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Aviation History
1924
1924 - 0117.PDF
FEBRUARY 28, 1924 RELIABLE FORMUL/E FOR ESTIMATING AEROPLANE PERFORMANCE REPORT NO. 173 of the American National Advisory Committee for Aeronautics, prepared by Walter S. Diehl, contains the derivation and the verification of formulae for predicting the speed range ratio, the initial rate of climb, and the absolute ceiling of an aeroplane. In addition, the derivation of the formulae for time of climb and for endurance, is given, while towards the end of the report is given a collection of other formulae dealing with performance. It is shown in the Report that the ratio of the maximum speed VMto the minimum speed Vs is given by VM __ Kj Vtim the two curves, which give the absolute ceiling on a basis HP of power reserve, i.e. "'. It will be observed that the HF„ two curves give somewhat dissimilar results. This is due to the fact that the curve on the left refers to the case when the ar The Vs Ay/Vs W HP speed of revolution N is proportional to right-hand curve refers to the case when N is constant, as- it is sometimes found to be in machines fitted with certain engines. Report No. 171 states that in a surprisingly large number of cases examined the formula i P Y' 10 k * was; where TJ„, is the maximum propeller efficiency and Kx is a constant with an average value of 20-3, when V is in W m.p.h. and-——(the power loading) is in lbs./b.h.p. The rate of climb at sea level, C„, is given by - K*m _ (2Vs + VM )\ 1125 (L/D) ] C„ = 33000 VHP/ where (L/D) is the overall value for the aeroplane at the found to hold true, and that in the absence of accurate data on the performance of a particular engine this should be used. It is also stated that a few cases were noted in which N was substantially constant from sea level to the highest altitude reached, and that it is to be expected that in some cases the variation will lie between these limits, i.e. the curve of absolute ceiling lie between the two given in the accompanying graphs. With reference to the formulae for speed range, initial rate of climb, and absolute ceiling, it is stated that these were developed at the Bureau of Aeronautics of the Navy Department by Mr. Walter S. Diehl, and that they have been 32000 28000 84000 8" \aoooo «j 16000 o 12000 V) 8000 4000 n / / / / / f 10 32000 28000 24000 to z20000 » ceitm i oI200O 8000 4000 n 1 / / / / F | -' ,~* 2.0 3.0 40 Ratio Curves of absolute ceiling against 5.0 Wgg MPro HPa 6.0 7.0 SO 1.0 2.0 3.0 4.0 Rat.o p&& '• ro 5.0 60 7.0 HP,, (Ratio of horse-power available at ground level to horse-power S Jh "yo.10. required at ground level). The curve on the left applies to the case when the revolutions N « I — I The curve on the right applies to cases where N (i.e., speed of revolutions) is constant. These curves are for use in conjunction with the formula. angle for best climb (maximum value of (L/D) is to be used) j , • / VM\-0,27 and K2 is a constant found to be K« = I -^- 1 The absolute ceiling is given indirectly by HPgc _ K4(L/D) HP„ / 1 T7 W \ 0.80 l^ • Vs • HP J in which K, has an average value of 61.7, when Vs is in W m.p.h., and =— is in lbs./b.h.p. It is to be observed that HP„„ is the horse-power available at sea level, and HPr„ the horse-power required at sea level. The formula is for use with two curves for absolute ceiling given in American N.A.C.A. Report No. 171. As the formula is of little use without the curves, we have reproduced, from Report No. 171, used for over a year with gratifying results, particularly in case of the formulae for speed range and rate of climb. The formula for absolute ceiling, the Report states, has just been developed, and has not been given a thorough verification. However, it appears to fulfil the requirements for accurate work, especially when it is desired to calculate the effect of changes in wing loading and power loading. *'•' In Report No. 173 the value of Kz in the speed range formula has been determined for each of 30 combinations of wing and power loadings, the former ranging from 4 lbs. to 14 lbs./sq. ft., and the latter from 6 lbs. to 24 lbs./h.p. From these it appears that so long as ( —— j is greater than 1.70, K, is substantially constant, with an average value of 20.3. The values of K, have also been determined from reliable, performance data for a number of well-known machines. 117
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