Genghis,
The five variables for lateral control that are taken into account are the runway crab angle, main gear reactions, lateral control deflections, rudder deflection, and the nose gear steering angle.
Two assumptions are made, that the pilot want to keep the aircraft on the runway, and does so without winging over, so the nose gear steering angle and aileron deflections are assumed values.
The other control deflections are a function of dynamic pressure.
The longitudinal control equations (3 of) includes the drag coefficient of the aircraft in ground effect, all as a function of dynamic pressure.
Using these equations, and the engine thrust model one can deduce the takeoff ground run, not that I have seen anyone go to all the effort, just longitudinal control.
The Jeppesen airport analysis manual we use only factors head and tail winds.
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It is possible to fly without motors, but not without knowledge and skill.
— Wilbur Wright