Dynamics - Relative Flows

Relative Flows

Opening Note: I never got around to issues regarding relative velocity in my propulsion series. So, why bother now? Good question; I have no answer. For those of you with absolutely no appetite for Math, skip to the Summary So Far section, if you’re so inclined.

Consider some stationary frame of reference. In this frame the water particle velocity will be given by,

[indent]u = ux i + uy j[/indent]and surfboard velocity by,

[indent]v = vx i + vy j + vz k[/indent], see figure 1.

As experience by a surfboard moving with velocity v, the water particle velocity will be given by,

[indent]w = wx i + wy j + wz k[/indent] where,

[indent]wx = (ux - vx)

wy = (uy - vy)

wz = - vz[/indent]Consider the special case when the board has the same forward velocity as that of the water particles, [indent] vx = ux [/indent] and isn’t climbing or dropping on the wave, [indent] vy = 0 [/indent] Then we have, [indent]w = uy j - vz k[/indent]See figure 2.

Now v, is generally modeled as the motion of the curl – i.e. where the surfer is most likely to be. Of course he need not be sitting in the curl, or some nearby region, but for modeling this is convenient. If this assumption is made, than it becomes apparent that the faster the curl, the more dominant the role of - vz k possibly becomes. Or, conversely, the slower the curl, the more important the term the other terms possibly become.

It is possible to put this is a form which allows for some quick calculations of angles, particularly the angle at which the flow will be hitting the board bottom, just divide [indent]w = wx i + wy j + wz k[/indent] by |w| = w, which will allow for the calculation of the cosine angles. To keep things simple lets take the no climbing or dropping case. [indent]n = uy/w j - vz/w k[/indent]Where n is a unit vector pointing in the direction of w and here, [indent]w = (uy* uy + vz*vz)[/indent]Then you simple take the arccosine as follows,[indent] arcCos(uy/w)[/indent][indent]arcCos(- vz/w)[/indent] Which will give you the respective angles from the y-axis and z-axis.

Summary So Far?

I plan on plugging in some numbers in my next post. But for now, there are a few things worth pointing out. Firstly, for this special case - of moving with forward water particle speed and no climbing or dropping - the flow as experience by the bottom of the surfboard seems to happen in one plane, the yz-plane. Second there is a upward component, the importance of which seems to depend on how the magnitude and direction of v.

To put this in perspective, here I’ve made the assumption that the board is pointing in the direction of v, which is not vz, vz is just the z-component of v. This of course, need not be the case, but if it is, than the flow interaction with the fins is, in the very least, not which most might visualize it to be. In particular, you’ve also got the upward component smacking the bottom of the board and fins - especially if they’re toe-canted. Worse, that upward component become more important the slower the curl, e.g. the smaller the vz component. But even if the vz is dominating, unless it also dominates or is the largest component of v, you’ve got a nice rail-to-rail kind of flow impacting the bottom and fins.

Though I plan of continuing this is subsequent posts, for now you’ve just got to wonder what toe-cant are doing. I haven’t dealt with changing angle of the bottom or fins with respect to this flow, but its not that hard to visual how a given change in board and fin orientation might change the interaction - (…gets even stranger.)

Am I Correct?

Hell, I’m open to correction. I know this, from a lot of the comments that have been made in this forum, as well as those made on the Net (fin manufacturer sites, fin research sites, various manufacturer sites, etc.) such a treatment seems to be somewhat off the mark. The flow past fins seems to be viewed in a manner similar to the flow past a submerged wing traveling in the opposite direction to the flow, but more or less parallel to it - kind of a classical view of how things might be working. Some authors have given consideration to the angle of attack for toe-cant, but still the flow seems to be seen as coming virtually head on - which is not necessarily the case as presented here. Then again, the case primarily described above is limited -i.e. a trim, or quasi-steady-state sort of case. It’s kind of an understatement, but if you start making turns - things do change.

kc

PS

Somebody please check my Math, and hopefully, reasoning.


