I'll try to post this myself, rather than asking Bob Green to do it for me. He deserves a break...

The last couple days I've been evaluating the effect of using different values for the ratio of the Breaker Depth versus the Breaking Wave Height, given the same Wave Height of 25 feet.

This ratio is known as the "Breaker Depth Index, which I'll call "BDI".

The deeper the water where the waves break, the faster the Wave Speed will be in the surf zone. Bigger waves break in deeper water, so they are moving faster.

In the open ocean, where the waves are in water that's deeper than about half of their deepwater wavelength, the Wave Propagation Speed is proportional to the Wavelength and the Period. The Wave Speed in knots, Ckts = Tseconds / 0.33.

But, in 'Transitional Depth water' that is less than about half of the open-ocean wavelength, the swell starts 'feeling the bottom', and begins slowing down. This is where the first refraction of the swell begins to take place. A 20-second swell has a deep-water wavelength over 2000 ft long, so it first starts slowing in water that's still over 1000 feet deep. At that depth, it's still moving at freeway speeds.

When the swell gets into water that's only about 1/20th of the original open-ocean wavelength, it's considered to be in 'Shallow Water'. In such shallow water, which could be about 100 feet deep for that long 20-second swell that's approaching, the wave speed is becoming mostly independent of the period, only affected now by the Depth of the water.

In 'Shallow Water', Wave Speed, Vwave = SQRT(g times d), where g=acceleration of gravity at that Latitude, and d is the water depth. But d = BDI times Hb, so, if I use feet, d,ft = BDI x Hb,ft.

I used 25 feet for the Breaking Wave Height, Hb,ft. Then, as I increased the Breaker Depth Index from unity (one, or 1) to (1 / 0.78) or BDI = 1.282051282, the Breaking Depth also increased, and therefore the Wave Speed ALSO increased.

If the Maximum Makeable Break Angle, or Ride Angle, was calculated according to the Energy Budget formula, the Maximum Makeable Ride Angle, B (measured away from 'Straight Off' where B = 0 degrees) is: the Angle B whose Cosine = SQRT[BDI/(2+BDI)].

I discovered that as the 25-foot wave got faster in the deeper water, the Maximum Makeable Ride Angle got smaller (and the Peel Angle A got larger). Remember, A = (90-B) degrees, as it's measured away from the crest of the wave.

But, here's what's REALLY interesting: As I tried various values of BDI, the Curl Speed, i.e., "Vcurl", the speed of the surfer ACROSS THE WATER, remained the SAME! That's the speed you would measure using a boat speedometer, NOT the GPS speed, which is given in the formulas as "Vsurfer". Remember, Vsurfer is the speed relative to the BOTTOM, (or the Earth).

It seems that ONLY the Breaking Wave Height has any effect on how fast you can go!

That makes perfect sense, since it's the Height of the wave that gave you all that Energy to play with. You obtained all that Energy Budget at the Drop-In! How fast you CAN go is dependent ONLY on the Energy you have available to you!

For a 25-foot wave, I got a Maximum Vcurl speed of 27.33040833 MPH

For a 26.24' wave, I get a Maximum Vcurl speed of 28 MPH

To find Vcurl, max, in MPH, Use:

Vcurl, max (MPH) = 5.466081666 x SQUAREROOT(Hb, ft).

Comments, anyone?

As I understand it, your Vcurl is the speed at which the break point of the curl progresses along the length of the wave crest. If that's the case, I don't see how the curl speed has any limit -- at least at the speeds we're talking about in surfing. For example, a long-crested wave moving nearly perpendicular to shoaling isobaths can break virtually simultaneously along its length (I'm sure that most of us have seen long-crested curling waves break in which the curl moves along hundreds of feet down the length of the crest within a couple of seconds.)

Whether or not a surfboard can keep up is another question. You assume that the board and rider have an energy budget comprised of both kinetic energy and potential energy -- and that total energy remains constant during a ride. This assumption is equivalent to assuming that there is no gain or loss of total energy during the ride, or that any loss of energy is compensated by an associated gain of energy of equal magnitude from another mechanism. It is relatively easy to demonstrate that there is a loss of energy -- for example, when the board and surfer plane across a level sea surface and there is no source of energy they quickly slow to a stop (e.g. when coasting straight off out into the flats) rather than continuing at the same speed as at the end of the drop. Conversely, if the energy budget consisted solely of the potential energy available when starting to catch a wave, and there is no gain or loss of total energy during the ride, then if or when the surfer and board go up the face of the wave, they should come to a halt (relative to the wave face) as they reach the crest. Yet all of us have seen bodies and boards launched at speed into the air above the crest of the wave during a late kickout.

