As an avid mountain biker who also peruses bike forums - this article really unlocked my understanding of how pumping a foil works (from a physics standpoint) and helped me refine my technique:
How to Pump Your Bike, According to Physics - Pinkbike
Pumping a foil uses the same technique of increasing speed through conservation of angular momentum - except with a foil we are free to move the foil through a curve anywhere (similar to how you pump a surf skate on flat pavement).
If you watch good pumpers on the foil - they extend their arms upwards as the extend their legs through the pump. This works to further raise their center of mass off the foil and gives more speed / a more effective pump.
This video is a breakdown of the same technique, but used to generate speed on a surfboard:
How to Generate Speed | The Pumping Technique - Learn How Advanced Surfers Accelerate. (youtube.com)
Here’s an old video of me which shows the leg extension timing through the pump (my pumping has gotten a lot better since this was taken):
Hope this helps someone!
