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Aviation History
1929
1929 - 1347.PDF
JUNE 27, 1»29 SI THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT FIG I • Fig. 2 gives the tail setting required to trim for an aircraft with the C.G. arranged to give: (1) Stability, (2) Neutral stability, and (3) Instability. Consider the aircraft in steady flight at a speed A, now reduce the speed to B without altering the tail setting. The machine is still in trim in case 2 but is out of trim in cases 1 and 3. In case 1 the tail will be set too positively and the machine will tend to dive until it again reaches speed A, when it will continue in steady flight as before. In case 3, however, the tail setting at the reduced speed will be too negative and the machine will tend to climb and cause a further reduction of speed and will eventually lead to stalling. This latter condition is, of course, an undesirable feature in civil aircraft although it may be necessary to a small degree in special cases in order to obtain manoeuvrability. It is a well-known fact that if a machine is neutrally stable at small angles of attack it is invariably stable at larger angles. The fact that no change of trim takes place in the neutrally stable region gives a convenient starting point for a mathe- matical treatment of the problem. The most important assumption made is that the drag of the whole aircraft acts at the centre of gravity and has, therefore, no influence on the tail load. For a normal biplane this is approximately correct, and generally the moment of drag is so small compared with the moment of lift, &c, that the assumption is justified. It is also assumed that the lift coefficient curve is propor- tional to incidence at small angles of attack and that the moment coefficient about the leading edge of the wing is roughly a straight line when plotted against the lift coefficient. This latter assumption is stated as above because the usual conception of moment is that about the leading edge. Actually this is slightly altered for the purpose of the article, and a point on the chord is chosen where the moment coeffi- cient is constant and has a value of K,w) which is the moment at no lift. The position of this point expressed as a fraction of the chord is given by the slope of the moment curve about the leading edge. So that if the moment with respect to the leading edge Km = -eKL + KHi0 (1) Then the point about which the moment is constant is c times the chord back from the leading edge. Theory suggests that the value of e should be 0 • 25, actual values as measured in the wind tunnel vary slightly from this but for any section whose characteristics are not known it is safe, for a monoplane, to use this figure. The value of e is taken as being independent of Aspect Ratio, but changes from monoplane to biplane as a function of the gap-chord ratio, thus :— (2)e (biplane) = e (monoplane) 1 —J ( — where c = Mean chord in feet. g = Gap in feet. The'definition of mean chord (for moments) of a biplane is _ (3) where Swi an<i Sw» represent the areas of top and bottom planes and cx and c2 the corresponding chord. If the ratio of the hit coefficients of upper and lower wiag is given by KL Upper Lower then the height of the equivalent chord above the mean chord of the bottom plane is V = 9 r S'W!\r + S, where g is the gap between the mean planes. The fore and aft position of the equivalent chord is deter- mined by the position of ex. The points ex clt e c and etct must be on a straight fine. Having fixed the equivalent plane the necessary conditions for stability can now be investigated. From considerations of lift and moments only the moment of the wings about the C.G. at small angles of incidenoe can be expressed by :— Mw = a-Swc[(*-e)Kl+KllJ (5) where q — a-p-V1 and xc. is the distance measured parallel to the wind direction between the leading edge of the equivalent plane and the C.G. The moment of the tail plane (considered as all elevator) about the C.G. is M, = q-Sth.Kv (6) where Ky is the tail-lift coefficient and " L " is the tail arm measured parallel to the chord. (See Fig. 1.) For steady flight the moment of the tail must balance the moment of the wings in all cases, i.e.: MW = M, from which we obtain If «, is the setting of the tail plane with respect to the chord of the equivalent plane and 3 is the downwash angle at the tail, and a is the incidence of the main planes, measured from no hit, then K-,, = at (a + a/ — ji) where " a< " is the slope of the tail lift curve. TAIL SETTING ANGLES TO TRIM (8) FIG.2. 1? 8 4 0 •4 uA* /AJ 7// // 1 © \ o Q U [L 1 • • _—.—- '< Q •—H ato 50 IOO 150 a» reo JOO V - SPEEO (M PM)
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