I'd like to thank "Strychnine" for his comments regarding the ability of skateborders and snowboarders to "pump" at the bottom of the Half-pipe or the Transition and thereby gain more speed in preparation for the next maneuver. I guess that's really what ice-skaters and roller-bladers have been doing for a long time. OK...not really rocket science, after all.

Yes, but...the power dissipated by the surfboard in the case of the simulated ride I posted a couple of posts ago was about 3 hp. An Olympic class athlete can briefly generate a bit over 1 hp. So at best (i.e. a 100% power transfer efficiency, etc.) the addition of power by the surfer extending and contracting his leg muscles will only increase the power input into the craft and rider by 33 percent. At 30 ft/sec (~20 mph), most of the drag (force) on the surfboard is
proportional to the square of the speed "through" the water (skin
friction and form drag). Hence the associated power loss is proportional to the cube of speed through the
water. Raising the power input from 3 hp (associated with gravity) to 4
hp (associated with gravity plus the surfer pumping) will cause an
increase in speed. Since power is proportional to the cube of the speed,
we can solve for the increase in speed associated with this increase in
power. More specifically:

V4 / V3 = cube-root (P4 / P3) = 1.10 (V3 = speed with 3 hp; V4 = speed with 4 hp, P3 and P4 are the associated powers)

So under the most optimistic conditions (i.e. 100 efficiency in transferring power, Olympic class athlete, etc. the direct input of additional power by the surfer will only increase the speed by about 10 percent (i.e. 25 mph would become 27.5 mph). In the real world situation (i.e. lower efficiency, typical surfer, etc.) the increase in speed would likely much less.

The situation for skateboarders and ice skateris is substantially different. In particular the total drag force (associated with bearings, tire contact, skate blade, air drag, etc.) is much less. Hence the input of power by the skateboarder or ice skater is typically much greater than than the power lost to drag -- and therefore the rider, by putting out the same power as in our surfboard case ( ~1 hp), will have a much bigger influence on the speed (in fact, on level ground, the board and rider won't move without it).

However, there is at least one other means by which pumping might significantly alter the speed of a surfboard and rider -- and that is if the sequence of motions involved in pumping (or some other maneuver) change the hydrodynamic efficiency of the board. The speeds calculated by the simulation mode are for a steady-state condition. But in the real world, the rider may be constantly maneuvering the board and rider into configurations that can be briefly more efficient (but which cannot sustained as they are unstable). If the net result of this varying efficiency results in an increase in the power input to the board, the speed of the board will be increased. Since the rider only has to supply the effort to change the angle-of-attack of the board, and/or bank the board, he might be able to substantially increase the speed of the board with much less effort (in a manner similar to flying an airplane where the control forces are much less than the load carrying capacity).However, simulating a constantly changing situation like this is far beyond the capabilities of the steady-state model and would require a much greater development effort.

LarryG wrote:

Well, "mtb", how do we quantify THAT? I'm about ready to give up on this...It's getting too complex for my puny brain do handle.

If the shape of the wave face of a good (i.e., "Plunging" or curling) wave is that of a Logarithmic Spiral (a Logarithmic function when plotted on a Polar Coordinate system), then we could use calculus to find the Slope of the curve (Derivative) at any point on the wave face.

That's true. But that's a mighty big "IF" (in regard to the shape/flow of the wave face).

LarryG wrote:

But, I think a surfer tracking at a point on the face of a 16-foot wave where the slope is, say, the Optimum 48 degrees, would be going FASTER than a surfer on an 8-foot wave who is ALSO riding where the slope is 48 degrees. We need to find out...

I would agree. I would be VERY surprised if that were not the case.

LarryG wrote:

I'm talking about "Steady-State" conditions, here; No climbing and dropping, and NO pumping!

Me too!

LarryG wrote:

Including the surfer's speed-increasing maneuvers complicates the situation significantly, so let's try to deal with that separately, after we have accumulated more experimental data in the surf.

Oh well...I guess I need to brush up on my calculus. This is going to be interesting!

Are any of you guys using the "S-Box" to measure and plot your rides on the waves?

Pardon my ignorance, but what is a "S-Box"?

LarryG wrote:

We need to "Shake the Bushes" some more, trying to find more people interested in determining just "How Fast CAN a Surfer Go on a Wave?" Hopefully, some day we'll have a better idea...

Actually, it called the "SBOX", and it's a device that contains accelerometers and other electronic devices packaged in a small box that is about as large as a pack of playing cards. It can be mounted on a surfboard and used to measure motions in 3 dimensions. It has been used at Jeffrey's Bay in South Africa to measure alleged surfboard speeds attained at "SuperTubes".

I say "alleged" because IF it's mounted near the nose, then the highest speeds detected during the bottom turn will be exaggerated by the speed of the nose of the board snapping around rapidly. That's NOT a true measure of the surfboard speed on the wave!

If you're interested, you can read about the use of the SBOX at the "J-Bay Speed Run" at:

In one of the statements, the surf size was given as "5 feet", and the Measured speeds at the bottom turns was given as 62.5 KM/HR, with a maximum recorded speed of 83 KM/HR.

Using the 62.5 Kilometers per Hour figure: if you multiply by 1000 to get Meters per Hour, then divide by 3600 seconds in an hour, you get a speed of about 17.361 m/sec, or (dividing by 0.3048 to get feet/sec) about 56.959 ft/sec. Multiplying by 15/22 to get MPH, you get about 38.8357 MPH. WOW!!! Almost 39 MPH on only a "5 foot" wave. Ha! I don't think so...

Maybe they were using "Local Scale", or "Hawaiian Scale", which is actually "Half-Meters"?

If so, then the wave "looked" like about 8 feet, (about 3 ft overhead), WITHOUT the Trough, in which case the TRUE Crest-to-Trough (Top-to-Bottom) Breaking Wave Height was about 10 feet, or about TWICE as big as reported.

If the breaking wave height WAS actually 10 feet, then it would have been breaking in about 12.8 feet of water, and the wave speed, in ft/sec, i.e., Vwave = SQRT(gd), = 20.281 fps.

The wave speed in MPH = (15/22) times (Vwave, fps), = 13.828 MPH

That means that the surfer was going about 2.808 times as fast as the wave! And that gives a "Peel Angle" (measured away from the wave crest) of only 20.859 degrees...,

or a Ride Angle (measured away from Straight-Off) of a whopping 69.141 degrees! WOW!

I know SuperTubes is fast, but I don't think the Makeable tube rides are THAT fast.

Oh well...I wasn't here, so who knows for sure?

I'd like to get my hands on one of those SBOX devices, just to try out on a paipo board on Hawaiian waves.

