# Dynamics - An Area Tool (And A Segue Into Design)

Area Tool

The diagram hopefully makes things clear; you can estimate the bottom surface area of a surfboard by using rectangles, and the Area Tool offers a quick way to do just that. The tool uses a well know and established way of obtaining quick area estimates, (see any introductory Calculus book.)

You can make your estimates more accurate by reducing the width of the tool from 4 in to 2 or even 1 in. Though I’ve shown the tool using inches, you could use the metric system instead (e.g. centimeters). You could also make the Area Tool out of Plexiglas; it will make reading the various h values a lot easier. Of course, if you’re clever and understand the concept, you don’t even need a special tool, a simple ruler will do.

… Segue Into Design

The bottom area is of particular importance if propulsion in surfing is derived from the flow of water in a wave (see ‘Dynamic – The Trim Equation’.) Given that force is equal to pressure times area, the pressure coming from the flow in a wave, area becomes a design tool.

F = PA

(See, ‘Dynamics – The Trim Equation’ for way to estimate P using wave particle velocity.)

Increasing the area, for a given pressure would increase the force.

Though matters are rarely that simple, nevertheless comparing a fish to a standard shortboard, and then possibly to a gun, is likely to be interesting exercise. (I suggest exploring how surface area increases from the tail end forward, and correlating it with where the surfer usually stands while riding the respective board.) Fishes were designed for low flow conditions –i.e. small water particle velocities, whereas for guns, the opposite. Smaller water particle velocities means less pressure, the fish strategy compensating for this by using greater area. Higher water particle velocities means you can reduce the area and still have sufficient propulsion. Of course these are not the sole determining factors in the design of these two solutions (fishes and guns.)

But you could take this a little further. Narrower rear section boards, unless they are ridden on sufficiently large waves, tend to push the surfer to ride more forward on the board. Boards with wider rear sections tend to allow the surfer to surf farther back, but in general, tends to cause problems on larger waves (you generally loose the ability to remove or bring surface area on line –i.e. you loose a degree of control over propulsion.)

Of course, I am sure there are other explanations as to why surface area matters. This is just one take from a given perspective –i.e. if propulsion was derived from the flow in a wave. Also, the above discussion on area as a design tool is in no way complete, nor does the above discussion prove or disprove anything.

(Edit:Remove this line. 06/18/06, KC)

The next step will be an attempt to explore how propulsion as outlined in ‘Dynamics - The Trim Equation’ might impact design through bottom contours.

The next step will be an attempt to explore how bottom contours might impact propulsion as outlined in ‘Dynamics - The Trim Equation’ .

Kevin

PS

My apologies for the edit. I’m not very good at proof reading my own work.

Have you ever been called “prolific”?

(only with the most complimentary sentiment)

Nice area tool.

The catch is that F=PA is incorrect. (edit: can’t be solved in this context)

Without a force opposing the water movement you have zero pressure. . . . area by itsef does not resist the water movement. . . mass is required !!. . . and the trouble is that F=PA presupposes that there is a given and fixed pressure (and thus not only mass, but a changing mass) when in fact there is not a given pressure. . . the formula represents a fallacious circular argument in this case.

Why is there not a given pressure?

There is no given pressure because pressure due to horizontal movement depends upon the inertia of the object. . . . and once the object is moving with the water at the same speed as the water the pressure goes to zero no matter how much area (and mass) the object has.

The bottom line is that horizontal water movement cannot apply any force to the object once the object is moving with the water . . . for the water to apply a force there must be an opposing force

The pressure between the water and the object will be greatest when the water meets a stationary object ( or one moving in the opposite direction to the water movement) . . . . once the object accelerates in the direction of the water movement the pressure will decrease and will reach zero when the water and the object are travelling in the same speed and direction)

Furthermore, once the water and the object are travelling in the same direction it is impossible for the object to change its direction by angling itself in relation to the water movement. . . . because the object cannot provide any force which opposes the water movement.

