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EDITOR'S NOTE

Adapted from equations appearing in HPeJ article 010, here is a useful method to work out the speed for downhill coasting at a specified time after starting from rest.

First solve the following intermediates;

X = mass
Y = mass * g * [sine(angle) - Crr]
Z = CdA * air density * 0.5

Complete by solving for speed (v);

v = sqrt(Y/Z) * tanh(sqrt(Y*Z)/X*time)

Example:

Inputs:  time = 60 (seconds),mass = 102 (kg), g = 9.81 (m/s^2), angle = .05 (rad), Crr = 0.005 (n/n), air density = 1.05 (kg/m2),CdA = 0.5 (m2), X = 102 (calculated), Y = 45.01 (calculated), Z = 0.25 (calculated)

Results:  v = 12.66 m/s

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