# 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,:

lP

where

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.

f

— is the dihedral-effect parameter given by

(C/p) r=o

where

Г is the geometric dihedral angle, positive for the wing tip above the plane of the root chord.

 (6) X. = 0.50

 Н=ї.0 PA

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

CL= 0

M

(B.10,6)

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).