Data for Estimating. Aerodynamic Derivatives

This appendix contains a limited amount of data on stability and control derivatives. It is not intended to be used for design. That requires much more detail than could possibly be provided here. It is intended to display some representative orders of magnitude and trends, and to provide numerical data that teachers and students can use for exercises. All the data pertain to subsonic flight of rigid airplanes. Much of the information comes from either the USAF Datcom (USAF, 1978) or from the data sheets of the Royal Aeronautical Society of Great Britain (now out of print), which is also the source for some of the Datcom data. We have taken some liberties in extract­ing and presenting this information, but have not changed any essential content. For information about derivatives at transonic and supersonic speeds and for geometries different from those covered in the following, the reader is referred to the USAF Dat­com. When estimating derivatives, reference should also be made to Tables 5.1 and


A. l Lift-Curve Slope, C,

A. 2 Control Effectiveness, CLs

B. 3 Control Hinge Moments B.4 Tab Effectiveness, b3 де

B.5 Downwash, —— da

B.6 Effect of Bodies on Neutral Point and Cm >

B. 7 Propeller and Slipstream Effects

B.8 Wing Pitching Derivative, Cmq

B.9 Wing Sideslip Derivatives Clp, Cnp

B.10 Wing Rolling Derivatives Clp, C„p

В.11 Wing Yawing Derivatives Cir, C„r

B. l2 Changes in Inertias and Stability Derivatives with
Change of Body Axes


• The source of the data for airfoils and wings is USAF datcom. It applies to rigid straight-tapered wings at subsonic speeds and small angle of attack.

• The section lift-curve slope is given by


Cla = — K(Claheory (B.1,1)

where К is given in Fig. B. l,la and (C;Jtheory in Fig. B.1,1Z>. У90 and У99 are the air­foil thicknesses, in percent of chord, at 90% and 99% of the chord back from the leading edge, as illustrated, and the trailing edge angle is defined in terms of these thicknesses by


• The lift-curve slope C, a of the wing alone is given in Fig. B.1,2. The inset equation is seen to approach the theoretically correct limits of тгА/2 as A —> 0 and 27ras {A—» °°, к—> 1, Л—» 0, (3—> 1}.

• Figure B.1,3 gives some theoretical values of the body effect on CLa for unswept wings in mid-wing combination with an infinite circular cylinder body. For values of A < 1, the theory also applies to delta wings with pointed tips.

In Fig. B. l,3a the wing angle of attack is the same as that of the fuselage; that is, e = 0. In this case the lift of the wing-body combination increases to a maximum value, then decreases with increasing body diameter. Where there is a wing setting,

i. e., e Ф 0, and aB = 0 (Fig. В. 1,3i>), the lift of the combination decreases with in­creasing a.

B.2 Control Effectiveness, CLs


Figure B.2,la presents theoretical values of the two-dimensional control derivative C, s for simple flaps in incompressible flow. These values can be corrected by the em-

4 [P2+ tan2 Лс/2]2

Figure B.1,2 Subsonic wing lift-curve slope.

pineal data of Fig. B.2,1 b for the strong effect of nonideal lift-curve slope of the main surface to which the control is attached.


The derivative CLs for a finite lifting surface with a part span control flap is obtained from the section derivative by

where CLo and Cla are as defined in B. l, C, s is the corrected value from Fig. B.2,1 b and Kl and K2 are the factors given in Figs. B.2,2 and B.2,3. In these figures the para­meter (as)Cl is the rate of change of zero-lift angle with flap deflection, given by the inset graph, and Aw and A are, respectively, the aspect ratio and taper ratio of the main surface.