Actually, it called the "SBOX", and it's a device that contains accelerometers and other electronic devices packaged in a small box that is about as large as a pack of playing cards. It can be mounted on a surfboard and used to measure motions in 3 dimensions. It has been used at Jeffrey's Bay in South Africa to measure alleged surfboard speeds attained at "SuperTubes".

Thanks for the information and links -- very interesting! Several years ago one of the UCSD lab exercises in a science/engineering course was using small, self-contained, internally-recording accelerometers mounted on a surfboard (or surfer --I don't remember which) to measure speeds while surfing. Unfortunately I never heard about how successful that effort turned out.

The addition of the missing GPS and gyros in the SBOX should provide not only better measurements of the motions in 3 linear dimensions, but also measurements of rotations around another 3 axes (pitch, roll, yaw).

LarryG wrote:

I say "alleged" because IF it's mounted near the nose, then the highest speeds detected during the bottom turn will be exaggerated by the speed of the nose of the board snapping around rapidly. That's NOT a true measure of the surfboard speed on the wave!

If you're interested, you can read about the use of the SBOX at the "J-Bay Speed Run" at:

In one of the statements, the surf size was given as "5 feet", and the Measured speeds at the bottom turns was given as 62.5 KM/HR, with a maximum recorded speed of 83 KM/HR.

Using the 62.5 Kilometers per Hour figure: if you multiply by 1000 to get Meters per Hour, then divide by 3600 seconds in an hour, you get a speed of about 17.361 m/sec, or (dividing by 0.3048 to get feet/sec) about 56.959 ft/sec. Multiplying by 15/22 to get MPH, you get about 38.8357 MPH. WOW!!!Almost 39 MPH on only a "5 foot" wave. Ha! I don't think so...

They did say that the fastest speeds were during the bottom turn, so it's not the steady-state situation we've been discussing. However, I do agree that even with that consideration the speed seems a bit high.

LarryG wrote:

Maybe they were using "Local Scale", or "Hawaiian Scale", which is actually "Half-Meters"?

If so, then the wave "looked" like about 8 feet, (about 3 ft overhead), WITHOUT the Trough, in which case the TRUE Crest-to-Trough (Top-to-Bottom) Breaking Wave Height was about 10 feet, or about TWICE as big as reported.

If the breaking wave height WAS actually 10 feet, then it would have been breaking in about 12.8 feet of water, and the wave speed, in ft/sec, i.e., Vwave = SQRT(gd), = 20.281 fps.

The wave speed in MPH = (15/22) times (Vwave, fps), = 13.828 MPH

That means that the surfer was going about 2.808 times as fast as the wave! And that gives a "Peel Angle" (measured away from the wave crest) of only 20.859 degrees...,

or a Ride Angle (measured away from Straight-Off) of a whopping 69.141 degrees! WOW!

I know SuperTubes is fast, but I don't think the Makeable tube rides are THAT fast.

Oh well...I wasn't here, so who knows for sure?

Agreed.

BTW ...a question:

Do you know how the wave speed is measured at the point where it begins to break?

I don't.

It's pretty easy to measure in deep water, or in shallow water with a constant depth. All you need to do is to measure the time it takes for the crest of the wave to cover a known distance. However, in shoaling water, as the wave begins to break, it's less obvious what/where on the wave form you should be making your measurements. For example, in the case of a plunging wave that is really throwing out, the speed of the lip of the wave toward shore can be on the order of twice the speed of motion where the slope of the face of the same wave is vertical.

LarryG wrote:

I'd like to get my hands on one of those SBOX devices, just to try out on a paipo board on Hawaiian waves.

Hi, guys!
"mtb" asked how wave speed is (or could be) measured at the point of breaking. I'm not sure whether he was referring to the calculated Wave Propagation Speed over the Shoaling Bottom, or the speed of a surfer on the wave who's staying just ahead of the curling vertical face.
It is known that the speed of forward motion of a wave in shallow water is proportional to the square root of the water depth. We already have a proven formula for describing the speed of a Shallow Water Wave, where Vwave = SQRT(gd).
For a Breaking Wave, where the Depth of water at the point of breaking, d = BDI times Hb.
The ratio of (breaker depth) / (breaker height), d/Hb, is called the "Breaker Depth Index", which I call "BDI", and it is typically about 1.28 for waves breaking over a sloping bottom that is typical for most decent surf breaks.
Good surf spots have slopes of around 1 in 30, and Easy" surf (like Waikiki) probably involves average bottom slopes of around 1:80 or 1:100. The bottom slope affects the shape of the breaking wave. The steeper slopes create the "Plunging" waves preferred by advanced surfers. Inexperienced surfers and intermediate surfers enjoy easier-breaking "Spilling Waves". No curling, tubing, pitching lips to contend with.
When a deep-water swell starts running over a bottom that is getting shallower, the front of the swell slows down more than the rear of the swell, which is still out in deeper water. As the rear of the swell is in the process of 'catching up' to the front of the same swell, the wave HEIGHT has to increase, because the wave LENGTH is getting shorter, and water is incompressible.
As the water depth decreases, and the wave crest rises higher, it increasingly is travelling in water that is deeper than the Trough, and therefore is moving faster and faster. The water surface in the trough is actually being 'sucked' out, i.e., moving out toward the approaching wave. Eventually the top of the wave is moving at the SAME speed as the bottom of the wave, and at that point the wave face is going vertical.
A moment later, the top of the wave is moving FASTER than the bottom of the wave, and the lip pitches out from the top, moving maybe twice as fast as the bottom by now. If the bottom slope is NOT very steep, the wave face becomes unstable when the face is approaching 60 degrees from horizontal, just ahead of the crest of the wave. The top of the wave then starts sliding down the wave face, and you have a softly breaking wave.
On a smaller scale, out at sea in deep water, the growing wavelets can get too steep and become unstable when the wave height is too great for the still-short wavelengths, and the result is seen as breaking 'whitecaps'.
So, is the 'calculated Wave Speed' actually the speed of the TOP of the wave, or of the part of the wave that is equivalent to the Average height of the wave? Certainly, it is not the speed of the Bottom of the wave. That's the slowest part of the wave! I always assumed that it was the speed of the top of the wave. It's calculated using the Crest-to-Trough height of the wave, H, by definition.
I've spent years calculating Average Wave Speed, but the bottom is generally getting shallower as the wave moves in towards shore, so the wave is slowing down all the time. I observe the wave length shorten, and I can compare the wavelengths out in the lineup, maybe 400 yards from shore, with the wavelengths when the waves reach the beach. The speed is proportional to the wavelengths, but I can only determine the average depth that way. The formula does seem to agree with my observations.
But, I still don't know the Instantaneous Wave Speed. The bottom here in Hawaii is usually pretty uneven, being a coral bottom. I'm constantly amazed that the waves can get as good as they do, here. The more solid or even the bottom, the cleaner, crisper the waves are. Really uneven bottoms produce thicker waves. Easier to ride, but not as exciting for the expert surfers.
Bob Shepherd had the right idea: mount a pitot tube on the bottom of the board, in front of the skeg. But you want a continuous record of the pressures measured during your ride on a wave, so that requires a way to transmit the results to a recorder on the beach. He had a pressure gauge mounted on his surfboard which he could observe during the ride. That would be easy to do now, 30-40 years later.
I think the "SBOX" is going to be the most promising device in the near future for real-time measurements of surfboard motion on waves. Just, don't mount it on the NOSE of the board!
Maybe a guy in the water without his surfboard could wear a GPS device or an "SBOX" on a harness around his chest and be able to accurately measure wave motion before the wave starts to break. That would give us actual wave height and surface water movement ahead of and at the top of the wave. If he could bodysurf the wave (going straight off, just before it breaks on him), maybe that would eliminate the errors associated with putting the device on a surfboard. Hmmm...
So, "How do you measure wave speed at the point of breaking?" I guess I don't know, either!
We're not there yet, are we? Definitely getting closer, tho'...
Thanks again!

