Dynamics - A Simple Vector Model

General Discussion
1

[=Black][=1][ 2](Edit 10/07/06. Notes on rewrite. KC)

[/]

Rewrite Notes.

After reading the replies it was fairly clear that these posts didn’t accomplish what had I had hoped they would. I then rewrote the posts, but while in the process of resubmitting them, I realized that my rewrite wasn’t likely to make matters any better. At that point I just decide to leave it be for a while, though I left the diagrams, which virtually contain all that was written, but in a more condensed form.

So whatever turns out to be the case, it should be noted that the comments which have been posted by others may or may not apply to what is eventually the final form of this thread.

Those that have posted to date will be notified of what I am doing and given the opportunity to remove (if only the body) of their post. If they choose not to do so, please make sure you observe the time of their post. If it’s prior to the time of this edit, then there is a good chance they are referring to something that’s not there anymore.

Thanks,

Kevin

[/][/]

Part 1 A Simple Vector Model of A Surfboard on A Wave

We can broadly group the forces acting on a surfer/surfboard system into two groups, those that provide propulsion (thrust), or propulsive forces and those that act to resist motion, or resistive forces.

Whatever the forces involved, or how they operate to achieve one thing or another, ultimately it will be necessary to relate those forces to the surfer/surfboard system and its environment. That is, we need a model of a surfer/surfboard system and its environment.

In the following I attempt to sketch out a simple vector model of a surfer/surfboard system in its environment. It’s not the only model. Models are usually made to investigate or ‘model’ particular aspects of some thing, which usually means leaving everything that is not of immediate interest out of the model. In this respect a model at best is an abstraction, or a simplification - and the model that is developed here is no exception – it leaves a whole lot out. Often the bits left out of the model can be incorporated by assigning ‘lumped’ properties to the model, like a total surface area and possibly its orientation, without providing much more detail about that property -i.e. its exact shape. This is basically the approach taken here. However, the approach does not prevent one from incorporating more information (whether it be additional properties or detail, in general) at later time.

What follows is fairly mathematical, but nothing more than a first year college level course in calculus, possibly less, wouldn’t allow you to handle.

The Model

We start with a surfer/surfboard system on a wave, see figure 1 insert of a surfer/surfboard system on a wave. We identify the following; the unit normal to the surfboard, the unit vector directed along the centerline of the surfboard, the wetted area of the bottom of the surfboard (and its leading wetted edge) and the unit vector in the direction of fluid motion, see figure 1.

These unit vectors (which basically represent the direction only as they only have a magnitude of unity) are assumed knowable. Of course this may not be the case, but here they are. From this set it is possible to generate a lot of information, or in this case a lot of other unit vectors and those that will be derived here are given in figure 2. (Actually, one more assumption will be required, see next below.)

The fluid motion vectors have not been placed in the inserts because they are somewhat controversial, at least they may require some additional explanation. In the end however, exactly how the orientation of the flow vector is arbitrary (that is, up to the modeler) and should not have any impact on the correctness of the model itself. Well, that’s assuming the model is correct.

In figure 3 the calculation of the unit vector perpendicular to the long length of the surfboard is made. The remaining vectors are derived in Part 1 cont. in a following post.

Kevin



2

Part 1 A Simple Vector Model of A Surfboard on A Wave, Cont.

The next vector to be derived is the unit vector perpendicular to the unit vector representing the motion of the fluid, in particular a unit vector that will allow for a Lift/Drag treatment using the model.

Classic Lift/Drag

Basically a Lift/Drag treatment resolves the forces of a fluid flowing past an object into a force in the direction of the fluid flow, called Drag and one perpendicular to the fluid flow, called Lift. The resolution of forces in the way makes immediate sense, at least most of the time. However, it should be understood that the choice is arbitrary, that is you could resolve the forces anyway you like.

Here the angle of attack is taken to be the angle between the unit vector of fluid motion and the bottom of the board, the derivation is straight forward, see figure 4.