Request for Example Data

If anyone has some cant, toe, water particle, or surfboard velocities they like to suggest as examples please let me know. Right now, I’m inclined to go with a range of cant from (off the vertical) 0, 5, 7, 9 degrees (9 degrees being unlikely in practice, but possibly interesting), a range of toe from (off the center-line) 0, 2, 4, 5, 7 degrees (7 degrees being unlikely in practice, but possibly interesting), and as for surfboard velocity (or curl velocity) whatever I can dig up in the archives or literature, same for water particle velocity.



Dig these videos, kc

http://www.liveleak.com/view?i=c33_1181213616

http://www.youtube.com/watch?v=93nVjY6iFjs

Hello Kevin

In figure 1 you have shown a surfboard which has a beachward movement which is equivalent to the horizontal beachward movement in the top of the wave (Ux = Vx)

The problem with that is that with a beachward movement only equal to that of water particle movement, the board will lose the wave as the wave travels towards the beach much faster than the horizontal beachward component of the circular water particle movement in the top section of the wave.

This mistake is revealed again where you say:

Quote:

"Consider the special case when the board has the same forward velocity as that of the water particles, [indent]vx = ux [/indent]

and isn’t climbing or dropping on the wave"

The problem with that statement is that if the board has a beachward velocity equal to the ‘beachward’ velocity of the water particles, then the board will be climbing on the wave and will lose the wave. . . . this is for the same reason given above: namely that the wave travels towards the beach much faster than the beachward component of the water particle rotation . . . . . thus if the surfboard is to stay on the wave its beachward velocity must be equal to that of the wave, which is not what you have shown.

In all of your previous writing on this subject you have made the same mistake.

.

Aside from the fact that I could watch Curren work it all day, and the river clip was excellent, can I assume that, maybe you’re seeing, at least bits of this ‘vista of countersense’ that I seem to be suggesting?

Agreeing with it is another matter - its just a hypothesis.

kc

Agreed- in fact, this ( http://www.youtube.com/results?search_query=flowrider ) provides some interesting insights to the question.

Now, what are all the vectors involved here? As in what forces are acting on a trimmed board moving along a board in a steady-state condition? I dunno if the centerline of the board is paralell to the direction the board is moving through the water, even in that steady state, though I suspect I am anticipating Kevin’s next.

doc…

If you look at Kevin’s post it shows that he is still assuming that a beachward flow of water particles propels surfboard and rider towards the beach, which is clearly nonsense as in order to travel beachward with the wave the beachward velocity of the board must exceed the speed of the rotational movement of water particles within the wave. . . . and one can’t be pushed by a flow which is moving more slowly in any direction than one is oneself.

Of course Kevin isn’t coming out and saying it directly but it’s apparent from his drawings and formulae that he hasn’t figured it out yet.

.

Kevin, what do you hhave to say about the fact that the following statement from your first post describes a situation which cannot occur ?

Quote:

Consider the special case when the board has the same forward velocity as that of the water particles, [indent]vx = ux [/indent]

and isn’t climbing or dropping on the wave,

It cannot happen because if the board has only as much forward velocity as the beachward movent of water particles which occurs at the top of the circular rotation, then it is moving beachward more slowly than the wave and thus will climb up the wave and go over the back, losing the wave !

The ‘special case’ is not in the realm of physical possibility. . . . .

:slight_smile:

Tom, I think I understand your point.

That is, if your point is that not all water particles on the face are traveling at the propagation speed. So, yes I’ve oversimplified things to at least get us to the point where we could work out the particulars, my apologies, but simple is often a good start.

But you’ve also introduce a topic which is close to my heart, in particular, what is happening to the forward component of the flow under the board once the board is moving with, if only close to the velocity of the forward moving water particles - definitely worthy of a post, and if you don’t, I will.

However, for the moment, consider, if the forward component of the board is not sufficient, then it will, as you say ‘climb’, but how different is propagation speed from the maximum forward water particle velocity (and I didn’t say this in my post!. Thanks for pointing this out.) The difference is likely to be small under the trim or quasi-steady state conditions, that is the board is traveling at propagation speed, or possibly the forward speed of the curl region, that I described, which would make the component very small, but still present nevertheless. It’s worth noting, but I’m not sure it would significantly change the argument.