Attached is a graphic showing the output from a (1980's to 1990's) computer simulation model of surfing on a wave and how the speed achieved (steady-state conditions) is affected by how the surfer trims the board ("angle-of-attack") and where one places the board on the face of the wave ("wave slope"). The contour lines are essentially your "Ride Angle" (smaller angle -> increasing speed). In this particular simulation, the optimum trim position (relates to AOA) is predicted to be about 11 degrees, and the optimum position on the wave is where the slope of the sea surface (measured inshore to offshore) is about 48 degrees, This resulted in a predicted speed of about 22.7 mph. Other predicted quantities (not shown) are: speed, wetted area, wetted length, and location of the surfer's center-of-mass (AOA trim).

It seems that ONLY the Breaking Wave Height has any effect on how fast you can go!

That makes perfect sense, since it's the Height of the wave that gave you all that Energy to play with. You obtained all that Energy Budget at the Drop-In! How fast you CAN go is dependent ONLY on the Energy you have available to you!

...

Comments, anyone?

Great stuff here! I think your above assumption only applies to big single drop waves like Waimea. The way that I see it, the surfers muscles are effectively an engine that converts potential energy into kinetic energy. The engergy put into doing a bottom turn allows the surfer to go back up to the top of the wave for another drop. Like a forced pendulum, if you make several little pushes at the right times, then you can really get going fast. The image that comes to my mind is of Laird riding a wave at Jaws. He seems to be moving the fastest after making a few turns and drops. He is rythmically increasing his velocity as he travels at an angle across the wave.

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.

The formula I originally described in the "Part 1" essay on "Surfer Speed...etc" was for GPS speed of a surfer, relative to the BOTTOM. So, "Surfer Speed" is the Resultant of two motions: Curl Speed and Wave Speed, moving at right angles to each other, where:

Note that Curl Speed is also the speed of a surfboard relative to the WATER, but only IF the board stays in the same relative position on the wave face. It is the speed you can measure with a boat speedometer on the board.

The fastest trim line on a wave is the HIGHEST line that you can maintain. Bodyboards and Paipo boards can trim WAY higher than a surfboard, and the riders that DO go up there are maximizing their speed.

The formula I derived for Curl Speed is:

Curl Speed = SQUAREROOT(2gHb), or, Vcurl = SQRT(2g times Hb)

where, Vcurl is in ft/sec, g = 32 + (13550 / 99999) exactly, (or about 32.13550136, rounded),

and Hb = True, Total Breaking Wave Height, in feet (including the Trough).

If you know or can calculate Surfer Speed, Vcurl = Vsurfer x SIN B, (or =Vsurfer x COS A)

If you know or can calculate Wave Speed, Vcurl = Vwave x TAN B, (or =Vwave / TAN A)

The reason I posted all this stuff in the first place (on several websites) was to 'shake the bushes' and see if anybody out there was trying to measure surfboard speeds in a reliable manner. The worldwide response was not as great as I had hoped for, but what few responses I DID get were very helpful and I want to thank all you guys for your input.

By the way (I almost forgot)...

(for "mtb"): I have a question for you.

Did you use a Logarithmic Curve for the Wave Face, or a Circular function, to get the slope of the wave face? Terry Hendricks used a circular wave face shape for his calculations of board speeds. I always considered it a logarithmic curve from the trough up to at least the point where the wave goes vertical, just before breaking.

Also, on your interesting graph of "Track Angle (which I label Peel Angle "A" in my formulas) vs. Angle of Attack and wave-face Slope", there is a 'Minimum' Track Angle of somewhat >51 degrees shown at about 11 degrees AOA and 48 degrees Slope. That's very interesting to me, because MY "Maximum Makeable Ride Angle" or "Break Angle B" came out to about 51.34 degrees. That would be about 38.66 degrees for the Minimum Peel Angle.

What do you make of that? Could I be validating your graph? (or vice-versa?). Hmmmm...

Anyway, Many Thanks, again! Your input has been very helpful!

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.

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.

I wanted to clarify what I believed were the real-world ramifications of my "Surfer Speed, etc" formulas, which were based on a surfer's Total Energy Budget.

