Foil dynamics questions.

[kenwstr]

Hi

Australian Sailing mag did a piece on foiled International Moth class.
So got into discussions on foils.

I did some figuring to see whether a 2 handed dinghy could power a foil
but as this was based on aerodynamic knowledge, I just wanted to veryfy a few things.

The following is ball park estimate, not intended to be an exhaustive analasys.

First, If we use a V foil so the tips rise above the surface, there should be no induced drag so only need to consider profile drag with a skin friction componant. I expect there will be some interference or wave drag at the surface but I don't know how to figure these last 2.

Also, because the foil is a V, it will rise until the lift from the submerged protion is = the total weight of boat and cew, say 250 kg, 2450N. That means we only have the required area submerged at any speed that is sufficient to raise the hull. Therefore the form drag = weight * Cdf / Cl at all speeds in question. Lets also taper the foil (small chord in deep centre) so aspect ratio and Rn are reasonably constant at all lifted speeds. Remember we are after a rough ball park figure.

So assuming Cl = 1 I get:

Speed Foil Area
Kts sqm
5 0.8
10 0.2
20 0.05
40 0.0125


I need Reynolds number to look up some polars.
I found viscosity for water of 1cp on the net and I think this works out around
944 x 10^-6 kg/m/s
If the mean chord a is .44 m at 5kts and .055m at 40Kts (tapered foil)
Rn approx = 1 000 000
Airfoil polars show a Cdf of around 0.015 at Cl = 1 at this Rn

Now can I assume this figure for water given that I accounted for density and viscosity in the Rn calculation ????
Is fluid compresability an issue???

That means dragg = 2450N * 0.015 / 1 = 36.75N or 3.75Kg force.


That seems a low figure that suggests almost any sailing dinghy could be foiled. Are my calcs and assumptions correct?
Are there other major drag componants to consider and how important are they to the final drag value?


Regards,
Ken

In the Moth class surface piercing foils were on the first boat to win a race in that class on foils. They were soon supplanted by the fully submerged foils designed and built by John Ilett of fastacraft( www.fastacraft.com ).
A Moth mainfoil may have an area around 1.08 sq. ft. and the rear foil about 60% of that. The fully submerged foil does require an altitude control system(wand).
Go to the International Moth class Australia forum for an in depth discussion of foils.
Go to www.monofoiler.com for pictures of several dinghy foilers.
The Moth Class outlawed surface piercing foils mounted off each wing as violating the anti-multihull rule so only foils mounted on the cl are acceptable.
Foil loading of around 177 pounds per sq.ft. (based on 80% load on mainfoil)works good on a two foil system but loadings have been much higher on some dinghy foilers such as the I14 on monofoiler.com Also, the Rave multifoiler operates at much higher loadings but also develops all the righting moment for the boat whereas the Moth foilers RM is from the crew(and crew technique). It's all about when you want to takeoff and whether low speed and mid range foiling is more important than max top end speed. The Moth guys appear to be going for early takeoff....
See the "foiler design" topic under "sailboats" here.
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Before the two foil Moth(with the possible exception of some windsurfer designs) all sailing hydrofoils were at least three foils. The Moth was a breakthru in foiler design for dinghies and flies with only two surface penetrations; you want to keep struts/surface penetrations to a minimum.....
=========================
Moth forum(click on message board):
http://www.moth.asn.au

[tspeer]

Originally Posted by kenwstr

...
First, If we use a V foil so the tips rise above the surface, there should be no induced drag so only need to consider profile drag with a skin friction componant.

Wrong. Even if the water's surface acted like a solid boundary there would still be induced drag. Contrary to the popular explanation of "flow around the ends", induced drag comes from getting lift by deflecting a mass of water over a finite span. You can tinker with the ends, but you can't eliminate it entirely.

At very low speeds, the free water surface acts like a solid boundary, but at high speeds it has just the opposite effect. Induced drag is actually doubled at the free surface, and increased by a lesser factor for the portions of the foil that are more deeply immersed.

[quote]I expect there will be some interference or wave drag at the surface but I don't know how to figure these last 2.[\QUOTE]

The simplest method is called "biplane theory". The idea is the foil acts as though it were one demi-wing of a biplane with a phantom demi-wing equidistant from the surface and producing the same lift. See http://naca.larc.nasa.gov/reports/19...ca-tn-4168.pdf and http://naca.larc.nasa.gov/reports/19...eport-1232.pdf

The physics goes like this. At very slow speeds, the force of gravity is large compared to the dynamic pressure from the foil's motion. So the vertical component of the velocities is suppressed at the surface and the pressure at the mean water level will change by small changes in the height of the water.

To represent this kind of a boundary you use an image system of sources/sinks or vortices that has the mirror geometry of the foil and all the strengths of the singularities are of opposite sign. The image system cancels the vertical components of the velocity, making the surface a plane of symmetry, and doubles the tangential components of the velocity induced by the sources or vortices.

At very high speeds, picture a hydrofoil that zips by and is gone before the water has much of a chance to react. In this case, the pressure at the surface is a constant - it's atmospheric everywhere. But the water at the surface has had a vertical velocity imparted to it - it just hasn't had time yet for that velocity to move it way from its originally flat shape.

In order to represent this condition, you use the same mirror geometry that you used for the solid boundary, but all the sources or vortices have the same sign as the physical foil's. This cancels the horizontal velocity - resulting in zero change in pressure at the surface, but doubles the vertical component at the surface.

Since the induced drag depends on the vertical component of velocity induced by the wake shed by the finite span foil, the induced drag is doubled at the surface.

Also, because the foil is a V, it will rise until the lift from the submerged protion is = the total weight of boat and cew, say 250 kg, 2450N. That means we only have the required area submerged at any speed that is sufficient to raise the hull.

If you do it this way, you will get a very steep increase in induced drag as the speed increases. And that takes some doing, because if the span is kept fixed the induced drag will go down with the square of the speed. The reason for the increase in induced drag is the shrinking of the span as less and less of the V is immersed.

Therefore the form drag = weight * Cdf / Cl at all speeds in question. Lets also taper the foil (small chord in deep centre) so aspect ratio and Rn are reasonably constant at all lifted speeds.

By tapering the chord as you suggest you get a very poor spanload distribution to start with, because the tips are heavily loaded and they are at the surface. But you do slow down the decrease in span with the decrease in area.

A better approach is to recognize that the lift on the V foil is a function not just of area but of angle of attack, too. You want to reduce the angle of attack as the speed increases so that the area, and span, reduce more slowly with speed than is the case with the constant-attitude approach. The reduction in area offsets some of the increase in profile drag with speed. The decrease in span gives up some of the decrease in induced drag with speed. The result can be a near-constant drag, independent of speed.

See http://www.tspeer.com/Hydrofoils/generic.pdf for an analysis of different types of hydrofoils, similar to what you are trying to do, and a comparison with experimental data. The experimental data for the V foil shows the drag can increase or decrease with speed, depending on how the attitude is controlled.