Everything you know is wrong, but it doesn't really matter.
Dave Gardner came over to the house yesterday. He brought some plots of flap control horn angles. He convinced me that if the bellcrank is in the plane of the wing, it's best to have the flap control horn input arm vertical. Then I used my cool program to check this, and either the program has an error, or the three-dimensionality of the problem complicates it more than we thought. Attached is the upchuck. As you can see from the inputs, it's a 4" bellcrank and 1.5" flap control horn, the bellcrank is straight in neutral, and the leadouts come straight out the wing. I had Excel put some "trendlines" (the fine, black lines) on the flap plots. They are the second-order curves that best fit the flap curves. Trendline equations are next to each flap curve.
Pretty cool, but I'd expect that wing centerline, thrust line, and placement of the horizontal tail (all three WRT their vertical realtionship to the
airplane's center of gravity play a larger role in control response) and any differences between inside and outside manuvers than the relatively small changes in surface deflections due the control geometry shown.
Let's say the wing is below the entire aircraft's CG. The drag from the wing is causing a nose-down pitching moment. The tail is above the CG, now we have a nose up contribution. If the engine is also above the CG, we get a negative moment from the thrust. There are also pitching moments due to the lift of the wing and the lift of the tail.
Without calculating the stability derivatives and knowing the control derivatives it's all just a crapshoot, and once again, it's the response of an airplane that matters.
Remember, Quantum Physics is for the guys that flunked out of Stability and Control, he, he.