Pressure is not a useful way of understanding the effect of horizontal water movement on a surfboard. . . . . and your design conclusions, which are based on a physical fallacy, are also incorrect.

.

F=PA is correct. Force per unit area is the definition of pressure. Also, a fluid moving across a surface can cause pressure on that surface. These are basic principles. You can argue about the interpretation and application of the principles, but F=PA will always apply.

Paul

The idea is correct, I’m dumb with formulas and calculations. But It’s true, the comparison between a fish and a gun (in extremis) is valid and makes sense even to a Physics idiot like me.

The deal is: there’s always a oposing force at least in two ways: the pressure as a result of the surfers weight at the same time that a board is running a wave. The board’s bottom doesn’t ‘goes’ with the wave, there’s a flow of water going against the bottom that makes the board lifts, so, there’s no lack of the ‘opposing force’. Both forces (surfer’s pressure and bottom flow) are ever present in surfing. What Tom Bloke said is true if you just pull your board into a wave without no surfer over it, then, the lack of surfer’s pressure over the board will make the board miss the wave or be out of control ('coz none is adjusting the ‘pressure X flow’ conditions to a proper ride).

At least it’s the understanding of someone who stop studying physics at high school and never been a great student.

J.

Quote:

F=PA is correct. Force per unit area is the definition of pressure. Also, a fluid moving across a surface can cause pressure on that surface. These are basic principles. You can argue about the interpretation and application of the principles, but F=PA will always apply.

Paul

Yes the equation is correct in itself but it can’t be solved in the context of horizontal water motion. . . . . in case you hadn’t noticed, area does not imply pressure. … . a mass is required, and there is no mass in that equation. . . . .

Regards,

Roy

Quote:

The idea is correct, I’m dumb with formulas and calculations. But It’s true, the comparison between a fish and a gun (in extremis) is valid and makes sense even to a Physics idiot like me.

Quote:

There’s a well known logical fallacy happening here. … . the truth of the conclusion does not imply the validity of the argument.

The deal is: there’s always a oposing force at least in two ways: the pressure as a result of the surfers weight at the same time that a board is running a wave. The board’s bottom doesn’t ‘goes’ with the wave, there’s a flow of water going against the bottom that makes the board lifts, so, there’s no lack of the ‘opposing force’.

No, you are attempting to use the downwards force of gravity as the “opposing force”. . … . this won’t work as an opposing force to horizontal flow, because it occurs at right angles to the horizontal flow. . . . the reason it seems so right when you say it is because the force of gravity is working against vertical flow constantly. . . .but what Kevin has been trying to do all this time is to use gravity as a ‘counterbalancing force’ against horizontal water movement. . . which it can never be. . . . . The only force opposing horizontal water movement is the inertia of the surfboard and rider, and once this is overcome no further force can be applied by the wave in the horizontal direction. . .

Ok here’s some more:

Let’s try to solve F=PA in the given context.

We are going to need a value for 2 out of the 3 variables

Let’s try finding a value for F (Force)

Can we establish a value for F?

The Reason: Even if we have a value for the kinetic energy of a mass of water in motion (which we don’t), this cannot be expressed as a force because kinetic energy does not apply force until it meets an opposing force. There is no opposing force in the equation.

Now let’s try finding a value for P (Pressure)

Can we find a value for P ?

No

The reason: Pressure is Force/Area, we have no value for force, therefore we cannot calculate pressure, even though we have an Area

So we cannot solve the equation with a value for only 1 out of 3 variables.

.

(There are lot of words in the following post and this thread generally about wave dynamics and other physical aspects of the physical act of surfing, but no argumentation–if you opened this thread in error, or do not wish to read many words about wave dynamics, even in the absence of argumentation, please use your BACK button to exit this thread now)

Roy, I think there isn’t any argument present that there is significant shear flow on the surface, although the verbiage is a touch confusing

But Kevin has always been aligned with the rest of the literature on wave dynamics in the understanding that the water particles in a wave (seen from profile) are simply describing a circle, the initial half circle crestward (seaward) and up, curvilinearly, and the other half of the circle beachward and down as/when the crest passes. Any differential between the particles at the surface and those below being quite small, since the particles below surface are describing the same pattern in smaller circles–all the literature by the experts in the field is in agreement. The whole thing is of course simply the manifestation of the energy pulse in the waveform throughout. No shear occurs independently or in opposition, of course.

