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Aviation History
1929
1929 - 1122.PDF
SUPPLEMENT TO FLIGHT MAY 30, 1H29THE AIRCRAFT ENGINEER In fact, the tails of most aircraft can be raised by the action of static slipstream alone. (B) Run while dropping tail. ' . V . •; When minimum flying speed is reached it is assumed that one second is taken to drop the tail till the wings are at the maximum angle of attack. During this second, the aircraft IB supposed to be moving forward with a uniform speed equal to the minimum flying speed, i.e., there is no accelera- tion. The choice of one second for the time to drop the tail has been made after comparing predicted results with values obtained from deck landing trials, and is considered to be quite a reasonable assumption. Also the assumption of no acceleration during this time leads to only a very small error, and is justified by the simplification obtained by its use. Using the above assumptions and the fundamental aero- dynamic data of the aircraft, the following method will be found to be very straightforward, though fairly laborious, and will yield results of real value, especially in the case of deck launching machines. The first part of the calculation consists of finding the value of the total accelerating force at every point in the run. During the run the datum line of the aircraft is assumed to be horizontal. . •. at any instant :— Accelerating force — thrust x cos 6 — total drag, where 8 is the angle between the thrust line and the datum line of the machine. 0 is usually small, and it is sufficiently accurate to take cos 0=1. . •. Accelerating force = thrust — total drag. (1) To Find the Thrust:—If the actual airscrew character- istics, torque coefficient KQ, thrust-coefficient KT, and efficiency »/ are available from test or design, the thrust at all forward speeds can be found accurately with the aid of the engine power curve, but if the aircraft is still in the design stage and these characteristics are'unknown, a more genera] method will have to be used. HORIZONTAL DIRECTION oF MOTION FIG Assuming that the maximum power and revolutions of the engine, and a reasonably correct value of the top speed of the aircraft are known, it is an easy matter to obtain an approximate value for the airscrew diameter. The V/nD at top speed can then be found, and from this a good idea of the airscrew efficiency is obtained, followed by the calculation of the thrust at top speed. Then, if Tt, = thrust at top speed, and Vi, = top speed, the following empirical factors may be used to find the thrust T at any speed V. V/Vt 1-00 0-80 0-60 0-40 0-20 0-00 T/TL 1000 1124 1-250 1-370 1-460 1-50 A curve of thrust T against forward speed V is thus obtained. From the thrust curve it is possible to obtain a curve of slipstream velocity using the formula T = 0-00331 D2 V* a (1 + a) to find a. •where a — inflow velocity ratio. T = thrust in lbs. . D = airscrew diameter in feet. V = forward speed in ft./sec. The final slipstream velocity (V -j- v) is then given by (V + v) = V (1 + 2a) ft./sec. This formula assumes that the effective airscrew disc area is an annulus with external diameter D, and internal diameter 1 '3D. and the diameter of the final slipstream can be shown to be Dt = D\/ /1 + 1-llaft. ..•.•1 +2a" , on the assump- tion thatjthe'external diameter contracts from D tu D,. while the diameter of the centre core remains equal to I) 3. i Curves of slipstream speed, and slipstream diameter can therefore be plotted on a base of forward speed. (2) Total Drag of the Machine.—The total drag of tie aircraft during the run can be divided into six parts :— (a) Wing drag in slipstream. (b) Wing drag outside slipstream. (c) Backward component of lift in slipstream. (d) Parasite drag in slipstream. (e) Parasite drag outside slipstream. (/) Drag due to wheel friction. It will first be necessary to define by symbols the'attitude of the machine during the run, and to collect the following data from a 3-view G.A. :— A = Total wing area in sq. ft. Aj = Wing area in slipstream. A2 = Wing area outside slipstream. A1 depends on the slipstream diameter, D1( found as explained above, and hence varies with the forward speed. It will be sufficiently accurate, however, to take a mean value for the slipstream diameter, and a constant value for Aj found by using this mean. at0 =" main plane incidence, i.e., angle of wings to datum line of machine. a°0 = angle of main planes to thrust line. The aircraft is running with its datum line horizontal. Therefore the angle of attack of the wings (outside slipstream) is oc°, and the thrust line is inclined at an angle of (a — Oj)0 to the horizontal. The characteristic curves of Kt, KD, and L/D plotted against angle of attack a for the aerofoil will be required, and theae must be corrected for the appropriate wing arrangement in the usual manner. Then the following quantities are calculated for several values of the speed, from no forward speed to 5 or 10 m.p.h. above the minimum flying speed. (a) Wing Drag in Slipstream.—Treating the air velocities vectorially and referring to Fig. 1, it can be shown that x1 = angle of attack of wings in slipstream. V Then at any forward speed :— Lift in slipstream = Ki.jpA! (V + vf. Wing drag in slipstream = DWl lift in slipstream X (L/D), where V = forward speed in ft./sec. V + v = slipstream speed in ft./sec. found previously. Aj = wing area in slipstream. Kn = lift coefficient appropriate to angle of attack «V(L/uJj = Lift-drag ratio appropriate to angle of attack aV p = 0-00237 at S.L. KL and (L/n), are taken from the wing characteristic curves. (b) Wing Drag Outside Slipstream:—Lift outside slip- stream is given by KipAjV2, and wing drag outside slip- stream = DW2 = lift outside slipstream X (L/D) where KL and L/D are appropriate to the angle of attack a°. (c) Backward Component, of Lift in Slipstream :—A stud of Fig. 1 will show that the lift in the slipstream is inclined backward at an angle of (a — aj)0 to the vertical. i'llis causes a drag component DW3, which is equal to Lift in slipstream x sin (a — ccj 0. (d) Parasite Drag in Slipstream .-—The parasite drap 'at 100 ft./sec. is found by the usual methods (model te^r or detail estimation), and the proportions inside and outside the slipstream obtained. Then parasite drag in slipstream = T)Bl = dx X —j^T where dt = parasite drag in slipstream at 100 ft./eec. V +t'= slipstream velocity in ft./'sec. 4466
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