Pumping a Foil Board Explained . . . with Skateboard

[surfinJ]

That is the reaction that the hop can bring out in the esthetically inspired surfer.
Watching the hop used past the needed one or two is a visual equivalent to the auditory nails on the chalkboard.

[peterwSUPr]

I'll admit I have not read all of the posts here in detail and watched the full length of the videos, but here are a few thoughts. 

I think the dude jumping up and down on the shortboard, if it works, might be trying to get up onto a plane.  A boat needs a lot more energy to get up onto a plane than to stay up on a plane.  He's trying to keep it up and planing perhaps?  Pumping a board windsurfing is trying to push it unto a plane.

I think the pumping of a foil is exactly the same as pumping a bike on a pump track, but I'm not sure we need to look at the radius and use angular momentum.  If you are high up on the foil and it has a downward glide angle it will glide forward and down.  If you accelerate your body upward it helps to drive the board forward more.  If you could instantly, once at the bottom, incline the board and foil upward, and bend your legs and sink down, the board would rise up as it glides forward.  Now, once at the top, instantly incline the board down and repeat.  Now of course we can't instantly change the angle, so it does end up looking more like a sine wave than a triangular wave, but I don't think the radius is a key to this, other than it has to match how we can move our board and body.

As for pumping side to side, you are essentially falling of to one side and pushing your body one way and the board accelerates the other way, then you catch yourself and go the other way.  I've done it on ice skates, but can't say I'd ever seen the upper body motion like that on a skate board in the first video.

Peter