This leaves determining the unit vector for the Lift force. Here it is assumed to be in the plane formed by both the unit normal to the board and the unit vector for fluid motion. This is not a unique choice, as other equally suited vectors are available (e.g. one could have been chosen to lie in the plane formed by the unit vector of fluid motion and the vertical.) Given this choice, the unit vector is derived in figure 5.

Using these two vectors, one for the unit vector in the direction of fluid motion and the perpendicular derived in figure 5, and the assumption that the velocity of the fluid would be available, the treatment is outline in figure 6.

I don’t actually know if this treatment makes much sense. I’ve introduced it as an example exercise in using the model. Given that the treatment is somewhat arbitrary, I’m simply not in the position to evaluate its value.

Kevin



3

Holy crap, Kevin. My brain hurts just looking at that stuff.

You have demonstrated time and again your ability to generate models of the dynamics involved with surfing. You also manage to do it in such a way that it is beyond the grasp of most of the non-PhD holding members here. I’m sure it will be a good resource, in an easily-to-search format, for the next person wishing to research some really in-depth and math-driven analysis of surfing physics, and in that sense it is a valuable contribution to the forum.

I am sure that there are a few here who are totally on board with all of the equations and diagrams you post up (probably blakestah, and I’m sure others I can’t think of right off hand), but I am certainly not one of them. I just can’t wrap my brain around them, never had the schooling in those disciplines, the aptitude, or the desire. And yes, to be fair, I have seen plenty of plain-language posts of yours that are well within my ability to digest and comprehend.

But theory is theory, math is math, and a surfboard is a surfboard.

I guess what I’m trying to say, as respectfully as possible so as not to minimize your contributions here, is lets see some practical application! You have demonstrated a thorough knowledge of surfing physics, so you are in a unique position to design a surfboard based upon science and not trial-and-error and intuition.

Now, this is just my own selfish desire to see what would kind of surfcraft would come from one with your background (although I’m sure chipper will have my back on this) but why don’t you make a surfboard, post some photos, and then explain (in as simple terms as possible) why it has the design elements it does… Then go surf it and let us know how it works!

And if you’ve already done this, and I’ve missed it somehow, post up the link.

4

Part 1 A Simple Vector Model of A Surfboard on A Wave, Cont.

Originally, I had also included a derivation of the wet edge unit vector, but I’ve now removed it, so things end here.

It was fun.

Kevin

It is my impression that none of the comments that follow the initial posting of the thread addressed the wet edge derivation.

5

Where is the unit vector for GRAVITY? I’m beginning to think you really don’t feel that GRAVITY is a significant factor. Also where is the unit vector for the WAVE’s motion?

I gather from a that you’re GOOFY.

“They will also come in handy when fins are placed on the board, as it is now possible to relate toe-in and cant angle to the flow.” One, it’s the height of arrogance and ignorance, unwittingly displayed, in the face of reality ie people like Greg Griffin et al.

And two, the direction of oncoming flow changes all the time, through something like 70 degrees in one plane alone. There is no one angle to mount your fins. I believe Dave Blake has something like the answer for that.

But your whole line of stuff is really just about TRIM, isn’t it?

Straight trim speed is not at all the most important thing in anyone’s surfboard design. (Well–I can think of one guy actually, but I think you guys don’t get along) Exposures that engender drag are potential control surfaces. Toed-in fins can be turned more aggressively, also once oriented to a positive AOA they can be “pumped.” Concaved bottoms can too.

Photos that you posted in your other thread with attached remarks about the flow hitting the fins betray a misunderstanding of what’s going on down there in those photos and generally.

Volume of equations doesn’t/can’t overwhelm the results of ignorance of these several basic elemental factors.

And Jarrod has a very important point, as well.

6

Another thing, how much force should be applied to rub the wax? :wink:

7

I actually agree with a lot of what you have written.

A couple of things.

