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TECHNICAL NOTES NATION AL ADVISORY CO •. iMITTEE FOR AERONAUTICS.
No. 218 THE ESTI1~TION OF AIRPLANE PERFORMANCE FROM WIND TUNNEL TESTS ON CONVENTIONAL AIRPLANE MODELS.
By Edward P . Warner and Shatswell Ober.
Mass achusetts Institute of Technology .
May, 1 925 .
NATIONAL ADVISORY O O A~ nTTZE FOR AEJWNAUTIOS.
TE OHNIOAL NOTE NO. 2 18.
THE E ST I N~T I ON OF AI RPLA NE PERFORMANCE FROM ViIND 'IUNiJEL TESTS ON CO NVENTIONAL AIRPLANE MODELS.
By Edward P. Warner and Shatswell Ober.
For nearly fifteen yea r s wind tunnels have been in use as an invaluable too l of the ai r p l ane designer, and no move in the calculation of a new a i rplan e is ever made today without refer- ence to data obtained in the l aboratory. The proc ess of calcu- lating p erformance by t h e accepted me t h ods is one of summation of elementary res i stances determined from the records of wind tunnel experiments on model airfoils, struts, fuselages and other parts , and in the eva l uation of inte rfe rences between tho se parts J too, wind tum1el figures are relied upon.
Alt h ou gh it h as bee n an in creasingly common p racti ce to bu ild wind tunnel mode ls of c om p lete airplanes and to use the results o bta ined in testing them for the pred i ction of balanc e , stability and contro l characteristics, attempt to pred i ct per- formance characteristics directly from the same tunnel test h as been infre quen t, as there are several obvious sources of error in any such ca l culation . The slipstream effect does not a pp ear in a wind tunnel test . The model is no t an exact representation of the c om p leted airplane , as it w ould be p~ctical ly imp o3siblc to sinulate to scale all of the fittin gs and wiTes used on the aiTplane, and , even if those minute pa rts weT e m ade with the ut- r.A . C.A. Technical Note No. 218 2 most faithfulness and included, the scale effect in their re- sistance would be so enormous as probably to cause an error greater than that to which their complete omission leads. Even on some of the parts that are included, such as the interplane struts, the absolute dimensions are so small as to bring the values of Reynolds number for those members down into a region where coefficients of resistance change very rapidly with small changes of speed or scale, and it is scarcely worth while try- ing to reproduce accurately such members, for example, as struts of streamline section.
Serious as these difficulties are, it is yet true that the total error from all sou r c es in a performance prediction from a test of a conventi o nal model is likely to be more a function of the general typ e of airplane than of the particular design, and the ratios between the performance so calculated and that actu- ally obtained from the airplane on flight test may be expected to lie within a comparatively narrow range for all airplanes of generally similar type. With a view to determining the ma g ni- tude of theBe cor re c tion facto rs and the range of their varia- tions, an extended series of performance calculations have been made for a series of conv entional models, which have been tested in the past four years at the wind tunnel of the Massachusetts Institute of . Technology, and calculated performances have been compared with those actually determined for such of the air- planes as have been buil t and put through flight test.
~.A . C . A . Technical Note NOI 218 r' The clements of performance calculated include the maximum speed, minimum speed, absolute ceiling, ancc rate of climb at soa level. In the case of minimum speed the comparison with fli g ht test results is of little significance, as the difficulty of measuring minimum speed in flight is suc~ that an accurate de- termination is not to be hoped for i n the ordinary performance test. The mode l result is undoubtedly closer to tho true minimum in most cases than is that determined in a test of the full size airplane. For the model the speed is of course calculated by the forImlla: V min where L is the max imum lift of the model as tested, s mmax the reciprocal of t he sca le ratio (24 in case the model is built
to a scale of one-half inch to a foot), w the weight of the
airplane, and Vm the wind speed in the tunnel.
