All this fancy aerodynamics stuff is all well and good, but has nothing to do with a body moving along a surface under a constant force.
Well yes, that's the point really. A body moving along a surface under a constant [net] force (your analysis) is not very closely related to reality.
The problem is that it
doesn't err on the side of safety. You could well be and 45 kt 2500 ft into your 5000 ft runway and not make it to 60 kts by 5000 ft. That's because your acceleration decreases as your speed increases. Your assumption of constant acceleration is optimistic.
I think the principle of assessing your speed at some point on the runway and aborting if it is below a certain speed is a good principle. But if someone takes your numbers literally, they could end up in the fence at the end.
I wrote:
You also neglect the wind in your assessment. A headwind makes matters worse still.
to which kingy replied:
Ok, if I understand this correctly you are saying a headwind on takeoff makes take off distance Longer!
I could have chosen my words better! -- that's
not what I meant. I meant that in the case of a headwind, the proportion of distance at which 71% speed is reached is even further away from the 50% distance in slim_slag's constant acceleration case. Does that clarify?