Surfer & wave speed (measurement and technical considerations)

General Discussion
41

Nor do I. The last time the model was used for a simulation was back around 1994 and unfortunately the file containing the input parameters were lost in a subsequent drive crash-- so I can’t look them up. As best I recall most (but not all) of the simulations were executed assuming 6 to 8 foot waves.

The model is a steady-state model, it only computes the steady-state situation, not the history as to how it arrived at that state. The steady-state results are determined by the balance of forces (that’s why it’s “steady-state”–there is no net force to cause a change in speed or direction. That also means that the result is independent of the initial state.

Both are important. As to which is more important, let’s get a rough estimate of how much of a doubling of Wave Height would increase the steady-state speed; then compute the speed increase if the slope were doubled instead–and then compare the two predicted increases.

First we examine the effect of doubling the wave height.

We begin by noting that the surfer’s speed is roughly linearly proportional to wave speed, and that wave speed is proportional to the square-root of the effective water depth (i.e. adjusted for wave height):

Vwave = sq-root (g x (h + 3H/4))    h = water depth inj absence of waves, H = wave height (See: Van Dorn - Oceanography and Seamanship)

The change in wave height as the waves move into shoaling water and breaks depends on the ratio of the of the slope of the wave face of the deep water waves to the slope of the ocean bottom, but normally lies within the range of 0.78 to 1.2 (Van Dorn). As an approximation, let’s assume a ratio of 1. Now let’s see how much a doubling the wave height (H) will increase the wave speed:

Vwave1 = sq-root (g x (H +(3/4) x H) = sq-root ((7/4) x H)

Vwave2 = sq-root (g x (2H + (3/4) x (2H)) = sq-root ((7/2) x H)

So the ratio is:

Vwave2 / Vwave1 = sq-root (2)

…hence doubling the wave size can be expected to roughly increase the surfer’s speed by roughly 40%.

 

Now let’s estimate what change in speed will occur by doubling the slope of the wave face at the position of the surfer.

The steady-state speed is achieved when the thrust generated by the combination of the sloping face of the wave and gravity (via the weight of the surfer and board) is equal to the drag. For a 1st-order approximation, we assume that the surfboard is moving sufficiently fast that the primary source of drag is from skin friction, In that case, the drag will be proportional to the square of the speed.  We also note that the force associated with the sloping sea surface is linearly proportional to the slope of the wave face. So doubling the slope of the wave approximately doubles the thrust associated with gravity. The system responds by increasing the speed of the surfer so as to double the associated drag. Since drag increases as the square of the surfer’s speed, increasing the speed of the surfer by a factor = sq-root (2) will double the drag and thus offset the doubling of the thrust associated with gravity and the sloping wave face.

So the end result is that the two factors are roughly equal – and to get a better estimate, one must go to a higher order of approximation (which greatly complicates the analysis).

There are many difficulties in computing an estimate of the speed of a board. Not the least of these is that changes in any one factor affects the magnitudes of many other factors. By way of an example, increasing the angle-of-attack of the board relative to the face of the wave not only changes the lift generated, but also the induced drag. Moreover, the altered lift and drag change the wetted area of the board. The change in wetted area changes the aspect ratio of the wetted surface, thus changing the lift coefficient for the bottom of the board. The change in lift coefficient changes the lift generated by the board, which in turn changes the aspect ratio, …etc. And so it goes. Only nature has an easy time in accounting for all these changes.

The situation is much simpler for a hydrofoil board with fully submerged foils since the wetted area (and aspect ratio) is normally constant. For the interested reader, I’ve attached a MS Word file that contains an outline of a procedure to determine the steady-state speed of a hydrofoil-based board utilizing fully submerged foil(s) to illustrate the representations of the various forces involved in solving this simpler case. Unlike the surfboard model (which requires a computer to execute the simulations) this model can be (and has been) executed using a spread-sheet. Although less representative of surfboard hydrodynamics, it still can provide some insight as to the relative importance of various processes.

 

UPDATE:  I was unable to attach the MS Word file as it exceeds the file size limit by about 20% (and I don’t have the time to rewrite it). Sorry!

42

MTB,

 

Rod Rodgers is in California at the moment but I suspect he would be happy to post your MS Word file as is, to complement Larry’s writings and the articles on the exisiting Terry Hendricks articles he has up. Could pm me or Rod if you are interested in this as an option.

