# Wave resistance of rudder, using Michlet

Discussion in 'Hydrodynamics and Aerodynamics' started by Remmlinger, Sep 1, 2012.

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### Remmlingerengineer

I use the VPP for different purposes:

1.) The simulation of a towing tank. The purpose is to test the physical models in the VPP. If the modeling is valid, the measured data from the tank should be met. In this case a short executable like you described it would be helpful.

2.) My main interest, as described on my website, is optimization. The VPP is practically the merit function. Since the optimization runs almost a week, computing time is absolutely crucial. For resistance calculations anything else than a look-up table (Delft method) or a closed mathematical formula is just too costly in time.

Michlet is already a great tool as it is.
Appreciate you interest in my search for a straw to hang on to.

Uli

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### Leo LazauskasSenior Member

Too late!!!!!
ULIMICH has been released. LOL WTF.

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### Remmlingerengineer

Update

Attached are the equations that include the influence of submergence.
The diagram compares the approximation for the aspect ratio 2.0
To be honest, I have not yet checked other AR.
To produce a foil with a flat top beneath the surface in Michlet is tricky!
Uli

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• ###### Wavedrag_NACA0012.pdf
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### DCockeySenior Member

Uli, thanks for sharing the results. Is "h" the depth of the top below the surface?

I'm skeptical of the validity of modeling a flat top over foil in Michlet (or any other "thin ship" code).

Leo, any suggestions on how to estimate the wave drag of an isolated, vertical lifting foil in a computationally efficient manner similar to thin ship theory for symmetric foils? Vortex lattice method or the equivalent constant strength doublet panels? Possibly determine the approximate vortex/doublet strength using a conventional aerodynamics code, and then apply that strength to a vortex/doublet distribution using singularities which satisfy the linear free-surface conditions. Doublets would be attractive since a doublet can be obtained by differentiating a source.

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### Leo LazauskasSenior Member

1.For a non-lifting surface, I can't see that a keel could have
very large wave resistance. Deep submergence will damp out the
diverging waves; the short chord implies a high Froude number and,
therefore, small transverse waves.

2. I have not thought about how to solve the full lifting surface
equation in the presence of a free-surface. It's just too tough
and there are difficulties with hydraulic jumps behind the trailing-
edge of surface-piercing bodies.

Any of the methods you proposed would be a reasonable 1st attempt
for straight-edged surfaces. Curved planforms might be awkward for
some VLM codes.

You could try using Havelock sources and vortices (or dipoles)
but they can be tough to calculate.

3. I cheat by prescribing a vortex distribution, as did Tuck in
"Can lateral asymmetry of the hulls reduce catamaran wave resistance"