There is also a danger, which I always fail to point out when switching from talking about water particles and then whole bottoms of surfboards. It’s that the various water particles interacting with the bottom are not all moving with the same velocity. I suspect you understand this, but I thought I’d mention anyway.

As for making this same mistake in prior posts, my guess this isn’t the only one, nor likely to be the last - hopefully, you’ll look elsewhere for perfection.

kc


Doc, no forces discussed, just trying to get the relative issue introduced so I could start considering flow around the fins. Once the flow hits the bottom or fin, forces are imparted (momentum exchanged etc.) and flows change.

Here the arguement is that the flow is probably, at least in a wide range of conditions, not nose-to-tail as it is often visualized to be. I’ve argued this before without providing the kind of arguement provided here. The motivation here is to try and touch on what toe-cant are doing when surfing a slow curl, as opposed to a fast curl, among other things.

I do intend on posting a bit about the development of force (see my reply to Tom’s post.)

kc

Tom, again, perhaps I should have written ‘approximately equal’ so as to make the term virtually vanish? I know now, I wish I did.

Also, and I didn’t want to revisit this, but its not the forward component of the flow that makes the surfboard move forward, but the total flow with respect to the bottom orientation.

kc

Better be careful Mr Casey : that brand they are about to stamp on the poor novitiate might become fashionable, then all the kids will be lining up to get theirs.

Quote:

Tom, I think I understand your point.

That is, if your point is that not all water particles on the face are traveling at the propagation speed.

Firstly thanks for the cartoons, we are enjoying them a lot, my partner was ROFL at the “get some air?” one.

Actually isn’t it the case that none of the particles travel beachward at the propagation speed and thus the average beachward speed of the surfboard always exceeds the beachward water particle speed . . . . and always exceeds it when in trim or dropping down the wave

Quote:

But you’ve also introduce a topic which is close to my heart, in particular, what is happening to the forward component of the flow under the board once the board is moving with, if only close to the velocity of the forward moving water particles - definitely worthy of a post, and if you don’t, I will.

Isn’t it the case that the board is nearly always moving faster beachwards than the forward moving water particles ?

I seem to remember that according to figures we looked at last time this topic came up the speed of the water particles is only about 10% of the speed of the wave front so on a wave doing 10 mph beachward the beachward water particle movement is only about 1mph or so.

Quote:

However, for the moment, consider, if the forward component of the board is not sufficient, then it will, as you say ‘climb’, but how different is propagation speed from the maximum forward water particle velocity (and I didn’t say this in my post!. Thanks for pointing this out.) The difference is likely to be small under the trim or quasi-steady state conditions

The propagation speed is many times greater than the forward water particle speed at the top of the wave ( there was an online wave physics calculator we were using last time, will see if I can find it)

Thus when ‘in trim’ the board is moving beachwards many times faster than the water particles in the top of the wave

.

RS, I am pretty sure Kevin is talking about the anti-beachward component of the surface particles’ hydraulic circular when he mounts the plank in the face for his visual aid about the “propulsive” effect of that flow as a component of the surfer’s trim rate. I’ll buy that repulsive force combined with gravity can deflect you laterally but you look at the flow rate in the river clip to derive the trim rate that dork achieves and then look at the rapid rate of shoaling and what must be correspondingly high rates of the flow he talks about in the Sandspit clip-- and you have to watch to see what TC is doing and able to do and with what, versus what the river dork (sorry, but why bother?) in Germany is doing etc. They are two very different sets of surfing dynamics. There is relativity but the dynamic/act sets are so different that they are almost completely different. BY the way, the guy in the river is using some force to stay ahead of the crest, which makes the whole thing work, and you can watch TC use the same force to accelerate from the top to the bottom of the wave.

Roy, first off, there is no excuse for my referring to you as Tom, my apologies. I’ve believe I’ve done this before, and it was not intentional. Still, as far as I am concerned e-nicknames are a plague for the ‘slow’, though I understand how they might be valuable e.g. duplicate names, etc


For the moment, please allow me to restrict the question to how it could be that wave propagation velocity, which is not necessarily curl velocity, could be faster than any of the respective forward components of the velocities of the water particles in a wave. I don’t know how this could be, but I’d love to understand how. So, please explain, if you’re so inclined.