I had misunderstood him to say that he was positing a really significant shear flow up and over the crest, which didn’t make any sense, since one, everyone working in the actual field says there isn’t, and two, a significant surface flow shearing seaward would shear the top of the wave pulse off, and kill the wave pretty quickly, but I was mistaken–how could that be, anyway–but I was wrong–he’s not positing any particular flow, although it does appear to be a term he is reluctant to not use, and I think I don’t understand why he doesn’t pick a different one to talk about whatever he’s talking about, which, again, does not conflict with any of the literature by the actual experts who actually know far more about all of this than any of us.

Or at least I think that’s his position–he said he finds nothing in any of the lit opposing his thesis, and it all says the water doesn’t go anywhere much to speak of, except up and down…

with a pretty small percentage of net beachward drift, gained at the crest. That forward motion being completely subsumed by the combined wave motion forward and the gravitational acceleration coefficient of the surfer.

I misunderstood because I kept seeing other people’s diagrams of this circular motion to (I thought) advance what I thought was his mistaken argument that there was a flow, that in fact (I misunderstood him to say) provided all our propulsion, but he wasn’t–I was confused–he assures me he is in complete agreement with the rest of the world’s understanding of these physical facts of wave water particle movement. Good thing–I thought he was just a crank when I had that mistaken reading of his ideas.

Boy, am I glad he got me straightened out on what he was actually saying. That there is no flow.

Also, Roy, are you meaning “down the line,” “beachward,” or “seaward” when you say “horizontal” “flow?” I’m having a hard time following you. And I guess I don’t understand why youre using that term either when you really seem to be talking about the overall procession of the waveform/pulse.

The flat area the formula calculator above measures seems to be pretty isolated from the entire sphere of variables in actual surfing, in that it completely ignores the reduced or enhanced efficacy of surfaces given by concave, outline bumps, rocker, rails (penetration,) speed, and wave curvature, but I guess it helps you make a surfboard that’s appropriate to the size of your feet–I think variability of leverage that appendage can impart depending on its size gets ignored a lot.

And as long as everyone’s having fun!

: )

Hi Janklow,

My argument has been that even if there is a real water flow towards the beach, that it can’t possibly propel a surfboard and rider in the way that Kevin has described.

Thus I have been granting a beachward flow so that I can more effectively show that Kevin’s propulsion theory doesn’t work.

However in regard to water movement towards the beach, net movement isn’t necessary for there to be kinetic wave energy in the beachward direction. . … it’s similar to a stationary wheel. . . a stationary wheel can drive another wheel at the top of its rotation. . . . but it can’t drive anything which is already moving faster than the wheel’s rotation . . . . and in the case of surfing, if the surfer is travelling with the wave , then he is already travelling faster than the beachward water movement at the top of the wave and can’t be propelled by it. . . all the beachward water movement can do in that case is to reduce friction slightly.

Cheers,

Roy

I’m glad that you’ve discovered things. But one thing you haven’t discovered is that I have said, “That there is no flow.” There is a flow of water in a wave, its just that the ‘net’ flow is close to zero, at least in deep water. I refer you to the literature you sent me.

As for the rest of what you think I’ve said, if have ever used the term ‘shear flow’ I apologize, but I don’t think I have, in fact I’m not sure it means anything. A flow is usually taken to be the movement of a volume per unit time, or a mass per unit time (in every book or source on fluid mechanics that I have read.) If you’ve actually encountered the term “shear flow” in the literature, please be kind enough to post the reference.

Flow (as defined above) is precisely what I have meant when I have use the term, particularly with regards to what the water in a waveform is doing - its just that for the complete waveform (in deep water) there is little to no ‘net’ flow. There is not need to find another term.

