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Side Force and Yawing Moment Coefficients
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A further development of the theory leads to an explicit expression for the side force coefficient:
where H(k) is the magnitude of the transfer function H(k); pg = Lref/2b is the gust parameter; w/V is the gust amplitude; f (k, ko) is an oscillatory function quickly damped on both sides of the frequency ko. Finally,
,/ X 1 frr s, s 1 /sin(wo(2T – T)) – sin(woT) ф(т) = W(.T- T)coS(Mlr) – — — J (15)
is the gust auto-correlation function evaluated at t = 0. In Eq. 15, T is the time needed by the gust to travel the reference length with the speed V; и o is the frequency associated to ko.
The integral term in Eq. 14 depends on the admittance over the whole spectrum of frequencies and on the reference frequency k0. The integral is a constant with respect to the gust amplitude. Hence fcs* varies linearly with the
root mean square gust angle V^2 This linear dependence is also valid for the yawing moment coefficient, CY. In the latter case, replace the admittance for the moment, Eq. 11, into Eq. 14 to obtain the coefficient of proportionality. Results from this theory are compared in Fig. 2 with the experimental data of Bearman & Mullarkey for the road vehicle BA20 (scant angle 20 degrees). The figure shows both the side force coefficient CY and the pitching moment coefficient CS as a function of the RMS of the gust angle. The correlation is quite satisfactory.