But maybe that’s really not what you asking. I can’t help but wonder if what you are suggesting is that there is a range of water particle velocities, some may have a forward component as fast as propagation speed, some slower, and over an area, say defined as big as the wetted area of the board, water particle velocity (forward and upward components) ranges quiet a bit. Which, I would agree with.

In fact, it leads to some interesting design considerations, some of which were touched upon in the recent rocker thread - the notion of template and rocker, bringing bottom surface area on- and off-line. Is is possible to bring a the same amount of surface area on-line with different templates, however the nature of the interaction with the flow will be different depending on the template. Longer narrower templates experiencing different flow profiles than shorter wider templates in general, for the same amount of wetted surface area -i.e. they will experience a different range of water particle velocities. Of course how and where on the wave they [different templates] are surfed will matter, but the point is meant as a general one.

kc


PS

I believe the site you have in mind is http://www.coastal.udel.edu/faculty/rad/linearplot.html. It’s by Robert A. Dalrymple of the Center For Applied Coastal Research (CACR).

Hi Kevin, yes that’s the claculator thanks.

If we look at some of the maximum horizontal particle velocities they do appear to be much lower than the wave speed, for example a 2 metre wave with a 10 second period shows a maximum horizontal particle velocity of only 1.4 mph in 100 metre deep water, and only still only 4.1 mph in 3 metre deep water.

.

Quote:

As for making this same mistake in prior posts, my guess this isn’t the only one, nor likely to be the last - hopefully, you’ll look elsewhere for perfection.

kc


KC, I admire your thoughts on the topic and your cartoons deserve a place in the Sways book !

Looking forward to more.

Regards, SF.

Some Notes On Propagation Speed and Forward Water Particle Speed In A Breaking Wave

Roy,

It is my assumption, that a rapidly shoaling wave, virtually one that is about to break is a somewhat different beast than that of a deep water wave – things change rapidly as the wave begins to ‘break’ or is near breaking. It is my interpretation that in the case of a rapidly shoaling or breaking wave, the assumption that forward water particle speed of some of the particles is close to, if not equal to the propagation speed, in fact, the more vertical the face in the curl region, the more so.

Beside: Trying To Avoid A-Hot-Poker-Up-the-Ass Note

Though I could probably regurgitate one of a number of models used to model breaking waves, I wouldn’t feel comfortable doing so – my understanding of these models is pretty superficial. Luckily, at this point I’m not really convinced that it’s necessary – but ultimately I could be wrong.

My guess is that my statements above will not satisfy you, but it’s about as far as I’m capable of going at this point. (That point being determined by ignorance, and not an anal tendency to hold things back.) Please consider either researching breaking waves, or possibly finding an expert in the field to explain the various models to you. Or perhaps you feel confident in your own interpretation from experience. Either way, perhaps a hot poker awaits me in the future. (It’s getting crowded up ‘there’ [my ass] and a line of hot-pokerers seems to have formed, not necessarily in this forum, so anticipate a small wait.)

Back on topic… sort of

Nevertheless, the idea that not all the water particles involved are moving at the same forward velocity is an important one. This would imply the presence of a x-component term (see figure 1 in initial post.) In my view, how large this term is, or how big the collective contributions will be, will depend on where the surfboard is with respect to the curl, its orientation, and the geometry of the wetted surface area.

That said, I can see what’s at stake, it’s the role of that nose-to-tail component of the flow, which seems to be pretty important to many of the current views as to what is happening under a surfboard. I surely don’t deny its existence; I’m just inclined to include consideration of a rail-to-rail component, as well as a vertical component. In fact they all will contribute to planing, propulsion and fin interaction.

