Side Fin Physics

Ok, I’ve been trying to work some of this out for a while now, and if anyone can point me to some data I’d love them forever, but as yet I can’t find anything solid on this anywhere. I’ve attached a JPEG with some diagrams at the bottom, and, for the sake of simplicity, have made a few assumptions, they are;

1. One main purpose of any side fin is to help keep the rail engaged in the face of the wave, thus creating hold and drive.
2. To do this, the fin works, in part, as a hydrodynamic foil (similar to an aircraft’s wing), using laminar flow to generate lift at 90 degrees to the outside edge.
3. To maintain smooth laminar flow, the “angle of attack” of the fin is very important (Fig. 1-3)

Now, assuming that these assumptions are correct, what I’ve been trying to work out is why the fins on most surfboards are “Towed in” by between 3 & 7 degrees (Fig. 4). This causes a negative angle of attack to the flow of water and would actively prevent them from generating lift. I know from talking to several shapers that the more a fin is towed in, the more maneuverable a board becomes, while fins placed in-line with the stringer can cause a board to “track” down the line. FCS and Futures are very keen to point out the effectiveness of their foils, but I can’t see how their foils are having any effect given that they’re pointing the wrong way on the board.

All this leads me to my actual questions;
1. Are my assumptions correct?
2. If so are there any reasons, other than maneuverability, for fins to be towed in?
3. Is board maneuverability ACTIVELY affected by the tow angle of the fins, or is it just a by-product of the fins not working properly making it easier to go rail-to-rail?
4. What would happen if you used smaller fins and towed them outwards to get a better angle of attack?

I like to think I have a reasonable handle on most aspects of board design, but this whole thing has stumped me well and truly, any help would be greatly appreciated.


Hans & Jameskiri - Firstly, and this is a little off topic, but I have to disagree with you both on the issue of pumping. I have spent many hours breaking down slow motion footage and I promise you that at no point is the board “Pushed sideways down the wave face”. Pumping, if done properly, should be a series of smooth, linked top & bottom turns, combined with a compression and expansion of the surfers body. The whole point is to keep the fins and rail engaged in the wave to generate forward speed, and so if the board slid sideways at any point it would destroy any forward momentum. If you doubt me, try going frame-frame on a video and watch the tail of the board, it will never move sideways.

Also I realise that tow is not obligatory, and I understand the Pros and Cons of having fins in line with the stringer. What I want to know is WHY this happens. I would love to try and draw a velocity triangle, but since this, like Reynold’s Number, can’t be done without actual numbers, which as yet no one has been able to provide, this does not help to answer my questions.

GTFD - There is a lot of data from sailing/powerboats out there that could be used for approximation, but unfortunately it’s all based on flat water and a major component of any equation would be the speed and direction of the water flowing up the face of the wave (see below!).

Obproud & Stoneburner - If I understand your points about the flow of water, I think you are talking about something similar to “Apparent Wind theory” in sailing, where you have the True Wind blowing over the boat and then the “Induced Wind” which is created by the boat moving forwards through the air. The Apparent Wind is a vector of those two and is what you actually set your sails by.

I’ve attached a diagram of this theory, altered for a surfboard on a wave. In Figure 1 the board is travelling across the wave with the “True Flow” of water up the face of the wave at 90 degrees to the direction of travel. If we assume that the board and the wave are moving at about the same speed (in reality the board would be moving faster) then the “Apparent Flow” would be at 45 degrees to the direction of travel, and the the angle of attack would be perfect for generating lift. In principle, I can see how this theory could work and make sense, but I have a few problems in my head, maybe you can help me understand:

1. If this is correct it means the effectiveness of your fins is directly related to your direction of travel on the wave. If you drop down the face of the wave, the “True Flow” and “Induced Flow” are in the same direction, and we still have a negative angle of attack (Fig. 2). While if the board is turned up the face of the wave the “True Flow” and “Induced Flow” are opposing, and would cancel each other out leaving no water flowing over the fins (fig. 3).

2. For this theory to be correct, the board would have to be sliding sideways on the face of the wave. On a boat the air flows uninterrupted over the deck, allowing the sail to affect the flow and create lift. However the rail of the board is designed to grip and re-direct the flow of water behind it, so that a board angled at 90 degrees across the face of a wave, will gently rise up and off the back (and we all know how it feels when the rail actually slips on a steep face) By my understanding, the use of concaves on the bottom of a board is to re-direct as much water out the back of the board as possible, this would mean that the flow past the fins is running nose to tail. Maybe I’m wrong, and despite the best efforts of rail, concave and fins, most of the “true flow” up the face of the wave does pass under the board and out the other side, in which case there is still the first problem that the effectiveness of the fin would be altered by your angle to the wave face. Again maybe this is the case, and as with a sailing boat, the fastest direction of travel is the equivilent of a “Beam Reach” when the Apparent flow is just right for your fin set-up.

"I think in my experience (I do a lot of video coaching) during most carving turns the off-side fin is either out of the water or only just below the surface,"

While reviewing various photographs, I came to a different conclusion.  It is only rarely that I see an outside fin actually out of the water.  

