just to add the chordwise load distribution over flapped wing sections was given special treatment by Julian Allen in a paper titled " calculation of chordwise load distribution over airfoil sections with plain split or serially hinged trailing edged flaps". NACA report 634,1938
just as an aside in engineering the way certain comparisons in terms of 'efficiency are made' is to compare an ideal [or simplified] theoretical condition to the real condition as mentioned above this simpliedied section is basically a simple flap compared to the real flap this is the flap chord ratio and it is this ration that is the 'efficiency factor mentioned in one of the above post,...so how does one do so?
well the equations are too cumbersome for here but basically when design ing the section,...data from other designs is used,...so that makes these questions well within the realm of experiemtnal engineering would not everyone agree
Munk's integrals have also proven useful in this area