The formulas assumed that there was NO energy loss as the surfer continued his ride across a wave. That's patently impossible, of course. I'm looking for the Theoretical Maximum Energy here, which assumes NO LOSS.

It was also assumed that the surfer dropped in from the very TOP of the wave. That probably also is rarely the case (unless you're a paipo boarder, making a VERY late takeoff...not unusual at all!).

Then, it was assumed that the very BOTTOM of the wave is reached when making the bottom turn. Never happens! But, that was the assumption I made so I could use the ENTIRE Breaking Wave Height, Hb, in the energy calculations.

Note that I was looking for the Fastest-Possible "MAKEABLE" Curl Speed that a surfer could keep up with. That is a function of of the Wave Height and the Peel Angle. There is absolutely nothing in the formulas that put a limit on how fast the wave itself can peel across the crest of the wave. The only limit on Curl Speed is...Infinity! That's when you have a total close-out of the entire remaining portion of the breaking wave. The Peel Angle A at that moment is ZERO degrees (and the "Ride Angle", or Break Angle, B, measured away from 'straight-off, is 90 degrees.

The maximum possible energy is obtained if the surfer uses the ENTIRE wave height, and if there is NO loss of energy during the ride. In that unlikely case, what is the theoretical angle of ride CLOSEST to the wave crest that would enable the surfer to make the wave?

In the real world, the Maximum Ride Angle seems to be around 50 or 51 degrees away from straight-off (Angle B), or 39 or 40 degrees away from the crest of the wave (Minimum Peel Angle, A).

The wave can, and often will, peel off faster than the surfer can go across the wave. Ask the regulars at Maui's Maalaea Bay, or Supertubes, or Snapper Rocks...On some swell directions, the wave, or portions of it, are simply UNmakeable! You get closed out...somebody else further down the line drops in on your now-empty wave, and goes as far as HE can on it.

Some day, we will have rocket-powered boards that can go around close-out sections at will, but don't collide with another rocket-powered board. If the fuel tanks rupture, the resulting explosion will take out the entire lineup! Ha!

You're too fast for me! I can't respond as rapidly to your posts in this thread as quickly as you produce them. Hence you're already posting a new post before I can even respond to your previous one. So I've decided to stop posting to this thread until I can respond to your set of posts via a single post. When I complete that task I'll post my response here in the form of an attached MS Word *.doc file.

But first, a couple of comments relating to your most recent posting:

LarryG wrote:

Howzit, again!

I wanted to clarify what I believed were the real-world ramifications of my "Surfer Speed, etc" formulas, which were based on a surfer's Total Energy Budget.

The formulas assumed that there was NO energy loss as the surfer continued his ride across a wave. That's patently impossible, of course. I'm looking for the Theoretical Maximum Energy here, which assumes NO LOSS.

That's almost correct. What is really assumed is that there is no net gain or loss of energy in the system. An obvious source of energy loss is via the various mechanisms that produce drag (e.g. skin friction, induced, form, wave train generation, etc.). But where does the input of energy into the system come from? It comes from gravity, the combined weight of the surfer and board, and the wave shape and the wave-associated motions of water.

The surfer has some degree of control over the rate of energy loss, and/or the rate of energy gain, by how he positions the board on the face of the wave, and how he trims the board for minimum drag. As long as the rate of energy loss due to drag is less than the rate of gain of energy gain, the total energy in the "energy budget" will be increasing and thus permitting increasing speeds, or allowing the board to be positioned increasingly higher on the wave, or some combination of the two. In the extreme (i.e. no energy loss to drag at all), the maximum speed that can be obtained builds indefinitely -- or at least until limited by some other factor (such as the availability of wave face space).

mtb

ps. In support of this view, I call attention to the statement that you made that maximum speed is achieved by riding as high as you can on the face of a wave. That speed condition would seem to be impossible in your unchanging 'Energy Budget' approach (even in the absence of energy losses) since it is the potential energy in the budget that increases with increasing position of the wave face while the kinetic energy decreases accordingly. Thus one would expect the board speed to be increasing the lower one is riding across the face of the wave.

Sorry about the frequency of my responses; I'm retired, and probably have more time on my hands than all you guys who still have time-consuming jobs to keep you busy.

