I'm renaming Crafty's post so that it's easier identify:
Can Someone Much Smarter Than Me Explain ...
No I'm not smarter, but I'd like to talk about it anyway...
I don't think Dan's reasoning is sound. This is not criticism of Dan because I can't explain the hydrodynamics of surfing, myself. So, I think we should give him some credit for trying.
Let me try to reason some things out conceptually:
(as always, if you know better than me, Please! correct me)
1)Dan's claim: If you decrease surface area, pressure drops which means velocity increases. I wasn't sure if he was referring to width of the board decreasing or thickness of the rail decreasing, or both. But either way, if you drop the pressure below the board or along its rail, that should effectively pull the board into the water. And if the board is deeper in the water, there is more resistance to movement. You can't increase velocity and displace more water because that would mean your doing more work on the water. The universe is lazy, it will always choose the path of least work. Does this mean that bernoulli and dan are wrong? Bernoulli's equation is a derivation of physical law, which means that it can't be wrong---however! it can be misapplied/misunderstood/misused. Same for Dan's lift equation, which I don't think is bernoulli's???
2)I think Bernoulli's equation essentially says that, if you push 1 gallon of water in one end of a pipe, 1 gallon of water must come out the other end of the pipe, water can't just disappear. If you have a CLOSED SYSTEM, the in-flux and the out-flux have to be the same (flux is change in volume over time). So if you take a pipe, where the entrance is twice as large as the the exit. The velocity going in must be 1/2 the the velocity going out, so that the flux is the same.
"Closed System" is the key phrase. When looking at a physical phenomenon, you have to draw a boundary around the subject (enclose the subject) then define the conditions on the boundaries (scientist call these boundary conditions). In my experience, 90% of error comes from people drawing the wrong boundaries and defining the wrong boundary conditions (academic engineers say "trash in = trash out"). Enclosing a surfer on a wave (drawing the boundaries and defining boundary conditions) is more difficult than any engineering problem today, I'm not kidding or exaggerating. That's why the Millennium Prize was created for whoever makes gains with the Navier-Stokes equations. It's easy to identify which boundary conditions are wrong, but quite difficult to say what conditions are right. It's easy to say Dan is wrong, but much more difficult to say what is right.
3) Back to Dan's Lift equation. I think he made the wrong assumptions. The equation may apply better for a foil moving through a homogeneous fluid like air. But, a surfboard is traveling on the boundary of two fluids, water and air. To make things worse! one fluid is 800 times as dense as the other, AND one likes to cling to itself while the other repels itself. So pressure diffusion will be different in all directions...or water will move in some directions easier than others.
That's about as far as I can go at this point. I'll think about this for the next few years and get back to you guys.