Since the power output of an airplane propeller in lovel flight is equal to the product of the total drag by the speed, wi th an appropria te h or sep ower conversion constant, and the re- sistance of the airplane is proportional to the 6quare of the speed, maximum speed is obvio us ly given by t:1e forImlla: 3 375 P i] V 2 m where Dm is the appropriate drag of the model, P the e ng ine V.A.C.A. Technical Note No . 218 4 horsepower, ~ the propeller efficiency, and the other symbols have the same menning 2.S before, all speeds being given i n M .p.a, In making the calculations tab'~L::t cri in th::' s paper the ac tual engine horsepowe:r de"termi.[.J.8d by ti?st was usee.. The propeller efficiency was dctermined by making n. preliminary estimate of the maximum speed, an . estimate whi ch may be very rough wi thou t entailing appreciable error in the final result, calculating the V/ND at which a propeller desi gned to g ive its peak effi- c iency at maxi®lm speed of fli rrh t will work, nnd Qetermini ng the maximum efficiency from Li3ut. Diehl's (Reference 1) curves based on th e p ropeller , tests made by Dr. W. F. Durand at L elan d Stanford Junior University . The model drag has to be found by tria l, as it is, of c ourse , taken at the angle of attack corre- spond in g to max imum speed . I t is necessary, therefore, to make a successi on of approximations to the maximum speed, and to take the appropriate model dra g for each one) continuing until a figure is found for wh i ch the maximum calculated by the fo rmu- la just gi ven ag rees wi t :1 the approximation on which the calcula- tion was based . , The proces s of calculation is not a very tedious one, but, it would neve rtheless be d esirable to simp lify it still further, and that can be done by mak i ng the further assumptions that the maximum prope ller efficiency always has a fixed value of 75%, and that the angle of attack at which the airplane flies at r:laxim'J.m speed is a lways that giving mi nimum total drag. The first assump- !.A . C· A. Technica l Note o . 21 8 tion is obviously invalid, but i s unlikely to introduce errors of rr:o re than 7% or 8-% in the power, 'Which would correspond to errors of less ti.1an 3% in the determination of maximum speed.
The second assumpt io n approximates closely to the truth in most cases, as the d ra g cu rve is very flat in the neighborhood of the minimum, and there can b e a considerabl e change in an g le of at- tack; and so in speed ran g e, without much effect on the drag at a g iven speed . O bv i ous ly., the m ini mum dra g , if it is in error at all, will always be too low., and it would therefore be ex- pected that ther e would b e a ten d en cy to over-estimate the rmxi - mum speed when calculation is m ade by this simplified procodure .
The c alculations have actually been made for 23 models, a nd the results are tabulated b elow, w it h some re mark s on the model construction and on any sp e c ial peculiarities of the air planes .
Ex c ept as ot h erwise n oted, all the models have interplane st ruts and diagonal st ruts fo r m ed to streamline shape, and wires were om itted in all in stances . All of t h e models were about 1 8 inches i n sp an and wer e tested in the 4- foo t wind tunnel at the \~assa chus etts Institut e of Technolo gy except as otherwise noted.
N.A.C.AI Technica l Note No . 2 18 6 Table I.
E st i mation of Maximum Speed .
.
t::st.
Model Model Test Est . Test Test Remarks Speed Speed Method I Meth od II 1st .:2 d ·.
VE7 30 124 109 . 5 110 1.13 1,13 Cable used for interplane
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bracing designed I very clean otherwise.
VE7a 30 114 108 108 1.06 1.06 Streamline wire for int erplane bracing.
DH4 30 123 . 7 1 25 125 .99 .99 Round struts used on model~ Airplane con- '.
tains much round wire and many exposed fittings T3 40 94 . 6 98 . 5 1 00 . 96 .95 Much parasite resistance.
Side radiator used.
MB3 30 152 145 140 1~05 1.09 Tail not exactly like model.
Wing radiator used.
MB3a 30 140 . 6 1 45 142 . 97 .99 Side radiators used .
l~uch in- terplanc bracing of streamline wire.
Mess . 30 96.7 89 88 1.09 1.10 Very few wires
I
I on airplane.
Diagonal strut represented on model ~ NO i 218 N. A. C. A. Technica l Note Table I ( Cont. ) on of :.iaximum Speed.
EstilYlD.ti Test Est . Test Model M :o de1 Test Est .
Remarks 1st 2d deti10d II I Speed I.1ethod Speed 1.01 Much wire and 98 . 7 96 . 5 98 1.02 NBSI 40 many external I Free fittings.
I air radiators in slipstream.
3-foot model tested in lar ge wind tu :me 1.
119 1.05 40 125 .3 1 20 1.04 Side radiators TP1 used • . 95 Free air radi- PWI 30 146 1 54 1 53 .9 5 ( none ators represented on model) .
