Surfboard and Fin Hydrodynamics at Swansea University

After reading the thread commenced by Chris Cochran on foils, I thought it would be a good time to let your readers know about a new research project that we have started at the University of Wales Swansea (United Kingdom). (By the way I would just like to commend the work done by Michael Paler in maintaining this forum, which is absolutely superb).

The project funding has been derived from previous work in aerospace engineering and consists of a panel of engineers supervising a three-year PhD position taken on by a computer scientist. The project intends to look at various aspects of the hydrodynamics of surfboards for differing board and fin designs, using 3D Computational Fluid Dynamics (CFD) and stress analysis modelling coupled with experimental validation and some new prototype designs for both boards and fins.

As mentioned by Simonc in a previous thread, “surfboards are extreme craft in hydro/fluid dynamic terms, exceptionally high Froude numbers and very low Reynolds numbers”. This presents many challenges in modelling the highly complex flow, (E.g. 3D complex geometry, Turbulence, Two-phase flow with solid interaction and sometimes deformation, plus free surface effects).

Surfboard design is at a critical stage in which it would greatly benefit from the type of computational modelling previously only associated with more lucrative industries such as hull design in yachts and powerboats, not to mention aerodynamic design in the aerospace and automotive industries. The application of CFD to sport is very topical, in particular in attempting to improve performance of sports equipment and technique enhancement, with articles in the spring issue of FLUENT news (2004) and the Journal of Sports Science, case studying research into advanced swimwear (sponsored by Speedo) for the Athens Olympics.

Due to the complexity of the flow, we have decided to validate our computational models experimentally using two sets of experimental rigs, one of which is nearing completion as I write this. This particular rig has been developed to fix fins into a flow tank allowing pressure distributions, drag forces and velocity boundary layers to be measured. The work will involve testing a number of existing fin designs as well as a number of new prototypes. Benchmark objects will also be placed in the rig to get free surface distributions for verification of “simple” modelling test cases.

The second set of experiments will use of a larger tow-tank with higher speeds to tow scaled models of surfboards with fins and will allow verification of free-surface heights of bow waves and wake heights, pressure distributions on boards and overall drag data.

As part of the work we are developing Computer Aided Design (CAD) tools for fins and surfboards, demos of which can be downloaded from our website. These have an advantage over commercial CAD packages in that they have been specific created for the design of fins and surfboards and hence do not require such a steep learning curve.

[=1]Preliminary computational findings were presented in a paper at the 4th International Surfing Reef Symposium, Natural and Artificial Surfing Reefs, Surf Science and Coastal Management held at Manhattan Beach, California on January 12-14, 2005, and was highlighted in a recent article reviewing the symposium at surfline.com ([ 3]http://www.surfline.com/home/SurfNews/2005_02_24_artificial.cfm)[/]. Part of the work demonstrated that for double-foiled fins (e.g. middle fins), glassed on fins produced less drag than boxed fins which did not have a fillet. However, the argument was not cut and dry as this was not the case for the outer fins.[/]

We have a website (http://cetic.swan.ac.uk/surfs) from which the actual paper can be downloaded, and my e-mail is (N.P.Lavery@swansea.ac.uk) if anyone wants to correspond directly with us regarding any of this work.

thats a really big call …

and im sure it will be a real challenge , one of the biggest reasons surfboards still havent gone through a major scientific evaluation , is because of the amount of variables thrown in …

just to highlight one point …

you could drag a board through a test tunnel/tank , by a number of experiments you could conclude that a particular set of fins created more drag than another …

those very same fins when surfed by an energetic surfer would produce way more speed and drive than any other set …??

the variable was the riders input and skill level …

some fins dont start to work well till there is angle of attack , a surfer constantly working his board rail to rail gives the required angle of attack to gain thrust …

that presents a challange to any flow models being accurate , that all variables are represented and taken into consideration …

if one is missing nothing adds up …

a change in fin cant can cause drag , but can also make your board faster depending on the rocker of the board ??

so for any of this to be of any use in the future , it can only be as good as the interpretation of results , based on the programmers knowledge of all the known variables …

your gonna have to find all the best minds if you want even a fraction of accuracy …

i would say tom would have a good idea of whats happening in this area…

its all good , to do anything that establishes design principles …

itll stop the hype and crazy retro trends , when you have sound scientific formulas to back the subject …

regards

BERT

Yes…GIGO is very very difficult to avoid when it comes to surfboard fin testing. Nick, I hope this research group is aware of the extreme large AOAs (at times approaching 90 degrees!!!) involved in modern surfing…IMO I think its the reason why objective test data and analysis is so challenging and elusive.

