M. a. Chord and m. a. Center for Swept and Tapered. Wings (Subsonic)
The ratio c/cr is plotted against A in Fig. C.2 for straight tapered wings with stream – wise tips. The spanwise position of the m. a. center of the half-wing (or the center of pressure of the additional load) for uniform spanwise loading is also given in Fig. C.2. These functions are given in Table C. l.
The m. a. chord is located by means of the distance x of the leading edge of the m. a. chord aft of the wing apex:
where A0 = sweepback of wing leading edge, degrees.
The sweepback of the leading edge is related to the sweep of the nth-chord line A„ by the relation
Using (C.3,2) and the expression for c/cn x can be obtained in terms of c and An from
The fractional distance of the m. a. center aft of the leading edge of the m. a. chord, hnw, is given for swept and tapered wings at low speeds and small incidences in Fig. C.3. The dotted lines show the aerodynamic-center position for wings with unswept trailing edges. The curves have been obtained from theoretical and experimental data. The curves apply only within the linear range of the curve of wing lift against pitching moment, provided that the flow is subsonic over the entire wing. The probable error of h„n given by the curves is within 3%.
The total load on each section of a wing has three parts as illustrated by Fig. CAa. The resultant of the local additional lift la, is the lift La acting through the m. a. center (Fig. CAb).
The resultant of the distribution of the local basic lift lh is a pitching couple whenever the line of aerodynamic centers is not straight and perpendicular to x. This couple is given by
(x — x)lh dy = 2 J xlh dy о Jo
Figure C.3 Chordwise position of the mean aerodynamic center of swept and tapered wings at low speeds expressed as a fraction of the mean aerodynamic chord. (From Royal Aeronautical Data Sheet Wings 08.01.01.)
The total pitching-moment coefficient about the m. a. center is then
= Cm] + Cm2 = const (C.4,3)
If Cmar is constant across the span, and equals Cm2, then (C.4,2) also becomes the defining equation for c.