114. 5 114 1.01 1.01 Cantilever bi- T A6 40 115 . 2 plane . No wires in inter- plilne bracing .
Eng ine cowl on model not an ex- act repre sen ta- tion . 3-foot model tested in lar ge tunnel .
I
124 . 94 . 94 Fuselage unusu- PGl 30 1116 . 5 124 ally a:1Qllar in
I forn . !.loCel
cor~e " ra ti ve1y
I roue;h in con-
struction.
I I I 1.11 Cilntilcver V40 40 144 . 5 132 130 1.09 I monoplane.
I 109 1 . 02 Cantilever 11.05 'Pilr- 40 115 112 . 5 D8 !
I
I asol monoplane I ltvi t~ : expo s ed I strut.
1T . A. C. A. Technical Note No. 218 Table I (Cont.)
E stir.llat ion of Maximum Speed; I ~~odel E st. Test .:odel Test Est .
I Test
Rer,larks _ 2d. . ~ Method Speed Speed I ~Jlethod I II I ~l£t I 116 1.01 Cantilever mon- 1 .
COl 30 117 . 7 116 01 oplane vii th some expo sed struts . Wing covered with co rruga ted meta 1 Free air radia- tor.
I MS 30 85 .3 80 79 1.08 Externally [1.07 braced monop lane I of parasol typc.
Bracing wires not represented on model, but model containe d I 4 snort struts
. not actually on
airplane.
JL6 98 1.16 1.14 Cantilever mon- 30 111 . 2 96 oplane wing low on fuselage .
No wi res· . 99 Several wires ' 170 172 .97 MB6 40 175 in slipstream.
I
1 23 1.11 Streamline wire 1.10 C02a 40 137 125 used. Reported speed based on test .
single
I
radiators 1 00 . 99 ~99 Si d e TW2 30 99 used. Some un- certainty about speed and power .
182 1. 03 1.05 Cantilever mon- 19 1 . 1 186 R3 30 oplane . Lamblin radia tor s , rep- resented on model .
1 . A.C.A . Tcchnical Note ~b . 218 9 Tablo I (Cont . ) E stimation of Maximum Sp eed .
I Est . t.:st. Test Modell ~~odel Tcst :1 Test Remar ks Method I lIst 2d 1 Speed SD ~ ed Method I I 40 145 . 6 149 145 .98 1.00 Serr.i cant i lever PSI
I
paTasol mono - plane tested vii th landing , .
retracted.
gGar PS1' 40 129 . 8 137 1 34 . 95 .97 Same airplane,
I
l anding gea r down. Holes in fuseJ.age on airplane to al- low for retrac- tion of wheels not repre3ented on model.
Mean 1 . 03 1.03 In examinin g these tabulations and, in pa rticular, the ratios of actual to calculated speeds, t~ere are a number of points which snould be kept in mind as likely to affect the val- ues of those ratios. Obviously, in the first pl ace, the ratio o~ actual to calculated speed will b e hiGhest, other things be- in g eq ual, when the scale effect on the model is largest, or , in ot h er vlords, wilen t ile model is small or the speed of test is low. T he p oint is illustrated by the 'i IB3 and VE7 at one ex- tr eme, the T3 and TA6 at the other . I t might be expect ed, too, that the ratio would be high for airplanes with thick airfoil sec tions, as such forms are likely to snow an exceptionally large scale effect on t ile minilillim dra g .
r.A . C·A. Tcchnical Notd Mo . 21B
Secondly, it is apparent t~1a t t he introductio n on the air- plane of parts not presen t on t i1 e m odel, and offering parasite resistance; would tend to decrease the ratio, whic~ ~ould there- fore have a low value for airp l anes braced wi th large amounts of external stran ded cable, or other round wire . For the salile reason, the ratio would ten d to be l ow when fittings are crude in design or completely exposed aoove the wing surface, as those pOints are not repres e nted in the wind tunnel. The DH4, with a ratio of le ss than unity, even thouGh tested at 30 LP .:;-I., is a case in point, whi le the VE 7a represents an opposite ex- treme . Conversely, it would be anticipated that a cantilever monoplane would show an exceptionally hi gh ratio of speeds, as there are on the airplane practically no wires or other bracing me mbers not represented in the test . The JL6 furnishes an in- stanc e of this, but the DB gives a much lower ratio than night be expected.
