Expert: Paul Soderman - 8/21/2009

Question
I need to know how much force does it take to move a flap from zero wind to knot and mach numbers thankyou for the calculators or formulas

Answer
As you have surmised, when a flap is deflected the flap loading will increase, which can be represented by a single force operating a certain distance from the flap hinge.  The resulting hinge moment must then be countered by a moment generated by the control system or the flap will float to a new position.  As there are many kinds of flaps, there is no one formula that can be derived to handle all situations.  In fact, wind tunnel tests are usually employed to get this type of information because the theoretical predictions are very complex and often in error.  Some flaps change area as well as angle.  The hinge line itself can be any distance aft of the nose as chosen by the designer to control the hinge moment.  And the wing boundary layer is involved.  So to answer your question I need to know much more about the details of your flap assuming I could find the proper wind tunnel data.

The hinge moment depends on moment due to control surface deflection plus moment due to change in angle of attack. As an example, consider an NACA 0009 airfoil flap.  The hinge moment depends on flap chord relative to airfoil chord.  For a flap chord to airfoil chord ratio of 0.2, the hinge moment coefficient due to flap deflection is -.012 and the hinge moment coefficient due to angle of attack is -.0045 where the coefficient is defined as:

Ch = HM/(q S c)

HM = hinge moment
q = dynamic pressure
S = control surface area aft of the hinge line
c = root mean square chord of the control surface aft of the hinge line

A negative moment coefficient means that the flap is trying to float up.  For a flap chord to wing chord ratio of 0.4, the coefficients become -.015 and -.010 respectively.  (The curves are linear above a chord ratio of 0.2.)

For details see:  R. Sears -  Wind Tunnel Data on the Aerodynamic Characteristics of Airplane Control Surfaces, NACA WR L-663 (date unknown).  I found this in Airplane Performance Stability and Control by Perkins and Hage, Wiley  & Sons pub, 1963.  The above data must be corrected for flap nose gap and hinge line setback.
Paul