Hi, guys!
"mtb" asked how wave speed is (or could be) measured at the point of breaking. I'm not sure whether he was referring to the calculated Wave Propagation Speed over the Shoaling Bottom, or the speed of a surfer on the wave who's staying just ahead of the curling vertical face.

I was referring to the calculated Wave Propagation Speed.

LarryG wrote:

It is known that the speed of forward motion of a wave in shallow water is proportional to the square root of the water depth. We already have a proven formula for describing the speed of a Shallow Water Wave, where Vwave = SQRT(gd).

Yes, that is approximately correct for small amplitude, long-crested, "rigid" profile waves moving through shallow water of constant depth (e.g. see "Wind Waves", B. Kinsman, 1965 for the derivation of the equation.) I'm personally not aware of any study that shows that the wave speed "instantly" changes with changing water depth. Are you? If so, I'd appreciate the reference.

In regard to the relationship between water depth and wave speed in shallow water it is also worth noting that Van Dorn ("Oceanography and Seamanship", 1974) comments that "...more precise analysis shows that the shallow water wave velocity is also a function of wave height..." where: Speed = sq-root (g x (0.75 x H +h)) where H = wave height and h = water depth.

LarryG wrote:

For a Breaking Wave, where the Depth of water at the point of breaking, d = BDI times Hb.
The ratio of (breaker depth) / (breaker height), d/Hb, is called the "Breaker Depth Index", which I call "BDI", and it is typically about 1.28 for waves breaking over a sloping bottom that is typical for most decent surf breaks.
Good surf spots have slopes of around 1 in 30, and Easy" surf (like Waikiki) probably involves average bottom slopes of around 1:80 or 1:100. The bottom slope affects the shape of the breaking wave. The steeper slopes create the "Plunging" waves preferred by advanced surfers. Inexperienced surfers and intermediate surfers enjoy easier-breaking "Spilling Waves". No curling, tubing, pitching lips to contend with.
When a deep-water swell starts running over a bottom that is getting shallower, the front of the swell slows down more than the rear of the swell, which is still out in deeper water. As the rear of the swell is in the process of 'catching up' to the front of the same swell, the wave HEIGHT has to increase, because the wave LENGTH is getting shorter, and water is incompressible.
As the water depth decreases, and the wave crest rises higher, it increasingly is travelling in water that is deeper than the Trough, and therefore is moving faster and faster. The water surface in the trough is actually being 'sucked' out, i.e., moving out toward the approaching wave. Eventually the top of the wave is moving at the SAME speed as the bottom of the wave, and at that point the wave face is going vertical.
A moment later, the top of the wave is moving FASTER than the bottom of the wave, and the lip pitches out from the top, moving maybe twice as fast as the bottom by now. If the bottom slope is NOT very steep, the wave face becomes unstable when the face is approaching 60 degrees from horizontal, just ahead of the crest of the wave. The top of the wave then starts sliding down the wave face, and you have a softly breaking wave.
On a smaller scale, out at sea in deep water, the growing wavelets can get too steep and become unstable when the wave height is too great for the still-short wavelengths, and the result is seen as breaking 'whitecaps'.
So, is the 'calculated Wave Speed' actually the speed of the TOP of the wave, or of the part of the wave that is equivalent to the Average height of the wave? Certainly, it is not the speed of the Bottom of the wave. That's the slowest part of the wave! I always assumed that it was the speed of the top of the wave. It's calculated using the Crest-to-Trough height of the wave, H, by definition.

You commented in one of your early posts to this thread that when estimating wave height (e.g. by the line of sight method) the trough lies below sea level and a correction must be added to the measured height from sea level to the crest of the wave to get the true wave height. You suggested that correction should be about 1/5 -1/4 the measured height from sea level to the crest. I think that this correction factor is a function of wave slope and bottom slope as well as I have seen evidence that this correction can be as large as 1/2 the measured height above sea level in the case of a steeply sloped bottom. (S. Grilli et.al. - URI)

LarryG wrote:

I've spent years calculating Average Wave Speed, but the bottom is generally getting shallower as the wave moves in towards shore, so the wave is slowing down all the time. I observe the wave length shorten, and I can compare the wavelengths out in the lineup, maybe 400 yards from shore, with the wavelengths when the waves reach the beach. The speed is proportional to the wavelengths, but I can only determine the average depth that way. The formula does seem to agree with my observations.

What is the typical water depth 400m from shore? Are you sure that you satisfy the restrictions/conditions for using the "deep" and/or "shallow" water equations (water depth restrictions in particular)?

LarryG wrote:

But, I still don't know the Instantaneous Wave Speed. The bottom here in Hawaii is usually pretty uneven, being a coral bottom. I'm constantly amazed that the waves can get as good as they do, here. The more solid or even the bottom, the cleaner, crisper the waves are. Really uneven bottoms produce thicker waves. Easier to ride, but not as exciting for the expert surfers.
Bob Shepherd had the right idea: mount a pitot tube on the bottom of the board, in front of the skeg. But you want a continuous record of the pressures measured during your ride on a wave, so that requires a way to transmit the results to a recorder on the beach. He had a pressure gauge mounted on his surfboard which he could observe during the ride. That would be easy to do now, 30-40 years later.

Keep in mind that with a pitot tube you're measuring speeds relative to the board, not to the bottom. For example, if doing a re-entry your speed relative to the water can be very low (approaching zero), but your speed relative to the bottom will generally be much higher.

