Steam Piston Pogo Stick

A piston steam engine, for a pogo stick, is likely rather technically simpler than an internal-combustion-engine pogo stick. You need a water tank, a "flash" boiler (link), a steam-condenser, and a water pump (for moving water from the tank into the steam generator, against the steam pressure).

I think a quite-small-diameter piston-powered water pump, and a simple connecting rod between it and the main pogo-stick piston-shaft, can be workable. More complicated (but still necessarily mechanical, for this Idea to qualify as "steam-punk") will be the control system for the main power cylinder valves.

The best thing about this Idea is that the rate at which steam needs to be generated is much lower than in any other type of steam engine, simply because the piston cycles so slowly in normal pogo-stick operation. This should make it quite easy to condense the steam as fast as it is generated (normally it is very difficult to completely recycle the water used in a steam engine, because there is too much waste heat to dump).

It should be noted that as the water is recycled, the temperature of the water in the water tank should rise to almost --but not quite-- the boiling point. There is no reason to try to cool the condensed steam any more, than a little below the boiling point, after it condenses from vapor to liquid.

In fact, what we would like to have happen, to the extent possible, is for some of the steam to condense inside the power cylinder near the end of the power stroke. Use of the "heat of vaporization" (linked) qualifies as a loophole in how the "Carnot Cycle" (linked) specifies the efficiency of a heat-engine (allows the engine to be MORE efficient). Only the steam that doesn't condense needs some cooling to become also-condensed.

Well, that's all.