Warning: This is a little off topic. Also numbers are involved, but in a good way. That said…
Quick Summary
Free falling on your surfboard and landing upright can be brutal, even when falling a mere meter.
How much force?
Case 1. Free Falling (… when the ‘air’ goes bad?)
Lets say you find yourself and board a mere 1 meter above the surface of the water and dropping towards that surface. An ‘air’ gone bad? Who knows.
We know that, neglecting air resistance (you’re only dropping a meter with zero initial velocity, so this isn’t that much of a stretch), the time it will take you to fall will be given by the square root of [ 2 times the distance you’re about to fall divided by the acceleration due to gravity (9.8 meter per second squared)]. Here, falling a mere meter means you’ll fall for a short 0.45 seconds. We also know that in falling through the gravitational field you’ll acquire some velocity, and it can be calculated by the time you just calculated (0.45 s) times the acceleration due to gravity, which gives a speed 4.4 meters per second upon impact with the water.
Now for a collision with a head on flow, you can approximate the mayhem using something engineers call stagnation pressure, its given by one-half times the density of the fluid times the fluid velocity squared. If you want the total force, you just times that by the area of impact. Here, using a density of sea water of 1025 kg per meter cubed, and say your where on your 6’6” or something like that, which has a total bottom area of say 0.8 meter squared, you get a force of 793 N. Big deal? Lets see, we’ll compare it to your weight.
Your mass is a mere 63.5 kg, or in the Land of the Free (and slightly retarded when it comes to things metric), your weight is 145 lb. In metric, you weight is of course, 622 N –i.e. mass times the acceleration due to gravity.
What a difference a little air makes, huh? Here the fall is only a meter. You may wish to do it for 2 meters, or use the bottom area of your big boy thruster(?) But the real killer, in the free fall case, is the surface area - it works against you. Here, when coming down from such a drop, virtually the whole board can impact the water, in fact its a matter of style to make it so. However, most of the time, when surfing, the wetted area is usually significantly less than half the value of the whole board’s bottom.
So, you’ve got the formulae, you’ve got the logic, you’ve got all you need to estimate the 'slap’ force an ‘air gone bad.’
One point is certain, free falling and ‘slapping’ the surface like a belly flop is likely to be brutal on a board. As a design consideration, it is a unique case. Factor it in if you care to, or simply request that customers avoid the full belly flop when ‘airs go bad’, or on air landings of any kind (… yeah, good luck with that.)
As always, somebody check my Math, please.
kc