LarryG wrote:

I think the "SBOX" is going to be the most promising device in the near future for real-time measurements of surfboard motion on waves. Just, don't mount it on the NOSE of the board!
Maybe a guy in the water without his surfboard could wear a GPS device or an "SBOX" on a harness around his chest and be able to accurately measure wave motion before the wave starts to break. That would give us actual wave height and surface water movement ahead of and at the top of the wave.

I think it will be a great device as well. But keep in mind the limitations of GPS. Sea water is an electrical conductor, so if you're riding deep in the tube it will be like standing in a Faraday cage and the GPS won't be "seeing" the satellites at all--and hence no valid readings. Even riding close to the tube (but not in it) may block out enough lines of sight to the GPS satellites so that computations are not possible. GPS's of this class are also relatively inaccurate at measuring vertical displacements. Fortunately, the 3-axis accelerometers should help in getting past some of these problems.

A similar problem exists with where to mount it. Mounting it on the board has not only the turning accelerations you commented on, but by being close to the sea surface, has some of the GPS reception problems I just mentioned. Mounting it on the rider's chest may block off signals to the GPS receiver as well. The best location for optimizing the reception is probably on top of a helmet (but this may increase the likelihood of endangering the neck muscles and joints during a wipe-out)). From a scientific point of view, mounting it on the rider also has the problem of recording body motions rather than board motion (think "snapbacks" for example).

LarryG wrote:

If he could bodysurf the wave (going straight off, just before it breaks on him), maybe that would eliminate the errors associated with putting the device on a surfboard. Hmmm...
So, "How do you measure wave speed at the point of breaking?" I guess I don't know, either!
We're not there yet, are we? Definitely getting closer, tho'...
Thanks again!

In our Hawaiian summer surf season, we can see swells with periods ranging from 14 to 24 seconds, but typically they start out in the range of about 17-20 seconds (forerunners) for swells that have travelled somewhere between 2500 NM and 4500 NM. The longest swells come up from near Antarctica, with a period of near 25 seconds after maybe a 10-day trip (Decay Distance of 5500-6000 NM).

A 20-second swell has a wavelength of more than 2000 feet, so a "Shallow Water" wave would be one where the water depth is less than about 1/20th of the wavelength, or about 100 feet. Only Tow-In surfers would be likely to ride any waves in water THAT deep.

In water that is 100 feet deep, the waves could be up to 100 feet in height, depending on how steep the bottom slope is in the breaker zone. Most likely about 78 feet high. Not counting the Trough, that would leave a Height "Above Sea Level" of about 5/6th of 78 ft, or Hasl = 65 feet.

I know a guy who may have ridden a wave that big: Ken Bradshaw called his ride "50 feet". That's what it looked like without the trough. So, it had to be at least 60 feet total height.

It was about 11:30 AM on Wednesday, January 26th, 1998 (some people called it "Biggest Wednesday"). You may have seen the video, shot from a helicopter, up close! The video is titled "Condition Black" You probably have seen it. It's spectacular! It was the biggest swell since December 4th, 1969.

But, I have yet to see any reports of how FAST the guys driving the jet skis were going when they towed their friends into the waves that day. Somebody must know...

If the water depth was 100 ft, and if I use a wave height of 78 feet, then Van Dorn's formula says:

Vwave = SQRT[g x (0.75H + h)]

= SQRT[32.13550136(0.75 x 78 + 100)]

=SQRT[32.13550136 x 158.5]

= 71.369 ft/sec

And, Vmph = (15/22) x Vfps = 48.66 MPH.

If they could make a wave breaking with a Peel Angle of 45 degrees, they would have to go about 1.414 times the wave speed, or about 68.8 MPH...Freeway Speed! I doubt if they were angling that much in those huge waves.

For my 25-foot Makaha waves, My formula gives a wave speed of 21.86 MPH, and a maximum board speed (Vcurl) of 1.6 times that, or about 35 MPH.

If the water depth is 1.28 times 25 feet, or 32 feet, Van Dorn's formula gives a Wave Speed of 27.53 MPH, and if they could angle across the wave at 45 degrees, they would have to go 38.94 MPH. But, THEN, a 1200-foot ride would only take 21.0 seconds. Very few surfers ever beat 24 seconds, though...which is equivalent to about 34 MPH.

Well, Maybe there are too many pitfalls with using GPS for measuring board speeds on a wave. I think maybe a police radar-gun could handle that task more reliably. It would be hard to beat a 3-axis accelerometor-based self-contained device, but where could it be mounted on the board or surfer that would be close enough to his center of rotation (or center of gravity) to give truly representative readings of motion?

By the way, I have many of those old publications that you mentioned. I even had Bowditch's book on seamanship, etc. I loaned it to a friend years ago...and never saw it again! Oh well...

Take a look at this graph of a variation of a Logarithmic Curve: (it's close to the shape of a breaking wave of a Plunging type):

What do you think? The "trough' looks like it's a little too close to the vertical part of the breaking wave...i.e., not far enough out in front of the wave. The easy-breaking waves in Waikiki have their troughs located about 3 1/2 wave-heights out in front of the wave crest.

Well, Maybe there are too many pitfalls with using GPS for measuring board speeds on a wave. I think maybe a police radar-gun could handle that task more reliably. It would be hard to beat a 3-axis accelerometor-based self-contained device, but where could it be mounted on the board or surfer that would be close enough to his center of rotation (or center of gravity) to give truly representative readings of motion?

I think one should include measurements from 3 orthogonal gyros as well as the 3-axis accelerometers. All sensors to be sampled at a sufficiently short interval to resolve the effect of "spikes" in the data--said spikes to be "removed" in post processing of the data.

These mods should allow the data collection package to be mounted to the board and resolve the primary motions of interest in post processing..

LarryG wrote:

By the way, I have many of those old publications that you mentioned. I even had Bowditch's book on seamanship, etc. I loaned it to a friend years ago...and never saw it again! Oh well...

Bummer isn't it? I had the same thing happen with a GPS.

LarryG wrote:

Take a look at this graph of a variation of a Logarithmic Curve: (it's close to the shape of a breaking wave of a Plunging type):

What do you think? The "trough' looks like it's a little too close to the vertical part of the breaking wave...i.e., not far enough out in front of the wave. The easy-breaking waves in Waikiki have their troughs located about 3 1/2 wave-heights out in front of the wave crest.

I'm curious as to why you think that a logararithmic curve should be a good approximation to the shape of the forward face of a plunging wave? Simple physics says that once the lip pitches forward (horizontally), it will follow a parabolic trajectory until the lip strikes the wave face (or trough).

