Importance of a prismatic coefficient for a hull design

Hi everyone,

I've been reading a lot about hull design and the number I have to keep control. According to "Principles of Yacht Design br L. Larsson and R. Eliasson", one of then is the prismatic coefficient. It's stated in the book that for every designed speed you have a optimal coefficient.
But when you see the recent design, the sailboat become wider and the max beam shifted aft and still more or less constant towards the transom.
I was playing with some designs I found in the manufactures websites and it turns that the prismatic coefficient is larger than what is stated for the length and speed. As far as I drew it right.
This is easy to see if get a body plan view. The hull is becoming boxy.
My questions here are:

How much this high prismatic coefficient influences the design?
What I have found is a trend or I missed something?

I'd like to have your thoughts on that.

BR
Paulo

 

Neither beam nor a dart-shaped hull directly lead to higher prismatic coefficients. But an immersed transom certainly will. Very high speed sailboats will run pretty high CPs, like 0.57.

With sailboats, there is a lot more going on than with motorboats. The normal condition is heeled. For best pointing, you might design for 20 degrees of heel and a speed of 8 knots, with no chance of planing when sailing close hauled. But when broad reaching, you might hit 15 knots at 12 degrees of heel. The fun part is to design a hull that has the correct displacement curves and generates the correct RMs to make both those happen.

Prismatic Coefficient is really just a checksum. If you design a hull and don't like the CP, fiddling with the hull to "improve" the CP probably won't help. You have to get the entire displacement curve correct. The CP is just a way to categorize good displacement curves. It doesn't tell you what one looks like. You can have really rotten displacement curves that evaluate to reasonable-looking CPs.

There's also the problem of what to include in the displacement calculations. For full keel boats, normally everything is included. For strut fins with ballast bulbs, normally you just include the canoe body. For fin keel boats, you sorta have to get a feel for what the curves look like with the fin attached. The fin often has ten percent or more of the displaced volume, and it has a significant interaction with the hull on wave formation. It seems pretty common to apply some sort of draft-based attenuation factor to the fin volume, but then you have to have your own set of target displacement curves for the type of boat and the way you handle fin volumes.

One last consideration with sailboats - the hull shape that develops the best righting moment for a given length, displacement, and wetted surface area probably doesn't have an ideal CP. At least not if you just roll about the centerline of the hull. So you have to make some compromises on displacement, wetted area, RM generation, and heeled trim in order to work towards better CPs.

 

Nicely put.

 

In Olympic sprint kayaks, the Cp played a BIG part of speed improvements. Prior to 1986 most single sprint kayak hulls had a Cp of 0.58. After Ted Vandusen introduced a fleet of modern designs funded by the US Olympic Committee, the Cp for the single jumped to 0.61. Newer designs globally are in the 0.62-0.63 area.

 

Some very high performance dinghies are also well into the 0.63 region.

It seems to me human powered racing craft like Kayaks must be a bit of a special case. I assume they can be optimised for a very narrow speed range, because efficiency when not being paddled flat out is surely of minimal interest.

 

I repeat one sentence of yours, also quoted in bold font type in context:
"The fin often has ten percent or more of the displaced volume"

In most common ballasted monohull sailboats, keel weight is about 30% of total weight or a little more.
For each cubic meter of displacement, keel displacement for a steel is about 0.040 cubic meter resulting mass of 314 kg. In seawater that displacement of one cubic meter means mass of 1020kg, and therefore ballast ratio of 314kg / 1020 kg = 0.308
Displacement volume of (fin + bulb) / total displacement volume of boat is therefore 0.040 cubicmeter / 1 cubic meter = 4%.
For lead bulb that ratio is less with the same ballast ratio of 0.308. And with a bulb, only part of fin + bulb displacement is in the fin.
To have 10% of more displacement volume in fin without a bulb requires either hollow fin, or aluminium solid fin, neither are common. With a bulb, the fin must be even smaller in volume, 2...3 % of total displacement volume. Or even less if made of solid carbon laminate, as those are usually made in order to minimize hydrodynamic drag, and that means minimum wetted area and cross section, resulting also minimum displacement volume for the fin.

Can you name any common production sailboat with 10% volume in a fin keel?
With a solid steel construction, that would mean ballast ratio of 785 kg/1020 kg = 0.7696, or even more if there is also a bulb.
Should such extreme case exist, could you please specify materials used for such a fin?

Easy to find a boat with 10% displacement volume in the keel for a hollow full keel design though, but that was not the claim.

 

Hi @philSweet,

I've been quite busy from the date I asked my question about the Cp. I didn't even thank you properly. Sorry about that.
So, thanks a lot for the answer. Now I understand a little bit better how the design works. I need to study more about the displacement curves and its impact in performance/design though.

My plan is to resume my project now in a very slow pace. Anyhow, I appreciate all the input you gave.

BR
Paulo Neuenschwander

 

I've noticed that mentioned in various books. Is that done merely because it isn't worth the extra effort of estimating displacement for appendages, using traditional techniques? I.e., if you're using a 3D CAD method that allows fins and other appendages to be easily included in the displacement calculation, is there any reason you wouldn't do it?

 

I suspect that, the further away from the free surface of the water you get, the less relevant prismatic coefficient is. I imagine, for instance, that a keel bulb 4 feet long, 1 foot in diameter, and 6 feet below the surface makes very few waves.

As far as the displacement of fins, how many are made of solid steel all the way from the bulb to the hull? I don't think that would be very efficient.

 

A version of Goodhart's Law: when a measure becomes a target, it ceases to be a good measure.

 

I decided to do some extremely approximate reality testing on that 10 percent figure. Turns out it's quite reasonable, at least in some cases. I looked at the Mini-Transat 6.5 listed at Duckworks.
Transat 6.5 Plans https://duckworks.com/transat-6-5-plans/
It's supposed to displace 2800 lbs or so. Scaling approximately off the sketch provided, I get that the fin is about 5.4 feet deep and 2.3 feet wide, on average. (A tapered fin with that average chord would have more volume, but I'm going to assume a prismatic shape, because I want to make this easy. I'm also going to ignore the bulb for the same reason. If we use a NACA 0015, then the cross sectional area is about a tenth of the square of the chord. Working that out, I get a volume of something like 2.86 cubic feet, or 182 lbs of displacement in salt water. That's about 6.5 percent of total displacement. However, that's an awfully deep fin. We might want a fin half as long. In that case, it would have twice the displacement and would be 13 percent of total displacement.

No one, except maybe fastsailing, says that fin has to be solid steel. I suggest making the lower part steel and flooding the upper part, or at least making it from something less dense. I suppose we could leave it dry and just add some more steel at the bottom.

Many boats have fins of lower aspect ratios. For instance, Trekka.