# Some notes on toe and drag

Quick review,

Drag is the component of the resultant force exerted by a fluid on a body parallel to the relative motion of the fluid.

Lift refers to the component of the resultant force exerted by a fluid on a body perpendicular to the relative motion of the fluid.

Qualitatively if you graph lift vs drag forces for a given body and for a given velocity of relative flow, you get something like seen in figure 2. Increasing or decreasing angle of attack (see figure 1) moves you alone the curve. (For those of you who look at a lot of these kinds of curves you may find the curve in figure 2 a bit exaggerated. Think of it as a matter of scaling, or just cut me a little slack, or not.)

Also, the exact shape of these kinds of curves changes significantly with foil, shape, etc. Here, just think of something relatively streamline and symmetric. (For those who think terms of NACA nomenclature (and I don’t) think of something 0 0 as its first two arguments. Knowing NACA nomenclature however isn’t critical here, at least not in this post. Issues of foil are not specifically address in this initial post.)

You’ll notice there are no numbers in my graphs. Numbers surely matter. Regrettably, I don’t have any. But maybe that’s just as well for purposes here. My approach is going to be the quick and dirty qualitative kind, sort of a ‘thought experiment’ approach.

Assertion: Toe increases drag

Intuitively, the directionally opposed nature of toed fins suggests that additional drag might be expected, so lets build a fin system and see what turns up, but lets start with a parallel system.

Lets add two parallel similar fins in a symmetric manner about the initial fin. Given the nature of forces - components along a given direction add - then the addition of two additional similar fins might create a graph like that seen in figure 3.

This is truly a simplification, issues like spatial positioning of the fins plays a big role, but I’m assuming you’re cutting me some slack, at least to make my point, …or not. Also, I’ve conveniently left out other factors like, foil, cant, etc., all of which can be important too, but again, I’m counting on you giving me a little license here – as dangerous as that might be.

As suggest by figure 3, by adding the parallel fins (no toe or cant) the curve kind of flattens out over the range shown, at least relative to the single fin case. The drag at all angles of attack increases somewhat, its as if the whole curve is lifted - like you’ve dropped a little sea-anchor.

Time to toe…

Lets toe the lateral fins (nothing else just toe.) Relative to the central fin, their individual graphs would appear shifted as shown in figure 4. The respectively ‘bottom’ or point of zero angle of attack for these toed fins are located at a positions relative to the central fin’s curve which corresponds to the toe angle. We then sum the respective forces for our system. The resultant is also given in figure.

Figure 5, compares the all parallel 3-fin system and 3-fin 2-toed fin system results.

Perhaps not surprisingly, by toeing the lateral fins, the whole response of the system seems to be shifted up and slightly flatter (the flatten out is admittedly hard to see in my diagram… trust me?)

In fact, in this model, if you increase the toe, the two lateral graphs corresponding to the individual toed fins mover further apart, the result curve flattens even more and the overall drag of the system increases a little more, and conversely so if you decrease toe.

Also, things get better or worse, depending on your point of view, if you just started adding more toed fins sets: additional curves appearing outside the original toed curves for sets with greater toe, for those with less, appearing inside, flattening out the resultant curve and increaseing the overall drag. If you just add more fins with similar toe, you just add more drag, or shift the resultant curve upward. Giving what is happening, if you found it important, there would seem to be a whole bunch of different scenarios available to fine tune it.

All that said, and sure, this is all pretty crude and sketchy, but I don’t think its unreasonable to ask, who needs the extra drag? There would seem to be great benefit given the popularity of the toed fins. So what’s the benefit? At least with respect to drag.

Here’s my take…

It has been a while (late 60’s?), but my first shortboard had a single fin. On steep or late take-offs I’d literally rocket out of the pocket. When I finally bought a tri-finned toed shortboard, I rocketed much less, the take-offs where far more controlled, at least controlling acceleration during take-offs was less of a critical issue, or at least it felt so. Sure template or other factors played some role, but I’m inclined to believe most of it was due to the cluster.

Something similar also seems to apply to (single fin) longboard take-offs on steep or late take-offs. You can angle in a little, but often during big drops you, okay maybe just I, find myself leaning back struggling to put on the breaks, this, in addition to trying to keep the nose up. Otherwise you just rocket out of the pocket, and it’s a bitch to get back in it, as least as tight as you can on a shorter tri-finned board.