(Edit: 08/21/06, the last line in the above paragraph should read, “There is no need to find another term.” KC)

I have told you nothing that changes anything I have written so far, please don’t suggest otherwise.

(Nevertheless, I’m sure if asked Swaylock would be willing to make the private messages we exchanged available to any who would want to read them.)

Kevin

Apparently there is a number of references to ‘shear flow’ on the Net, so the term exists. It’s a shorten reference used when the interest is in the shear stress and subsequent velocity profiles developed by a flowing liquid under a particular set of circumstances. And perhaps there are other usages too. Nevertheless, I have not used the term, nor remember encountering it, let alone I understand why its been invoked here -i.e. with reference to the flow in a wave.

Kevin

Roy,

You seem to disagree with me, great. You’ve made this clear time and time again.

Kevin

The lay- and scholarly- (they never told us different–and you know how pedants with PhDs are–they’d tell us) consensus:

The surfer and his board are driven before the wave by simple push of the waveform overall, elementary grade of the face, and common gravity of the common variety.

Whereas, you think there are propulsive forces overriding those primary ones.

For the sake of those who didn’t bother to read the other threads

What is your “flow’s” vector in relation to the waveform’s overall motion?

What’s its net rate vs. the crest’s beachward V?

What’s it doing to surfers?

Inquiring minds and all

Quote:

Roy,

You seem to disagree with me, great. You’ve made this clear time and time again.

Kevin

Kevin,

In my humble opinion a theory isn’t worth 2 pins if you can’t defend it.

Personally, I welcome questions and objections, because in answering them I either strengthen my theory or get rid of a flaw in that theory.

Thus I have no interest in starting a mutual self congratulation thread, it just isn’t interesting. . . . . . this thread, on the other hand, is interesting, which is why I am here.

Furthermore, I am not going to stand aside and let you preach a theory which has fatal flaws without raising objections.

Having said that, I have to say also that I have learned something very important about water particle movement in waves through your posts, and if I am learning by participating in your thread, then I’m hanging around !

Please don’t ask your most interested discussion partners to leave, we have put lots of energy and thought into this topic. . . I have spent at least 10 hours of concentrated mental effort on the subject of surfboard propulsion since you started these threads, so be a good chap and defend your position, or alter it.

Now, to get down to brass tacks, so to speak, are you aware that pressure cannot exist without opposing forces ?

?

Roy/Tom

Not to defend anyone or take sides,

But…

if force equals pressure x area F=p*a

and force equals mass x acceleration, F=m*a

wouldn’t the following be true:

massacceleration=pressurearea and the totals balance out in a steady state

(trimming down the line)

And of course acceleration is from gravity.

However, (and there is always a however)

This is an over simplification of the physical dynamics of surfing.

if anybody has the time to breakout the other variables:

plan shape and board aspect ratio,

surface roughness

centers of pressure of the board,

wave shape and viscosity,

differing lift/drag ratios of boards, fins, etc

and thats just a quick list.

Book learning and theory aside,

doesn’t it really come down to the rider??

Enjoying this,

Pete

What he said about two pins–

and, while you may think you’ve been utterly clear, you haven’t, and you aren’t here.

How do you think you’ve been so clear, when the two people who have paid the most attention, and challenged your theories with the most direct and clear sort of questions, have two distinct ideas of what you’re on about?

You owe the other people who might be trying to understand (hello to you all, teeming masses) a reiteration on THIS thread of where this flow you mention HERE is and what it does… because you confuse (us) with the circular particle model that all experts in the field use to illustrate that the water in a wave doesn’t really go much of anywhere, and you are unclear about terms.

I would say that for their understanding, and for the sake of your integrity, now that you’ve asked us to leave, you owe them an answer to the 4 questions Roy and I asked above.

