But the process isn’t energy-limited — it’s displacement limited. Your arms have a certain length, your body has a certain mass distribution, and you can force

But the process isn’t energy-limited — it’s displacement limited. Your arms have a certain length, your body has a certain mass distribution, and you can force the angle by a certain amount. So, if you want a heuristic, integrate pumping displacement times swing position, where the pumping displacement has a fixed maximum. The result is maximized by a square wave.