Lets for moment say this makes a kind of sense. All sorts of questions come to mind. Does this relate to what is now the traditional method of establishing toe angle -i.e. drawing a line to the nose? What’s up with quads, etc? How does this fit in with backing off the toe angle on a (true) fish? And how does backing off on the toe on a (true) fish fit relate to the method of establishing toe? When do side bites on longboards really start to make a lot of sense? I think all these questions can be at least touched on now, at least from a drag perspective… if you buy into my nonsense… if only a little.

I haven’t even touched on cant, foil, fin shape/size,fin flex, etc., all of which can be pretty important. I just wanted to begin laying down a sort of base (for a possible cluster f%\$k of a thread.) Of course, what would really be nice is, if the powers that be at FCS unleashed one of their engineers long enough to explain to me and all, how much nonsense this (as in what I’ve sketched out here) is? They have data, right?

Anyway, as this post is now way too long, I’ll leave subsequent posts for more nonsense (that’s assuming this one doesn’t die a quick death…)

kc

All well and good if the water adjacent to the bottom of the board is all flowing parallel…

However, this is not even close to the pattern of flow. The water next to the board aggressively flows towards the rails in addition to flowing from nose to tail.

A little deeper to the hull, the vector points closer to nose-to-tail, but is still angled towards the rail.

Somewhere in the range of 3-4 inches deep of the hull, the water flow is pretty close to nose-to-tail.

With an appropriate angle of attack (nose-lift), the water is net parallel to all three fins on a thruster. Lift the nose more and the inside surface of the rail fins is high pressure. Nose down and the outside surface of the rail fins is high pressure.

Good riders ALWAYS keep their nose up enough that the inside surfaces of the rail fins is high pressure.

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All well and good if the water adjacent to the bottom of the board is all flowing parallel…

However, this is not even close to the pattern of flow. The water next to the board aggressively flows towards the rails in addition to flowing from nose to tail.

It seems to me that when talking about a surfboard moving “down the line” of a wave you have to think about the water flow relative to the board.

I think that most of the “water flow” relative to the board really comes from the board moving down the line (or whatever direction the board is moving).

Am I wrong?

However, this is not even close to the pattern of flow. The water next to the board aggressively flows towards the rails in addition to flowing from nose to tail.

A little deeper to the hull, the vector points closer to nose-to-tail, but is still angled towards the rail.

Somewhere in the range of 3-4 inches deep of the hull, the water flow is pretty close to nose-to-tail.

This is based on the assumption that the board is being surfed dead flat off the face in the flats. I would guess that represents a small fraction of actual surfing.

Once on the face, or slightly on rail including level trim on the face, this is no longer the case and represents the vast majority of actual surfing.

Kcasey, have you looked into sail physics yet?

http://www.lksc.org/myhtml/howsailswork.pdf

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However, this is not even close to the pattern of flow. The water next to the board aggressively flows towards the rails in addition to flowing from nose to tail.

A little deeper to the hull, the vector points closer to nose-to-tail, but is still angled towards the rail.

Somewhere in the range of 3-4 inches deep of the hull, the water flow is pretty close to nose-to-tail.

This is based on the assumption that the board is being surfed dead flat off the face in the flats. I would guess that represents a small fraction of actual surfing.

Once on the face, or slightly on rail including level trim on the face, this is no longer the case and represents the vast majority of actual surfing.

Kcasey, have you looked into sail physics yet?

http://www.lksc.org/myhtml/howsailswork.pdf

Sorry, but you’ve got it backwards. Cross-flow increases as aspect ratio decreases. Angling across the face of a wave reduces the max width of the wetted surface (wetted length also typically increases a little). Makes for a reduced aspect ratio and more cross-flow. (The narrower the bottom is, compared with its length, the more likely the water will flow off to the side rather than being deflected deeper)

Going staight off wets the full width of the board (and typically decreases the wetted length–at least until you slow down). Maximizes aspect ratio, minimizes cross-flow. The wider the bottom, relative to the length, the less likely the flow is going to go the long way around instead of just a little deeper to get to the end of the board)

Far away from the board the water doesn’t “feel” the presence of the distant bottom so it just more or less continues on it merry way. (If that weren’t the case then the dynamic lift–i.e. the lift leading to planing–would be roughly proportional to the depth of the water). [Could make it really difficult to catch a wave]

Hence: Blakestah is more correct.

mtb

Hey KC,

What you are saying does make sense: essentially drag for control.

