# theoretical displacement hull shape for min drag

Discussion in 'Software' started by Padava, Jun 21, 2009.

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What differential ( ordinary ODE or partial PDE ) equation describes a hull shape for minimum resistance and/or mimimum fuel consumption of displacement boats/ships operating at around the 1.34 sqrt (loa or lpp) ? I like to look at fundamentals to compare "pure" form with hull softwares now available to see how or which design parameters characterize different power displacement curves. Regards

Last edited: Jun 21, 2009
2. ### Guest625101138Previous Member

What you seek is not available.

The lowest drag hull for calm water is primarily a function of both speed AND displacement not just speed.

A common parametric hull that is used for drag analysis is the Wigley hull. It is simply a function of LWL (L), BWL (B), and draft (D). The equation for beam at any point on the hull is:

y = B/2 * (1 - (2x/L)^2) * (1 - (2z/D)^2)

You can find tow test data on these hulls if you search around the web.

Rick W

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You need to define a bit more clearly what you're objective is...is it mathetical, ie equations, or hydrodynamic, for example, since these two are not always compatible.

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### mydauphinSenior Member

A canoe... a very long light canoe...

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Is that a "whafer thin" infinitely long hull in an inviscid fluid?

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### mydauphinSenior Member

Might as well make it a vacuum

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### Leo LazauskasSenior Member

You should get hold of:
"The Wave Resistance of Ships"
John V. Wehausen
Ships of minimum resistance.

A few other references that might be useful...

"Ships of Minimum Total Resistance"
Lin, Wen-Chin, Webster, W.C. and Wehausen, J.V.,
College of Engineering,
Uni. of California, Berkeley,
Report No. NA-63-7
Aug. 1963.

"Optimal Ship Forms of Minimum Wave Resistance"
Chi-Chao Hsiung
College of Engineering,
Uni. of California, Berkeley,
Report No. NA 72-1
Aug. 1972.

Some formulations are just quadratic programming exercises,
but there are others available that require calculating Mathieu
functions. Unless you know some numerical analysis, they will
have you tearing your hair out! Hunt through Wehausen's work

Good luck!
Leo.

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Leo

You have been quoted as saying "...Leo advises that there are two lowest drag hulls but I have never seen this....", in reference to hull shapes and drag, would you care to elaborate on this please?

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### Leo LazauskasSenior Member

In some cases, and at some Froude numbers, it is possible to get more than one "optimal" hull. Think of it this way: a short beamy hull has low skin-friction and high wave resistance. At the same speed (and for the same displacement), a long thin hull can have high skin-friction and low wave resistance. Theefore it is possible to have two hulls with the same total drag, but different proportions of wave resistance and skin-friction.

For more, see:

Leo.

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Leo

Ok, so the statement is referring to the obvious aspects, as you have noted, when designing a hull-form, theoretically, both ends of the spectrum as such. Not some "holy grail" as appear the poster was eluding too! But I'm skipping over the obvious, the the difference in actual hull forms of such a theoretical exercise renders both hulls somewhat impractical in reality and hence, is just an "interesting" theoretical debate.

Since a short beamy hull will have poor length displacement ratio and all the consequential knock on affects.

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### Leo LazauskasSenior Member

I don't agree that they are impractical.

I gave an example of two extremes as an illustration. Instead, think slightly shorter and beamier, and slightly longer and thinner (instead of the extremes) and the conclusion is the same: there can be two hulls with the same total drag but different proportions of skin-friction and wave resistance.

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Leo

Interesting article. But, this is related to long thin rowing boats, of sorts.

A rowing boat is basically a skin, to keep the water out, a seat and method of "moving the boat" oars/rowlocks etc, that is all.

A real boat, in the sense that it is for more than just going up and down in a straight line for several thousand meters - that is to say a design brief of one line, is somewhat different to a real boat. A real boat in terms of what the hull form must provide has a design brief that runs into many pages such as outfitting, compliance with class requirements, payloads, propulsion, structural arrangement etc. This is where the "theoretical debate" breaks down between "hull-forms" and real hulls used for a working design.

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### Leo LazauskasSenior Member

The same "trick" can be done with real hulls.
Keep the shape the same but scale one hull so it is slightly shorter and beamier, and make another that is slightly longer and narrower. Now all three hulls have the same total drag, different proportions of wave drag and skin-friction, and, of course, different performance characteristics, seakindliness, etc.

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Leo

But your study is based upon volumetric Froude numbers, yes?..so there are 3 variables for any given volume and hence 3 solutions not 2.

So if the theory is correct, why are the assumptions for an "idealised hull", what is wrong with "any shape", a true "ship shape" becomes irrelevant for your study, just any shape is applicable, that is moving through a fluid.?

You even acknowledge this to an extent viz:

"..In this study, we present results for one hullform only - a canoe body defined by parabolic waterlines, elliptical cross-sections, and a parabolic keel-line. Although this form is an obvious idealisation.... Clearly this is a much finer type of hull than that of a typical merchant ship, but is relevant to sporting canoes and hulls of special high-speed vessels..."

"..When there are length restrictions, and hence a greater contribution of wave resistance to the total drag, multihulls can have less total drag than monohulls of the same length..."

"...In any case, the hulls resulting from the optimisation process also have the property that their wave resistance is generally only about 10% of the total, so that the absolute accuracy of the wave resistance measure is not critical..."

So, as i stated, it is a nice theoretical exercise for a 3D shape and finding a low drag shape, at low speeds for that 3D shape. But for a real hull ship shape, not so.

Since i don't see any reference to sinkage and trim, hence change of LCG/LCB, nor transom sterns etc, as one finds on higher froude number vessels etc.

The rowing boat study you provided is fine for one type of "hull form" at low Fn's, (which in itself i rather interesting) but i fail to see how this is applicable to real hull shapes given the endless caveats required to arrive at a conclusion in your study.

15. ### apex1Guest

Ahh, nice to see that finally they found each other (Ad Hoc and Leo).

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