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Aviation History
1945
1945 - 1814.PDF
SEPTEMBER 13TH, 1945 287 Some Theoretical Considerations of an Unorthodox Method - 0/ Increasing Jet Efficiency By F. UMPLEBY ACCORDING to Newton's Third Law, action and r"i reaction are equal and opposite, but .before we can j- -*• utilise reaction to propel an aircraft we must have some abutment upon which the reaction can take effect. ,;; a piston engine the reaction of the explosion takes effect ;:-)on the cylinder head, and the active working forces aretransmitted through the piston and connecting rod to the crank pin and thence-to the main bearings. The constraint if these reactive, and working forces tends to lift the cylinder head from the engine struc- ture. In reaction propulsion the unconstrained forces are free to take effect upon a number of fixed abutment •joints from which they are transmitted to the body of the propulsion machine and thence to the aircraft in which it is installed. The reactive force generated is due tii the increase in momentum imparted to the fluid gas stream by thermal and mechanical operations as it passes trough the machine. A simple case is that in which an axial-flow air com- c.ressor is driven by an axial-flow turbine, with simple axial combustion between the two. The fluid medium is driven through the machine axially from the inlet to the discharge outlet. Reaction is also obtained when a fluid gas stream :•. deflected around a bend, or in the blades of a turbine, ..ad both increases in momentum and bend deflection reaction can be utilised to provide propulsive forces, i.e. the propulsion machine as a whole may operate on the .mpulse-reaction principle. . Axial and Bend Reactions Each of these actions can be seen at work in a river. For example, where a change in the section of the river bed occurs, a hydraulic jump is created from which a wave may often be seen travelling up stream against the current. This may be said to illustrate axial fluid reaction. Where the stream sweeps around a bend, the outer bank is washed away, which illustrates the effect of bend reaction upon the river bank. In the case of purely axial flow, the momentum of the gas stream in relation to the acceleration of the fluid is decreased by an amount equivalent to the velocity of flight. As the velocity of flight increases, the effective propulsion force decreases, except in so far as the ram effect increases the density and mass flow of the air entering the air com- pressor. On the other hand, in the case of bend deflection or impulse-reaction, the whole of the fluid gas stream and the abutment elements upon which it reacts move as one body, and the resultant effective pro- , pulsion force is constant at all flight \ speeds, >and is enhanced by the ram uftuct. In considering these forces in detail the following simple formula; will be used, and one pound of air per second will" be taken as the basic quantity consumed. • 'Static Axial Thrust T =- Static Resultant BendW W(V v.) Reaction Force R = — (Vj cos a) -f (Vj'cos b) g g THE following article is of c controversial nature, and no: everyone will accept the author's deflection theory which, to many, will appear reminiscent of a man trying to lift himself by his boot straps. We shall welcome the opinions of readers as the subject needs to be thoroughly discussed in view of the great increases in efficiency claimed by the author. Static Thrust component T = K sin c Axial Thrust in Flight R or T = (W 4- w) (V - v) (5) C) Axial Thrust in Flight, for sloping pipe, from 4, T = R cos c Reaction 3i5end Thrust in Flight, R found from 2, T = R sin cw Where T = Thrust,.pounds. R = Resultant of velocity forces. W = Weight of gases, pounds per second. ID — Weight of gases, pounds per second, added due to ram effect. V = Velocity of gases, feet per second. V — V, = Difference in gas velocity, i.e. change in momentum. Vz = Velocity of gases entering bend, fee-1: per second. Vs = Velocity of gases leaving ber.d, feet per second. v = Velocity of flight, feet per second. a — Angle through which entering gases are deflected. b — Angle through which leaving gases are deflected. c = Component angle of resultant thrust force. g = 32-2. ' - W ;. —for air = -03105. : ' • s ••.-•' w • —for combustion products = -0316. g The actions and reactions of the gases may be illustrated by means of simple velocity or force diagrams in which the line of action is shown by an arrow and the intensity of ths action is indicated by the length of the arrow, to scale. The double-headed arrows indicate the direction of flight in all cases. Fig. 1 shows the simple' axial flow in which action, and reaction are indicated by arrows pointing in opposite direc- tions and the propulsive force generated is obtained from formula (1). Fig. 2 shows the case where a simple 45 deg. bend is Fife? 1. Diagram of simple axial flow. Fig. 2. Flow <n a 45-deg. bend; negative Fig. 3. Flow in a 90-deg. bend; positive thrust. - thrust. .'C
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