Now for some of your questions…

“Does this relate to what is now the traditional method of establishing toe angle -i.e. drawing a line to the nose? What’s up with quads, etc? How does this fit in with backing off the toe angle on a (true) fish? And how does backing off on the toe on a (true) fish fit relate to the method of establishing toe? When do side bites on longboards really start to make a lot of sense?”

I think the traditional methods for establishing toe were arrived at by both trial and error and convenience (line to nose). I think that toe-in helps to make sure that the asymmetrically foiled side fins are at a zero-lift orientation, but craftee’s experiments with under-board flow kinda shut that down near the board…but for flow neat the tip, it begins to make sense…

I think quads try to take advantage of a multi-element lifting surface effect. The forward fins help deflect the flow so that the back fins can work at their lesser toe angle…

The backing off of toe on a traditional fish I think has to do with its symmetrically foiled keels (zero lift is zero toe, and I do understand that I am not taking into account craftee’s and blakestah’s flow conditions). Another reason could be that keels have a tremendously low aspect ratio and high quarter-chord sweep, and because of this they are less sensitive to angle of attack changes…their lift v AOA curves are much flatter and stall occurs much later than a more upright, les swept planform (and asymmetrical foil).

As to when side-bites make sense on a longboard, I think it depends on the person. Having 3 vortex genertors on the underside of the board will have more drag than one…but can also potentially generate more lift when needed (if total fin areas are kept the same; larger single and smaller center fin on the 2+1 setup).

I imagine you are mainly taking into account induced drag, the dominant drag force at ‘slower’ speeds…I’m not sure what the speed is that marks the transition point at which parasitic and form drag become the major drag determinant, and not induced drag…any ideas?

JSS

That’s a really interesting reference (the URI) - very nice, great reading! Thanks.

I guess the discussion could go there, but here I just wanted to argue that shortboards ‘need to be on a leash’, and I am not referring to the one tethered to your leg.

The things are acceleration animals, at least when compared to what came before them. There acceleration needs to be restrained. That kind of statement (assertion) is not something you’re likely to read a lot.

Whether the flow is rail to rail; or, up and rail to rail; or, up, rail-to-rail and with a variable nose- to-tail component, or how flow changes with depth from the bottom of the board, are some of my favorite questions (I’m sure you’ve got better things to do, but just take a peak at some of my prior threads.) But I didn’t want to go there in this thread.

Also, turning, carving, etc. involves rails (and other aspects of the template) in a big way, but all that is relatively all over the place dynamically, that is you don’t turn the same way each time you turn, whereas with toe, you set it once and ‘walk away.’

Here, I was interested in exploring the role of toe with respect to drag, and that curious method of determining toe –i.e. drawing a line to the nose approach.

Regardless of the flow characteristic, in general, the opposed nature of toed fins means more drag than a set of similar un-toed fins. I thought it might be an interesting exercise to explore this further.

Really, what are we building here? Some weird meta-foil?

Maybe we’re not seeing the forest kind of thing. With each additional toed set, whether they be outside or inside the original toed set, a little bit more of the leading portion of some giant foil is added, all crammed into a limited space; each surfboard, more or less having its own meta-foil.

For now, I’d rather leave the particular dynamics of each individual foil to you foilophiles to thrash out – there’s money in them wee’lil shapes.

Anyway, I’d thought I take the opportunity to complete some thoughts….

kc

Regarding the method of establishing the toe angle…

Fins aren’t the only thing that drags, so to speak – wetted surface area is the other big culprit. More surface area, more drag, at least in general.

A simple notion… always a dangerous thing…

My guess is that, at least to a significant degree, the common technique of establishing toe angle, tries to account for increased drag that is associated with surface area by reducing the toe as a function of board length. Its not perfect, its not precise, but in the bay, board length is kind of a real quick and dirty way of adjusting toe – longer the board, more surface area, less toe, and conversely so.

The point being, that drag is good, but too much of a good thing is bad.

Surface area, or bottom area is not an exact match to board length e.g. the fish, and more on that later, but its not a bad dipstick, as dipsticks go.

There’s a lot of play here. A small difference in toe means that you’ll likely adjust your technique to the board – different position on the board, etc…

The point being its pretty hard to set a specific toe angle for a board out of the box (so to speak), but something reasonably close to where it should be is usually sufficient - the surfer making the necessary adjustments by modifying his technique.

