My brother and I both agree that ultimate surfer speed on a wave is accurately described by by Vult = C + Vmax.

While not a perfect example, the following is a good example demonstrating the additive speed of a surfboard dropping down the face of a wave traveling at speed C.

A train is moving down the ttrack at 8.2 mph. There is a skateboarder on top of a 5-ft ramp inside a car pulled by the train. The stationary skateboarder and the ramp are moving along with the train at 8.2 mph.

Now the skateboarder leans forward and drops down the ramp. At the bottom of the ramp, the skateboarder shoots forward at 12.2 mph (Vmax) towards the front of the train -- 12.2 mph faster than the train is moving. Relative to the ground outside the train, the skateboarder is traveling at a speed of 20.4 mph (8.2 mph + 12.2 mph = 20.4 mph).

I am thinking an effective technology for measuring surfer/surfboard speed might be a hot-wire anemometer. It could be placed in the leading edge of a center fin or just in front of a center fin (minimal sensor drag).

I'm happy and thrilled that somebody else decided to analyze the question of wave speed and surfboard speed. It is not as straightforward a problem in Physics as some people might think.You want to calculate how fast the surfboard CAN or MUST go to stay just ahead of the breaking wave.

First, the analyst must make a few Assumptions (known mathematically as 'Prior Conditions'). Then, from that starting point, you only need a knowledge of wave dynamics and Physics, plus some first-year Algebra, to derive a Mathematical Model for finding the Surfer Speed, given the ACTUAL or TRUE Wave Height and the Peel Angle.

The TRUE height of anything means 'Top-to-Bottom', so that INCLUDES the unrideable portion of the wave that we call the TROUGH. It's below sea level, and the wave face is not steep enough down there to keep your board moving. After all, the board is sliding downhill, so If you go TOO low on a wave, your board will start to mush out and eventually will STALL. You want to calculate how fast the surfboard CAN or MUST go in order to stay just ahead of the breaking wave. Note that if you are riding a 'Head High' wave, your board is still about a foot or more ABOVE the bottom of the wave. If it LOOKS LIKE 5 feet (from the deck of your your surfboard to the top of the wave) , the TRUE height is actually about 6 to 6.25 feet.

You must use the TRUE height of the wave in my Surfer Speed model.
My model says that (for a Spilling wave, at least), you can go AS FAST in MPH, as 7 times the Square Root of the True Height, in feet, for a maximum Peel Angle of 53 degrees from Straight-Off. In GIANT surf, the maximum 'make-able' wave peel angle will be much less.

4 ft = 14 MPH

9 ft = 21 MPH
16 ft = 28 MPH
25 ft = 35 MPH (looks like 20 ft at Waimea Bay)
36 ft = 42 MPH (looks like 30 ft at Waimea Bay)
49 ft = 49 MPH

but,

100 ft = 70 MPH! (The peel angle at Nazare in Portugal is much lees than Makaha Point Break.

My model shows that the HIGHER you can get on a wave, (before it goes vertical), the STEEPER the wave face surface is, and the FASTER you can go! This works best for Spilling-type, fast-breaking long walls like Point Breaks. If you are approaching a fast section up ahead, and want to get around it, you need to climb HIGHER on the wave face so you can then dive lower going thru that section. You EXCHANGE Altitude (Potential Energy) for Speed (Kinetic Energy). Your Total Energy while riding on a wave is the SUM of Potential Energy and Kinetic Energy.

BUT, If you wish to position yourself INSIDE the Tube, you must ride well down on the face of a Plunging-Type Wave, where the wave face is not as STEEP. And LESS steep means you go SLOWER! So, you might even need to slow the board down a bit to match the speed of the tube. That's all right: It's pretty exciting inside the 'Green Room'!

Surfers who use so-called "LOCAL Scale", which is based on the old 'Hawaiian Scale' from the 1950s and 1960s, should be aware that the old U.S. Weather Bureau used METRIC, only expressed in "HALF-Meters" rather than METERS. So, a Half meter is about half of 39.37", or about 19.685 inches. If you round that up slightly to simply 20 inches, then a wave that looks like '5 feet' (or 60") is "3 Half-meters, Hawaiian Scale (NOT FEET!). The True Height might be 6 feet, so the Hawaiian Scale is about 1/2 of the True Height, if you include the Trough.