I am not an engineer, academic, nor professional of any kind. I bang nails, and do other similar kinds of crap for a living at the moment. I post this stuff because it is interesting to me. I post it on Swaylocks because its the kind of forum where I might find others with similar interests. But one thing is for sure, you don’t need any of this stuff to build a great board, nor eventually become a world class journeyman. Of which, I am not - hell, I’m not even in the running to be a bad one.

I have a couple of immediate objects in mind. First, to understand the current set of design elements in current use. With regards to this I believe it is important to understand propulsion (or to use the engineering term thrust) in surfing. Second, to understand the consequences of that propulsion, or the flow characteristics which result from motion on the wave, and how design elements interact with this flow. Third, the possiblity exists, or at least at this point seems to exist for a simulation, most importantly with respect to design, but also as a game (think of the normal to the surfboard in the diagrams as a joystick.) I’m broke though, so either I sit on this stuff or pass it on and maybe at least have a dialog with others about it.

As for suggesting or building a design based on what ‘I think I know’, its not likely anytime soon. Experimenting costs money - this much I know for sure - and I will not be asking others to finance my nonsense, nor at the moment can I finance my nonsense.

I started a small board making operation which eventually failed. Though my quality control was improving, I have to admit that virtually most of my shapes at the time I closed down my little shack were driven by my mistakes (or by my attempts to correct them.) Eventually, the costs of the operation, and other financial pressures forced me to give up operation. I broke the last board I had, which I had made, over two years ago. At the moment I know of only one fellow who still has a board I made and he’s an ass-hole, so I won’t be bother him for photos.

So what you get, if you want to read this stuff is the possiblity of a discovering why design element works, and even more exciting why something else that you have though of, as a result of that understanding, may work too, or not. In this regard, completely disagreeing with my nonsense is as good as agreeing with it.

Those who can, do, those who can’t, yak too much, or my case post too much.

Take is or leave it, its just a post… it will go away with the click of a mouse.

All that written, there is one more reason for all this. Its one thing to just say this and that is true, its another to at least try and argue the point physically.

Thanks,

Kevin

8

You could add one at this point, if you liked.

Gravity will come into play when the equations of motion are developed. At this point all that’s been described is sort of a frame work of unit vectors, which will be required for the equations of motion.

Thanks,

Kevin

9

Depends.

What kind of wax - tropical, cold climate, ear…?

Thanks,

Kevin

10

… who’s chipper?

Kevin

11

Chipfish61… You know, ol’ “show me the photos!”

12

Lets not get fooled… its easy to think that complex maths must be right if we can’t understand it…

Personally, I don’t know if I like your methods KCasey… no offence, thats just my opinion. I think it comes across a bit too much as

you saying this is how it is, not hey guys, what do you think of these ideas?

How are you working out the wetted area? and more to the point, if we are talking about forces, isn’t it a bit too simplistic to think most forces are acting

through one point in the board? I think it would make more sense if the forces were treated as integrals and summed up… which will definately become more complex without even thinking about fins.

I think you might need to bring it back to bite size peices… not try to make these sweeping leaps and pass them as fact… like shwuz said, maybe try something small, say just finding out wetted area, and see if you can find a bit of practical evidence to support it and then go to the next bite…

The more you learn, the more you realise you dont know…

Ant

13
Quote:

……maybe try something small, say just finding out wetted area, and see if you can find a bit of practical evidence to support it and then go to the next bite…

I don’t remember if I’ve posted these results on Swaylock’s before, but here’s some predicted output from a simulation model I wrote in 1994 which you can compare with your observations from the “real world”.