Although the speed ratios from calculation by the ITDrC ex- act method range from . 94 to 1 . 16, and by the more a,proximate one from .94 to 1 . 1 4, this disturbin gly large variation can be lar gely accounted for if the points mentioned in the preceding two paragraphs, as well as ot h er le ss important but equally ob- vious causes of the d ifferences, are borne in mind. The mean deviations of the ratio s from the average values, all the tests being thro1.VTI in together wi th no attempt to interpret or fore- cast the variations of the correction factors, were 4 . 9% a~d N .A.C·A. Technical Not e No . 218 11 5 .0 {o by the two methods, respectively. As the m et hods are so nearly equal in ac cu racy, the us e of t he mor e complicated on e seens unjustified . The mean deviation of the maximum speeds as determined by a f ormula derived by one of the authors (Ref- erence 2 ) f ro m t he true max i ma for this same group of airplanes was 6.7% . Th e direct us e of the tunnel test thus gives results somewhat superior to those from t h e formula.
The assumption that no intelli gence will be used in inter- preting and app lyi ng the m odel test is, however, an obviously unfair one. To see what might b e done by an experienced man, a member of the faculty at th e Massachusetts Insti tute of Technol- ogy was re quest ed to m ake, fro~ an examination of the wind tun - ne l mode ls and a knowl edge of the a ppearance of the correspond - ing airplanes but without making any calculations or having ac- cess to t he wi nd tunnel test data, an estiwate of the probable ratio b etwe en the actual and ca l cu lated speeds in each case .
The mean d eviation of h is esti mates from the actual ratios was 4 .1 %, and in only one cas e did the error exce ed 8% . As the man who made the experiment had never tried anything of the sort befor e, there is li tt le doubt that the average error of predic- tion cou ld be cut to b elow 2t% after a little practice .
I
The c li mb ing p owers, as well a s the speed, can of course be p redicted fr om a w ind tunnel test . To determine the rate of climb at s ea level as a ccu r ately as possible it is necessary , instead of using a s in g le fo r mula, actually to compute from the F . A.C · A. Technical Note No . 218 12 wi nd tunnel test the power requi red for several speeds of fligi.l t, employing the formula :
V 2 W 3 /2 D V J(01f 3
(m .\. = m m (_ \ Lm S2 / s \ Le/ and, then, plotting a curve of power available, to find the point of maximum sepa r ation between the two and calculate the rate of climb at that point by the usual method. In getting the second curve, Lieut. Diehl 1s propel l er efficiency cu rves, contained in the report to which reference has already be en made, were used in combination with an allowance for the change of speed of the engine with chang i ng speed of flight based on a mean curve pub- lished some years ago (Reference 2).
A rougher approximation was based on the assumption that the propeller efficiency under conditions at maximum climb is uniformly equal to 60%, and that the angle of attack for best climb is that of maximum L ID of t11e airplane as whole. If the propeller efficiency were independent of speed, the best climb would, of course, be secured under the condition which L3 /2 the makes a maximum, but variation of propeller efficien- D cy flight results in the maximun with speed of climb actually being obtained at a considerably lower angle.
As befo re, calculations have been made by both Llet:lods for all airplanes f0r which the necessary datu were at : land, and the resul ts have been compared wi th the actual rates of climb as measured in flight test. T he first part of Table II gives the N.A,C·A . Te ch nica l Note No . 218 fi gu re s . Th e remarks on the models a re of c ourse t he s a me a s in Ta b le r..
Table II .
E st i m ation o f Ra te of Clim b and c eili ng .
I ni . ti al Rate of Cli mb
I
1:o d el (ft. per min .)