I've been surfing since 1950, and riding paipos since 1964. My experience with the paipos has been that I can go significantly FASTER if I stay as HIGH on the wave as possible. Part of the reason, though, is that I maintain VERY close trim to minimize drag. I would guess that my angle of attack is less than 5 degrees, maybe even approaching zero degrees when at high planing speeds. My board has a planing hull, but it is also buoyant, so as to minimize wetted area and the amount of water being disturbed as I pass by.

If you go low on the wave, you will go slower. Gravity is your 'engine', but the steeper upper reaches of the wave gives you more 'drive' from that engine powering your ride. Try it yourself.

I have no trouble passing surfboards. The typical surfer on a longboard maintains excessively high angles of attack on most of his ride. All that drag keeps them from going as fast as they could. And the large amount of rocker on the board's bottom also means lots of drag.

In 1970 I told Dewey Weber and Harold "Iggy" Ige, his shaper, about my experiments at Makaha, Sunset Beach and Waimea Bay using flattened bottom curves and minimal nose kick for very short boards. My fastest boards had wide tails, shallow concave bottoms and a single skeg for minimal drag.

Iggy had shaped a VERY fast 6' 2" short board in 1969 that he rode in 12-ft surf at Malibu, and he had the fastest board in the water. That design became the Weber "Ski", which my surfing buddy, Jimmy Blears used to win the 1972 World Surfing Campionships at San Diego, California.

My Conclusion: Flat is Fast! Wanna go really fast? Ride a paipo board! And stay High!

Not convinced? Take a look at this video of "Flyin' Fearless Phyllis" Dameron at Waimea Bay:

The thrust of this thread seems to be changing. In your
earlier posts to this thread, you were presenting your 'Total Energy
Budget' model as means of estimating the maximum speed that can be
achieved. One of the assumptions implicit in the model is that it is a
'closed' system and the total energy of the system is constant (and is
equal to the total energy at the time the surfer catches a wave). I
commented that one of the model predictions you listed was that the
fastest speeds occur low on the wave face (as all the potential energy
is converted to kinetic energy), and vice-versa high on the wave face (i.e. all the kinetic
energy has been converted into potential energy). From your subsequent postings we seem to be in agreement that
observations indicate that the fastest speeds are associated with surfing
high on the wave face instead of low. Hence there is a serious discrepancy between the Total Energy Budget model prediction and direct observation. This led me to point out that the model is
not a closed system and that there are both losses of energy associated with
drag, etc., and energy gains associated with the interaction of the
board with gravity and the sloping face of the wave.

With respect
to energy loss, you responded that since you were interested in
predicting upper bound for the maximum kinetic energy it was
appropriate to assume no energy loss. That's fair enough. But you have
not addressed how to arrive at an upper bound for the rate of energy
input and which doesn't lead to a total energy value that continues to
increase with the passage of time (normally the magnitude would be limited by the rate of loss of energy equalling the rate of input--but you've assumed that to be zero).

The guy you saw at Waimea Bay on his own designed 'Guitar Pick" style skegless wood paipo in the '60s was John Waidelich. He was a pioneer of big-wave surfing on paipo boards. There is video of him and his paipo buddy (forgot his name) surfing big Sunset and Waimea.

Those wide-tailed paipos are the fastest thing in the water, at least on waves that aren't too big and fast to be caught by a paipo rider. We can only paddle and kick maybe 3-4 MPH on those short boards (they're about 1/3rd as long as a big-wave gun). A surfer can paddle maybe twice as fast, so they are limited to about 35 ft waves (or 40 ft if you're Greg Noll!). Any bigger than that, and you need to be towed in. A 50-foot wave is travelling nearly 31 MPH, about 4 or 5 times as fast as a surfer can paddle his big gun, so he needs some help from that Yamaha WaveRunner.

I didn't surf Waimea Bay until the beginning of the '69/'70 winter season, not long after I came over here. I lived at Makaha for the first 15 years. In fact, I lived on Makau street for 4 years (from '73-'77). You must have seen me in the lineup if you went out early in the morning. I was usually the first guy out (at 'first light').

As I understand it, your Vcurl is the speed at which the break point of the curl progresses along the length of the wave crest. If that's the case, I don't see how the curl speed has any limit -- at least at the speeds we're talking about in surfing. For example, a long-crested wave moving nearly perpendicular to shoaling isobaths can break virtually simultaneously along its length (I'm sure that most of us have seen long-crested curling waves break in which the curl moves along hundreds of feet down the length of the crest within a couple of seconds.)