Classic single fin surfing assumptions/inputs would be much easier, but any conclusions would be tricky (perhaps erroneous) to extrapolate into modern rail to rail surfing.

Nick,

I think you’re going to have a tough time convincing some people that a lifetime’s empirical knowledge can be even touched on by a PhD, personally I reckon it’s about time…

Something I think that needs to be looked at is basic dimensionless characteristics, something akin to prismatic etc coefficients used in naval architecture, and how this relates to wave shape and height, and the rider. Too many of a surfboard’s physical properties are described subjectively rather than hard numbers. Maybe it’s about time someone undertook to do this then set up a database similar to the Delft series? I think it would definitely allow non-math’s based thinkers to put your work in better perspective.

Simon

Hi Simon, Bert and Co,

You are all right, it is a big call, but the 3-year PhD itself is just the tip of the iceberg, and really represents an exercise in building the knowledge required to start tackling a relatively new area in science. Of the six engineers supervising the PhD student, five of us have PhDs in computational modelling of fluid flow with many years of experience (up to 20+). Furthermore, all of us surf to various levels, so we also have some understanding of the more subjective issues involved in translating what surfers are feeling when riding the board to what is going on scientifically.

We have already looked at empirical theory, using methods such as one-dimensional, boundary layer type flow analysis over the board bottom, but this rapidly becomes constricting once you try more complex geometry which might include features such as the “V” or channel bottoms. So the only real way to approach this is to do a full blown 3-D flow analysis, broken down into parts to be manageable. For example, we will look at one middle fin, look at all components of drag and pressure and match them with our experimental data. Then look at side fins, do the same. Match it with experimental data. Then we look at free-surfaces on simple objects, match with experiment, then a small board, model and match to experiment. And so on. Little by little we improve our knowledge, and build a database of results with computer models verified at each step, enabling us to isolate what is doing what, e.g. is what percentage is due to pressure drag and what is due to friction drag. With the models verified, we can then get creative and comparatively look at series of fins, and get data on angles of attack versus drag and lift, or the effect of aspect ratio of fins.

Each of these small “packets” of understanding can then be built into a more comprehensive understanding of what is actually going on in the flow round the board, even during complex “rail-to-rail” modern maneuvers, i.e. projecting our understanding of the hydrodynamics of the boards/fins onto the larger scale problem of the surfing dynamics. At this stage, as you said Simon, we will have to make the link between science and surfing terminology to describe effects such as drive, maneuverability etc and how they relate to board design.

The hydrodynamics of fins is work which in fairness has already been done commercially to a certain extent by the likes of FCS, but unfortunately and understandably their data is not public knowledge, so how much of their conclusions are marketing is debatable. While this type of data may not necessarily be easily digestible to the layman, we are in the extraordinarily lucky position that, as academics, we don’t need to convince anyone to make a sale, and we will make all our findings public knowledge, eventually.

Best regards,

Nick

Back in the early 70’s I constructed a numerical model to examine the hydrodynamics of a surfboard, and the speed that it may achieve on a wave. It addresses only the “steady-state” case where the surfer is driving across the face of a wave and moving at the same lateral speed as the progressing curl (i.e. the surfer remains at the same position relative to the curl). It does not include any energy input by the surfer (i.e. equivalent to being so far back in the tube that there is either no room to pump, or any pumping contributes minimal energy to the surfer and board compared to that being delivered by the combination of the wave motion and the force of gravity).

Processes incorporated into the model include: static pressure (buoyancy), dynamic pressure (planing), wetted area (and wetted planform) of the hull, aspect ratio of the wetted area and it’s effects on the lift coefficient, parasitic and induced drag of the hull, (estimates) of the drag associated with the fin(s), and an approximation to the flow field in the face of a breaking wave. The board is assumed to have “natural” rocker (i.e. the curvature of the wetted portion of the bottom of the board matches the curvature of the wave face as determined in a vertical plane passing through the pathline of (and within the wetted area of) the board. Solutions are computed over a matrix of angles-of-attack (“trim angle” and (local) wave face slope (“slope angle”) governing the location of the board on the face of the wave. The model is programmed on a computer and computes a solution for each pair of trim and slope angles by successive approximation to convergence. The parameters (e.g. drag coefficient(s), lift coefficient slope, etc.) are estimated from third party studies and reports on craft with hulls with similar aspect ratios and hull forms (e.g. sea plane floats). A remaining major uncertainty is the details of the flow field in the face of a breaking wave.

