Fall Speed and Time with Air Resistance (from Distance)
From terminal velocity and fall distance, compute the impact speed and time with air resistance, and compare with a vacuum drop.
Input
Enter the terminal velocity and fall distance to compute the impact speed and time including air resistance.
The final fall speed where drag balances gravity.
Distance fallen starting from rest.
Gravity uses standard gravity g = 9.80665 m/s squared.
Result
Impact speed
36.866882m/s
Time taken
4.816221s
Terminal velocity
50 m/s
Fraction of terminal velocity
73.733763 %
Impact speed (km/h)
132.720774 km/h
Vacuum speed
44.286906 m/s
Speed difference vs vacuum
7.420024 m/s
Time difference vs vacuum
0.300213 s
Speed uses v = v_t × sqrt(1 − exp(−2gd / v_t squared)) and time uses t = (v_t / g) × artanh(v / v_t). Vacuum uses v = sqrt(2gd) and t = sqrt(2d / g).
How it works
- Assumes quadratic drag (proportional to the square of speed), parameterized by the terminal velocity v_t.
- The speed at distance d is v=v_t·sqrt(1−exp(−2gd/v_t squared)) in m/s.
- The time follows from v=v_t·tanh(gt/v_t), giving t=(v_t/g)·artanh(v/v_t) in seconds.
- Vacuum (no drag) reference values are v=sqrt(2gd) and t=sqrt(2d/g).
- Gravity uses standard gravity g=9.80665 m/s squared.
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Fall Speed and Time with Air Resistance (from Distance)