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Aviation History
1938
1938 - 1105.PDF
APRIL 21, 1938 27 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT 394C BALANCE CALCULATIONS An Alternative Method to Those of Air Publications 970 and 1208 Greater Simplicity Claimed By W. WILSON IN determining the loads for calculating the strength ofan aircraft structure, especially the wing structure, itis necessary to carry out " balance calculations " for certain flight conditions (Refs. i and 2). The following procedure is usually adopted :—A diagram, to scale, is "drawn for each case. Each known and unknown load is placed in its appropriate position. The moment arms about the centre of gravity are scaled off .parallel and normal to the flight path. Balance equations can then be written, the solution of which give the unknown loads. In no case is it possible, by the above method, to determine the loads for any particular case from a previous one. This is because every new case involves (i) A fresh centre of pressure position on the wing. '•• (ii) A fresh datum line (i.e., the flight path) parallel . . . ; and normal to which the moment arms are ••"->"••• measured. The present article attempts to simplify and save time on balance calculations by (a) Abandoning the conception of a centre of pressure of load on the wing, but instead applying the wing load -•. at the mean aerodynamic centre of the wing. This involves the introduction of a moment, i.e., the no lift moment. (b) Using a fixed datum which has no reference to the flight path. (c) Adopting a tabular method for the solution of the balance equations. , CENTRE OF AIRSCREW CENTRE of PRESSURE MEAN AEROPVNAMlC v Wl P1-ANE CENTRE \ NW FIG. J. Fig. 1 shows a diagram of balance centres, which remain fixed for any flight condition. The known and unknown loads are applied at five centres, i.e. : (1) The mean aerodynamic centre of the wing. (2) The centre of gravity. (3) The centre of body drag (extra to wing). (4) The centre of airscrew. (5) The centre of pressure of the tail plane. The definition and methods of determining the mean aerodynamic centre were given in an article in the Aircraft Engineer (Ref. 3). The centre of gravity and centre of resistance are deter- mined by the usual method. The centre of the airscrew is obtained from a drawing of the aircraft. The centre of pressure of the tail plane is assumed to be at one-third the tail plane mean chord. All moment arms are measured parallel and normal to a convenient horizontal datum, e.g., the thrust line or the horizontal datum of the aircraft. The notation used for the moment arms and loads follows that used in A.P. 970 and A.P. 1208 (the moment arms being now measured, however, parallel and normal to the horizontal datum chosen), with the following additions :— Mo = no lift moment on wing. Q = component of thrust normal to flight path. : . / = horizontal moment arm of centre of airscrew.• v . c = horizontal moment arm of centre of body drag. m — vertical moment arm of centre of pressure of tail plane. It should be noted that moment arms and loads are considered positive in sign as shown in Fig. i, the reference lines for the moment arms being horizontal and vertical lines drawn through the centre of gravity. Referring to Fig. i :— Q = T sin (a — <f>) = T(a - 4) :.:• : ., '•'.•"•'•.. ' .. (1) since the angle a — <f> will usually be small. In the case when the horizontal datum is parallel to the thrust line, <f> = o Resolving loads parallel to the flight path :— F = D +DB — T (2) Resolving loads normal to the flight path :••- NW = L + Q + P (3) or L = NW—Q-P .. .. .. .. (4) Taking moments about the centre of gravity :— — T (e cos a + / sin a) + Q (/ cos a — « sin a) + L (a cos a — b sin a) + D (p cos a + a sin a) + Mo + DB (d cos a — c sin a) — P (/ cos a + m sin d) = o In this equation, very little loss of accuracy will result by putting cos a = I and sin a = a, since a will usually be small. If the quantities in brackets (which are the " resultant "' moment arms obtained by scaling off a diagram by the usual method) are therefore written <?j = e + fit y::,'- j. . . • • «, = '•: d\ = h =the equation -T*, + Q/,from which P = - T/; - a b d I • -6a •-; :-•.;-••;- 4- aoL •' • ; '-••- .- — CO. i- mm •>*'•"• becomes 4- La, + Db, + ? % + L/7 + D/ -• • ,. .•_•:. \\,. -f- DBi 1 I' -r M 0/- 1 '1 P/, = o (0) Equation (6) is used in conjunction with equation (3) when NW is unknown (e.g., gust cases). Substituting for L in equation (5) from equation (4) : — , + Dfcj + Mo + DBd, - P(/, + ax) = o From which P= -Tr + Qh NW; (7) Equation (7) is used in conjunction with equation (4) when L is unknown (e.g., level flight and glide cases). In the above equations for engines-off cases, — DA is substituted for T and Q — o. The application of the method is shown by the following example :—The following data refer to a normal category, twin-engined aircraft for passenger transport, designed to civil requirements. It should be emphasised that these data are purely imaginary and refer to no particular aeroplane. All up weight Stalling speed Normal top speed Wing area 20,000 pounds. 75 miles per hour 180 miles per hour. I.A.S. at 10,000 ft. (,i/T=.86) 1,000 sq. ft.
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