slim_slag
Despite this being a splendid walk-through of Newtonian Physics, sadly it has limited real-world applicability...
Ignoring, for a moment, the non-linear acceleration of aircraft on the ground
, the 71% Vr by 50% distance is really only relevant when the TORA is equal to distance required to achieve Vr - which in the majority of cases is not true...
If
all continue/stop decisions were based on being at 75% Vr by 50% of
theoretical "d", most take-offs would be abandoned despite miles of clear runway ahead - perhaps a little too conservative if we want to be pilots and not taxi-ers
But I can see where you're coming from and agree that if you aren't at 75% Vr by 50% of TORA you should abandon (which I think is what you set-out to prove
)
Remembering that this whole discussion started with a comment from a student (with instructor present) who struggled to get airborne on a faltering engine, it would have been an excellent learning experience for said student to have calculated accelerate distances
under those specific conditions and seen where his go/no-go point should have been. I doubt the instructor asked for this to be done though, either pre or post-flight.