I've attached a graphic from a computer model of a breaking wave (Grilli, URI) that incorporates more extensive physics in its formulation. In this example, it is simulating the wave cross-section at a sequence of times for a 2D, plunging-type breaker in shoal water. Note that the lip trajectory predicted by this model also supports my contention that the lip will follow a parabolic-like trajectory.

LarryG wrote:

Catch ya later!

(edit - addition below)

FWIW, note that in this simulation, the max "depth" of the trough below sea level is about equal to one-half of the max height of the crest above sea level.

I absolutely agree that the top, or lip, of a plunging a wave, once it starts to pitch out over the wave face below, is following a ballistic trajectory, i.e., a Parabolic Curve, assuming no wind is acting on it.

But, a surfer is normally riding the wave face well BELOW the lip, where it is not yet vertical. You can go up on the steeper part of the wave face only for a moment when you 'bang off the lip'. Only Bodyboarders are ever able to actually 'ride upside down' under the lip. But that is only a momentary stunt, performed at places like the Banzai Pipeline. I have pictures of a guy doing that, taken by my friend, Bernie Baker.

(see attachment)

The part of the wave face that I think looks very similar to the curve in the graph I showed in the previous post, is that part of the wave face that is BELOW the point where the face has gone vertical.

Note that the horizontal distance from the bottom of the 'trough' to the point where the face is vertical, is about the same distance as the vertical distance from the bottom of the trough to the point up the wave face that is vertical. In other words, the wave face is vertical at a point that is about HALF-WAY up the front of the wave.

Now look at the graphs of the 6 wave cross-sectional profiles, or shapes, that you provided in your last post:

The bottom of the trough is about -0.12 units, and the top of the wave is about +0.18 units (n/H values), so the wave's total vertical distance is about 0.3 units. The wave face is vertical at about +0.03 units, so the distance from the Bottom of the trough to the Vertical point is about about +0.15 units, or HALF-WAY up the wave face. Hmmm! That's the same as the shape of the curve I referred you to, the "Catacaustic" variation of the Logarithmic Curve!

Take a look at some of the graphs in these websites:

Maybe the shape of such extreme plunging waves as Teahupoo in Tahiti would more closely fit these idealized mathematical curves.

For smaller, more typical waves as seen here in Hawaii (with Tradewinds blowing offshore into the face of the breaking wave) here is the shape you'll likely see:

(see attachment)

We need more real-world photos, I think, so we can compare the ACTUAL shapes of the best waves in the world with these theoretical mathematical models.

By the way, "mtb", did you ever surf in Hawaii? When you were going to school in San Diego, you had access to some of the best waves in California! I had to drive all the way down from the crowded South Bay area (Hermosa Beach) to enjoy your great waves down there. From Trestles to Baja was my favorite surfing grounds along the entire coastline.

I absolutely agree that the top, or lip, of a plunging a wave, once it starts to pitch out over the wave face below, is following a ballistic trajectory, i.e., a Parabolic Curve, assuming no wind is acting on it.

But, a surfer is normally riding the wave face well BELOW the lip, where it is not yet vertical. You can go up on the steeper part of the wave face only for a moment when you 'bang off the lip'. Only Bodyboarders are ever able to actually 'ride upside down' under the lip. But that is only a momentary stunt, performed at places like the Banzai Pipeline. I have pictures of a guy doing that, taken by my friend, Bernie Baker.

(see attachment)

The model that I have referred to was developed to estimate the maximum steady-state speed of a rider racing across the face of a hypothetical plunging-type wave, and the combination of positioning on the face of a wave, and trimming the board, that results in that speed. In order to achieve this estimate, simulations are carried out in a systematic manner for a large number of combinations of the slope of the wave face and the trim (angle-of-attack) angle of the board on the face of the wave (i.e. a 2-dimensional array). This array is examined to locate he combination of slope and trim that produces the fastest speed across the face of a wave.

So far, the shape of the wave face has not been required to produce a simulation -- only trial values for the slope of the wave. The next step is to determine if this is a feasible solution -- i.e. whether the combination of trim and (especially) slope can actually be achieved. This is where the description of the profile of the wave plays an important role. For example, consider Bernie Baker's tube-riding picture from Vals Reef that you posted. The slope of the wave face at the location of the board in the picture appears to be something like 18 to 30 degrees. The surfing model projects that the maximum speed should be achieved where the wave face slope is about 47 degrees (and the board is trimmed for an angle-of-attack of 11 degrees). But clearly the rider in the picture at Vals cannot increase his speed by moving up the face of the wave to where the slope is 47 degrees since his is already encapsulated between the wave face, the lip overhead, and lower face of the wave profile, and has virtually no discretionary maneuvering capability in this condition.

LarryG wrote:

The part of the wave face that I think looks very similar to the curve in the graph I showed in the previous post, is that part of the wave face that is BELOW the point where the face has gone vertical.

Note that the horizontal distance from the bottom of the 'trough' to the point where the face is vertical, is about the same distance as the vertical distance from the bottom of the trough to the point up the wave face that is vertical. In other words, the wave face is vertical at a point that is about HALF-WAY up the front of the wave.

It doesn't look like that's the case for the first (left-most) profile to me. It looks like the slope becomes vertical at around 80% of the wave height.

Larry G wrote:

Now look at the graphs of the 6 wave cross-sectional profiles, or shapes, that you provided in your last post:

The bottom of the trough is about -0.12 units, and the top of the wave is about +0.18 units (n/H values), so the wave's total vertical distance is about 0.3 units. The wave face is vertical at about +0.03 units, so the distance from the Bottom of the trough to the Vertical point is about about +0.15 units, or HALF-WAY up the wave face. Hmmm! That's the same as the shape of the curve I referred you to, the "Catacaustic" variation of the Logarithmic Curve!

Take a look at some of the graphs in these websites:

Maybe the shape of such extreme plunging waves as Teahupoo in Tahiti would more closely fit these idealized mathematical curves.

The Logarithmic Spiral Catacaustic looks pretty good for the lower portions of each of the profiles when you overlay it onto the profiles I posted previously. But there's a bit too much curvature more or less midway between the two ends of the figure. Perhaps this could be reduced by playing a bit with the generating parameters for the spiral catacaustic curve.

LarryG wrote:

For smaller, more typical waves as seen here in Hawaii (with Tradewinds blowing offshore into the face of the breaking wave) here is the shape you'll likely see:

(see attachment)

We need more real-world photos, I think, so we can compare the ACTUAL shapes of the best waves in the world with these theoretical mathematical models.

That would be nice, but perhaps difficult to carry out . If done with pictures I would suspect that one would need a minimum of 3 synchronized still or video cameras at (optimized) surveyed locations in order to have at least a chance of success. The models have been compared with observations from physical models (laboratory wave tanks) with pretty good success.