With conventional side fins, once the board is up on rail the resistance of the outer surface of the outer fin has already been broken.

With the CRVs (and hoops) the initial transition of the turns is when the beneficial release effect of the outside fins in a CRV set-up is most likely to be felt.  People I know who have tried the CRV fins have also told me they noticed the difference during rail to rail changes.  They just seem to feel 'looser' during rail to rail transitions even as they feel more positive during the maneuvers. 

My point is not to pimp the CRVs... just to illustrate the underestimated effect of the outer surface of the outside fin.

[quote="$1"] Just out of interest, are all 3 fins double foiled? [/quote]

They can be.     It does not present any problems if they are.

Bill Thrailkill: To my mind, the speed of a board is directly related to how well the rail grips the wave face. Theoretically fins are not needed for this, but they help maintain grip when you want to shift your weight and turn. Any fin will cause turbulent flow; how much will be directly related to how big the fin is, however since a fin with a good angle of attack will generate more lift than drag, it should therefore give the rail more grip, thus producing more speed. Therefore my thought would be that a smaller but properly angled side fin would give more speed and for the same manoverability. Interested to understand how your methords.

GTFD: That is a good point, but since the Reynold’s Number cannot really be applied without quantifiable numbers, it is irrelevant unless someone has some access to test tank data (which I would love to see, hand it over FCS!).

Johnmellor: I think in my experience (I do a lot of video coaching) during most carving turns the off-side fin is either out of the water or only just below the surface, where the surface tension of the water would make it tricky to work out the dynamics. In straight line trim or gentle turns however I agree the off-side fin could cause problems, esp as it may have a better angle of attack than the near-side fin. As a side note, the whole reason for this post is that the more I think about it, the less the near-side fin makes sense to me!

Retrothis: Thank you for your explanation of the video, makes a lot more sense now. Maybe my use of the term “Laminar Flow” is wrong, but there must be some mechanism by which a foil can generate lift in water at high speed, as Hydrofoils on powerboats seem pretty efficient. Whatever mechanism that is should work on a foiled fin too, as long as the angle of attack is good.


Cool, thanks Bill!

Cheer up, while there is no Tooth Fairy, there IS hydrodynamic lift as a function of both foil shape, as well as AoA.   When you think of side fins,  you don't really need as much depth or surface area, as many people think.     Believe me when I tell you there is a point of diminishing return.   As a worldly woman once said, SIZE MATTERS.


Toeing in the side fins is not obligatory. When going in a straigth line, they would only induce drag.

however, you are never going in a straigth line.

Toe-in will help generating speed while pumping, especially on small waves at low speeds. When you push your board down, you are actually pushing it sideways down on the wave face. Toe-in will then lower the angle of attack of the waveside fin.

If you draw the velocity triangles of whats happening, the above should become clear.

Toe-in has more value on small waves where generating speed by pumping is important, on big waves it only results in drag.

Academically speaking mostly. Reynold's number is right in there for this conversation. I don't deeply understand it enouph to chime in with its principles and direct application. Using Reynol's number and similar fluid dynamic theories does demand solid numbers but we could approximate the range of velocities and Aof attacks in the range of higher speed sailing craft and motor boats about in the water skiing speed range. There is much written in such design tomes, also very basic aircraft design keeps the considerations simple and model airplane design books are quite good for the amateur fluid designer. The reading and near understanding of the academics is helpful, to me anyway. Seems,  the billion$, pro aero/hydro designers, space age included, would be hard pressed to design on paper or supercomputer, with all their formulas and numbers, what surfboard builders have managed to cobble together over the years.   first time attemt to copy/paste sway to sway, hope it goes.  Nice! it went. The first paragrph says it all academically, then down the line Bert Burger chimes in with some real world words. Gotta love Sways.


There it is! The second sentence answers the question.

You must also consider the moving water in the wave.

(Angle of) Moving board over water + (Angle of) moving water under board = Angle of Attack

Wakeboard fins have no toe for the same reason.

Then there is the turning thing… if ther is no toe, and you go to turn the AoA becomes to large too quickly… so with more toe you can turn the board further and faster before the lift to drag ratio becomes inefficient.


As you turn the board, the toe-in angle of the outside fin, wave face side, should be minimized and lift should be generated (assuming an asymmetric foil), helping to pull the nose of the board into the turn.  The outside fin, relative to the wave face, is pulled out of the water as the cutback lean angle increases. 

In a straight line path, toed-in fins create more drag than fins that are not toed.  Also, as the number of fins increases, the drag increases.

Effective cutback radius increases as speed increases.

Should centrifugal acceleration be a consideration?

In general, I believe water flow should remain relatively laminar along a surface as long as it does not exceed 480 ft/min.

But alas, I am only a shade-tree engineer.

