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Aviation History
1926
1926 - 0295.PDF
APRIL 29, 1923 39 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT a = alteration of angle of pitch, in degrees. p = density of air in slugs. v = speed, along flight path, in feet per second. The small suffix letters tagged on to all the coefficient symbols serve to indicate the element of the aeroplane to which they are due. A negative sign for a moment-coefficient indicates that the moment is an " instable " one, a positive sign (or no sign) that the moment is a '' stable " one ; an " instable " moment of pitch or of yaw is one which tends to increase the divergence from the initial attitude, an " instable " moment of roll is one which tends to depress the port wing tip when the tail of the machine is yawed to port; " stable " moments are, of course, those which produce the opposite effects. To revert then to stability in pitching :—Having calculated the values of SMP, §MB and §MW for the design under exami- nation, it remains to give such area to the tail surface that :— SMT = - C, (SM,, + SM,, -f SMW) (1) ('„ the empirical " measure " of stability in pitching, should The rate of change of pitching moment due to wings is smaller the farther forward the C.G., and (though to a consi- derably lesser degree) is smaller the greater the distance of the C.G. below the " mean "' chord ; or, expressed in the 1* symbols of Fig. 6 the smaller the value of ~ the smaller will be the value of §MW, ami the greater the value of "^- the smaller will be the value of §MM , and vice-versa. Neglecting the effect of variation of '-^ as of secondary importance t M within the usual limits of its variation and assuming, for simplicity, that yt = 0 (i.e., that C.G. lies on " mean " chord), for a wing of R.A.F. 15 section :— When xx = 0-27 CM [8MW H- (AW X CM )] = 0-0014 „ = 0-30 CM [§MW Hr (AW X CM)] = 0-00255 „ =0-33 CM [$MW ~ (Aw X C,, )]--•• 0-0037 "Lw= ANGLE OP INCIDENCE , W\»J&- CHORD Tb X-X- O^ = 'ANGLEOPPITCH^ X-XTP FuGHT-rATH. ~L - Af\fGL E OP AT TACK , Wi^G-CHORD TO FLIGHT- r*ftTM . l_ = TOTAL LIFT-TORCE ON WIKJG-SURFACE • D- _:. DRAG •• i . ('y, ist"E WHC^I CM IS Go IF S«I = 'EaU'VALENT MEWJ SPAN^OF WINGS 5^. V " DIHEDRAL ANGLE '.— C^XM = £00007 •+- -cooofsV^) Aw 5LW = ICOOOO7 + -OOOI3V~)XAW^SW1 +• r&Ywxry,"| C'M. ^T'^HCT CW IS ABOVE C.G) (§MW =(^IA%IMUt«; VALUE FOR Mw PER 1° ALTE.KATIOM OFAMGLE OF PITCHJ -r- Fig. 6.—Values for lateral force and moments due to wing surface. have some value between 1-5 and 3-5 depending upon the degree of stability required. For the same degree of stability, however, the value of Cj is dependent to some extent upon the pitching moment of inertia (moment of inertia about axis Z-Z) of the aeroplane and upon the location of the C.G. with respect to the " mean "' wing chord (apart from the effect of this relation upon §M,V). It is probable that the former factor may be neglected in this empirical procedure, unless one has reason to suppose that the length of the radius of gyration in pitch is of abnormal value compared to, say, the length of the " tail-lever" (LT in Fig. 5). It would appear reasonable to expect that, for the same degree of stability, the value of C2 should vary linearly as does the value j— kv being the radius of gyration in pitch. Now for the " Bristol Fighter "' Z'P 4-56 . rT = i5^i = °-29- Hence we might say that, assuming one has calculated the values for the radii of gyration (a simple but tedious business), should have some value between 5-0 p- and 12-0 T^ LIT -LiT depending upon the degree of stability required. As regards effect of location of C.G. with respect to " mean ' wing chord :— x1 =0-27 CM „ =0-30CM ,. =0-33 CM Assuming that for the case ,r, = 0-27 CM the value of [§M,. -i- §M,,1 be 0-5 of the value of SMW it follows that, if j'j be the only variable, when [&MP + &MB + §MW] = 0-0021 (Aw xCM ) [SMr + SMI( -f SMW] =0-00325(Aw xCM ) I8MP - SMB + §MW| =0-0044 (Aw xCM ) In other words, if nothing except ,r, be varied, an aeroplane with a-j = 0-30CM would need about 1-55 times the tail area that it would if x1 = 0-27 CM, whilst with xx — 0-33 CM it would need about 2-10 times the tail area that it would if a-i = 0-27 CM and about 1-35 times the tail area it would if xx — 0-30 CM . in order to retain the same value for C,. Now the equation of motion in pitching is of the form •(2) 260c In which Iz = Moment of inertia about axis Z-Z. M = Pitching-moment, assumed to vary linearly as a the angle, of pitch. MP = " Damping factor " or pitching-moment due to rate of pitching ; this factor is due almost wholly to the tail surface. I7, is constant, for an aeroplane in which x, and area of tail are the only variables, hence, if the area of the tail-surface were increased so as to retain (in equation (1)) the same value for C, as Z, is increased, both M and MP (in equation (2)) would be increased ; this means that the amplitude of pitch E 2
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