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Aviation History
1927
1927 - 0646.PDF
52 SUPPLEMENT TO FLIGHT AUGUST 25, 1927THE AIRCRAFT ENGINEER TOO 650 600 550 500 450 400 350 300 250 200 150 100 50 .1(11 "lu r f i I LABL 1 M 1 -Q lit :a-<u •flr \ 11 J i ! 1 t 1 1 1 1 1 1 \ (Ml MM Z^ Vt .... \ D LOCI MM* / 'Y A \P.H 1 A1 i M t 1 >A i 1 M 1 f MM 1 A E ; : ) / M [ \ - I I I I I \ \ i i ir 0 10 20 30 40 50 60 70 80 90 100 110 120 Fig. 1. Typical Curves of Power required and Power available. Where Al = The area of a flat plate which has the same resistance as the wing profile drag plus all the structural items and tail surfaces. Dind. = - „., (fundamental Prandtl equation) W = Total weight of airplane. S = Span of wings. K/,= Coefficient which raises the span of a biplane to the equivalent monoplane span and depends upon ratio of gap to span. This quantity is given by the curve of Fig. 2. Substituting in equation 2. PK = (o 00327 A,,V- - 12'J ^ j — = 0-00000872 A,,V:!- (K,,S)2V- -375 W- , = P,,,xc. (1) As the speed changes, both the propeller efficiency, e, and the motor power, P,,(, change. The revolutions of the motor, and also the efficiency decrease as V decreases. These two variations, tending to reduce the power available, may be grouped into one quantity, overall efficiency, e,,. H. C. Watts has given a number of curves of overall efficiency in " Design of Air Screws." e,, may be expressed approximately by — )e<> = e,liax. I » des. / (8) When s. = Velocity at which propeller is designed to absorb the power of the motor at the required revolutions. / V I/2, (~J (9) v » des. Then P,, = POTemax. K,, (10) Mr. F. W. Herman uses a curve for maximum propeller efficiency which gives very excellent results in practice. This curve_can be expressed quite accurately, between all limits in use, by the expression :— I _ 1- 0-425 P,,//"N'/:' Where N = Revolutions of propeller at Vjes. Summary The curves of Fig. 1 are expressed approximately by :— Pfi = 0•00000872 A,,V -f When fnlax. = 1-0-425 PJ/' (10) (11) and K,: = (/ V •.'/- • Vdes. ' MAXIMUM VELOCITY Referring to Fig. 1, it is seen that the maximum speed obtainable is at the point " A " where the curves P,, and P,. intersect. That is, Where P,, = P,. Then at Vmax. P,,/max.K,, = 0-00000872 A;,Ynlax.' - "- ...(12) •$(XV,O)-\ max. It is convenient to consider all terms of the above equation as fractions of the total weight, W. Then ,, = 0-00000872^ Vmax.-' 4- ^Tv^v— (12a V\ C)(1S.)>)"\ max. Let -^ = Fp, the power factor (inverse of power loading) ~—*i = Fr, the parasite resistance factor. AVERAGE GAP OVER LARGER SPAN •05' -10 15 2. 25 Fig 2. Values of Coefficient K,, for various Biplanes. 5966
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