 

Bob

43

Yesterday I attempted to attach a MS Word file outlining a simple model of a surfboard and rider traversing across the face of a wave if the rider maintains his position on the wave relative to the breaking point of the wave crest (i.e. the break point and the rider move along the face at the same speed). 

However, I was unable to do so as the file exceeded the attachment limits for posting here. So I broke the original file into two parts and have attached them to this post. I hope you find it interesting.

(Please let me know if you find any mistakes)

https://swaylocks7stage.s3.us-east-2.amazonaws.com/s3fs-public/BrdSimP0.doc

https://swaylocks7stage.s3.us-east-2.amazonaws.com/s3fs-public/BrdSimP2.doc

44

Hi, guys!

This is for "mtb":

If anybody asks the question: "Where's the Beef?", you have certainly provided it, in spades! Thanks! I hate the vagueness in most people's answers in the various forums that I frequent.

Now, I wonder how many surfers on this forum can follow your mathematical formulas with full understanding. You definitely need to have a solid background in math to be able to digest it all. At least, you didn't get into Vector math or Calculus! We thank you for that...

Let's put this to a test: How about a mind-experiment?

Which surfer, riding identical surfboards, would be able to go faster on a wave that is peeling fast enough, where:

1): Surfer #1 is ONE-THIRD of the way up on the face of a 24-ft wave, where it's not too steep

and

2): Surfer #2 is HALF-WAY way up on a 16-ft wave, where it is steeper, but not TOO steep to handle

AND...

3): Hey! How about that bodyboarder (or paipo rider) tracking way up high at 3/4ths of the way up the face of the 16-ft wave, where it's really steep!

I'm curious to know what kind of speeds the different riders would be capable of reaching, IF the wave wasn't peeling too radically. What IS the maximum makeable peel angle in each case above? The faster rider will be able to make it across a faster-peeling wave, right?

So, which of the two stand-up surfers would be able to go faster: the one on the steeper part of the smaller wave, but at about the same height above sea level as the other guy, who's tracking lower on the face of a bigger wave, (which is breaking in deeper water, so is moving faster)?

I think maybe the surfer speed could be simply related to: HOW HIGH he is above sea level (or the bottom of the wave, say) and HOW STEEP the wave face is where he's tracking. The results would probably be different from what we have already theorized so far.

This is maddening! Mind-boggling! Ha!

I guess we will have to await more experimental results from guys who tow-in, or who enter speed contests. But, they need to report wave heights and wave speeds more reliably and consistently, otherwise the data is almost useless to a statistician. (Garbage IN, Garbage OUT)

Thanks again for the formulas!

 

45

[quote="$1"]

Hi, "mtb",

I have often wondered if a surfer, after dropping in on a wave, could continue his bottom turn all the way around 180 degrees, and then climb immediately all the back way up to the top of the wave with enough excess speed (or Momentum) to be able to launch himself up into the air ABOVE the wave, to an altitude that was even HIGHER than the top of the wave where he started.

I doubt it...

The fact they they CAN 'get big air' on waves farther down the line, where the wave is smaller, only shows that they still have enough Energy left, and excess speed on tap, to do it where the wave has lost some of its initial height.

However, if they COULD do it right after the 'drop-in-and-turn' phase of their ride, that would surprise me, especially if the wave height is undiminished after they make their their turn. Most surfers take off at the peak of the wave, where the shallow spot on the bottom precipitates the initial breaking of the wave, (i.e., in the lineup), where the top of the wave might be 20% higher than the shoulder immediately following their take-off.

[/quote]

 

Hey Larry, this musing struck a chord with me, as I have been watching a movie called 'Modern Collective' on and off for the last few weeks and have been trying to figure something out;

 

In one section, Dane Reynolds takes off, bottoms turns and launches (and lands) a big backside air 360 on a shoulder-high left, in France, I believe. How he manages that is beyond me, and I would never be able to start to quantify it in terms of physics, but there must be some merit in investigating the element of rider input in 'pumping' for speed out of the curve of the wave, in the same way a skater pumps the transition for speed on a halfpipe?

 

One can assume that this element does not apply to big waves, where simply hanging in there to make it to the bottom and around the first section is hard enough in itself!

 

Apologies for bringing the discussion down to my layman undrstanding, but I thought it was an interesting example of how we (well, a select few!)  must be able to 'create' speed very quickly.

