That’s just how pendulum frequency scales with size. You have a sqrt(X) period with X distance, so sqrt(X) speed, so X energy over sqrt(X) time.
You can also consider a jumping robot, which accelerates at a constant rate for a fixed % of its height. The final speed and time taken are both sqrt(X).
Why is this? Is there some reason why the power available goes as height^3.5, or is this a requirement for achieving the height^0.5 walking speed?
That’s just how pendulum frequency scales with size. You have a sqrt(X) period with X distance, so sqrt(X) speed, so X energy over sqrt(X) time.
You can also consider a jumping robot, which accelerates at a constant rate for a fixed % of its height. The final speed and time taken are both sqrt(X).