Newcomers to this line of discussion, please see the link in my signature below, and pay CLOSE ATTENTION to Kevin

EDIT: If Roy is accurate in stating that your belief is in a beachward “flow,” as you call it, it’s embarrassingly obvious that you’re really talking about a wave, and the elements of our surfing motion on it I describe above. In that case, my confusion stems from the fact that you’re talking about us riding a “flow,” instead of a wave. If you’re talking about a crestward flow, as I’ve thought could only be the case, and you’re talking about us deflecting across that “flow,” (as in river surfing, to which ocean wave surfing is roughly as similar as it is water-skiing) well then you’re talking about a surfer who has a very subjective view of what’s happening under him–the operative motion-inducing elements being wave push and grade with gravity, his deflection (pressure) against those and inertia.

I hadn’t thought we were badgering you unduly, inasmuch as you haven’t kept these specific points clear enough for anyone to have objected and given their clear understanding of you in support.

But I should address the forum: would anyone like to answer the questions I asked of Kevin?:

What is your “flow’s” vector in relation to the waveform’s overall motion? (Please, if you only answer one question, Kevin…)

What’s its net rate vs. the crest’s beachward V? (Note that if he’s saying it’s going crestward, to be meaningful in a net value its velocity would have to significantly exceed the beachward motion of the overall wave in the opposite direction–otherwise it’s just the wave’s speed, isn’t it–which would put the primary seaward flow at like, what, 25 knots? A river indeed. One you couldn’t miss, or ride with a moving wave’s beachward V combining with it for a surfer effective velocity over water of like 40 knots?! Wahhh! I’m flying! Why am I not going anywhere?! LOL!)

What’s it doing to surfers? (“Aaaaaaaa!!! Help!!!”)

using his modelling?

Or explain, if Roy’s understanding of KCsey’s thesis of flow is correct, how we would surf a “flow” going beachward–how would Kelly Slater do what he does riding a river-like flow toward the beach? (I don’t think Roy’s on it, even taking the piss here, but again, according to Kevin, this “flow’s” impact or value on surfing’s progress in any direction altogether overwhelms the combined influence of the wave’s overall beachward motion and gravity’s accelerative influence, so we’re talking about a flow speed of about 35-500 knots! LOL–is anyone else drinking?)

v

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Wouldn’t the water that is not in motion provide the opposing force required to produce a value for F? How can something (water) ‘move’ at all if there is no force? Isn’t air an opposing force? The sea bottom? I guess I do not understand how F can not be assigned a value save for some mass of suspended water self-contained in and of itself.

–snip

Let’s try finding a value for F (Force)

Can we establish a value for F?

The Reason: Even if we have a value for the kinetic energy of a mass of water in motion (which we don’t), this cannot be expressed as a force because kinetic energy does not apply force until it meets an opposing force. There is no opposing force in the equation.

And doesn’t anything in ‘motion’ provide pressure? You can’t have pressure without force and you can’t have motion without force, which assumes the existence of pressure… so…

force has it’s own value for pressure as it cannot exist without one

F must be applied to another value to be measured, most likely the medium taking the brunt of all this force and pressure. So, moving water, has force, has pressure, area has value… to what then, are we going to bash all this force with?

F=P(previously configured moving mass)*A(previously configured area which I’ll assume, in this case, has it’s own values for F and P)

P can not not have a value

A can of course have a value

F can not not have a value due to the existence of P, and visa versa

so the whole equation is invalid in it’s application here no? regardless of whether or not we can find a value for F or P.

We want the force resulting(r) from the redirection or refocusing of the original values of F and P (which we can not not have with something in motion and it’s velocity, (v)) and the added values of applied area and it’s Fs and Ps and Vs

So :O) R = P(F(vF) + (P(vP))) * A(A(avP + avF)) where a = a + avp and avf consideration

I know that doesn’t make any sense but what I think is missing is maybe velocity.?.

so… the area tool is effectively worthless, as is the area you’re designing, if you do not take into account the range of force and pressure applied to the area.

Your 39 square inches of perfectly contoured tail area has a very small window of applied perfection to any given moving surface. So the tough part is, I would think, finding the perfect area and contours that provide the widest range of advantage to the widest range of force and pressure to be applied to and from it etc etc so on and so forth