In my shaping experience with hollow timber boards I use no toe in for side fins (I only build twin fins and alaias). Its correct about the toe in and pumping, but I have never surfed a wave small enough where I have needed to pump, or perhaps the wider, faster low drag shape of the board and fin characteristics makes pumping obsolete. Either way I do not see value in toe in unless you are designing a board that utilises the increased drag of the fins as a pivot or turning point or you are designing a board that has to remain in a state of constant agitation (turning pumping etc) to maintain speed… I do find my boards dont snap off the lip as well, probably due to a combination of the greater swing weight and hold of the parallel fins, but for me this is a small price to pay for effortless speed and flow on any size wave…

Laminar flow…laminar flow… To be honest I don’t think laminar flow can be applied to the flow of water past the fin surface. The forces that determine the flow are different. In laminar flow viscosity and diffusion are some of the primary forces that determine the flow. For these forces to be of any consequence, the scale must microscopic. At these scales, momentum and mass has little influence if any. Additionally the flow velocities are tiny…micro meters per second…  I think to say that the flow is laminar, one has to be able to predict the location of a water molecule. The most noticeable aspect of laminar flow is absence of mixing, the only way two streams of fluid can mix when in state of laminar flow is by diffusion. See here, this is a video of what laminar flow looks like inside a 2 mm wide channel:

The flow of water past the fin is influenced largely by momentum I think. The fin moves through stationary liquid, at speed, pushing water out of its way with the leading edge. The fin has mass, it has velocity, hence it has momentum.


Only because one can’t see any turbulent mixing at the fin surface in those underwater photos, does not mean its not occurring.


With regards to angle of attack…this changes once the board starts to turn. So, the toe is there to take the advantage of change in direction of relative flow of water.


Your assumptions are correct.

Thrailkill - if so then am I also correct in saying that right now fins are NOT using hydrodynamic lift, and the clames by FCS and Futures are false? If so then are fins just points of lateral resistance?

Retrothis - Trying to understand everything you’ve said (and I may be on the edge of my physics knowlege, so please bare with me)
It is possable that my use of the term “Laminar Flow” is incorrect. Most of my knowledge is from a basic understanding of Aerodynamics (where laminar flow is created by momentum), and I maybe don’t fully understand the differences with Hydrodynamics. I watched your video, but was unclear of what I was watching, where is the flow, and where would I see mixing if it was taking place? You say that Flow Velocities on fins are tiny, but boards on average waves have been clocked at 11m/s, which sounds pretty quick to me, and given that in high school science a spoon under a tap manages to produce lift, I feel a fin at these speeds should work IF it has a good angle of attack, but if I’m right about the poor angle of attack, then there would be turbulant mixing of water at the trailing edge of the fin.

I agree that with a fin most of the flow is created by momentum, but in that case I can’t see how the direction of flow can change unless the board actually starts to slide sideways in the water. Although the board may change the direction it is facing on the wave, it still continues to have forwards momentum, so the flow of water is always from nose-tail. If the flow does change direction, what direction does it go, as to have a positive angle of attack on the inside fin, it would surely have to flow accross the board from the outside edge to the inside one.

I’m happy to be wrong on all this, but I want to understand WHY I’m wrong.



[quote="$1"] ... so the flow of water is always from nose-tail. [/quote]

With that statement, you have set your feet on the path of knowledge.     The relative flow is alway nose to tail, in line with the stringer.  I NEVER toe in side fins on 3 fin systems.     There are ''secret'' tweeks, that I will not go into here, but you have a good initial grip on the topic.     Toe in, or toe out, is a guarantee of increased drag, slowing the boards max speed.    My experience with 3 fin setups began in 1964, so I'm no stranger to them.   I will not give up speed for maneuverability.    I require both.

In the academic physics of it all, don't forget Reynold's number.

Hi harrington -

I agree with Bill and generally set my side more parallel than is the norm. 

One aspect of the equation that hasn't been mentioned is the effect of the outer fin.  With my own experiments with keels, FCS CRVs, and hoops there is definitely some resistance associated with the outer surface of the outer fins in rail-to-rail transitions and turning in general.  By 'outer' fin I mean the fin opposite of the direction of your turn.... in an off-the-top/cutback maneuver it can quickly become the fin opposite of 'outer' as in bottom turning/trimming. 

Foil thickness, leading edge shape, and outer surface vertical curvature can play a big role in rail-to-rail transitioning and general turning/trimming situations.  

It is pretty easy to imagine what's going on with the inside fin during a bottom turn but the outer fin is having an effect as well.

Hey Harrington

No no, the speed of the water flowing past the fin is as you say. Its relativly fast.

What i was trying to point out is that to achieve laminar flow with water, the flow speeds have to be much much lower. The volumes must be tiny to eliminate the effects of momentum. Hence, why I think that the flow of water past the fins is not laminar.

With regards to the video, that was just to show what laminar flow actually looks like.

Here is an image to explain what you were seeing:

The mixing occurs at the border of green and black streams. The mixing only occurs via diffusion. One of the hallmarks of lamiar flow.

With regards to direction of flow, I am probably wrong myself. So I would go with Bill T on this point.

My view was based on trying to rationalize why would a fin have toe. The only thing that I could come up with was that during a turn the direction of flow must be altered.

But again It looks like im wrong in this regard.