The model assumes:

  1. The wave face in the immediate area of the surfer and board can be approximated by a sloping planar surface.

  2. Steady-state conditions. Namely the surfer remains at the same vertical position on the face of the wave and moves parallel to the curl of the wave at the same rate the curl is progressing along the crest of the wave (both the wave and the surfer are simultaneously moving towards shore as well at the onshore rate of progression of the wave at the breaking point). The diagonal track that the path of the surfer and board traces out when viewed from overhead makes an angle relative to the alignment of the crest of the wave. I call this angle the “path” angle. Since steady-state conditions are assumed, this is the same as the “peel” angle of the wave (as used by modelers simulating or measuring breaking waves).

  3. The board has “natural rocker”. That is, the rocker in the board is congruent with the (undisturbed) curve of the wave face along the wetted portion of the board.

  4. The wetted width of the bottom (not counting wetted by spray) is constant along the wetted length.

  5. The board is flat from side to side, and all the wetted rails are “hard”.

  6. The board has a single fin aligned with the longitudinal axis of the board.

  7. The lift-slope coefficient for the board is a function of both the aspect ratio of the wetted area, and the transverse slope angle (the angle between the bottom of the board and the sea surface as measured from side to side of the board). The effect of the latter is estimated from the change in lift coefficient associated with the presence of dihedral (“V”) in a planing hull.

  8. The angle-of-attack (AOA) of the hull relative to the sea surface along the pathline is sufficiently small that cosine(AOA) is approximately = 1.

  9. The combined weight of the rider and board is 160 lbs.

  10. The wave height is either (don’t remember which) 6 or 8 feet (measured in oceanographer’s height, not necessarily a surfer’s estimate).

Fig.1 - Speed

Figure 1 shows the predicted dependence of the board speed over the bottom (along the pathline) on where the board is positioned on the face of the wave (wave slope), and how the surfer has trimmed the board (AOA). The model predicts that the maximum speed (approx. 22.7 mph, no pumping) will be attained where the wave face slope angle is about 47 degrees (as seen in a cross-section through the wave), and the board is trimmed to an angle-of-attack of about 11 degrees.

Fig.2 - Maximum wetted length

Figure 2 shows the predicted maximum wetted length (i.e. from where the water first contacts the rail on the wave side of the board back to the tail block) as a function of position on the face of the wave and the trim angle. When positioned for maximum speed, the predicted wetted length is a bit under 5 feet.

Fig.3 - Wetted area

Figure 3 shows the predicted wetted area on the bottom of the board as a function of position on the face of the wave and the trim angle. When positioned for maximum speed, the predicted wetted area is a little less than 3 square-feet.

Fig.4 - Center of mass

[Apparently the forum software limits the number of inline graphics per post to three, so I’ll present this figure in another post]

14

I applaud the effort to quantitate the forces involved in surfboard design and wave dynamics. A Simple Vector Model is an admirable attempt at assigning numeric value to the overall situation.

The problem (IMO) lies in the unknown and constantly changing variables - especially in regards to the breaking wave. Areas that I have problems with on a regular basis generally involve the unpredictable nature of the elements encountered in the real world…

How does one assign a numerical value to a sudden shallow spot on the reef that turns that slow peeling wave into a suck out grinder? What about a sudden gust blowing up the face on an offshore wind day? A rebound off a rockpile or converging swells from different directions can turn an otherwise predictable take off spot into a wedging monster.

Many theoretical ideas, which look so good on paper, fail in actual practice. Isn’t that what led to the old saying, “Back to the drawing board?”

15

Fig.4 - Center of Mass

Figure 4 shows the position of the center of mass of the surfer (measured forward from the tailblock) to achieve the indicated angle-of-attack (left axis) as a function of the position of the board on the face of the wave (wave slope). When positioned and trimmed for maximum speed, the predicted location of the surfer’s center-of-mass is slightly more than three feet forward of the tail of the board.

Fig.5 - Average wetted width

And, for completeness, Figure 5 shows the average wetted width of the board as a function of location on the face of the wave and how the board is trimmed by the rider. When positioned and trimmed for maximum speed, the average wetted width is predicted to be about 0.57 feet (6.8 inches).