The following figures illustrate the type of output generated by the model. Unfortunately, the most recent runs were 11 years ago, so I don’t remember the exact details of this simulation. However, virtually all the simulations were carried out for breaker heights of 6-8 feet (trough to crest) and a combined weight for the surfer and board of around 170 lbs.

Board Speed

http://home.pacbell.net/surfwiz/surf101/image002.gif

The first figure illustrates the relationship between where the rider positions the board on the face of the wave, and how he trims the board (via shifting his weight fore and aft to alter the angle-of-attack of the hull) and the maximum speed he will achieve. As can be seen from the figure, in this particular simulation the maximum possible speed predicted (for this combination of surfboard and wave) is achieved where the slope of the wave face is 46 degrees, and the angle-of-attack of the board (relative to the local sea surface at the mean position of the wetted area of the board) is 11 degrees, and is predicted to be 22.65 mph (speed over the bottom).

Board Wetted Area

http://home.pacbell.net/surfwiz/surf101/image004.gif

The second plot shows the wetted area on the bottom of the board (in square-feet) as a function of position on the wave face and trim. The wetted area when positioned and trimmed for maximum speed is about 2.55 square-feet.

Wetted Length

http://home.pacbell.net/surfwiz/surf101/image006.gif

The third graphic shows the distance from where the rail of the board first contacts the wave surface to back to the tail of the board. The wetted length when positioned on the wave and trimmed for maximum speed is predicted to be 4.5 feet.

Board Trim

http://home.pacbell.net/surfwiz/surf101/image008.gif

The fourth plot shows the location of the center-of-mass of the surfer and board (measured in ft from the tail) as a function of wave slope and angle-of-attack. Note that the trim position that produces the maximum speed is about 2.8 feet forward of the tail.

Discussion

Analysis of photographs of expert surfers carefully selected to minimize the effects of viewpoint uncertainty show that the slope of the wave face at the mean location of the wetted area of the board when in trim for maximum speed is probably close to the predicted 46 degrees. Direct measurements of speeds (over the bottom) of skilled surfers on waves of a size and shape comparable to those used in generating these plots are also close to the predicted maximum speed. Similarly, the entry point of the rail of the board with the face of the wave and the location of the center-of-mass of the rider on the board seem reasonably close to the predicted values (although admittedly I haven’t made a careful comparison). Hence it would appear that this model may be useful in providing some guidance on the relative importance of the various processes governing the “unassisted” speed potential of a surfboard.

It will be interesting to see how the predictions of this (relatively) simple model compare with the (hopefully) more realistic and accurate predictions from a suitable CFD program of the type proposed in this thread. However, I would like to emphasize again that present uncertainties in describing the details of the flow field in the face of a wave may limit the validity and accuracy of such simulations until/unless a better description becomes available and can provide the boundary conditions for the CFD simulations.

mtb

Quote:
Nick, I hope this research group is aware of the extreme large AOAs (at times approaching 90 degrees!!!) involved in modern surfing...

I do not think AOAs, measured in terms of water flow relative to the stringer line, ever exceed 15 degrees, and probably not usually 12. You can measure this with a rotating fin box by using different end-stop angles.

I’m not in any position to add to this discussion, as I have no formal education on this subject, but I do, like many others here, have my own years of hands-on experimenting formulating my own conclusions.

I understand the complexities of this subject and it is very intersting following the direction of all the formal studies that are being undertaken, and as much as I agree with the difficulty of documenting the dynamics of a surfboard and fins, the sound way of starting is with a static model.

The outside influences, like energy input from an individual rider or individual wave shape, are more infintisimal than most design theories. I have had boards and fins that trim well but hate being pumped, and others that would not trim but would fly when pumped.

As for having no room to pump in a tight tube is bullshit, what are ankles and toes for? I’ve seen guys pump their way out of what I thought were impossible situations. Talent, luck, board design or just will power??? Unmeasurable, no matter how many studies could be done.

It’s funny how the most simple of activities, a person on a board on a wave, can involve such incredibly complex physics.

Credit must go to anyone and everyone doing any sort of serious scientific study on sufboards and fins. Results found should never be taken lightly or irrelevant, as all information can only be constructive in the long run.

Wildy,

It’s funny how in so many things the simplest theories have the most complicated applications, say quantum theory, and the simplest activities can only be supported the most complicated of theories.