Whether or not a surfboard can keep up is another question. You assume that the board and rider have an energy budget comprised of both kinetic energy and potential energy -- and that total energy remains constant during a ride. This assumption is equivalent to assuming that there is no gain or loss of total energy during the ride, or that any loss of energy is compensated by an associated gain of energy of equal magnitude from another mechanism. It is relatively easy to demonstrate that there is a loss of energy -- for example, when the board and surfer plane across a level sea surface and there is no source of energy they quickly slow to a stop (e.g. when coasting straight off out into the flats) rather than continuing at the same speed as at the end of the drop. Conversely, if the energy budget consisted solely of the potential energy available when starting to catch a wave, and there is no gain or loss of total energy during the ride, then if or when the surfer and board go up the face of the wave, they should come to a halt (relative to the wave face) as they reach the crest. Yet all of us have seen bodies and boards launched at speed into the air above the crest of the wave during a late kickout.

Attached is a graphic showing the output from a (1980's to 1990's) computer simulation model of surfing on a wave and how the speed achieved (steady-state conditions) is affected by how the surfer trims the board ("angle-of-attack") and where one places the board on the face of the wave ("wave slope"). The contour lines are essentially your "Ride Angle" (smaller angle -> increasing speed). In this particular simulation, the optimum trim position (relates to AOA) is predicted to be about 11 degrees, and the optimum position on the wave is where the slope of the sea surface (measured inshore to offshore) is about 48 degrees, This resulted in a predicted speed of about 22.7 mph. Other predicted quantities (not shown) are: speed, wetted area, wetted length, and location of the surfer's center-of-mass (AOA trim).

mtb

## BOARDANG.GIF

Great stuff here! I think your above assumption only applies to big single drop waves like Waimea. The way that I see it, the surfers muscles are effectively an engine that converts potential energy into kinetic energy. The engergy put into doing a bottom turn allows the surfer to go back up to the top of the wave for another drop. Like a forced pendulum, if you make several little pushes at the right times, then you can really get going fast. The image that comes to my mind is of Laird riding a wave at Jaws. He seems to be moving the fastest after making a few turns and drops. He is rythmically increasing his velocity as he travels at an angle across the wave.

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.

The formula I originally described in the "Part 1" essay on "Surfer Speed...etc" was for GPS speed of a surfer, relative to the BOTTOM. So, "Surfer Speed" is the Resultant of two motions: Curl Speed and Wave Speed, moving at right angles to each other, where:

(Surfer Speed)^2 = (Curl Speed)^2 + (Wave Speed)^2

Note that Curl Speed is also the speed of a surfboard relative to the WATER, but only IF the board stays in the same relative position on the wave face. It is the speed you can measure with a boat speedometer on the board.

The fastest trim line on a wave is the HIGHEST line that you can maintain. Bodyboards and Paipo boards can trim WAY higher than a surfboard, and the riders that DO go up there are maximizing their speed.

The formula I derived for Curl Speed is:

Curl Speed = SQUAREROOT(2gHb), or, Vcurl = SQRT(2g times Hb)

where, Vcurl is in ft/sec, g = 32 + (13550 / 99999) exactly, (or about 32.13550136, rounded),

and Hb = True, Total Breaking Wave Height, in feet (including the Trough).

If you know or can calculate Surfer Speed, Vcurl = Vsurfer x SIN B, (or =Vsurfer x COS A)

If you know or can calculate Wave Speed, Vcurl = Vwave x TAN B, (or =Vwave / TAN A)

The reason I posted all this stuff in the first place (on several websites) was to 'shake the bushes' and see if anybody out there was trying to measure surfboard speeds in a reliable manner. The worldwide response was not as great as I had hoped for, but what few responses I DID get were very helpful and I want to thank all you guys for your input.

By the way (I almost forgot)...

(for "mtb"): I have a question for you.

Did you use a Logarithmic Curve for the Wave Face, or a Circular function, to get the slope of the wave face? Terry Hendricks used a circular wave face shape for his calculations of board speeds. I always considered it a logarithmic curve from the trough up to at least the point where the wave goes vertical, just before breaking.

Also, on your interesting graph of "Track Angle (which I label Peel Angle "A" in my formulas) vs. Angle of Attack and wave-face Slope", there is a 'Minimum' Track Angle of somewhat >51 degrees shown at about 11 degrees AOA and 48 degrees Slope. That's very interesting to me, because MY "Maximum Makeable Ride Angle" or "Break Angle B" came out to about 51.34 degrees. That would be about 38.66 degrees for the Minimum Peel Angle.

