For an explanation of the 'thruster
hypothesis' see BillBarnfield's
post above, and my
interpretation of this hypothesis, if for no other reason than to
understand what I mean by shedding flow.
...start simple
Curious
as to the direction of shedding flow relative to incident flow, I
modeled the impact of this shedding flow on an uncanted toed lateral
fin – just the one lateral fin is considered. I used Carswell's
experimental data for the RedX X1 L fin (the left asymmetrically
foiled fin), see Hydrodynamics of Surfboard Fins, Carswell, D. J.
(2007). Here, the incident flow does not have a upward direction, see
below. The point was to start simple.
...results, so far
Rather
than bore the shit of most of you with a lot of math, I'll get right
to the results, see next paragraph. For those interested, and I hope
some are, and will want to actually check my model and numbers,
please work though the iillustrations below. It's not a very complex model.
It's crude, but hopefully not unreasonable.
In a
nutshell, for the model here, a net positive contribution to the
actual propulsion of the surfboard doesn't start until the direction
of the shedding flow is about 50-degree (probably a little less, let's say 45 degree)
relative to the incident flow (in this model.) This isn't
inconsistent with BillBarnfield's
diagram of how he imagines the flow under a surfboard, see figure 3 below.
For
shedding flow angles of less than 45-degree the net contribution is
negative, that is, it amounts to a drag. But the amounts suggested
here for the one fin aren't all that critical; roughly times three,as it would be for the full configuration,
is another matter however. The same would be true for the positive
contribution, but times two, if the shedding flow was symmetrical.
I've
also compared different toe angles (3-degree, 4-degree, and 5-degree)
to try and get a feel for how toe might be contributing (in this
model.) It would appear that with increasing toe, the net positive
contribution, here for toe greater than 4%, to propulsion starts
earlier that 50-degree and the net drag is less for angles less than
45-degree. That would tend to contradict, at least my experience with
over-toed configurations. Nevertheless this is a very very simple
model, and such a finding neither proves nor disproves anything.
I
guess the next step would be to try and incorporate cant into the
picture, and off course the upward component of flow. It would seem
at this point, with a little (or, maybe a lot?) stretching of
Carswell's data, that the impact of cant could be accounted for, but not
today, at least by me it won't.
Then
after that, take into account the impact of all three fins (or more?,
gee that would be interesting to find out what's going on with quads,
etc. ) Which would likely be a real mess, as you've got to start to
make assumptions about how symmetric this shedding flow is.
Am I
convinced that such a mechanism is in play? Sure, It could be. Do I
believe that a 45-degree kind of direction of the shedding flow is
possible? Sure, it could be. The picture is hardly complete for me.
By the way, the
point here was the **45-degree plus or minus shedding angle** – and,
that has impact on more than just fins...bottom contours
(particularly the impact of concaves and convexes, and how to take
advantage of any further changes in this angle with toe and cant), on
how fin gizmos work (like turbo tubes or tunnels, or whatever they
are called), how configuration gizmos work (like swivel fins, etc.) and
more.
By the way,
Carswell's doesn't exhaustively treat gizmos (including flexible
fins) but he does touch on them. I recommend his thesis to anyone
interested in this kind of modeling.
… believe it or
not, for me that was fun. Hopefully, somebody will check all this and
confirm the model, or rip me a new one, or even better carry on to
cant and beyond.
kc
ps
In the spirit of
JohnMellor's thread, I'd like to identify myself as having no stake
in any particular industry related product or gizmo. I wish I did,
there's money to be made in 'dem gizmos – sit back and wait for the
cash to come in, kind of money. - the best kind of money.
pss
By the way, Carswell touches on the net
impact of a classic tri-fin configuration, but does not incorporate
the thruster hypothesis -i.e. the proposed role of shedding flow.
That is, in his model there is no shedding flow, its all incident
-i.e. all three fins experiencing the same incident flow. To say the
real picture lies somewhere in between the kind of shedding flow
assumed in the thruster hypothesis and the straightforward approach
taken by Carswell (and maybe others, Marsh, T. J. Development of an
Optimized Surfboard Fin? … and if anyone has a copy of this paper,
I'd love to read it!), is likely an understatement. Still, Carswell's
data is interesting.