Test Te s t Test
-Zd-
F. s t . Est. 1 s t "T" l il e tho d Method II .L VE7 10 70 975 930 1.10 1. 15 V E7 a 1 04 0 . 9 4 . 95 9 7 5 10 30 DH4 1160 . 8 7 1 00 0 11 50 · 86 T3 31 5 54 0 49 0 . 58 . 64 MB 3 1 93 0 22 10 2110 . 8 7 . 91 MB3 a 1 235 1630 1660 .73 . 74 Mes s - 7 00 8 2 6 800 . 85 . 87 NBS l 39 1 630 560 . 62 . 70 TP l 75 0 86 0 830 . 8 7 . SO PW l 1 24 0 1 37 0 14 50 . 9 1 . 86 TA 6 1 040 14 0 0 1370 .74 . 76 PGl 925 1 36 0 . 73 1 26 0 . 73 V4 0 1 585 1. 77 0 17 80 . 89 . 89 D8 1 50 0 1 57 0 1 470 . 95 1. 02 I COl 77 5 98 0 8t.-0 . 79 . 92 I MS 3<]0 I 700 5 65 1< 24 1. 79 I J16 580 6 40 560 . 81 1 003 I I Sr.
Mean . 93 • 0
I
I
!
Ceili ng .
I
I
VTl,7 21 200 19 9')0 1 8400 1 . 06 1 . 15
I
VE7a 2 14 00 1 9600 . 88 . 96 1 8900
I
1 9600 . 86 . 90 D 34 1 7600 2040 0
I
. 63 T3 9000 1 4300 13 200 . 68 I 1 , 00 MD3 24300 2 7 50 0 2 5000 . S O I MB3 a 21 20 0 2330 0 20700 . 91 1 ,,02 , 95 Mess . 1 5600 1 860 0 16 500 . 84
I
i NB Sl 1 000 0 13 80 0 1 2900 . 73 . 77 I
I
'I F l I
pv n 1. 0e)
21 000 22200 2 1 000 . 95
I
TA6 2060 0 24500 22S00 .8 4 . 91 I J PGl 1 6900 2.l S00 20400 . 79 . 83 .
26300 25400 28600 . 89 . 87 V 'l·O
I
252() 0 23200 . 88 . 95 DB 22 1 00
I
COl l S400 1 9200 1 650 0 . 96 1. 11 1.1 S 1 6500 1 2800 11 200 1. 29 1. 47 J1 6 1 5900 1 520 0 1 420 0 1 .05 1. 12
I
M ea n .84 . 87 I I ----------~ ---- --~----- -- -- N.A.C.A. Technical ~ote No . 218 The variations in climb ratios are even lar ger than those in speed, ranging as they do from . 58 to 1.24, and from . 64 to 1.79, by the mor e complex and the simplified method, respective- ly. The highest fie;ureo are, nowever, for a "freak" case stand- ing qu ite by itself . The mean deviations are 13.3% and 16.8%, respectively, but if tne one freak cas e, which seems likely to be chargeab le against some error in the specification of vveight or power, is eliminated, these figures are reduced to 12.2% and 11.410. A gain, the met~od involvi ng the larger number of assump- tions seems about o..s satisfactory as the one in which morc care was taken . Calculations of rate of cl imb by formula (Reference :1) gave a mean deviation from the actual rates of 17%. An ex- periment on the prediction of the r atios, identical TIith that mqde when maximum speeds were ~n question, reduced the mear- er- ror to 9 . 5% , and further partial tri21s with estimates made by men who had gained some experience, left little doubt that the mean error could be reduced below 8%. The same factors men- tioned in tee tiscussion of maximum ~peed enter in ~ere and serve to exulain these variations in part, but there are other pOints w:lich he lp to account for tn3 width of the spread of the figures . Scale effect is less impor~ant at large an31es than at small as a rule, and pal'asi te resistance is also of less relative import<...nce under climbing conditions than at max- imum speed , bu t the slipstream is vastly more important in its effect W_ 1Em climbing Vi i t~ full throttle, and it is probaole --~-- - ---- -- N. A,C.A. Technical Iote No . 218 15 that the variat~ons in slipstream effect very largely account for the discrepanc ies here observed. It would be expected, therefore, that the ratios would be smallest for airplanes vri th an unusual ly large sl ipstream ef fect on resistance, or, in other words, for the airplane hav i ng a lar ge amount of resisting sur- face behind the p ro pel ler, but not so placed as to be li~ely to be of much service i n increasing the tbrust, as it is, of course, well known that a prope rly shaped body close behind the central proportion of the prop e ller ll~y do. The ~ffiS-l and the T-3 exempli fy thi s . I n gene ral, the airplanes \7i t:1 :ree ai r radiators in the sl i ps trea m hav e low ratios.