Obviously, it is possible, in a gross way, to over- or under-do the toe. Shapers familiar with a given break will likely vary from the standard toe (or the way of setting it) if the feedback warrants it – no surprise there.

Some notes on fishes…

The fish, though its hardly a cut in stone, was made for those mushy days, usually small mushy days, or at least that is my understand of the original intent. With traditional fishes you get a little more surface area per length, which results in a little more translation of force from wave to board. But given their original application, the last thing you’d want is an excessive amount of drag, so you back off on the toe. Usually not completely, but I have seen twins on fishes that approach the toeless. Modern fishes are all over the place, so the rule is no longer generally true.

Some notes on longboard side bites…

Side bites on longboards are pretty popular. Whether or not they make sense is obviously up to the shaper and surfer. I’m inclined to think they make a lot of sense on modern longboards, particularly because of the change in longboard surfing style and of course the kind waves that modern longboarders are more willing what to be able to ride. The side bites offer a little more drag, probably enough for those hairier drops, and the additional drag can keep you closer to the pocket, but not enough to get in the way otherwise. On mushier days, they probably don’t cause enough of a problem to notice.

kc

Nice. Your taking matters further than I.

Please, if you get a moment, see the bottom half of my reply to craftee. The upper half isn’t too bad either.

kc

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I think quads try to take advantage of a multi-element lifting surface effect. The forward fins help deflect the flow so that the back fins can work at their lesser toe angle…

The backing off of toe on a traditional fish I think has to do with its symmetrically foiled keels (zero lift is zero toe, and I do understand that I am not taking into account craftee’s and blakestah’s flow conditions). Another reason could be that keels have a tremendously low aspect ratio and high quarter-chord sweep, and because of this they are less sensitive to angle of attack changes…their lift v AOA curves are much flatter and stall occurs much later than a more upright, les swept planform (and asymmetrical foil).

A reduction in toe-in “works” when the board hull length is longer and is ridden more “nose-down” or with more “front foot”.

In smaller waves it is highly desireable to be able to ride with a heavier front foot (all other things equal) because the heavier front foot flattens the board to the water and reduces the hull resistance (which is from skin resistance and water displacement and planing forces). This complements a lower rocker as well…when you combine these elements (flatter rocker, ridden more front foot, less toe-in), you have the modern quad/fish, a board that “works” better in smaller waves because the smaller waves do not have enough ooomph to complement the necessary heavy rear foot required on a thruster.

However, the ability to generate thrust suffers because it is highly sensitive to the differential angle between rear and rail fins, and quads ain’t got it the way a thruster does.

Now, if someone only came up with a way to generate the thrust of a thruster, while allowing the board to be ridden with more front foot, then you would have a small wave board that REALLY kicked as5. Something that would have less drag than a quad, but as much thrust as a thruster.

Here’s a picture that might clear up my meta-foil reference.

I think I’ll take the opportunity to briefly finishing up some thoughts …

A few notes on cant and hold…

The plane of a cant fin, far more often than not will tend to pull the tail of the board into the surface of the wave. This would seem to fly in the face of the usual concerns for ‘lift’ –i.e. lifting the tail of the surfboard, as cant tends to generate forces in the opposite direction.

However, the forces generated by cant can be viewed as ‘holding’ the board to the wave, in that they oppose planing forces. Planing forces during surfing tend to push the whole board up and out of the water; cant counteracts these forces to a degree allowing the surfer/surfboard to remain connected to the face of the wave.

Though their function on street vehicles is questionable, airfoils placed on racing cars tend to provide a similar function with respect to traction. But while I’m making automotive analogies, cant also plays some role in dampening shocks, similar to the suspension system of an automobile.

Like all such tweaks to fins, cant does come with a drag cost.

Can’t cant do other things too? Perhaps, but pigs cant fly…sorry can’t fly.

Summarizing…

Toe increases drag (among other things which weren’t addressed here) and that’s a good thing.

Cant works to counter some of the lift generated by planing forces and that’s also a good thing.

disturbing uh,… dragging and sinking being ‘good’ things… it all came to me when I gave up coffee… maybe its the withdrawl talking… must be?

kc

I think you misunderstood.

