see AC25-7C, 29.d(5)(d) (on page 131 of the AC) for an "official" description of the correction
That test method is doing the opposite - it's a parametric method of measuring the Cl(max) of a real aeroplane by observing that Cl(max) normally occurs just before the stall and then measuring stall speed. From that, using the equation for lift coefficient, it is possible to use the relevant factors (dynamic pressure, aircraft weight, load factor, reference area etc) to calculate the actual Cl at the stall (assumed to be Cl(max)).
The correction factors you are talking about are those which are then applied to attempt to remove the sources of error in that test method - like the tailplane download adding to weight, the vertical component of thrust from the engine reducing weight and mach number corrections.
So it is using the variation in stall speed with CG position to calculate the Cl(max), not measuring a variation in Cl(max) with CG position. To clarify this point I'll go back to your original question:
Originally Posted by
myrbobtat
Can anyone point me to the equation which corrects CLmax for a change in CG? In other words, if CLmax is measured to be 2.4 at 20% CG, what would the equation be to estimate CLmax at say 7% fwd CG? (all else being constant, e.g. weight + alt).
The answer would be that if the method works the Cl(max) calculated for the 7% fwd CG would also be 2.4, but the airspeeds at which the stalls occurred (the test parameter being measured) would be different. The algorithms given in AC25-7C, 29.d(5)(d) would then (hopefully) yield the same Cl(max) from the two different airspeeds.