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Aviation History
1942
1942 - 1408.PDF
22 FLIGHT JULY 2ND, 1942 Correspondence The Editor does not hold himself responsible for the views expressed by correspondents. The names and addresses of the writers, not necessarily for publication, must in all cases accompany letters. AD ASTRA Wright Bros.' First Machine WITH reference to the article " Ad Astra " by the Rt. Hon. Lord Brabazop, in your issue of June 4th, might I point out that the Wright Brothers' first machine was destroyed in a crash, and that the machine in the Science Museum, though built by them, is merely a replica, and has never been flown? REG. JUDSON. JET PROPULSION OF AIRCRAFT Formula for Calculating Thrust SOME weeks ago you printed a letter from me, in which I expressed some doubts on the feasibility of any system of jet propulsion for aircraft in which ' the thrust is obtained by the introduction of heat into the air stream. Since then I have given the problem further consideration, the results of which I would like to submit to your readers for criticism. As already pointed out by one of your correspondents, the tube through which the jet of air passes would have to be of the form shown in the figure. Using the following symbols :— p = air pressure to lb./ft.2 p •* air density in slugs/ft.8 T = air temperature in °C. absolute V m air velocity in f.p.s. A = cross sectional area of tube in ft.2 C„ = specific heat of air in ft. Ib./lb. °C. = 234 ft.lb./lb.°C. Cp y — rf- =1.4 (ratio ot specific heats) and assuming that at inlet px = 2,120 lb./ft.2, px = 0.00238 slugs/ft.*, T, = 288 °C, V, - 300 f.p.s. and At = 5 ft.2 we have : Mass of air flowing per second = px AjV, = 3.57 slugs. For a compressible fluid we have, instead of the ordinary Bernoulli equation, the formula Gain in internal energy = (Ts — T2)CcgM ft./lb. M Gain in kinetic energy = (V 3 3 — V 2 2) —ft./lb. . If the sum of the last three expressions be equated to the heat added and taking into account the momentum equation, we obtain :— v a = 237 f-P-s., p3 = 2,162.0 lb./ft.2, p3 = 0.00205 slug/ft.*, T3 = 340.8 °C. als. Using the modified Bernouille equation for compressible adiabatic flow, we next obtain (assuming A4 = Aj = 5ft.2), V4 = 356.0 f.p.s., T4 = 337 °C. als., Pi = 0.00201 slugs/ft.3, pt = 2,090 rb./ft.2. The conditions in the slip stream after adiabatic expansion to pb = 2,120 lb./ft.2 are V5 = 312.0 f.p.s., T5 = 338 °C. abs., p6 = 0.00205 slugs/ft.3. 2120 lb/sq.ft. 338 "Cabs YY = Vx2 +- * -(S 1 when the flow is (v-O^Pi]/ \pj J adiabatic. Applying this formula to the flow between sections 1 and 2 y—I = -290.3°C", <• m we obtain Vl = 200 f.p.s., T2 p2 — 0.00243 slugs/ft.3 and A8 = 7.35 ft.2. It is now assumed that between sections 2 and 3, 2 x io6 ft.lb. of energy are added to the air in the form of heat every second (= 3,640 h.p.). The effect of this heat on the pressure velocity, density and temperature of the air can be found from the following equations : Momentum equation :—(pt — />,) A2 = M(V3 - V, lb. Heat added Thrust x Velocity of aircraft _ 42.8 x 300 2 x ioG 0.0064; Work done against external pressure M (is- - h \Pa Pi ft./lb. BOOKS FOR WIRELESS TRAINING TX7IRELESS has become so important in the war, especially W to the air services, that reliable technical books are very much in demand. Technical books issued from the offices of the Wireless World have earned a high reputation in the past, and to-day they supply the needs of all branches of the Services. Theoretical books written from a practical point of view include " Foundations of Wireless." This book, from an elementary beginning, brings the student" up to the stage where he can read and understand circuit diagrams and pro-. vide himself with a good foundation of wireless theory. " Radio Designers' Handbook " might be described as a manual packed with practical information and describing the use of formulae required by the radio designer; a book specially imported from Australia because nothing like it had been produced here. Those whose business it is to maintain wireless equipment yr The resultant thrust can be calculated in two-ways. First, total change of momentum per second = 3.57 slugs x (Vs — V,) = 42.8 lb. Second. Average outward pressure between 1 and 2 is approxi- . , 2120 + 2180 mately = 2150 lb./ft.2. Average outward pressure between 3 and 4 is approximately 2162 + 2090 -—= 2126 lb./ft.2, 2 The resultant thrust due to these pressures is roughly (2150 — 2126) (Aj — Aj) = 24 x 2.35 = 56.4 lb. which agrees fairly well with the first value. _ „ . . , . . , Useful work Efficiency of propulsion is given by Heat added Or the efficiency of propulsion is 0.64 per cent. In the foregoing calculation no allowance has been made for y$» losses due to turbulence, which would surely be considerable in the divergent portion of the tube between 1 and 2. R. M. HELSDON. Technical College, Coventry. will find the " Wireless Servicing Manual " a really practical guide, where the object of the author has been to make the reader understand what he is doing in testing rather than working mechanically to a plan. Another volume, which may be regarded as a companion, is " Radio Laboratory Hand book," describing apparatus used in a testing laboratory and its operation. Specialised branches of radio are catered for,' and " Wireless Direction Finding " is a big volume which covers theory and practice of the various branches of this subject, whilst " Television Receiving Equipment " will meet the needs of those in training for work where cathode-ray tubes will be employed. The operating side of wireless has not been forgotten, and nearly a quarter of a million copies of a sixpenny booklet, " Learning Morse," have been sold since the beginning of the war. •P" •**-
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