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…)