Another poss ible ex p lanation of a part of the variation is found in the difficulty of secu ri ng accurate measurements of ra te of climb in flight test . iivl1ile a complete performance test should se:rve to g ive a clo se approxi::1a tion to the best of which the air91ane is capable under standard conaitions, Go~e of the figures here included are the results of scattered or incomplete tests, includ.ing only a single climb or an incoY.1- plete series of c li mbs , and the percenta:se of error is lil:ely to be considerably larger than in the measurement of actual maximum speed for the same airplanes .
To predict the absolute ceil in g of an airplene from 17ind tunnel test it i s necessary to make the usual assumptions of decrease in engine power wi th al ti tude, etc., so the furtncr assumption was made that the ceiling is given in feet b the J 0.A.J.A . Tecbnical Jote No. 218 16 for:imla (Rcferencc 2.) :.
hPa H = 40,000 lo glO EP r HP being the horsepower available at maximum speed and HP a r being the minimum horsepo~er required at any speed, both taken at sea level. Two me thods were used to find the power required and there were therefore two determinations of ceiling, as of speed and rate of climb. First, the power required curve drawn for estimating rate of cl imb vias prolonged to include the mini- mum . This should give the most ac curate estimate possible from the test. The more approximate method was use the power re- qui red already found for c li mb at the angle of attack corre- sponding to maximum LID instead of the true minimum power found by plotting the curve . I n the first case, the power available was the same as that determined in the course of the calculation of maximum speed by the first, and more complex, method. In the second m ethod of finding ceiling, a uniform propeller efficiency of 75% was used.
Calculations have been carried out for 16 airplanes (ceil- ing tests were lacking on the ot~ers) and the ratios of actual to predicted cei lin gs found, and the results are included in Table II ..
The variations in ceiling ratios, like those for climb, are large. The lovest figures are . 63 and .6 8 for the complex and simple meth ods, while the highest are 1.29 and 1.47. The mean deviations from the avera ge is 11.0% for the more careful N.A.C.&. Tech~icQl ~ote No . 2 18 method and only 11 06% for the s i mp l er. For a third time, there- fore, it appears that the gain by the use of the more careful and longer calculation is tr i vi al . As in the case of climb, figures near the extreme a r e ra re, the high values standing quite alone and relating to the same airplane which previously ha1 to be dismissed as a freak case. The mean deviation of the ceilings estimated by formu l a ( Reference 2) from the true ceil- ing is 15%. The excision of th e M-S model reduces the mean de- viation to 8,8 and 10 . 5% by the tw o methods based on the wind tunnel result, 10 . 8% for the calcu l ation by formula. Trials at the prediction of the ratios, simi l ar to those previously de- scribed, cut the mean variation to about 10%, wi th partial tests by men wi~h more experience in this particular line indi- cating easy possib i lity of a reduction of mean error to about 5% or 6%.
The same reasons given for variations in maxim~m speed and climb apply to the variations in ceilin g factor, t~e effe ct of added parasite and scale effect being somewhat less at the an- g le of attack at the ceil i ng than at maximum speed. An added element of uncertainty is the variation of en g ine power with altitude, which is different with engines of different types, especially in th e cas e of IIh i gh compression" en g ines and the rotary types .
In conclUSion , and in th e light of the study here made and the fi~lres ~ ere given , it appears that the wind tUnnel test is ~.t .C.A. Technical Note No . 2 18 18 a V8~y useful tool in performance calculation, Qnd that, Qt the very le~st, a wind tunnel t es t mad e on a conventional ~odel for the invcstign.tion of st ab ili ty and balance should be macte to prov~de information on pr ob ab le performance as well. If CQre- fully applied, the p redi ct ion of pe rforma nce from such a model test should be mor e accur a te t han the result secured from any formula , and sh o uld n ot co mpare very unfavorably wit h the prod- uct of the most exhaustive and careful computation by the usual process of summ ation of pa rtial drags.
Refere nces .
1. Walter S. Diehl: The Ge ne ral E fficiency Curve for Air p lane Pro p eller s . B. A. C.A . Technical Report No . 168 . 1923.
2. Edward P . Warne r: -Airp lane Perfor mance Formulas - IIJournal of Society of Automotive Engineers, II June, 1922 .
3. Edvvard P. Warner : The Variation of Engine Speed vli th Speed of Flight - II.J.U tomoti ve I ndustrlcs, II January 22 , 19 20 .