Originally Posted by
Patrick Illner
I got the equation from a Bachelor Thesis. Unfortunately the professor does not have time to explain neither the equation nor my calculations to me. That is why I am asking here.
I am by no means capable of coming up with this equation on my own.
The 1700m are from flyAPG. But you are correct it is the TODR. So I figure from Lift Off to 35/50feet takes about 200m. So the ground roll is about 1500m, which at 18100 pounds seems realistic for me.
I think the ratio for ground roll to TODR is probably closer to 2/3, so TODR 1700m, ground roll 1100m, but I am guessing here. I flew the CJ3, TODR is 3200ft, was almost always of the ground by 2000ft.
Honestly, I don't really understand the formula, but I will see how far I get:
The 1/2 and top of the equation is: 1/2 * m * v^2. This is the formula for kinetic energy.
The bottom of the equitation is T-D-F-Rwy slope.
So Thrust [N] - ("aerodynamic"(not really)) Drag [N] - (ground friction) Drag [N] - Loss/Gain of energy due to runway slope [N] , so basically the sum of all the horizontal forces or the net force on the aircraft.
Work is equal to the Force multiplied by the distance, so distance is Work divided by force.
The work done on an object by a net force equals the kinetic energy, so the distance traveled is the kinetic energy (top) divided by the total net force (bottom).
Where this equation doesn't make sense is that it puts the classic lift and drag formulas into a ground roll equation. Until you start your rotation the drag comes from 2 sources: the rolling drag from the wheels, and the aerodynamic drag from the whole aircraft. The D in the formula should be zero because it relates to induced drag associated with flying at an angle of attack that creates lift, and we really don't while rolling down the runway. I don't know where the friction coefficient of 0.04 comes from (scrambled eggs on a Teflon pan?), but I assume it is the friction coefficient for a tire on a runway, but we shouldn't subtract anything from it for lift until we rotate, so L should be zero until then. The part about runway slope could be correct. It uses v=.707vlof as an average speed but there is no L or D till rotation, and the formula has ZERO real aerodynamic drag in the equation.
I honestly think it isn't a time issue preventing your professor from explaining this equation, i think it is just plain incorrect, and unusable in any practical way.