Nick,

I fully understand and appreciate your approach, and can see the academic benefits. But if I can give an analogy compared to my everyday work: I design marine equipment over a range of sizes, when I do my structural calcs I’ll build up a set of algorithms in a spreadsheet. I do basic FE myself for stress concentrations etc, but I’ll often get a consultant to do a full nonlinear FE analysis (whole assemblies etc), if I have twenty sizes, I’ll get the FE done on three to benchmark my own algorithms then interpolate across the range. I can’t help feeling that your research would be of much greater non-academic value if there were an established set of algorithms to describe surfboard performance.

MTB appears to have done some work already on this, would it not be possible to integrate some kind of project to more fully establish some basic algorithms describing surfboard performance? (Integrate’s not the word I’m looking for, some kind of parallel project linked or associated with your work?)

Simon C

As an example, when you look at pic of someone nose riding and the sheet of water displaced is coming out nearly perpendicular to the stringer line…should one just throw this obvious effect out of the equation? When you bottom turn a thruster and the outside fin begins to exit the water things change dramatically…same when you do a sharp top turn. 15 degrees sounds like soft turning.

Buy a small (1’ x 2’) sheet of acrylic or lexan, cut out a shape, tape some streamers to the bottom and test in a calm pool…this is an accurate model of what’s happening. I stand by my observations.

http://www.swaylocks.com/forum/gforum.cgi?post=157948#157948

With regard to your linked reference…

I agree that experimentation of this type is often a great way to visualize the dominant characteristics of some process or effect. However, one has to be careful in how one generalizes those characteristics to a different environment or set of circumstances–and in particular, any quantative relationships that one deduces from their observations.

While your observations may well be correct, there’s still remains the question about whether your simulation environment (in this case, a flat, horizontal, sea/water surface) is representative of a wave face environment (which is characterized by a compound curved surface and a velocity field that varies not only with position on the face of the wave, but also with depth below the surface).

For example, in your study, does the combination of the curvature you bent into your sheet of plexiglass, the curved path of its motion, and the flat sea surface adequately simulate the combination of the rocker in a surfboard, a curved path while turning, and a curved sea surface? …if so, what is the relationship between the curvature of the wave face, the rocker of the surfboard, the curvature of the path, and and the curvature of the plexiglass to obtain an adequate approximation?

By way of another possible (and perhaps more subtle) example of the effects of these characteristics, here’s another question to ponder:

Build a board with a flat (from side-to-side) bottom. Have a rider ride it across the face of a wave such that he simultaneously maintains his position on the face of the wave and his position relative to the curl. Take a picture of him on the wave when his pathline is perpendicular to your line of sight to him (ideally the lens level should be at the same elevation as the centerline of the board), or, alternatively, as he heads straight toward you. Observe the orientation of the board in the picture. You will find that the shore-side rail of his board is typically lower than that on the wave side of the board (as long as your eye level isn’t too different from the board level).

Since presssure forces are always perpendicular to a surface (in this case, the wetted area of the board) and the board is flat from side-to-side, the pressure force must have a net component in the direction transverse to the pathline of the board (and directed towards shore). Unless compensated by an equal and oppositely directed transverse force, the board will not follow the pathline, but rather will be accelerated towards shore (relative to the pathline). Since the pathline remains constant, there must be some compensating force. What is the source of this force? …and (given one possible answer) why is there not a torque that rotates the board around it’s yaw axis?

As far as the spray from the nose-riding board, apart from the distorting effects of friction with the bottom (or air), my guess would be that it’s probably more likely to be directed approximately perpendicular to the line where the bottom of the board first intersects the sea surface as just “downstream” from this point is the stagnation point for the oncoming flow and the area of highest pressure. The latter can easily be observed (as I have done) by drilling a series of longitudinally spaced holes through the board down it’s length, bonding in straws trimmed flat (and sharp-edged) with the bottom surface of the board and terminating just above the deck of the board (each straw of equal length). Then observing the elevation of the water jetting up from each hole when underway. In your case, since the sea surface/wave face is sloping downward toward shore, and the wave side rail of the board contacts the sea surface before the shore side of the rail of the board, the locus of points connecting the points of initial contact is (approximately) a diagonal line across the board.

You are correct that this spray (which is also present even if not noseriding, but perhaps less evident) does affect the lift-drag characteristics of the hull. But to a first approximation, these effects are incorporated into empirically determined lift-drag coefficients for the hull if those are used for a simulation.