LarryG wrote:

By the way, "mtb", did you ever surf in Hawaii? When you were going to school in San Diego, you had access to some of the best waves in California! I had to drive all the way down from the crowded South Bay area (Hermosa Beach) to enjoy your great waves down there. From Trestles to Baja was my favorite surfing grounds along the entire coastline.

Yes.

LarryG wrote:

Catch ya later!

Good discussion (..and nice pictures. Thanks for posting them!)

I'm brand new to this group and came across this thread for probably the obvious reason; I saw this video of Carlos Burle on a 10-meter wave and wondered about his top speed: http://www.youtube.com/watch?v=466-swjGeO0

I note that there has been an effort to answer the various ways this question could be asked, speed in water, speed over ground, maximum velocity (meaning with the wave and including the vertical component). Since this was a casual inquiry on my part, but not wishing to stir the pot, I was hoping someone with some experience might help me estimate his maximum velocity, including the wave speed. My question is really the top speed of ANY surfer, but I figure this example has GOT to be close to that....

Yes, but...the power dissipated by the surfboard in the case of the simulated ride I posted a couple of posts ago was about 3 hp. An Olympic class athlete can briefly generate a bit over 1 hp. So at best (i.e. a 100% power transfer efficiency, etc.) the addition of power by the surfer extending and contracting his leg muscles will only increase the power input into the craft and rider by 33 percent. At 30 ft/sec (~20 mph), most of the drag (force) on the surfboard is proportional to the square of the speed "through" the water (skin friction and form drag). Hence the associated power loss is proportional to the cube of speed through the water. Raising the power input from 3 hp (associated with gravity) to 4 hp (associated with gravity plus the surfer pumping) will cause an increase in speed. Since power is proportional to the cube of the speed, we can solve for the increase in speed associated with this increase in power. More specifically:

V4 / V3 = cube-root (P4 / P3) = 1.10 (V3 = speed with 3 hp; V4 = speed with 4 hp, P3 and P4 are the associated powers)

So under the most optimistic conditions (i.e. 100 efficiency in transferring power, Olympic class athlete, etc. the direct input of additional power by the surfer will only increase the speed by about 10 percent (i.e. 25 mph would become 27.5 mph). In the real world situation (i.e. lower efficiency, typical surfer, etc.) the increase in speed would likely much less.

The situation for skateboarders and ice skateris is substantially different. In particular the total drag force (associated with bearings, tire contact, skate blade, air drag, etc.) is much less. Hence the input of power by the skateboarder or ice skater is typically much greater than than the power lost to drag -- and therefore the rider, by putting out the same power as in our surfboard case ( ~1 hp), will have a much bigger influence on the speed (in fact, on level ground, the board and rider won't move without it).

However, there is at least one other means by which pumping might significantly alter the speed of a surfboard and rider -- and that is if the sequence of motions involved in pumping (or some other maneuver) change the hydrodynamic efficiency of the board. The speeds calculated by the simulation mode are for a steady-state condition. But in the real world, the rider may be constantly maneuvering the board and rider into configurations that can be briefly more efficient (but which cannot sustained as they are unstable). If the net result of this varying efficiency results in an increase in the power input to the board, the speed of the board will be increased. Since the rider only has to supply the effort to change the angle-of-attack of the board, and/or bank the board, he might be able to substantially increase the speed of the board with much less effort (in a manner similar to flying an airplane where the control forces are much less than the load carrying capacity).However, simulating a constantly changing situation like this is far beyond the capabilities of the steady-state model and would require a much greater development effort.

That's true. But that's a mighty big "IF" (in regard to the shape/flow of the wave face).

I would agree. I would be VERY surprised if that were not the case.

Me too!

Pardon my ignorance, but what is a "S-Box"?

Hi, guys!

"mtb" asked "what is an S-box?"

Actually, it called the "SBOX", and it's a device that contains accelerometers and other electronic devices packaged in a small box that is about as large as a pack of playing cards. It can be mounted on a surfboard and used to measure motions in 3 dimensions. It has been used at Jeffrey's Bay in South Africa to measure alleged surfboard speeds attained at "SuperTubes".

I say "alleged" because IF it's mounted near the nose, then the highest speeds detected during the bottom turn will be exaggerated by the speed of the nose of the board snapping around rapidly. That's NOT a true measure of the surfboard speed on the wave!

If you're interested, you can read about the use of the SBOX at the "J-Bay Speed Run" at:

www.surfinglife.com.au/news/asl-news/4677--j-bay-speed-run

or:

www.zigzag.co.za/features/exclusives/6116/How-Fast-Can-You-Go

In one of the statements, the surf size was given as "5 feet", and the Measured speeds at the bottom turns was given as 62.5 KM/HR, with a maximum recorded speed of 83 KM/HR.

Using the 62.5 Kilometers per Hour figure: if you multiply by 1000 to get Meters per Hour, then divide by 3600 seconds in an hour, you get a speed of about 17.361 m/sec, or (dividing by 0.3048 to get feet/sec) about 56.959 ft/sec. Multiplying by 15/22 to get MPH, you get about 38.8357 MPH. WOW!!! Almost 39 MPH on only a "5 foot" wave. Ha! I don't think so...

Maybe they were using "Local Scale", or "Hawaiian Scale", which is actually "Half-Meters"?

If so, then the wave "looked" like about 8 feet, (about 3 ft overhead), WITHOUT the Trough, in which case the TRUE Crest-to-Trough (Top-to-Bottom) Breaking Wave Height was about 10 feet, or about TWICE as big as reported.

If the breaking wave height WAS actually 10 feet, then it would have been breaking in about 12.8 feet of water, and the wave speed, in ft/sec, i.e., Vwave = SQRT(gd), = 20.281 fps.

The wave speed in MPH = (15/22) times (Vwave, fps), = 13.828 MPH

That means that the surfer was going about 2.808 times as fast as the wave! And that gives a "Peel Angle" (measured away from the wave crest) of only 20.859 degrees...,

or a Ride Angle (measured away from Straight-Off) of a whopping 69.141 degrees! WOW!

I know SuperTubes is fast, but I don't think the Makeable tube rides are THAT fast.

Oh well...I wasn't here, so who knows for sure?

I'd like to get my hands on one of those SBOX devices, just to try out on a paipo board on Hawaiian waves.

Catch ya later...

Thanks for the information and links -- very interesting! Several years ago one of the UCSD lab exercises in a science/engineering course was using small, self-contained, internally-recording accelerometers mounted on a surfboard (or surfer --I don't remember which) to measure speeds while surfing. Unfortunately I never heard about how successful that effort turned out.

