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Aviation History
1932
1932 - 0185.PDF
FEBRUARY 26, 1932 11 THE AIRCRAFT ENGINEER SUPPLBMBNT TO FLIGHT values of b.h.p. must be equal. Eliminating the term b.h.p. from the two equations we find that for the airscrew to fulfil the design conditions it must satisfy the equation V KQ = 0-01118—- (xi) nD Unless equation (xi) holds good the b.h.p. absorbed by the airscrew at the design r.p.m. will not be the same as that developed by the engine at the same speed, and the result will be that the r.p.m. obtained will not be those for which the airscrew is designed. Fig. 2 gives curves of KQ against V/«D for various values of P/D. These curves have been obtained by interpolation in the values given in It. & M. 829, and have been corrected to fulfil the conditions laid down in equation (xi). It seldom occurs in practice that the exact value of the diameter obtained from equation (v) can be worked to. Not only does the fact that airscrew diameters are usually made in multiples of 3 in. lead to minor departures from the value, but considerations of tip clearance, etc., will frequently cause a considerable variation of the diameter from the ideal. When this occurs the value of KQ has to be brought to the neces sary amount by varying the blade width. The curves in When 20 per cent, over-revving is permitted, the relationship becomes / V ) =0-78/4 \wD/ci \wD/M Again, referring to equation (ii) we get K QCI B.H.P.ei /nM K(J B.H.P.M \fio, (xiii) (xiv) In the case of 10 per cent, over-revving this gives KQ C1 B.H.P.c, and in the case of 20 per cent, over-revving KQ ci B.H.P.ci —- = 1-728 -. KQM B.H.P.M Since B.H.P.C] is the b.h.p. of the engine at normal r.p.m., the ratio B.H.P.C|/B.H.P.M can be obtained from the power curve of the engine; and unless the value so found gives the same value of K„ ,/KQ as is given by the curve of K^ against V / nD for the par- ~* ^x\N |\N \ \ \ \ FIG. 2 \ \ \ \ \ \\\ 1-5 a ° S 10 V/nD 1-5 2-0 Fig. 2.—Torque coefficients for standard airscrews. Fig. 2 are for a maximum blade width of 0.082D : for any other ratio of blade width to diameter the curve of KQ can be made to apply by multiplying its ordinates by the factor fq which can be obtained from the curve in Fig. 3. We are now in a position to determine the diameter and pitch of an airscrew to meet with requirements of r.p.m., b.h.p. and maximum speed; but not to ensure that it will also comply with the requirement of normal r.p.m. on climb. The forward speed at which the rate of climb is a maximum will depend upon the characteristics of the whole machine; but on examination of a number of cases it will be found that the ratio of the climbing speed to the top speed is very nearly constant, the average value being approximately 0.65. Adopting this figure, and using the suffices CI and M to denote climb ing and maximum speed conditions, we have Vci = 0-65 VM If the r.p.m. on climb are normal we get, in the case of 10 per cent, over-revving being permitted, 10 »cl 11 »« and »D/ci V nD/x (xii) 10 0-5 FIG. 3 0-5 1-0 Neio Blade Widt+i / Normal Bl0a« W>drh 1-5 Fig. 3.—Relationship between torque coefficient and blade width. ticular value of P/D selected, the airscrew will not hold the engine down to exactly normal r.p.m. at full throttle. For each value of P/D the ratio KQ/KQ is constant for geometrically similar airscrews; as also is the value V ' V \ of (- - ) and ( - ) . From this it follows that for each \«D/ci \»D/JI value of P/D there is only one ratio of B.H.P.C]/B.H.P.M which will give maximum r.p.m. at maximum efficiency at top speed, and also normal r.p.m. on climb. Since D is fixed by B.H.P.M, V, and n, P is also fixed, and in consequence it appears that unless n can be varied any particular engine will fulfil the required con ditions only for a given and invariable value of V. For any other value of V the conditions of maximum and normal r.p.m. at top speed and climb respectively can be attained by adjusting the value of P/D and the blade area; but the alteration of P/D will affect the combination of speed and r.p.m. at which the point of maximum efficiency occurs. The curves in Fig. 4 have been drawn from Figs. 1 and 2, and show for any value of B.H.P.CI/B.H.P.M the 174 c
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