark Y“p-tt-=+;$:;.;-_“:;+ ,f-?!$: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 +- -+-
33、? ;* ;- ;+-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.COOV2,(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-aProvided by IHSNot for ResaleNo reproduction o
34、r networking permitted without license from IHS-,-,-$ t. N.A.C.A.Technical Note No. 557#“.9,7.8 1-IL7.,%.3L!.2r,1cE-/.1 .2 .3 a714 .5 .6 .7Controllablett.I/ iISpeed _ VMaximum speed Vm.,. , Figure 7,- General full-throttle thrust-horsepowercurves.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