The addition of the missing GPS and gyros in the SBOX should provide not only better measurements of the motions in 3 linear dimensions, but also measurements of rotations around another 3 axes (pitch, roll, yaw).

They did say that the fastest speeds were during the bottom turn, so it's not the steady-state situation we've been discussing. However, I do agree that even with that consideration the speed seems a bit high.

Agreed.

BTW ...a question:

Do you know how the wave speed is measured at the point where it begins to break?

I don't.

It's pretty easy to measure in deep water, or in shallow water with a constant depth. All you need to do is to measure the time it takes for the crest of the wave to cover a known distance. However, in shoaling water, as the wave begins to break, it's less obvious what/where on the wave form you should be making your measurements. For example, in the case of a plunging wave that is really throwing out, the speed of the lip of the wave toward shore can be on the order of twice the speed of motion where the slope of the face of the same wave is vertical.

I was referring to the calculated Wave Propagation Speed.

Yes, that is approximately correct for small amplitude, long-crested, "rigid" profile waves moving through shallow water of constant depth (e.g. see "Wind Waves", B. Kinsman, 1965 for the derivation of the equation.) I'm personally not aware of any study that shows that the wave speed "instantly" changes with changing water depth. Are you? If so, I'd appreciate the reference.

In regard to the relationship between water depth and wave speed in shallow water it is also worth noting that Van Dorn ("Oceanography and Seamanship", 1974) comments that "...more precise analysis shows that the shallow water wave velocity is also a function of wave height..." where: Speed = sq-root (g x (0.75 x H +h)) where H = wave height and h = water depth.

You commented in one of your early posts to this thread that when estimating wave height (e.g. by the line of sight method) the trough lies below sea level and a correction must be added to the measured height from sea level to the crest of the wave to get the true wave height. You suggested that correction should be about 1/5 -1/4 the measured height from sea level to the crest. I think that this correction factor is a function of wave slope and bottom slope as well as I have seen evidence that this correction can be as large as 1/2 the measured height above sea level in the case of a steeply sloped bottom. (S. Grilli et.al. - URI)

What is the typical water depth 400m from shore? Are you sure that you satisfy the restrictions/conditions for using the "deep" and/or "shallow" water equations (water depth restrictions in particular)?

Keep in mind that with a pitot tube you're measuring speeds relative to the board, not to the bottom. For example, if doing a re-entry your speed relative to the water can be very low (approaching zero), but your speed relative to the bottom will generally be much higher.

I think it will be a great device as well. But keep in mind the limitations of GPS. Sea water is an electrical conductor, so if you're riding deep in the tube it will be like standing in a Faraday cage and the GPS won't be "seeing" the satellites at all--and hence no valid readings. Even riding close to the tube (but not in it) may block out enough lines of sight to the GPS satellites so that computations are not possible. GPS's of this class are also relatively inaccurate at measuring vertical displacements. Fortunately, the 3-axis accelerometers should help in getting past some of these problems.

A similar problem exists with where to mount it. Mounting it on the board has not only the turning accelerations you commented on, but by being close to the sea surface, has some of the GPS reception problems I just mentioned. Mounting it on the rider's chest may block off signals to the GPS receiver as well. The best location for optimizing the reception is probably on top of a helmet (but this may increase the likelihood of endangering the neck muscles and joints during a wipe-out)). From a scientific point of view, mounting it on the rider also has the problem of recording body motions rather than board motion (think "snapbacks" for example).

mtb

Hi, again, "mtb"!

In our Hawaiian summer surf season, we can see swells with periods ranging from 14 to 24 seconds, but typically they start out in the range of about 17-20 seconds (forerunners) for swells that have travelled somewhere between 2500 NM and 4500 NM. The longest swells come up from near Antarctica, with a period of near 25 seconds after maybe a 10-day trip (Decay Distance of 5500-6000 NM).

A 20-second swell has a wavelength of more than 2000 feet, so a "Shallow Water" wave would be one where the water depth is less than about 1/20th of the wavelength, or about 100 feet. Only Tow-In surfers would be likely to ride any waves in water THAT deep.

In water that is 100 feet deep, the waves could be up to 100 feet in height, depending on how steep the bottom slope is in the breaker zone. Most likely about 78 feet high. Not counting the Trough, that would leave a Height "Above Sea Level" of about 5/6th of 78 ft, or Hasl = 65 feet.

I know a guy who may have ridden a wave that big: Ken Bradshaw called his ride "50 feet". That's what it looked like without the trough. So, it had to be at least 60 feet total height.

It was about 11:30 AM on Wednesday, January 26th, 1998 (some people called it "Biggest Wednesday"). You may have seen the video, shot from a helicopter, up close! The video is titled "Condition Black" You probably have seen it. It's spectacular! It was the biggest swell since December 4th, 1969.

But, I have yet to see any reports of how FAST the guys driving the jet skis were going when they towed their friends into the waves that day. Somebody must know...

If the water depth was 100 ft, and if I use a wave height of 78 feet, then Van Dorn's formula says:

Vwave = SQRT[g x (0.75H + h)]

= SQRT[32.13550136(0.75 x 78 + 100)]

=SQRT[32.13550136 x 158.5]

= 71.369 ft/sec

And, Vmph = (15/22) x Vfps = 48.66 MPH.

If they could make a wave breaking with a Peel Angle of 45 degrees, they would have to go about 1.414 times the wave speed, or about 68.8 MPH...Freeway Speed! I doubt if they were angling that much in those huge waves.

For my 25-foot Makaha waves, My formula gives a wave speed of 21.86 MPH, and a maximum board speed (Vcurl) of 1.6 times that, or about 35 MPH.

If the water depth is 1.28 times 25 feet, or 32 feet, Van Dorn's formula gives a Wave Speed of 27.53 MPH, and if they could angle across the wave at 45 degrees, they would have to go 38.94 MPH. But, THEN, a 1200-foot ride would only take 21.0 seconds. Very few surfers ever beat 24 seconds, though...which is equivalent to about 34 MPH.

Well, Maybe there are too many pitfalls with using GPS for measuring board speeds on a wave. I think maybe a police radar-gun could handle that task more reliably. It would be hard to beat a 3-axis accelerometor-based self-contained device, but where could it be mounted on the board or surfer that would be close enough to his center of rotation (or center of gravity) to give truly representative readings of motion?

By the way, I have many of those old publications that you mentioned. I even had Bowditch's book on seamanship, etc. I loaned it to a friend years ago...and never saw it again! Oh well...

Take a look at this graph of a variation of a Logarithmic Curve: (it's close to the shape of a breaking wave of a Plunging type):

www.2dcurves.com/spiral/spirallo.html

What do you think? The "trough' looks like it's a little too close to the vertical part of the breaking wave...i.e., not far enough out in front of the wave. The easy-breaking waves in Waikiki have their troughs located about 3 1/2 wave-heights out in front of the wave crest.