So, the more inclusive equation (?),

[indent]w = (ux – vx)i + uy j - vz k[/indent]

How big is the first term in the curl region? I suspect it depends on the nature of the curl and where in the curl you are. Still, there are, those nasty rail-to-rail and vertical components to deal with. Or perhaps not, I guess I’ll find out.

kc

PS

I could be wrong, but Dalrymple’s applet was introduced in a post as an aid to visualizing the nature of the motion of water particles in a wave, at least their overall general trajectory –i.e. the way they move in general. I don’t believe it was ever stated that it modeled a breaking wave. I don’t believe it does, nor do I believe Dalrymple meant it to. I may have used some of Dalrymple’s numbers at some point to illustrate the range of magnitude of the force from the impacting flow, but I don’t believe I went farther than that.


Regarding The Knistle’s Diagram

I’ve attached Knistle’s diagram of a typical trajectory of a surfer surfing a wave. It’s ‘thread related’ but not necessarily related to Roy’s post. I’ve modified it slightly to show the u and v vectors (see figure 1 in initial post)

Aloha Kevin

Your quote above…

"It is my assumption, that a rapidly shoaling wave, virtually one that is about to break is a somewhat different beast than that of a deep water wave "

… Points out an important issue that is continually missed when discussions around this subject surface.

Those who rarely ride steep, hollow breaking waves could easily miss this important point. (and apparently many do, miss it that is) There is no question that much of the water in a breaking wave is moving forward with great force toward the beach and that anything immersed in that water or that is hit by that water will get the positive or negative effects of that movement as the case may be.

Anyone sitting in the channel at Pipeline watching the waves break (pitch forward) can easily testify to the fact that the water is moving toward the beach with incredible force, not just cycling in circles. Where the “lip” actually begins its journey as a “lip” or how far down the wave the “Lip” area extends, could be debated endlessly for sure. But as a surfer I know, as do most, when it has gained “Lip” status and becomes valuable or dangerous to me in wave riding. Where it then ends up crashing FORWARD into the shore is usually a long, long way from where it began.

If one was to dye the water a couple of hundred yards out from there, the dye wouldn’t move very quickly to shore, due to Dalrymple’s example. But if you threw the die in an emerging “Lip” it would be on the beach in a few short seconds.

This can make for a very difficult and complicated discussion regarding how a surfboard is propelled as it is through an elaborate interaction of all the forces including air movements. Most surfing takes place in that neblus zone where the wave is transitioning from a green water swell into white water soup. With available energies being dispersed in all kind of directions and ways. Some water is circling, some is moving vertically, some horizontally forward, some downward, some angular… as does also the air.

A surfboard’s interaction with the breaking wave is not governed solely by Dalrymple’s example and in fact most contemporary wave riding in breaking waves has little to do with it. Even so, as Dalrymple’s example shows, the horizontal movement of the surface water particles shouldn’t be underestimated. For example, if one was to stand with their face right in front of a log floating perpendicular to the beach as waves pass under it, it would first pull back a bit from the previous wave and then rush forward knocking out a few teeth from the rush of a forward horizontal force. To believe this wouldn’t happen because one didn’t believe that water moves forward, would be a dangerous presumtion to say the least.

Quote:

It cannot happen because if the board has only as much forward velocity as the beachward movent of water particles which occurs at the top of the circular rotation, then it is moving beachward more slowly than the wave and thus will climb up the wave and go over the back, losing the wave !

I will not pretend to understand the details of what you guys are discussing. But I think that you are missing the point that water particles do not have to have any significant movement to transfer energy between one another.

For example. sound (waves) propagates through the air without much significant movement of the actual particles, but the energy is still moving through the air.

Hi Kevin,

The calculator shows us (as you point out ) that the horizontal particle movement increases in speed as the wave steepens in shallow water.

I wonder if this movement ever equals the speed of the wave front in an unbroken wave.

Assuming that the horizontal particle movement is less than the speed of the wave front, I have argued that the particle movement cannot push the surfboard, however after thinking about it some more, it seems to me that it is a bit like the following scenario: If a car is travelling at 60 mph with a following wind of 40 mph, the wind cannot be pushing the car. . . nevertheless the following wind will increase the speed of the car by reducing resistance. This analogy applies when going straight to the beach and I think also when trimming down the line although that is a bit harder to visualise

RS