# Displacement distribution

Discussion in 'Sailboats' started by Wardi, May 12, 2005.

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### WardiSenior Member

It is well documented that the prismatic coeffecient and distribution of displacement along the hull significantly influences its resistance.

Some of the older yacht design texts talk of an "ideal" Curve of Areas having a versed sines curve for the forebody and a trochoid for the aft sections.

Is this still valid and what "rules" are being applied today?

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### sorenfdkYacht Designer

I don't think these rules were ever valid - they just "looked right"!
In Design of Sailing Yachts , Pierre Gutelle suggests using the curves of the Gaussian distribution. I don't know why they should be better, but they also "look right"!
The designers behind the 12M Stars and Stripes did some research on this subject, but nothing really useful was ever published.
George Hazen once published a formula to calculate a curve of areas with given CP and LCB, but who knows if this formula is any better than the others?

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### MilanSenior Member

Today's rules usually relate volume distribution (most oftenly given as a prismatic coefficient) to the speed / length ratio. It means that you first decide for which speed you want to optimize your design, then calculate what's the speed / length ratio and than distribute the volume.
Speed / length Prism. coef.
0.8 0.52
1.0 0.54
1.2 0.55
1.3 0.57

Milan

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### MilanSenior Member

Sorry, editing in Word obviously don't work here. I hope this will be more readable:

Speed / length => Prism. coef.
0.8 => 0.52
1.0 => 0.54
1.2 => 0.55
1.3 => 0.57

Milan

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### Raggi_ThorNav.arch/Designer/Builder

That's ok Milan, but it doesn't tell us more about the distribution. There are many curves of area that will give a selected cp. Some designers look at the entrance angle for example. Given a fixed midship area, waterline and displacement how do you distribute the volume you need between the midship and the ends? I think this is done by "intuition" or what "looks right", not by calculation of pressure gradients etc.

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### CT 249Senior Member

Milan, can I ask where you got those figures from? What text or tests?

Most racing dinghies are quite high; Int Canoe .51 (class restrictions); National 12s range from .52 to .6; some competitive NS14s are around .62. The Laser is around .56, while the figure for modern skiff Moths is around .68.

Wardi may have many more figures etc....

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### MilanSenior Member

Yes Thor, there is still a lot of room for the guess work, but these "rules" put you in the good direction and narrow space for serious mistakes. They are further refined by differing forward and aft prism. coef.

CT 249, I think I took them from Steve Dashew, I'm not shore, I'll heave to check at home, don't have all my stuff here at the office. In any case, these numbers are for the sailing yachts, not sure how they correlate with a planing dinghy hulls. The best systematic tests for the sailing yachts which I'm aware of are Delft series of tests. However, being than in Europe, math used in tests is based on the metric system and often different formulas then those used in the Angl. Sax. parts of the world. Might be a bit okward to use for people used to Anglo- Sax. measuring units.

Milan

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### sorenfdkYacht Designer

I'd say that all papers by Gerritsma et al about the Delft Systematic Yacht Hull Series are required reading for anyone interested in sailing yacht design. If SI units pose a problem, then this is as good a time as any to learn about them - it is after all the most used system of units!

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### CT 249Senior Member

Thanks Milan.

Many people here use the Delft series for yachts AFAIK, we (Australia) and NZ and UK use metric. One good NZ designer uses the Delft series for dinghy designs IIRC.

I have checked with many people (including Americas Cup/skiff designers, VPP creators, etc) and no-one knows of a similar system of dinghy tests, unfortunately.

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### Raggi_ThorNav.arch/Designer/Builder

Many sources say that planing hulls should have cp from 0.6 to 0.7 for Speed/length ratios of 2 to 3. This is probably right for some of the dinghies.

11. ### Doug LordGuest

hull vary/ pc

Ian, you may find this interesting if you haven't already seen it:
http://www.newavesys.com/hullvary.htm
For those wanting to pursue Cp in dinghy designs there are many designs from the 60's onward shown on the Cherub site; it might be possible to print out the design and calculate the prismatic.
http://www.sailingsource.com/cherub/hismain.htm

There is also something floating around Cherub circles that I had printed out showing literally dozens of designs by a particular designer that I can't find(David somebody)- I'm still looking...
And there is this with designs by Andy Patterson who might be able to comment on Wardis question:
http://home.freeuk.net/axeman66/chdesign.htm

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### Andy PJunior Member

Dave Roe designed the bistro - very successul cherub late 80's - 90's

My dinghy designing ( axeman moths and Cherubs ) has been design for the rules, wetted surface, the desired shape for planing ( or not in moths ) , smooth curves, smooth displacement distribution...

Vertical topsides make a big difference to performance, but this doesn't come into any calcs ( cos the shape is above the waterline - but waves go up and down in an unmeasured way )

and then afterwards the prismatic is merely an interesting end result of 0.65 or whatever. ( but it seems to come out at the 'right' number )

Planing dinghies and prismatic coeff - there is so much variation of waterline , weight distribution, efects of planing that the coeff is a bit meaningless - most dinghies appear to have similar coeff, but can have vastly different performance.

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### CT 249Senior Member

"most dinghies appear to have similar coeff, but can have vastly different performance."

Yep, and the National 12 CPs indicate that you can have very different coefficients, and very similar performance! And like Andy says, by the time you figure in different weights, and perhaps allow for the huge changes created by moving crew weight. Anyone know what the CP for say a 29er is when floating to dwl, compared to its CP at actual static waterline and its CP with the crew on the bow in light airs?

Lorsail may be thinking of David Lee's page of Cherub/R/12 plans;

http://www.engineers.auckland.ac.nz/~dlee022/webphotos%2bvideo/compare12s/

David is the good NZ designer I know of who uses the Delft series results IIRC.

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### WardiSenior Member

Thanks for your contributions so far!

I had not considered dinghy designs when posing this question, because they tend to run well above theoretical "hull speed" much of the time and hence normal displacement distribution rules are not so applicable. It is best then to design with high prismatic coefficients and optimise wetted surface and planing performance for these designs.

With regard to yacht design, where we desire improved performance in displacement mode, well within the normal hull speed limitations, I am rather disappointed to hear that the Curve of Areas rules I mentioned do not seem to be applied these days and even more surprised that no other rules or methods have been developed to replace them.

Surely there is a better method than developing fair lines by eye! Does anyone know of any data available on successful boats which could be used for analysis?

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### gggGuest...

heel/prismatic

> Anyone know what the CP for say a 29er is when floating to dwl, compared > to its CP at actual static waterline and its CP with the crew on the bow in
> light airs?

I just took a Cherub design I had in hullform and ran it with a range of angles and so on, and in bow down trim with 15 degrees of heel the prismatic was .59, while upright with the transom immersed to the chine (as at speed) it was .67.

Jim C

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