Catch ya later!

I think one should include measurements from 3 orthogonal gyros as well as the 3-axis accelerometers. All sensors to be sampled at a sufficiently short interval to resolve the effect of "spikes" in the data--said spikes to be "removed" in post processing of the data.

These mods should allow the data collection package to be mounted to the board and resolve the primary motions of interest in post processing..

Bummer isn't it? I had the same thing happen with a GPS.

I'm curious as to why you think that a logararithmic curve should be a good approximation to the shape of the forward face of a plunging wave? Simple physics says that once the lip pitches forward (horizontally), it will follow a parabolic trajectory until the lip strikes the wave face (or trough).

I've attached a graphic from a computer model of a breaking wave (Grilli, URI) that incorporates more extensive physics in its formulation. In this example, it is simulating the wave cross-section at a sequence of times for a 2D, plunging-type breaker in shoal water. Note that the lip trajectory predicted by this model also supports my contention that the lip will follow a parabolic-like trajectory.

(edit - addition below)

FWIW, note that in this simulation, the max "depth" of the trough below sea level is about equal to one-half of the max height of the crest above sea level.

## BREAKING.GIF

Hi, "mtb"!

I absolutely agree that the top, or lip, of a plunging a wave, once it starts to pitch out over the wave face below, is following a ballistic trajectory, i.e., a Parabolic Curve, assuming no wind is acting on it.

But, a surfer is normally riding the wave face well BELOW the lip, where it is not yet vertical. You can go up on the steeper part of the wave face only for a moment when you 'bang off the lip'. Only Bodyboarders are ever able to actually 'ride upside down' under the lip. But that is only a momentary stunt, performed at places like the Banzai Pipeline. I have pictures of a guy doing that, taken by my friend, Bernie Baker.

(see attachment)

The part of the wave face that I think looks very similar to the curve in the graph I showed in the previous post, is that part of the wave face that is BELOW the point where the face has gone vertical.

Note that the horizontal distance from the bottom of the 'trough' to the point where the face is vertical, is about the same distance as the vertical distance from the bottom of the trough to the point up the wave face that is vertical. In other words, the wave face is vertical at a point that is about HALF-WAY up the front of the wave.

Now look at the graphs of the 6 wave cross-sectional profiles, or shapes, that you provided in your last post:

The bottom of the trough is about -0.12 units, and the top of the wave is about +0.18 units (n/H values), so the wave's total vertical distance is about 0.3 units. The wave face is vertical at about +0.03 units, so the distance from the Bottom of the trough to the Vertical point is about about +0.15 units, or HALF-WAY up the wave face. Hmmm! That's the same as the shape of the curve I referred you to, the "Catacaustic" variation of the Logarithmic Curve!

Take a look at some of the graphs in these websites:

http://mathworld.wolfram.com/LogarithmicSpiralCatacaustic.html

http://demonstrations.wolfram.com/CatacausticsGeneratedByAPointSource/

Maybe the shape of such extreme plunging waves as Teahupoo in Tahiti would more closely fit these idealized mathematical curves.

For smaller, more typical waves as seen here in Hawaii (with Tradewinds blowing offshore into the face of the breaking wave) here is the shape you'll likely see:

(see attachment)

We need more real-world photos, I think, so we can compare the ACTUAL shapes of the best waves in the world with these theoretical mathematical models.

By the way, "mtb", did you ever surf in Hawaii? When you were going to school in San Diego, you had access to some of the best waves in California! I had to drive all the way down from the crowded South Bay area (Hermosa Beach) to enjoy your great waves down there. From Trestles to Baja was my favorite surfing grounds along the entire coastline.

Catch ya later!

## Vals_Reef_21July2010_BBaker_.jpg

## Pipe_by_Bernie_Baker_DSC2651.jpg

The model that I have referred to was developed to estimate the maximum steady-state speed of a rider racing across the face of a hypothetical plunging-type wave, and the combination of positioning on the face of a wave, and trimming the board, that results in that speed. In order to achieve this estimate, simulations are carried out in a systematic manner for a large number of combinations of the slope of the wave face and the trim (angle-of-attack) angle of the board on the face of the wave (i.e. a 2-dimensional array). This array is examined to locate he combination of slope and trim that produces the fastest speed across the face of a wave.

So far, the shape of the wave face has not been required to produce a simulation -- only trial values for the slope of the wave. The next step is to determine if this is a feasible solution -- i.e. whether the combination of trim and (especially) slope can actually be achieved. This is where the description of the profile of the wave plays an important role. For example, consider Bernie Baker's tube-riding picture from Vals Reef that you posted. The slope of the wave face at the location of the board in the picture appears to be something like 18 to 30 degrees. The surfing model projects that the maximum speed should be achieved where the wave face slope is about 47 degrees (and the board is trimmed for an angle-of-attack of 11 degrees). But clearly the rider in the picture at Vals cannot increase his speed by moving up the face of the wave to where the slope is 47 degrees since his is already encapsulated between the wave face, the lip overhead, and lower face of the wave profile, and has virtually no discretionary maneuvering capability in this condition.

It doesn't look like that's the case for the first (left-most) profile to me. It looks like the slope becomes vertical at around 80% of the wave height.

The Logarithmic Spiral Catacaustic looks pretty good for the lower portions of each of the profiles when you overlay it onto the profiles I posted previously. But there's a bit too much curvature more or less midway between the two ends of the figure. Perhaps this could be reduced by playing a bit with the generating parameters for the spiral catacaustic curve.

That would be nice, but perhaps difficult to carry out . If done with pictures I would suspect that one would need a minimum of 3 synchronized still or video cameras at (optimized) surveyed locations in order to have at least a chance of success. The models have been compared with observations from physical models (laboratory wave tanks) with pretty good success.

Yes.

Good discussion (..and nice pictures. Thanks for posting them!)

mtb

Hi forum members,

I'm brand new to this group and came across this thread for probably the obvious reason; I saw this video of Carlos Burle on a 10-meter wave and wondered about his top speed: http://www.youtube.com/watch?v=466-swjGeO0

I note that there has been an effort to answer the various ways this question could be asked, speed in water, speed over ground, maximum velocity (meaning with the wave and including the vertical component). Since this was a casual inquiry on my part, but not wishing to stir the pot, I was hoping someone with some experience might help me estimate his maximum velocity, including the wave speed. My question is really the top speed of ANY surfer, but I figure this example has GOT to be close to that....

Many thanks for your input,

Robert Wyatt

landlocked in Austin, TX

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