# Prismatic Coefficient

Discussion in 'Boat Design' started by hwsiii, Aug 9, 2009.

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### hwsiiiJunior Member

I understand props very well and most analysis of hulls, but for some reason I cannot seem to get it straight in my head on how to figure the prismatic coefficient of a hull form.
For some reason I seem to have a mental block that precludes me from understanding something so simple as this.
Could someone please explain this in 9th Grade english so I can get the jist of what I am missing.

H

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### Mark VanJunior Member

Start with the area of the mid ship section. Multiply it by the LWL. Then take the volume of the actual hull. The prismatic coefficient is the ratio between those two numbers.

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### MikeJohnsSenior Member

The ratio of the volume of the displaced water to the volume of an imaginary shape made by extruding the largest cross section to the fore and aft static waterline extents.

In feet and tons its
(D X 35) / (L X A)

D is displ in tons multiply by 35 gives feet^3
L is LWL in ft
A is largest Xsectional area in ft^2

Cp is a very important measurement for the design of a hull and it should be chosen with care to match the operative speed length ratio for a displacment hull.

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### AlikSenior Member

Prismatic coefficient CP is ratio of:
- volume displacement of hull (V) to
- volume of prism based on midship section, with height equal to waterline length (LWL)

CP=V/(w*LWL)

where w-area of midship section

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### PARYacht Designer/Builder

Designers use several of these cute little things to help them understand the shape and employment of the hull type. What the prismatic coefficient does more then anything is tell the designer how fine the ends of the yacht are.

By way of a prismatic coefficient, there will be specifically targeted ranges for this coefficient on a particular yacht's S/L ratio, depending on it's expected performance envelope. It's part of the volumetric game playing, utilized working out an ideal underwater set of shapes, to incorporate into a specific set of design parameters. Did this help?

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### rwatsonSenior Member

Helped me a lot - thanks guys

Once question - why do they call it a Prism ? is that because the 'midship section' is irregular (not necessarily square), though the theoretical 'top' of the shap would be flat (waterline)

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### AlikSenior Member

Prism does not need to be square at base.
As well as cylinder does not need to have round base...

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### MikeJohnsSenior Member

For interest here's a plot of the design target relationship between CP and speed ratio for displacment craft.

For sailboats look also to the Paris curve that relates lateral plane and Cp.

#### Attached Files:

• ###### Cp.JPG
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If you're not so good with words...how about pictures?

#### Attached Files:

• ###### Cp diag.jpg
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### hwsiiiJunior Member

H

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### marshmatSenior Member

Care to explain/justify that generalization, ccdiver?

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### daiquiriEngineering and Design

Ccdiver, it depends... on what you want to achieve.
We are slowly and steadily going towards a future where oil wil be less and less available. So the energy efficiency will be a primary goal for ships and boats, not the speed. That's where displacement hulls are still unbeatable, if you consider the construction costs too.

Actually, we will probably have to move some models out of museums and put them in the water again, because some really efficient hulls have been created between the second half of the 19th and the first half of the 20th century, before the advent of planing V hulls.

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### rwatsonSenior Member

Oh sure - 85% of the worlds vital resources are moved by displacement hulls, and I prefer a boat you can put some gear in too.

And to intimate that displacement hulls are not safe ????

have you had a couple of heavy nights recently, need to get something off your liver ?

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