Wing Rolling Derivatives Clp, Cnp
The following methods are simplified versions of those given in USAF Datcom. They apply to rigid straight-tapered wings in subsonic flow, in the linear range of CL vs. a. The derivative C,:
j is the roll-damping parameter at zero lift, obtained from Fig. ‘Cl=о в.10,1 as a function of Af3 and /3A/к.
The parameter к is the ratio of the two-dimensional lift-curve slope at the appropriate Mach number to 2tt//3 that is, (C, JM/(2 77//З). The two-dimensional lift-curve slope is obtained from Sec. B. l. For wings with airfoil sections varying in a reasonably linear manner with span, the average value of the lift-curve slopes of the root and tip sections is adequate.
The parameter is the compressible sweep parameter given as
. , / tan Лс/4 .———
Ap = tan 1 f—- —— j, where /3 = Vl — M2.
and Лс/4 is the sweepback angle of the wing chord line.
— is the dihedral-effect parameter given by
Г is the geometric dihedral angle, positive for the wing tip above the plane of the root chord.
(6) X. = 0.50
z is the vertical distance between the CG and the wing root chord, positive for the CG above the root chord. b is the wing span.
(AC, p)drag is the increment in the roll-damping derivative due to drag, given by
(AQ„)drag = Cl-j CDo (B. 10,3)
where (C )
—lp is the drag-due-to-lift roll-damping parameter obtained from Fig.
<~’L B.10,2 as a function of A and Лс/4.
CL is the wing lift coefficient below the stall.
CDo is the profile or total zero-lift drag coefficient.
The derivative Cn
is the roll-damping derivative at the appropriate Mach number estimated above is the angle of attack, is the lift coefficient.
I is the slope of the yawing moment due to rolling at zero lift given by
is the effect of linear wing twist obtained from Fig. B.10,3.
is the wing twist between the root and tip stations in degrees, negative for washout (see Fig. B.10,3).