One final comment with regard to your streamer observations (in your linked reference)…

At least a portion of your sub-surface cross-flow (the flow you observed away from the sea-air interface line–although perhaps not if you had a streamer very close to it) is associated with the low aspect ratios (max wetted width divided by mean wetted length) of surfboard (and boat hulls) and the angle of attack that you gave to the “hull”. By way of an example, if you place a plate of some fixed length and width at some angle relative to a flow, some of the approaching fluid will be deflected more or less away from the plate (but approximately within the plane passing through the longitudinal axis and perpendicular to the plane of the plate), another portion of the flow will diverge and develop flows with components toward the sides of the plate. The degree to which the latter occurs is dependent on the ratio of the width of the plate, relative to its length–i.e. the aspect ratio. Most of the flow will be along the length of the plate for a short, wide plate (example: a plate 1" long and 1 block wide); most of the flow is to either side of the plate for a long, narrow plate (e.g. 1" wide, 1 block long). In computing lift and (induced) drag, the consequences of this cross-flow effect on lift and drag are usually estimated based on established empirical and theoretical relationships involving the aspect ratio of the plate (hull, foil, wing, etc.).

mtb

i can visualize a computerized board … a 9-2 tri-fin with “natural” rocker. The dashboard at the nose has speedometer and water temperature gages for the rider. The brain is sealed in the glove compartment. I like three types of flow meters for hull speed, including: six doppler meters mounted in the foam, homemade thermal-diffusion mats to cover the bottom, rails and fins that measure heat loss to calculate speed (these mats would measure speed at 1000 points on the hull), and pitot tubes at a minimum of three locations giving the velocity at the hull and 1 cm below the hull. GPS. Foot pressure sensors to determine rider input. Fluorescein dye release nipples in front of the fins with cameras to record eddy flow patterns along the hull, rails, fins. Hull vibration and flex, and fin flex sensors. Rider wears the battery pack, maybe the computer too, and is plugged in via the leash. Estimated cost $50,000. But I can’t visualize the testable hypothesis, maybe it has to do with single fin versus tri-fin.

Quote:

i can visualize a computerized board ……But I can’t visualize the testable hypothesis, maybe it has to do with single fin versus tri-fin.

I can think of a number of assumptions/approximations incorporated into my simulation model (e.g. the “natural” rocker approximation) that could be tested (/accuracy and domain of validity estimated/) with only a tiny fraction of the instrumentation you have listed.

mtb

PS. FWIW, the present HYPO board is fitted with means of measuring both “speed-through-the water” (SpeedMate impeller-type speedo), and “speed-over-the-bottom” (GPS with WAAS) – and means of in-situ measurements of the net force vector on the forward foil and the drag force on the main foil (plus struts) are being contemplated for the future.

Nick, I bet MTB would agree to fly over for a free consult if you paid his travel expenses, and you’d reap huge rewards from such a visit. I’d post some of the articles he wrote over 30 years ago if it wouldn’t blow his cover…but he is a PhD physicist who’se been interested in, and studying, waves for over 40 years.

good points MTB…but regarding the test method…how’bout that price/information ratio? Not bad huh…especially compared to the 1/4 mill mech test lab I used to work/manage…

Quote:

good points MTB…but regarding the test method…how’bout that price/information ratio? Not bad huh…especially compared to the 1/4 mill mech test lab I used to work/manage…

Yes, definitely! In a sense, I guess this is essentially another pair of examples of how the cost of adding another digit after the decimal place often increases exponentially but adds to the information base logarithmically.

mtb

Dear MTB and Blakestah,

I too would not want to blow MTB’s cover! I find it fascinating that we may have been surfing and working, in the same place and time and not have known each other. I admire the original articles that you have referred to, which I also referenced in our paper at the Artificial Surfing Reef symposium.

I see MTB’s work as providing a comprehensive overview of surfing dynamics from a force vector resolution aspect, and the data that we are working to acquire from our modelling and experiments would fit in with MTB’s model to enhance the specifics of the drag forces (friction, pressure etc), but therefore our models do depend on MTB’s models data to a certain extent (i.e. we used velocities for boundary condition for the CFD data derived from MTB’s equations).

I am very interested in talking to MTB about further development of an integrated model of surfing dynamics, particularly the equations which connect surfing velocity and wave velocity. However, and unfortunately, our budget is really small for this project!!

Nick

Simon,

Absolutely agree with what you are saying, i.e. integration of the project at two levels I call then surfing dynamics and detailed hydrodynamics.

Regards,

Nick

Should have posted this a few months ago, but on similar lines of scientific advancement in surfboard shape design, I and my partner devoted our thesis work to this type of design.

An article following our graduation is circulating (http://www.cfdreview.com/article.pl?sid=06/09/22/1352236&mode=nested).

And the beginnings of our website can be found at (www.db-surfaces.com).