dynamics&forces of hydrofoil wave surfing I'm puzzled by apparent ability of hydrofoil to surf [ocean's] wave, as evidenced by this footage.
Let's compare it to ordinary surfboard. Let's focus on "static" condition when the board is position is steady relatively to the wave crest. Then the board is inclined and the angle provides a fraction of gravitational force (green) opposing the friction (red) thus maintaining the board's horizontal movement together with wave front. 

The steeper the wave, the larger the green component of gravitational force, so that it would be higher than friction thus accelerating board down the slope. 
What happens when the board forces are defined not by the interaction board and water surface but hydrofoil under the surface? Horizontal movement dictates that hydrofoil has to be at zero angle (minus angle of attack necessary for hydrofoil overcome the weight). But then, what is the source of horizontal force necessary to counteract the friction?   
P.S. After drawing the image it seems to me that the picture for hydrofoil forces would be essentially the same (modulo the nature of the normal force). The only limitation is for the hydrofoil angle of attack being less than the wave slope (otherwise the normal force orientation is in wrong direction).
 A: You say:

Horizontal movement dictates that hydrofoil has to be at zero angle (minus angle of attack necessary for hydrofoil overcome the weight).

You could make the same argument about a surfboard; if it weren't horizontal, its movement across/through the water would make it go up or down. In both cases, you'd be missing the point.
At the point of contact of a surfboard, the water is moving upwards as part of the leading edge of the wave. Since the surfboard is moving forwards, the net motion of the board versus the water is a vector pointing down and forwards, matching the angle of the board. The weight of the surfer presses the board down against the water, resulting in a net force forward.
The exact same argument applies to the foilboard. The hydrofoil is only a little below the surface of the water, so it, too, contacts water that is rising with the leading edge of the wave. As the surfer moves forward, the net vector is again pointing down and forwards, matching the angle of the hydrofoil. And, the weight of the surfer presses the foil down against the water, resulting in a net force forward.