Bob, few surfers have the patience to read my original treatment of "Surfer Speed vs.Wave Height", so if you want to send the above to Swaylocks, I'd much appreciate it.

Thanks for that Bob. I didn’t know that Larry was still active in the surfing arena, he has some long standing design ideas that will probabaly prove to be prophetic in years to come.

Surfing is in his blood. He has some long term interests, such as surf forecasting. I haven't asked if he's getting wet much these days. His speed post was prompted by some photos I sent him of a recent South African trip.

Please thank Larry on my behalf for following the add-on discussion to your post of his work and Larry's accompanying posts. Larry did a great job. My work was/is in no way intended to refute Larry's.

I approached this to get a general idea about speed and foil size for hydrofoil surfboards. I read Larry's posts after I had done my first round of calculations that followed my post in Brett's hydrofoil thread.

My calculations were to determine the absolute maximum (ultimate) instantaneous surfer speed that is possible while obeying the laws of physics. My calculations also assume frictionless acceleration and velocity. Wave height is assumed to be measured from trough to crest/peak -- a liquid skateboarder's ramp. Also, I used Cyril J. Galvin's research (1968) for my wave speed estimates.

I think most of us realize that a frictionless (ideal) wave, without water movement in the wave's face, does not exist in the real world (i.e. the line-up). Water movement toward and up the wave face, as well as drag, prevent this "upper limit" speed from ever happening.

The ultimate surfer speed equation (in the ideal environment) can be simplified as shown below. To see the derivation of these equations, go to the end of the blog post at this link:

surface area .

Surface area for sure. And related to velocity...

Swaylocks Surfboard Design Forum:thoughts & theories ... practical & theoreticalRAIL PROFILE http://bgboard.blogspot.com/2014/03/march-82014-afterr-seeing-recent.html

My brother and I both agree that ultimate surfer speed on a wave is accurately described by by

Vult= C + Vmax.While not a perfect example, the following is a good example demonstrating the additive speed of a surfboard dropping down the face of a wave traveling at speed C.

A train is moving down the ttrack at 8.2 mph. There is a skateboarder on top of a 5-ft ramp inside a car pulled by the train. The stationary skateboarder and the ramp are moving along with the train at 8.2 mph.

Now the skateboarder leans forward and drops down the ramp. At the bottom of the ramp, the skateboarder shoots forward at 12.2 mph (Vmax) towards the front of the train -- 12.2 mph faster than the train is moving. Relative to the ground outside the train, the skateboarder is traveling at a speed of 20.4 mph (8.2 mph + 12.2 mph = 20.4 mph).

Swaylocks Surfboard Design Forum:thoughts & theories ... practical & theoreticalRAIL PROFILE http://bgboard.blogspot.com/2014/03/march-82014-afterr-seeing-recent.html

I am thinking an effective technology for measuring surfer/surfboard speed might be a hot-wire anemometer. It could be placed in the leading edge of a center fin or just in front of a center fin (minimal sensor drag).

Swaylocks Surfboard Design Forum:thoughts & theories ... practical & theoreticalRAIL PROFILE http://bgboard.blogspot.com/2014/03/march-82014-afterr-seeing-recent.html

Larry Goddard asked if I could post his reply:

I'm happy and thrilled that somebody else decided to analyze the question of wave speed and surfboard speed. It is not as straightforward a problem in Physics as some people might think.You want to calculate how fast the surfboard CAN or MUST go to stay just ahead of the breaking wave.

First, the analyst must make a few Assumptions (known mathematically as 'Prior Conditions'). Then, from that starting point, you only need a knowledge of wave dynamics and Physics, plus some first-year Algebra, to derive a Mathematical Model for finding the Surfer Speed, given the ACTUAL or TRUE Wave Height and the Peel Angle.

The TRUE height of anything means 'Top-to-Bottom', so that INCLUDES the unrideable portion of the wave that we call the TROUGH. It's below sea level, and the wave face is not steep enough down there to keep your board moving. After all, the board is sliding downhill, so If you go TOO low on a wave, your board will start to mush out and eventually will STALL. You want to calculate how fast the surfboard CAN or MUST go in order to stay just ahead of the breaking wave. Note that if you are riding a 'Head High' wave, your board is still about a foot or more ABOVE the bottom of the wave. If it LOOKS LIKE 5 feet (from the deck of your your surfboard to the top of the wave) , the TRUE height is actually about 6 to 6.25 feet.

