Larry G is Larry Goddard -
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Thanks! But now my head hurts! LOL!
Physics and Algebra. Civil dialogue. The Golden Era of Sways.
This may get exiled to a science only sub-forum.
Swaylocks Surfboard Design Forum: thoughts & theories ... practical & theoretical
RAIL PROFILE http://bgboard.blogspot.com/2014/03/march-82014-afterr-seeing-recent.html
Lol! physics and MATH!....PFFT!....there's an app for that!
Taking it to the max: Even recording EEG during a surf session!
Hopefully I have caught all of the typos.
The upper limit speed of a surfer/surfboard on a wave is a simple calculation. This upper limit speed assumes no drag/friction or upward movement of water in the wave face. Actual maximum surfing speed would be slower.
The calculation is simple high school physics and algebra. Maximum surfing speed cannot be greater than the free-fall speed (Vmax) of a surfer falling from a height equal to the height of the wave.
Vmax = square root of 2gh
g = gravity (32 ft/sec^2 or 9.8 m/sec^2)
h = height (in this case wave height)
The first table at the bottom of the post shows the upper limit, free-fall, surfing speeds for several wave heights (assuming no friction and no upward movement of water in the wave face.)
The minimum surfing speed cannot be less than the wave speed (C). Surfable waves are shallow water waves. Approximate wave speed can be calculated with the following equation.
C = square root of dg
d = depth
Water depth for breaking waves depends on wave types (Galvin, 1968; J. Geophys. Res.)
For plunging waves, d = 0.9h
For spilling waves, d = 1.2h
d = water depth
h = wave height
(Speeds for several heights of plunging and spilling waves are shown in the tables at the bottom of this post.)
The maximum angle of surfboard travel (A) relative the direction of wave travel is determined by the maximum surfing speed.
CosA = wave speed (C) divided by maximum surfing speed (Vmax)
CosA = C/Vmax
Assuming no friction or upward water movement in the wave face, (using high school trigonometry) approximate maximum values of angle A would be;
48 degrees for plunging waves,
39 degrees for spilling waves.
The form of surfing waves will range from plunging to spilling.
Maximum speed of a surfer at the bottom of a wave (curved ramp/inclined plane) cannot be faster than free-fall speed.
I'm not trying to fault your maths, but it seems that there are two components of speed. the first is resultant speed of the surfer in the direction of the wave. The second is the speed with which the surfer traverses the wave face. It would seem that the resultant vector would be longer than just the speed in the direction of the wave. I'm happy to be convinced otherwise.
"In Snapper Rocks, Mick Fanning is currently the fastest surfer. The Australian champion recorded a maximum speed of 39,1 km/h. In second place, Joel Parkinson stands with 34,6 km/h. Bede Durbidge is third (33,6 km/h) and 10-time world champion Kelly Slater places in fourth (32 km/h)."
The numbers in Imperial are 24.3; 21.5; 20.9; 19.9 mph which match well with your estimations for one vector.
Don't know which day they measured speeds in the article, but the surf looked to be in the 4-6' range http://www.worldsurfleague.com/posts/16096/round-4-and-5-highlights-2011-quiksilver-pro-australia?serializedFilterBy=e235
I meant to reply to Stoneburners post Nr 88, not Nr 89.
Stoneburner, I think your conclusion is wrong: The maximum attainable surfing speed on a wave is not limited by the free fall speed that would be attained when falling the height of the waves face.
I have measured a top speed of about 45km/h surfing waves with faces around 3-4m high, but according to your hypothesis, the waves would have had to have 8m faces.