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How can you predict the change in lift and pitching moment produced by control surface at a certain deflection angle?
I am aware that the effectiveness of the control surface is affected by compressibility. At subsonic speed the contribution to the change in lift force will be higher, but at supersonic speed it decreases significantly. How will the pitching moment change due to deflection of the control surface in either case?

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  • $\begingroup$ Sections 6.1.1 and 6.1.2 of this USAF DATCOM should answer your question in a very good and simple way. $\endgroup$
    – sophit
    Oct 11 at 17:11

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@sophit mentions DATCOM -- it is a good start.

In general, how are you predicting aerodynamic forces and moments in the first place? We generally predict control surface contributions to forces and moments using the same tools and techniques.

This can be as simple as thin airfoil theory -- there are tools based on thin airfoil theory to predict the effect of a plain flap deflection.

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