Originally posted by 3WE
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The REAL problem we discussed while beating this dead horse dead again and again is what happens when you DO NOT reject the take off, which is what (almost) ALWAYS happens in the accidents and incidents involving a sub-par take-off scenario. So Vr is the problem.
So say for example that you mixed up 2 numbers and instead of calculating the take off with your actual weight of 53000 lb you input 35000 lb.
Now you get a given Vr and a given distance, and with that Vr comes a Vlo (lift-off) which is not shown to the pilot but is part of the "internal" algorithm.
Is your filed length is more than the minimum needed, V1 is selectable within a range that ensures that you can reject at V1 and stop, or lose an engine at V1 and lift off, both within the the runway length (which is why Vlo is part of the internal algorithm).
Vr is NOT selectable. Is unique for each scenario. And a unique Vlo and lift-off distance comes with it.
But the acceleration will be 35/53=66% of the assumed one.
And, to make things worse, to generate a lift equal to the increased weight you will need a speed sqrt(53/35)= 1.23 the calculated speed
Since the distance needed to achieve a given speed is given by D = V^2 / 2A, we can write the assumed and real scenarios as
Assumed: D1 = V1^2 /2A1
Real: D2 = V2^2 / 2A2 = (1.23V1)^2 / 2(0.66A1) = 2.29 * V1^2 / 2A1 = 2.3 D1
The real distance you will need to get the plane in the air is more than twice what you thought it would take.
And there is NOTHING to alert you that you are accelerating less than expected and will need more speed and much more distance than expected.
Good luck.
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