Deflecting an aileron will increase or decrease the camber of the outer wing where the aileron is attached. I learnt on this platform that centre of pressure (c.p.) moves fore and aft with aileron deflection.
Is the c.p. movement as a result of aileron deflection significant? If it is significant, how does one calculate the difference in c.p. with respect to aileron upward or downward deflection?
The CP of local sections where the ailerons are deflected should shift aft. In an asymmetric deflection case, very little pitch moment would be generated. For symmetric deflection (e.g. maneuver load alleviation, flaperon), there will be a net pitch moment, but should be small due to the outboard location of the panels, unless the wing is highly swept.
To estimate the effect, you can view ailerons as part-span plain flaps. You can use any of the semi-analytical methods from ESDU, DATCOM or Roskam. You can also use any vortex lattice method to get the answer. The estimates should agree fairly well for small deflections and low Mach.