You must use the TRUE height of the wave in my Surfer Speed model.

My model says that (for a Spilling wave, at least), you can go AS FAST in MPH, as 7 times the Square Root of the True Height, in feet, for a maximum Peel Angle of 53 degrees from Straight-Off. In GIANT surf, the maximum 'make-able' wave peel angle will be much less.

4 ft = 14 MPH

9 ft = 21 MPH

16 ft = 28 MPH

25 ft = 35 MPH (looks like 20 ft at Waimea Bay)

36 ft = 42 MPH (looks like 30 ft at Waimea Bay)

49 ft = 49 MPH

but,

100 ft = 70 MPH! (The peel angle at Nazare in Portugal is much lees than Makaha Point Break.

My model shows that the HIGHER you can get on a wave, (before it goes vertical), the STEEPER the wave face surface is, and the FASTER you can go! This works best for Spilling-type, fast-breaking long walls like Point Breaks. If you are approaching a fast section up ahead, and want to get around it, you need to climb HIGHER on the wave face so you can then dive lower going thru that section. You EXCHANGE Altitude (Potential Energy) for Speed (Kinetic Energy). Your Total Energy while riding on a wave is the SUM of Potential Energy and Kinetic Energy.

BUT, If you wish to position yourself INSIDE the Tube, you must ride well down on the face of a Plunging-Type Wave, where the wave face is not as STEEP. And LESS steep means you go SLOWER! So, you might even need to slow the board down a bit to match the speed of the tube. That's all right: It's pretty exciting inside the 'Green Room'!

Surfers who use so-called "LOCAL Scale", which is based on the old 'Hawaiian Scale' from the 1950s and 1960s, should be aware that the old U.S. Weather Bureau used METRIC, only expressed in "HALF-Meters" rather than METERS. So, a Half meter is about half of 39.37", or about 19.685 inches. If you round that up slightly to simply 20 inches, then a wave that looks like '5 feet' (or 60") is "3 Half-meters, Hawaiian Scale (NOT FEET!). The True Height might be 6 feet, so the Hawaiian Scale is about 1/2 of the True Height, if you include the Trough.

Bob, few surfers have the patience to read my original treatment of "Surfer Speed vs.Wave Height", so if you want to send the above to Swaylocks, I'd much appreciate it.

Thanks for that Bob. I didn’t know that Larry was still active in the surfing arena, he has some long standing design ideas that will probabaly prove to be prophetic in years to come.

Gday Brett,

Surfing is in his blood. He has some long term interests, such as surf forecasting. I haven't asked if he's getting wet much these days. His speed post was prompted by some photos I sent him of a recent South African trip.

Regards

Bob

The bit on Hawaiian half meters explains why wave measures in Hawaiian feet seem about 30% understated.

Bob (bgreen),

Please thank Larry on my behalf for following the add-on discussion to your post of his work and Larry's accompanying posts. Larry did a great job. My work was/is in no way intended to refute Larry's.

I approached this to get a general idea about speed and foil size for hydrofoil surfboards. I read Larry's posts after I had done my first round of calculations that followed my post in Brett's hydrofoil thread.

My calculations were to determine the absolute maximum (ultimate) instantaneous surfer speed that is possible while obeying the laws of physics. My calculations also assume frictionless acceleration and velocity. Wave height is assumed to be measured from trough to crest/peak -- a liquid skateboarder's ramp. Also, I used Cyril J. Galvin's research (1968) for my wave speed estimates.

I think most of us realize that a frictionless (ideal) wave, without water movement in the wave's face, does not exist in the real world (i.e. the line-up). Water movement toward and up the wave face, as well as drag, prevent this "upper limit" speed from ever happening.

The ultimate surfer speed equation (in the ideal environment) can be simplified as shown below. To see the derivation of these equations, go to the end of the blog post at this link:

http://bgsurfphysics.blogspot.com/2018/08/wave-surfing-speeds.html

Bill Wurts

## Ult_Surf_Speed_EqB.jpg

Swaylocks Surfboard Design Forum:thoughts & theories ... practical & theoreticalRAIL PROFILE http://bgboard.blogspot.com/2014/03/march-82014-afterr-seeing-recent.html

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