What do you make of that? Could I be validating your graph? (or vice-versa?). Hmmmm...

Anyway, Many Thanks, again! Your input has been very helpful!

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.

Howzit, again!

I wanted to clarify what I believed were the real-world ramifications of my "Surfer Speed, etc" formulas, which were based on a surfer's Total Energy Budget.

The formulas assumed that there was NO energy loss as the surfer continued his ride across a wave. That's patently impossible, of course. I'm looking for the Theoretical Maximum Energy here, which assumes NO LOSS.

It was also assumed that the surfer dropped in from the very TOP of the wave. That probably also is rarely the case (unless you're a paipo boarder, making a VERY late takeoff...not unusual at all!).

Then, it was assumed that the very BOTTOM of the wave is reached when making the bottom turn. Never happens! But, that was the assumption I made so I could use the ENTIRE Breaking Wave Height, Hb, in the energy calculations.

Note that I was looking for the Fastest-Possible "MAKEABLE" Curl Speed that a surfer could keep up with. That is a function of of the Wave Height and the Peel Angle. There is absolutely nothing in the formulas that put a limit on how fast the wave itself can peel across the crest of the wave. The only limit on Curl Speed is...Infinity! That's when you have a total close-out of the entire remaining portion of the breaking wave. The Peel Angle A at that moment is ZERO degrees (and the "Ride Angle", or Break Angle, B, measured away from 'straight-off, is 90 degrees.

The maximum possible energy is obtained if the surfer uses the ENTIRE wave height, and if there is NO loss of energy during the ride. In that unlikely case, what is the theoretical angle of ride CLOSEST to the wave crest that would enable the surfer to make the wave?

In the real world, the Maximum Ride Angle seems to be around 50 or 51 degrees away from straight-off (Angle B), or 39 or 40 degrees away from the crest of the wave (Minimum Peel Angle, A).

The wave can, and often will, peel off faster than the surfer can go across the wave. Ask the regulars at Maui's Maalaea Bay, or Supertubes, or Snapper Rocks...On some swell directions, the wave, or portions of it, are simply UNmakeable! You get closed out...somebody else further down the line drops in on your now-empty wave, and goes as far as HE can on it.

Some day, we will have rocket-powered boards that can go around close-out sections at will, but don't collide with another rocket-powered board. If the fuel tanks rupture, the resulting explosion will take out the entire lineup! Ha!

Let's go surfing, now...

Hi Larry,

You're too fast for me! I can't respond as rapidly to your posts in this thread as quickly as you produce them. Hence you're already posting a new post before I can even respond to your previous one. So I've decided to stop posting to this thread until I can respond to your set of posts via a single post. When I complete that task I'll post my response here in the form of an attached MS Word *.doc file.

But first, a couple of comments relating to your most recent posting:

That's almost correct. What is really assumed is that there is no net gain or loss of energy in the system. An obvious source of energy loss is via the various mechanisms that produce drag (e.g. skin friction, induced, form, wave train generation, etc.). But where does the input of energy into the system come from? It comes from gravity, the combined weight of the surfer and board, and the wave shape and the wave-associated motions of water.

The surfer has some degree of control over the rate of energy loss, and/or the rate of energy gain, by how he positions the board on the face of the wave, and how he trims the board for minimum drag. As long as the rate of energy loss due to drag is less than the rate of gain of energy gain, the total energy in the "energy budget" will be increasing and thus permitting increasing speeds, or allowing the board to be positioned increasingly higher on the wave, or some combination of the two. In the extreme (i.e. no energy loss to drag at all), the maximum speed that can be obtained builds indefinitely -- or at least until limited by some other factor (such as the availability of wave face space).

mtb

ps. In support of this view, I call attention to the statement that you made that maximum speed is achieved by riding as high as you can on the face of a wave. That speed condition would seem to be impossible in your unchanging 'Energy Budget' approach (even in the absence of energy losses) since it is the potential energy in the budget that increases with increasing position of the wave face while the kinetic energy decreases accordingly. Thus one would expect the board speed to be increasing the lower one is riding across the face of the wave.

Hi, once again, "mtb",

Sorry about the frequency of my responses; I'm retired, and probably have more time on my hands than all you guys who still have time-consuming jobs to keep you busy.

