# Prismatic coefficient discussion

Discussion in 'Sailboats' started by AdrienJousset, Dec 31, 2010.

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Dear All,

I am currently designing a 40 ft hull for a racing sailing boat.

After having designed the hull (canoe body), I brought the keel, the bulb and the rudder and noticed that the Cp would considerably change. So far this is normal. I never really noticed that since we usually consider the Cp without the keel, bulb and rudder...
In fact during the calculation of the prismatic coefficient we never take into account the keel and the bulb. I am talking about a fin keel. For a high displacement long keel boat the keel will be included into the calculations. By the way this topic has already been partially discussed in a previous thread, but I would like to go a little further. So I am talking about a fin keel and a bulb and not a long keel.
Why do we not take into account the keel and bulb volume into the Cp calculation?
If we do it so, the canoe body will need to have major modifications in order to achieve ideal Cp. So a bit nose in the air I would have said that we should not take the appendages into account.
However Bruce Farr flattens the hull near the keel to reduce the pick in the area curve due to the keel volume. So does plane designer with Jetfighters. And I think it should be right to consider some effect of the keel on the canoe body.
The bulb is probably far enough from the bottom of the hull to not be taken into account.
Also the keel is usually wider, thicker, longer near the hull for mainly structural issues, so i would say that the effect on the canoe body hydrodynamic is even more important.

So my question or my discussion topic would be: would it not be interesting to partially consider the keel as part of the canoe body for Cp calculation? and if so how much should be taken? 30%, 50%

Thank you all for your replies. And Happy New Year!!!

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### gonzoSenior Member

Usually the keel is calculated as a foil separately. For example, it doesn't usually have wave resistance. Also, it is completely submerged unlike the hull which moves between two mediums.

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I agree but if we take the optimum Cp from the Deflt series, should we no take into acount apart of the keel volume? As a young unknowledged yacht designer (just kidding) I think so...
My theory is that we should take a part of the keel volume into acount. but how much?

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### gonzoSenior Member

I distrust a numbers only approach. They work for comparing similar hulls, so if you use the same percentage, they should give you a reasonable comparison. However, prismatic coefficient assumes the hull travels in a straight line.

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### AlikSenior Member

Adrien, those optimum CP's from Delft series are for canoe body only, pls refer to original publications on series. Taking canoe body and appendages separately is correct approach.

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### yipsterdesigner

discussing prismatic coefficent and planes as well.. hmm.. long as a foil gives lift in fluid
for race boats could we not check on area rule and Euler as well?

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### Perm StressSenior Member

Separate consideration of fin keel and hull is a standard approach, commonly used throughout industry at present. So you will not find anything numerical published on the opposite philosophy.
However, a few years ago, Yachting World publication on JuanK designed VO70 mentioned a towing tank discovery, that a hollow in the bottom around keel is beneficial in decreasing drag to a degree. Will JuanK ever publish detailed numbers? Unlikely for me. It is his bread and butter...
German designers Reinke did extensive research on keel influence on wave-making of hull. They (neither father nor son) do not publish design numbers nor many lines drawings. But they publish a periodically revised book "Yachtbau", so at least quite general info could be found here. As far as I remember, they present two photos of identical hulls of their design upwind, one with CL keel, the other with bilge keels. In photos it is obvious, that with bilge keels, there is almost no hollow in the water in midships area.

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### AlikSenior Member

There were some papers on the subject in CSYS-11 (1993) proceedings.

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### Perm StressSenior Member

I did not attend CSYS in 1993 . Where to find these papers?

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### AlikSenior Member

There is a detailed research of bulbkeels with CFD and wind tunnel.
I had those in paper copy before; now I believe one can get them from SNAME.

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### LPFlying Boatman

I think that the key here is, as mentioned before, that the canoe body functions between two mediums and physical perturbations can form because of the interaction between the two. Fluid dynamics associated with aircraft design cannot be applied here. However, the keel, operating in a single medium may display similar properties as an aircraft in it's medium. The constant cross-section theories in aircraft design are based on the incompressability of free air. Constant cross-sectional area aids in the flow of air around the aircraft.

A winged-keel, especially with an associated bulb, could also benefit from the same theories as it too functions in a single medium of incompressable fluid.

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Really interesting article from Yipster regarding the area rule:
"The shape itself was not as critical in the creation of drag, but the rate of change in that shape had the most significant effect. For the mathematically inclined, we can say that wave drag is related to the second-derivative (or curvature) of the volume distribution of the vehicle....The conclusion of this research was that shaping the vehicle to create a smooth cross-sectional area distribution from the nose to the tail could drastically reduce the drag on an aircraft. The area rule tells us that the volume of the body should be reduced in the presence of a wing, tail surface, or other projection so that there are no discontinuities in the cross-sectional area distribution of the vehicle shape."

In most racing rule it is not allowed to have hollow (or concave shape in cross section) in the hull. However by flattening the hull near the keel, it could possible to reduce the discontinuity in the area distribution.

I understand that the Deflt series did not take into account the keel in their Cp comparison and that they make conclusion of the optimum Cp only related to the canoe body.

I think it should be interesting to consider the keel, or part of the keel, as part of the hull.

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### yipsterdesigner

glad i'm not keelhauled for the racing idea, but au contraire, if JuanK talks about it..
papers perhaps here?: http://www.csysonline.com/call_for_papers_20.php

elasticity and compressability of water is way less than air yet like flows its there
f.e. on a raked keel water flows halfway the foil up to the hull bottom loading that area extra

was thinking of checking such hollow keel bottom in mlt808_180807
but never came around doing so and dont know it calculates on such eighter

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### Eric SponbergSenior Member

You may be aware that all of the design ratios were discussed in a previous thread here:

http://www.boatdesign.net/forums/boat-design/center-flotation-calculation-implications-30857.html

http://www.boatdesign.net/forums/boat-design/center-flotation-calculation-implications-30857-18.html

The discussion of prismatic coefficient is in chapter 3.

In that chapter, I give the following explanation:

Usually, in sailboat design, the keel and itâ€™s draft is left out of the calculation of volume. This is because, as in the Cb calculation, the keel tends to make Cp less sensitive. So we ignore the keel for calculation of Cp. In powerboat design, we do not do this. If we are designing a trawler or lobster boat, for example, we keep the keel in the calculation because it is a major portion of the hull.

If we left the keel and bulb in the Cp calculation, it would be harder to judge the nuances and distribution of volume of the hull itself, which is usually what we are trying to do with Cp. It muddies up the waters. Including the volume of the keel and bulb in the Cp calculation does not really tell us anything about either the keel or the hull.

I hope that helps.

Eric

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### tspeerSenior Member

I think there's another reason to ignore the bulb and fin keel, and that is because they are much deeper than the hull, so the effect on wave-making resistance is going to be less than the same volume placed in the hull. It might make sense to use the keel and bulb, but weight the cross-sectional area by depth, perhaps with an exponential function. That would include the area at the root of the keel at almost face value, but heavily discount the volume of the bulb.

Of course, when comparing different configurations, it is important to have a uniform standard of bookkeeping, and the coefficients used have definitions that obey agreed conventions. So even if it might be more accurate to include the fin keel and bulb, if the convention is to leave them out, then one should abide by the convention so as to be comparing apples to apples. As Eric has pointed out.

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