46

Good questions! – but virtually impossible for me to estimate without generating simulations for each case. Moreover, those simulations would need to be carried out not with the simple model that I described in my previous post, but rather with a more complex model (e.g. the model that generated the graphic output predictions that I presented two postings ago to this thread).

Agreed!

I agree that it would be a good beginning. But I think more information than just wave height and speed (combined with surfer speed and direction (e.g. peel angle)) would be required to construct a model with reasonable predictive capabilities. For example, a measurement of the slope of the wave face along the surfer’s pathline at the location of the surfboard on the wave would be very useful as (it is the slope at the position of the surfboard along his pathline at the position of the surfer on the face of the wave rather than his elevation above the sea level that is important.

 

47

Hi, guys!

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.

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.

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

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?

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...

Thanks again, guys!

 

 

48

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”?

 

49

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... 

50

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.

51

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!

52

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

 

53

 

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.

 

728×242 26.8 KB

54

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!

55

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!

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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

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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

58

Hi, Robert!

Aloha!! I didn't think there would be any more responses to our spirited discussions on "Surfer Speed...etc". It seemed to have played out. Conclusion: it remains to be determined just how fast surfers CAN and DO actually go on surfable waves.

But more answers will be forthcoming as more 'speed' events are staged around the world, with GPS devices such as the "SBOX" doing the actual measurements of instantaneous speeds over the bottom. Unfortunately, those devices can be fooled by wild body gyrations if the measuring unit is mounted ON THE SURFER. And they can report anomylously high momentary speeds when they are mounted on the front of the board. Think bottom turns, or banging off the lip.

I suggested that the device would best be mounted on a surfer's lower leg, or implanted IN the surfboard, between the surfer's foot positions (which don't shift much on a short board). That's impractical, so I think the leg-mount idea is best.

But...if you want to measure the surfer's speed ACROSS THE WATER, you would need to ALSO know the speed of the wave itself over the bottom (at the point on the wave face where the surfer is riding at any given moment in time, which would need to be synchronized with the GPS speed recorded at the SAME TIME). I suppose that could be done with computers, but it sure is complicated!

The surfer's speed over the bottom is a combination of wave motion AND his motion over the moving wave form. His GPS speed is the vector sum of those two motions. If you want to know how fast he's moving over the surface of the water, you need to separate those two motions.

I think the most reliable and simplest way to determine the ACTUAL SPEED of the surfboard OVER THE WATER is to just use something like a boat speedometer, or even better, a pressure-measuring "pitot tube" on the bottom of the board somewhere below the position of the surfer. It wouldn't be able to give accurate readings when the board was tail-sliding, but would be fine when the board is trimmed for high speed across the fast-peeling wall of water.

You were interested in the likely maximum speed of the surfer on the wave in the video, which you called 'a 10-meter wave'. You can easily measure a small wave directly...just take a measuring stick out and actually measure it! But, when the waves get over 10-15 feet, it gets much more difficult...not to mention dangerous!

All you need to do in those situations, is to position yourself on the beach so that the the top of the wave just "touches" the horizon. Then, find a landmark up or down the beach that is the SAME DISTANCE from you as the breaking waves. Where the horizon intersects the landmark, THAT part of the landmark is at the SAME HEIGHT ABOVE SEA LEVEL as the wave crest, above sea level. This technique is called "The Line-of-Sight Method" of wave-height measurement. It can be accurate down to the nearest inch!

Note that this method can NOT tell you how low the water is, below sea level, in the TROUGH at the bottom of the entire wave. But that TOTAL HEIGHT, including the trough, is the TRUE WAVE HEIGHT. To actually measure the trough, you need somebody in the water just outside the impact zone (so he doesn't get slammed by the breaking wave) holding a long pole pointed straight up toward the sky. Then, with binoculars or, even better, a movie camera on the beach, you can observe (or record) how far the pole moves up and down with the passing wave forms.

The steeper the Slope of the bottom where the wave rises and breaks, the harder a wave can break, and the deeper the trough relative to the total wave height. For easy-breaking waves (think Waikiki), the trough might only be 14-17% of the total height of the breaking wave. For hard-breaking waves (think Pipeline), the trough might be 17-20% of the entire wave. For insanely hollow waves (think Teahupo'o, or "Chopo", in Tahiti). I don't know how deep the fearful 'Pit' is at that scary place, but it must be pretty impressive!

