Control Hinge Moments


t trailing-edge angle defined by the tangents со the upper and

lower surfaces at the trailing edge

{b)(yr theoretical rate of change of hinge-moment coefficient with

angle of attack for incompressible inviscid two-dimensional flow

(b,)0 actual rate of change of hinge-moment coefficient with angle

of attack for incompressible two-dimensional flow

Rectangular wings infinite circular cylinder mid-wing configuration


Figure B.1,3 Body effect on lift-curve slope expressed as a ratio of lift of wing-body combination to lift of wing alone. (From “Lift and Lift Distribution of Wings in Combination with Slender Bodies of Revolution,” by H. J. Luckert, Can. Aero../., December 1955.)

(Ь2)от theoretical rate of change of hinge-moment coefficient with

control deflection for incompressible inviscid two-dimen­sional flow

(b2)о actual rate of change of hinge-moment coefficient with con­

trol deflection for incompressible two-dimensional flow

Figure B.2,2 Flap-chord factor.

(^l)obal’ (^2)0bal

rates of change of control hinge-moment coefficients with in­cidence and control-surface deflection, respectively, in two­dimensional flow for control surfaces with sealed gap and nose balance

F, aJ8

induced angle of attack correction to (&,)0 and (b2)Q, respec­tively, where F, is the value of (a,/S) [Q/C, J when cf = c

F2, Д(b2)

stream-line curvature correction to (bx)0 and (b2)0, respec­tively, where F2 is the value of Д(b2) when cf = c

factor to F2 and Д(b2) allowing for nose balance


ratio of control-surface area forward of hinge line to control – surface area behind hinge line


Figures B.3,1 and B.3,2

The curves of Fig. B.3,1 were derived for a standard series of airfoils with plain controls for which tan (|)r = t/c (referred to by an asterisk). To correct for airfoils

with tan (!)t different from t/c, values of (b,)*)74 (C, a)*heory and C*a are calculated for the given t/c ratio; then (b,)0 is calculated from

Oh) 0 = (bSo + 2[(CJ theory C;*J(tan (t) – t/c). (B.3,1)

Values of (C/a)*heory and C*a may be obtained as in Appendix B. l.

The curves apply for values of angle of attack and control deflection for which there is no flow separation over the airfoil; for these conditions (h,)0 can be estimated to within ±0.05. The data refer to sealed gaps but may be used if the gap is not greater than 0.002c.

The above discussion also applies to the data given in Fig. B.3,2 for (b2)0. The subscript 1 in Eq. B.3,1 becomes a subscript 2, a becomes 8, and values of (CZs)t*heory and C*ls may be obtained from Appendix B.2.


Figure B.3,1 Rate of change of hinge-moment coefficient with angle of attack for a plain control in incompressible two-dimensional flow. (From Royal Aeronautical Society Data Sheet Controls, 04.01.01.)

Figure B.3,3

The effect of nose balance on (£,)„ and (b2)0 can be estimated from the curves given on this figure. The data were obtained from wind-tunnel tests on airfoils with control-chord/airfoil-chord ratio of 0.3. Relatively small changes in nose and trailing – edge shape, and airflow over the control surface, may have a large effect on hinge moments for balanced control surfaces, so that estimates of nose-balance effect will be fairly inaccurate. If the control-surface gap is unsealed, the hinge-moment coeffi­cients of plain and nosebalanced controls will generally become more positive.

Figure B.3,4

Two-dimensional hinge-moment coefficients for control surfaces with nose bal­ance can be corrected for finite aspect ratio of the main surface using the factors given in the curves and the following equations:

bx = (Mo(l – F,) + F2F3Cla ^2 ~ (^2)0 — (сг,/<5)(£>і)0 + Mb2)F3C, li

For plain control surfaces the above equations are used with F3 = 1. (&,)0 and (b2)0 can be obtained from Fig. B.3,1 and B.3,2, respectively, for plain controls. For nose – balanced controls, the two-dimensional coefficients (&,)0 and (b2)0 must include the effect of nose-balance. Values of C/a can be obtained from Sec. B. l, and those for Cu from Fig. B.2,1.

Lifting-surface theory was applied to unswept wings with elliptic spanwise lift distribution to derive the factors. Full-span control surfaces were assumed together with constant ratios of cf/c and constant values of (&,)0 and (b2)0 across the span. The factors apply to wings with taper ratios of 2 to 3 if c/c, (/;. )„ and (b2)0 do not vary by more than ± 10% from their average values.

Figure B.3,4 Finite-aspect-ratio corrections for two-dimensional plain and nose-balanced control hinge-moment coefficients (Cla per radian). (From Royal Aeronautical Society Data Sheet Controls 04.01.05.) “