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Aviation History
1932
1932 - 0184.PDF
10 SUPPLEMENT TO FLIGHT FEBRUARY 26, 1932 THE AIRCRAFT ENGINEER it follows that the value of V/nD at top speed is high, and the airscrew requires a large value of the experi mental mean pitch. This in its turn causes the r.p.m. to vary more rapidly with speed than is the case with a lower pitch, and the holding down effect of the airscrew on the engine becomes more pronounced. To examine this effect more closely it is necessary to know the value of P/D for any airscrew under consideration. To obtain the greatest possible thrust horsepower at, any speed the airscrew must work at maximum efficiency at that speed. The diameter of the airscrew is found from a know ledge of the speed and r.p.m. at which maximum effici ency is required; generally the maximum speed of the machine and maximum permissible r.p.m. of the engine are the governing factors. A useful formula, given by Diehl in N.A.C.A. Report No. 178, is BJELP. pv 90fi00\* N (iv) Here N = airscrew r.p.m. and V = speed in m.p.h. As we are examining airscrew characteristics whose curves are given in terms of ft./sec. and revs./sec., it will be more convenient to express the formula used in these units. Equation (iv) now becomes: — 33 X 10s B.H.P. D4 = pV (V) n and V now being revs./sec. and ft./sec. respectively, and p being, as usual, the relative density of the air. Having found D and knowing V and n, the value of V/nD can be calculated. We have now to find what value of P/D will give maximum efficiency at this value of V/nD. The thrust function curve given on page 321 of Bair- stow's " Applied Aerodynamics " (and elsewhere) has for its equation 4ri KTTC UP/ (vi) Here Tc is the reciprocal of KT at V/nP = 0.5, and is therefore constant. The airscrew efficiency is given, by the equation 1 P KTTc V "=2r'D'K,Q, 'rcP (V11) Since at maximum efficiency V/nD is fixed, and = V/nP X P/D, the value of ij for any particular value of P/D is greatest when KTTc/KyQr is greatest. From equations (i) and (vi) KTTC KQQO [-GJ] 1 -f- 0-017 + 0-0738 l)[ 1 -8 V »P vm Differentiating and simplifying we find that maximum when 1-017+0-0738 KTTC KQQC D 1 nP > ( ~= ) (0-017 + 0-0738 - j = O nP/ \ D/ Re-writing this in terms of P/D and V/nD we get P D )> ahm 0-0738 D/ DUD/ UD -0-2303 (ix) If the values of P/D as given by this equation are plotted against V/nD the curve obtained is in good agreement with results found in tests up to a value of P/D of about 1.4 only. From R. & M. 829, which gives results of tests on a family of airscrews, values of P/D against V/nD at maximum efficiency can be obtained up to a value of P/D of about 1.8. To fit these values equation (ix) has to be modified, and very fair agree ment can be obtained by combining it with the equation P V - = 118 f 0-14. D nD The final equation for P/D and V/nD now becomes P 1) nD P\2 I) I» 0-1476 V \« 3(D/\ + 16 + 0-59 V \< V JID 0-045 (x) This curve is plotted in Fig. 1, and gives good agree ment with test results up to the maximum value of P/D tested. For values of P/D greater than 1.9 it cannot be relied on; almost certainly a further modification to the equation would be required, but without tests at 10 o •« "7 '5 / / / / / FlG.1 10 1-2 V/_ 1-8 Fig. 1.—Relationship between P/D and V/nD at maximum efficiency. higher values of P/D it is impossible to say what the modifications would be. In passing it may be remarked that it seems probable that terms involving P/D, (P/D)2 and log (V/nD) would have to be added, and the equation would become somewhat unwieldy. The breakdown in agreement after P/D = 1.4, and the nature of the curve obtained from equation (ix) after that value indicate that the general curves of KQQC against P/D as given by equation (i) are applic able only for values of P/D of less than 1.4. We will take, therefore, the curves of KQ against V/nD from R. & M. 829, using those for two-bladed airscrews whose maximum blade width is 0.082D. Returning to equations (ii) and (v) for Kq and D we have 550 B.H.P. 1 K Q = and J)1 0-00237 pn3D5 27t 33 x 10r' RI1.P. n2 pV di) (v) In equation (ii) the value of b.h.p. is that which the airscrew will absorb, while in equation (v) the value of b.h.p. is that which the airscrew is required to absorb, i.e., that of the engine. It is obvious that the two 174 b
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