16
Quote:
Holy crap, Kevin. My brain hurts just looking at that stuff.

You have demonstrated time and again your ability to generate models of the dynamics involved with surfing. You also manage to do it in such a way that it is beyond the grasp of most of the non-PhD holding members here. I’m sure it will be a good resource, in an easily-to-search format, for the next person wishing to research some really in-depth and math-driven analysis of surfing physics, and in that sense it is a valuable contribution to the forum.

If you cannot explain something in simple terms so a layman can understand it, you probably do not understand it yourself.

I have no problem understanding MTB. KCasey is another matter. However, far be it from me to inhibit the theoretical rantings of someone interested in surfing, I’ve sure flung enough in my time.

Carry on.

17
Quote:

I applaud the effort to quantitate the forces involved in surfboard design and wave dynamics. A Simple Vector Model is an admirable attempt at assigning numeric value to the overall situation.

The problem (IMO) lies in the unknown and constantly changing variables - especially in regards to the breaking wave. Areas that I have problems with on a regular basis generally involve the unpredictable nature of the elements encountered in the real world…

How does one assign a numerical value to a sudden shallow spot on the reef that turns that slow peeling wave into a suck out grinder? What about a sudden gust blowing up the face on an offshore wind day? A rebound off a rockpile or converging swells from different directions can turn an otherwise predictable take off spot into a wedging monster.

Many theoretical ideas, which look so good on paper, fail in actual practice. Isn’t that what led to the old saying, “Back to the drawing board?”

My feeling is that you have to learn to walk before you can learn to run. If one can predict attributes of a simple situation (as in the example I presented above–say something like Jeffrey’s Bay) that are representative of the real world, then one gains confidence that their approach and understanding of the problem to be solved may be on the right track. Once one has confidence in that, they can can then begin to consider examining/simulating more complex situations.

FWIW, the median and average (over the bottom) speeds that I have measured by GPS (60+ measurements) are just under 20 mph. Typical wave conditions for those measurements are comparable with the 6-8 ft wave height (trough to crest) assumed for and used in the simulation. Given all the uncertainties (and the details of the flow field in the face of the breaking part of the wave being one of the major contributors to this uncertainty), and approximations made regarding the board shape, I don’t think a predicted max speed of 22.7 mph is all that different from 20 mph (of course I may not be unbiased).

Similarly, although it is a little difficult to accurately measure wave face slopes in selected photographs looking “down” the tube at a surfer who appears to be in steady-state trim, one typically arrives at wave face angle slopes (at the location of the wetted portion of the board) that are in the range of 45-50 degrees wave slope. Again, in reasonable agreement with the prediction for the desired wave slope for maximum speed. The max wetted length and center-of-mass locations don’t seem greatly out of line either.

18

Your point about my style is taken. I’ll work on it.

The wetted area can will be tricky, but remember here its all lumped into a ‘particle’. Its not the most complete description, but you’ve (well, I) have to start somewhere.

Also, this is just a frame work. There really isn’t any equations of motion here, there is no need to sum things up yet. There will be though, hopefully.

As for breaking into pieces, the post isn’t going anywhere, no one will be tested after I’m done, take your time, or don’t, ask questions, or don’t, personally I’m not going to hold it against you. In fact I kind of flattered you’ve read the stuff, thanks.

Understanding this stuff isn’t going to make you better at building surfboards - building surfboards does that. This is supplimental, extra, but only if you’re interested.

As for practical evidence, I only have circumstantial evidence. I couldn’t afford to pop for an experiment, a new board say. And apparently my use of pictures found on the Net didn’t go over that big in prior posts. I try again though.

Kevin

19

Excellent. I agree. The question is how do you begin a journey?

As for a discussion of waves, that is breaking waves, I’m all for that… got a good model?

Thanks,

Kevin

20

If you don’t understand it how do you know I ‘flung’ a ‘rant’. If you understand it and disagree with it, please share your insight.

Thanks,

Kevin