My point is that the AOAs seen on fins is proportional to how much the board is railed. Flat surfed no railing means more straighter flow and reduced cross; railed, AOAs (cross) get steep, the harder the railing, the steeper the cross.

Call me crazy but I think we are saying the same thing, just using different terms and points of reference.

I like what you’re saying about toe being increased for shorter boards via the ‘point to the nose’ approach. Now I have to ask of the fluid dynamicists out there (MTB, you out there?) if on a shorter v longer board, how the flow next to the board would differ. Given the same weight surfer on each, my guess is that the shorter board would ride a little lower in the water, possibly making the flow next to the board angle more compared to the stringer. This would mean that for a zero-lift condition (or just for less drag), more toe-in would be necessary compared to a longer board (essentially what you said, just trying to figure out another reason why).

JSS

EDIT - Just saw Blakestah’s post; he essentially says the same thing…now doesn’t having a system like 4wfs, to adjust toe, or a self-adjusting system like SurfTrux seem like the way to go to really dial in a board? I think so…

Blakestah, about your Trux…is there a way to have more ‘toe-out’ range on the movement of the side fins so the outside fin can ‘disappear’ more? Just wondering…

Regardless of the flow characteristic, in general, the opposed nature of toed fins means more drag than a set of similar un-toed fins. I thought it might be an interesting exercise to explore this further.

K, if youre talking about thruster setups which are typically used on modern surfboards using modern surfing, toein REDUCES drag ON RAIL. And on rail is where I want to be, so you guessed right, Im biased.

IMO, looking at foils individually, they dont matter as much as people think. Or at least, not as important as other fin critical factors. Cant see the forrest for the trees if you will.

You seem to be implying that fin drag is not necessarily a bad thing. I dont have a problem with that. Ten years or so ago my thinking was to minimize finning in order to minimize drag, in order to maximize speed. Ive since learned. With modern multifin surfboards, fins are good, real good. For my style of surfing, they are energy transducers.

I wish I could debate and discuss more, but my way of thinking is much simpler now. Besides, you can always buy a set of 4WFS boxes and experiment to your hearts content. Field experiments is where the fun and answers are. MIght give it a go myself.

Btw, a fin/board guru told me that toein allows the fin to point in the direction of the wave’s energy. Not exactly sure what he meant, but it had me thinking.

Here’s the \$64,000 question:

If you could have a board with no drag, but doesnt generate thrust and doesnt turn, would you use it and ride it regularly?

THAT is the question.

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I like what you're saying about toe being increased for shorter boards via the 'point to the nose' approach. Now I have to ask of the fluid dynamicists out there (MTB, you out there?) if on a shorter v longer board, how the flow next to the board would differ. Given the same weight surfer on each, my guess is that the shorter board would ride a little lower in the water, possibly making the flow next to the board angle more compared to the stringer. This would mean that for a zero-lift condition (or just for less drag), more toe-in would be necessary compared to a longer board (essentially what you said, just trying to figure out another reason why).

The angle of attack and aspect ratio of the planing hull will be the major variables. If you make the planing hull longer, it will typically be ridden at less of an angle from tail to nose. The angle of attack reduction will reduce the water side-flow. This will happen even more than you might suppose, because the longer board will also generate more lift through water displacement (Galileo’s bathtub), so the amount of planing lift required is less (so you ride it even less nose-up). When it is all added up, the shorter board will need to be ridden a lot more “nose up”.

It changes again when you change the wave speed, everything straightens out a little.

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EDIT - Just saw Blakestah’s post; he essentially says the same thing…now doesn’t having a system like 4wfs, to adjust toe, or a self-adjusting system like SurfTrux seem like the way to go to really dial in a board? I think so…

Blakestah, about your Trux…is there a way to have more ‘toe-out’ range on the movement of the side fins so the outside fin can ‘disappear’ more? Just wondering…

I wondered about this a lot, because on my prototype boards the available toe-out was larger. Actually, both toe-in and toe-out were larger, so I independently dialed them in. I found, of course, that toe-in at the standard was optimal. But toe-out had a modest effect, but got better and better the more toe-out was allowed. For manufacturing ease I made them the same. You could hack up a box to change it pretty easily with 5 minutes and a file (if you knew where to file), if you are interested email me and I can walk you through it. It definitely will not hurt anything.

Through a lot of the range of action on a surfboard, it may be adequately controlled with no fins. When you get to the harder turning, obviously that changes, and that is sorta how the Trux work.