I've been surfing since 1950, and riding paipos since 1964. My experience with the paipos has been that I can go significantly FASTER if I stay as HIGH on the wave as possible. Part of the reason, though, is that I maintain VERY close trim to minimize drag. I would guess that my angle of attack is less than 5 degrees, maybe even approaching zero degrees when at high planing speeds. My board has a planing hull, but it is also buoyant, so as to minimize wetted area and the amount of water being disturbed as I pass by.

If you go low on the wave, you will go slower. Gravity is your 'engine', but the steeper upper reaches of the wave gives you more 'drive' from that engine powering your ride. Try it yourself.

I have no trouble passing surfboards. The typical surfer on a longboard maintains excessively high angles of attack on most of his ride. All that drag keeps them from going as fast as they could. And the large amount of rocker on the board's bottom also means lots of drag.

In 1970 I told Dewey Weber and Harold "Iggy" Ige, his shaper, about my experiments at Makaha, Sunset Beach and Waimea Bay using flattened bottom curves and minimal nose kick for very short boards. My fastest boards had wide tails, shallow concave bottoms and a single skeg for minimal drag.

Iggy had shaped a VERY fast 6' 2" short board in 1969 that he rode in 12-ft surf at Malibu, and he had the fastest board in the water. That design became the Weber "Ski", which my surfing buddy, Jimmy Blears used to win the 1972 World Surfing Campionships at San Diego, California.

My Conclusion: Flat is Fast! Wanna go really fast? Ride a paipo board! And stay High!

Not convinced? Take a look at this video of "Flyin' Fearless Phyllis" Dameron at Waimea Bay:

www.youtube.com/watch?v=fj3Y39gu1HY&NR=1

I've seen paipo's pass full guns, on the drop, at Waimea. Early to mid 60's. Was that you? Looked like big guitar pick.

Bill ThrailkillSHAPER SINCE 1958Hi Larry,

The thrust of this thread seems to be changing. In your earlier posts to this thread, you were presenting your 'Total Energy Budget' model as means of estimating the maximum speed that can be achieved. One of the assumptions implicit in the model is that it is a 'closed' system and the total energy of the system is constant (and is equal to the total energy at the time the surfer catches a wave). I commented that one of the model predictions you listed was that the fastest speeds occur low on the wave face (as all the potential energy is converted to kinetic energy), and vice-versa high on the wave face (i.e. all the kinetic energy has been converted into potential energy). From your subsequent postings we seem to be in agreement that observations indicate that the fastest speeds are associated with surfing high on the wave face instead of low. Hence there is a serious discrepancy between the Total Energy Budget model prediction and direct observation. This led me to point out that the model is not a closed system and that there are both losses of energy associated with drag, etc., and energy gains associated with the interaction of the board with gravity and the sloping face of the wave.

With respect to energy loss, you responded that since you were interested in predicting upper bound for the maximum kinetic energy it was appropriate to assume no energy loss. That's fair enough. But you have not addressed how to arrive at an upper bound for the rate of energy input and which doesn't lead to a total energy value that continues to increase with the passage of time (normally the magnitude would be limited by the rate of loss of energy equalling the rate of input--but you've assumed that to be zero).

mtb

Howzit, Bill,

The guy you saw at Waimea Bay on his own designed 'Guitar Pick" style skegless wood paipo in the '60s was John Waidelich. He was a pioneer of big-wave surfing on paipo boards. There is video of him and his paipo buddy (forgot his name) surfing big Sunset and Waimea.

Those wide-tailed paipos are the fastest thing in the water, at least on waves that aren't too big and fast to be caught by a paipo rider. We can only paddle and kick maybe 3-4 MPH on those short boards (they're about 1/3rd as long as a big-wave gun). A surfer can paddle maybe twice as fast, so they are limited to about 35 ft waves (or 40 ft if you're Greg Noll!). Any bigger than that, and you need to be towed in. A 50-foot wave is travelling nearly 31 MPH, about 4 or 5 times as fast as a surfer can paddle his big gun, so he needs some help from that Yamaha WaveRunner.

I didn't surf Waimea Bay until the beginning of the '69/'70 winter season, not long after I came over here. I lived at Makaha for the first 15 years. In fact, I lived on Makau street for 4 years (from '73-'77). You must have seen me in the lineup if you went out early in the morning. I was usually the first guy out (at 'first light').

Gotta go! Time for the Evening News. Aloha!

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