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Aviation History
1931
1931 - 0174.PDF
FLIGHT, FEBRUARY 20, 1931 CALCULATION OF AIRSCREW CHARACTERISTICS In our issues of October 31 and November 7, we published an article on the Avro Long-range " Avian " on which Kings- ford Smith flew from England to Australia in record time. The article was much appreciated by our readers, as our post- bag shows, but the method employed in calculating airscrew characteristics puzzled several readers. We therefore com- municated with Mr. Roy Chad wick, chief designer to A. V. Rot c/v Co., Ltd., and he very kindly instructed the Avro Technical Department to gel out for us an explanation of the method employed. The method is stated in the following article.-—ED. THE following notes have been compiled on the methodemployed in estimating the Airscrew Characteristiscfor the Long Range Avian. (FLIGHT, October 31 and November 7). The characteristics obtained are based on empirical curves deduced from the model test results of R. ct M.829. A few notes have also been included to explain the applica- tion of the method to general routine investigations where, probably, an airscrew has not, at the time, been designed. Data Necessary It is assumed that the full scale airscrew will satisfy the design conditions of forward speed and R.P.M. at top speed, and at the design height. In a preliminary investigation the diameter is estimated by means of one of the many reliable formulas available, viz., Dr. Watts' Nomogram. The face pitch can be taken as the advance per revolution under the design conditions. P/ = 5280 88.V60 x R.P.M. (1) where P/ = Face pitch ft., V = Forward speed m.p.h. The Experimental Mean Pitch The experimental mean pitcli is the advance per revolutionwhere the thrust is zero. For a normal design of airscrew the experimental meanpitch to diameter ratio can be expressed approximately as :— Pe/D = 1-05 (P//D + 0-16) (2) The Torque Coefficient The torque coefficient Kq is given by 550 P pe 1 D» (3)2.7t.p na o where P = B.H.P. of engine at G.L. n — Revolutions per second of airscrew. p = Standard ground level density = 0-002373. o = Relative density at height. p« = Engine power factor at height. D = Airscrew diameter in feet. For a given type of airscrew the shape of the Kj curve is dependent only on the experimental mean pitch to diameter ratio. For the purpose of generalising the shape of the curves a constant (Qc) is introduced for each airscrew, such that when J1 = = 0-5 then Kt] Qr =1-0 (See Bairstow's Applied Aerodynamics.) The empirical relationship for the evaluation of Kg Qt. is as follows :— K,Or=l-EF (4) For E and F see Figs. 1 and 2.By combining equations 3 and 4 the value of Qc, which remains constant for any altitude or value of Ji, is given by 1 - (5) P _ 1 — EF 1? = Qc 550 The Thrust Coefficient The thrust coefficient K* is given by the well known for- mula ; 550 P pf 1 K'= 7 77D' n The known value of K^ is at the design conditions of top speed and R.P.M. For any other value of Jt 5 is rearranged so that P/MS can be extracted thus :— The shape of the Ki curve does not vary considerably with P«/D ratio and is expressed as a generalised curve which satis- fies the conditions:— K(TC =1-0 when Jt = 0-5 where Tf = constant. This curve is given in Fig. 3. Airscrew Efficiency The airscrew efficiency in free air is given by Kr Tf"Ii" = L-V -BC] J l — (N A, 15 and C being obtained from Figs. 4 and 5 and are em- pirical relationships. Slip Factor The increase in drag of the parts of the aeroplane in thv slip stream is proportioned to the square of the airspeed over the body, viz. (slipstream velicity)2 This increase in drag can be expressed as Where Dx is the free air drag of parts in the airscrew di-t area at speed V and D2 is the drag of the same parts in tlir airscrew slipstream at speed V + v v is the increase in airspeed due to slip. This increase in drag can also be expressed as a fraction r: the free airspeed drag :— '•'Do —D, / V + v , where <p = j __ T, 1,810-Tj 8 2-2? (in p-a-V-9 4 T = The free air airscrew thrust. A close approximation to this over the working range ^ :" \ ~V" / ~ ~ V^rJ7!)2 which is equivalent to saying that the loss of thrust due to th effect of the slipstream over the body is approximately a con- stant percentage of the thrust supplied by the airscrew over the flying range. The " nett" thrust is the difference between the iree ai: thrust and the increase in drag of the part in the airscrew db< area due to slip. T. the " nett " thrust is then given by " Nett " thrust = T; — (D2 — Dx) Substituting for (D, — Dx) from 9 and 11. "T" D, x 1265= Ti -^2 TJ-D 1265 (6) Taking the values of P and n from the power curve for theengine used (see Fig. 1 and table FLIGHT, November 7, 1930).See Fig. 6 for a and p«. r 3-A-KB-stt.-- I D2 where h is obtained as follows Estimate the free air drag of the parts in the t! then Free air drag in disc area Total free air parasite drag of the <:>•• Total parasite drag Note KB = —— p • a•JW•Vi Where Sw = Total wing area. It is more convenient to combine the slip facto* free air airscrew efficiency and obtain a " nett .... ('- isc - 168
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