The hydraulic pogo

Here we are not trusting Hop's equations for time-of-flight, but trusting the basics for commutes local-enough to redo them linearly.

Notion is: power-source on the pogo pushes against the surface. Up you go into space. Expend more power: wind back the spring. Down you go onto the surface. Boing again. Repeat. Eventually you've got enough stored momentum that your last kick back can be at an angle. Orbit!

Oh what fun. Now, let's get started on something "practical". Say we want lunar pogo-bounce as does 200 meters at a time for about 28 mph sideways; hitting the ground at a 45° angle for 40 mph, each bounce. First let us anticipate the question - who wants this.

First answer: whoever hated those MAKO missions in the first Mass Effect. 45° will clear many obstacles. Maximum height won't be that full cos(π/4) x whatever-meters up; but with a 40 mph initial velocity-budget, you can adjust angle accordingly.

Also the mechanism can store and expend energy per bounce. Say the problem is 200 m out. You plot 100 m, 50 m, 25 m. Next jump can be more than 40 mph. This before we get into battery-storage perhaps with solar panels.

I'd assume the computer would auto-plot the best route in advance. Or at least assist you.

Major issue: safety. The inner cabin needs to cushion the blows. Start with Earthlings, Luna's first (so seasonal) visitors. We like it 9.8 m/s². As the pogo hits the ground, we exert 8.18 m/s² upward, to turn the 28 down mph into 28 up again whilst delivering that 9.8 m/s² to the passengers. So, about 6.9 seconds of upthrust.

Three and a half seconds away at maybe 18 m/s along this diagonal end of its arc means the pogo's "stick" has to extend 62.3 meters out. So a third of its time pushing up, a third swinging around the extended piston to point forward (1/6 to apex, 1/6 going down), last third pushing down. Will need to expend energy moving the piston.

I am thinking less "coiled metal spring" and more "hydraulic". Do we own a fluid that can compress 65 meters in 3.5 seconds, and bounce back? Probably; but how much total length would be needed? It would be a cylinder, so we'd also ask diameter. 20x150 m? Superheavy is 9 x 68 m; Empire State is 380 m. Why not.

Inertia of this mass filled with hydraulic fluid plus, you know, cargo will be an issue. Once set on its route, it cannot easily change said route. In case of emergency, dump the fluid and eject the passengers. (Loonies don't use parachutes; they use inflatable cushions.)

I already did the maths to pogo a mile at a time on the Moon: a full kilometer of pure hydraulics. LOL! But . . .

Ceres and Callisto let you boiiiing that mile faster and I think the angle be lower. And if they wanted total 9.8 m/s² they could get that with more upward force than 8.18 m/s². So less time to upthrust; less length of hydraulic.

I think the pogo is "feasible" on the Moon for 200 m at a bounce. Callisto and more so Ceres are looking good for 500 m bounces. And from Deimos... well, that station will be docked to it, not on it.

UPDATE 12/13: ... for certain values of "feasible". Dude. Just use electric-augmented trampolines. Or even Elon's vacu-suck.

UPDATE 3/8/22: Keeping in mind that the Moon is dusty. Offroad driving has speedlimits. For ballistic bounce the only limit - the only speed - is from Kepler.