That’s a pretty good approximation, actually. And yes, I am gonna regret getting into this one, but here we go.
Lets break these forces down into two vectors: those that accellerate the surfcraft in question and those that retard it. Push and drag, if you will.
Accelleration forces for something travelling along a wave in a straight path, not turning? Well, I make that to be MG sin A, where A is the angle taken with the horizontal. At the extremes, you’d be either freefalling down the face of the wave or slowing to a stop on the flat with no accelleration at all. No other forces are really having much effect on accelleration.
That’s Physics 1, ‘motion’ - see http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/index.htm , with videos. It’s kinda cool.
What’s slowing the thing down, or at any rate defining the terminal velocity? Drag. All surfcraft are planing hulls, not buoyant hulls ( displacement hulls) when in use on a wave. No matter what sort of silliness surf terminology give’s 'em.
Planing hulls can be defined as something travelling greater than 2 times the square root of the waterline length ( in feet ) expressed in miles per hour. Displacement hulls are those that travel at less than 1.34 times the square root, etc.
Doing the math, a displacement hull that’s travelling at 20 MPH ( a not unreasonable speed for a surfcraft) would have to be 225 feet long, which really would give a new meaning to the term ‘longboard’, ya know?
Nope, they’re all planing, the effect of buoyancy is nil. Take buoyancy and save it for paddling. Along with waterline length.
Okay, so how do they plane? They push against water, generating lift. The heavier the surfcraft-rider combination, the more lift needs to be generated. All other things being equal, though, the faster ya go, the more lift per unit area is generated, so that less of the board is in contact with the water. But the drag also goes up with speed, so ya reach a balance where acelleration times mass equals drag - terminal velocity, as Herb says. There’s also small drags from fins, rails and what have you, but pushing against the water to generate lift is prolly the main component of drag.
Waterflow up the face of the wave? Naaah. If you think about it, if there was waterflow up the face of the wave to any real extent then what would happen?
Ah huh. When a wave broke, it wouldn’t throw out a lip in front, it’s throw out a lip in back. But…it doesn’t. Instead, the elliptical form of the wave rolling along hits something shallow, breaks and throws out the front.
What would make you think there was something like this going on? Well now - as the wave is moving, the water actually stays put. So you’re going along in the direction the wave is moving through water that’s pretty much staying put until the wave itself is breaking and actually coming over.
Air drag - not a helluva lot compared to water drag unless you’re really, really moving fast. Like ( again, as Herb says ) 150 miles an hour. It’s not an important component.
Now, that’s simplified, but it’s a start. Also, if you think about surfcraft as things that kinda find their own dynamic equilibrium, it’s helpful.
have fun
doc…
also- have fun with http://ocw.mit.edu/OcwWeb/Mechanical-Engineering/2-20Spring-2005/CourseHome/index.htm MIT’s Marine Hydrodynamics intro course. Also very cool, but no videos…