You need to know how big the total or TRUE wave height is, if you want to calculate how fast the wave is moving past the bottom. Then, if you can determine the Peel Angle, you can find the speed of the peeling curl relative to the bottom, or relative to the wave form's crest line. That was the main thrust of the essay on "Surfer Speed...etc."

My formula, rounded off to give an easily-remembered form, was:

Max surfer speed, MPH (or GPS Curl Speed, relative to the reef bottom) = 7 x SQUAREROOT(True Height, ft)

So, for a 4 ft wave, Max Speed = 14 MPH

and, for a 25 ft wave, Vmax = 35 MPH

 

Then for a true 10-meter wave (32.81 ft), Max Speed = 40.1 MPH

Remember, that wave may only look like about 8 meters to you, (or 26+ ft) without the trough.

 

Some of the biggest waves that Tow-In surfers have successfully ridden probably were closer to 20 METERS high (or 65.6 ft...looked like 50+ ft! Ask Ken Bradshaw: he rode of those Monsters on January 28th, 1998, on the North Shore of Oahu, Hawaii. It was the biggest swell since December 4th, 1969, when the North shore was closed out at 55 ft (Waimea Bay), and 60-70 ft off Kaena Point.

A 20-meter wave would break in about 84 feet of water (14 fathoms!), and would be moving at about 52 ft/sec, or 35.4 MPH. That's about 5 times as fast as you can paddle a surfboard. So, after the Yamaha WaveRunner tows you onto the wave, you make your drawn-out turn,... then...how fast do you need to go to make the wave?

If the peel angle is 45 degrees, you will need to go 1.414 times as fast as the wave propagation speed, or 50.1 MPH!

If the peel angle is 50 degrees, you will need to go 1.556 times as fast...that's freeway speed...55.1 MPH

My formula says you might be able to go as fast as 56.7 MPH. That's my Surfer Speed Limit. Probably not attainable in really big surf like that. We'll find out some day in the not-too-distant future. Who knows what the distant future holds for big-wave surfers? Rocket-powered boards that can FLY? Hmmm...

You may want to study the Winter Olympics Speed Skaters and their fastest body positions. Or practice standing on the top of a surf van going 55 on the freeway. I think you might get blown off by the wind...HA!

 Thanks for your interest, Robert. Maybe "mtb" will weigh in, as well. That would be cool...

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Hi Larry,

With the interest in the sport it seems odd that we haven’t been able to do a direct measurement yet.

Thank you for the detailed answer; I knew that more rigorous minds than mine had been working on this question and it seems like I came to the right place!

Has anyone tried putting a radar reflector on a surfer? Maybe research-grade gps or laser range finding? I know there are some geologists on the islands with at least some of the right gear for it. I’m sure I sound naive asking, but one would think that there would have to be a way to do it.

Mahalo!

Robert

 

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Hi, Robert!

The Laser Range-Finder devices would be too dangerous for the surfer, because of the possibility of blinding light hitting his eyes. Not worth the risk.

The Radar speed-measuring devices only would be able to measure the motion of the surfer TOWARD the device, (using Doppler). That would be useful information only if the device was set up way down the beach, positioned carefully, so that the surfer trimming in a straight line across the fastest part of the wave was heading DIRECTLY TOWARD the radar unit. That could work, I guess. Couldn't be THAT hard to do! I haven't heard of anybody trying it.

Just remember, tho', that the radar instrument would only be measuring the speed of the surfer relative to the fixed ground-based position of the radar unit. That is the same as the GPS measurements that the "SBOX" provides. So, both the radar unit and the SBOX can only measure the instantaneous speed of the surfer over the BOTTOM, not across the water.

The device needed to measure 'over the water' speed therefore needs to be mounted ON the surfboard, itself. But anything that you stick on the bottom of the board is going to cause at least a little extra drag. The pitot tube is less disruptive of water flow than a boat speedometer, but no matter what kind of hardware device you use, it will still need to be calibrated. Yikes! No wonder so few attempts have been made to date. We need new ideas! Anybody listening?

Thanks again for your interest, Robert! Maybe your questions will get some inventive minds focused on this interesting problem: If we want to know "How fast CAN a surfer go on a wave?", we need to figure out a way to determine: "How fast IS a surfer going across a wave?"

Aloha!