# Wetted Surface Coefficient

Discussion in 'Boat Design' started by kvsgkvng, Nov 28, 2012.

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### kvsgkvngSenior Member

For your consideration I would like to introduce a dimensionless coefficient which would quantify wetted surface assessment and overall “roundness” of any floating body.

This measurement would numerically describe the “compactness” of any submerged body with arbitrary geometry. The proposed coefficient would allow numerical comparison of various bodies with different geometric parameters after being submerged in any liquid. I believe it may characterize any given hull in retrospect to and in addition to other coefficients used in naval architecture.

As it is known various vessel hulls have different wetted surface areas which in turn depend on vessel’s length, width and draft. These parameters are difficult to compare considering the assortment of hull shapes. In order to compare various hulls to each other I propose a coefficient which gives numerical interpretation for any given wetted surface compared to the most compact surface for any given volume – the sphere.

Geometric definition of a sphere’s volume is that has it has the absolute minimum surface area for any given volume; therefore it suits well to compare different hulls in regards to the “compactness” of a submerged volume and to describe a hull with the least wetted surface.

In order to make this comparison more understandable and pictorially resembling all other naval architecture coefficients, a half-sphere is proposed instead of the whole sphere. Yet it yields same comparative results as the whole sphere.

Formulae:
Half-Sphere Volume:V= 4/6*Pi*R^3
V=(HullDisplacement)/(SeawaterDensity)
Half-Sphere Surface:A=2*Pi*R^2

Below is an extract from the attached spreadsheet where different hulls are being compared according to the above principal description of the Wetted Surface Coefficient. As easily seen, the “Tasar” dinghy appears to have most “flattened" hull compared to others in the same category. In contrary, the Folkboat WSC is comparatively higher than those of dinghies. The Cape Henry is most “rounded” hull in the comparison series, considering that centerboard is raised.

I believe this numerical coefficient may serve well as an additional descriptor of any hull.

Procedure to calculate Wetted Surface Coefficient:

(1) Obtain volume by dividing the displacement by sea-water density
(2) Compute the radius of equivalent half-sphere volume (1)
(3) Compute submerged surface of equivalent half-sphere volume using (2) as the sphere radius
(4) Divide computed submerged surface (3) by wetted surface

The attached spreadsheet has these formulas coded.

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• ###### Wetted_Surface_Coefficient_Extract.gif
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Last edited: Nov 28, 2012
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### DCockeySenior Member

The wetted surface coefficent, Cs, is commonly defined as
Cs = S / (Del * LWL)^1/2
S is the wetted surface area
Del is the displacement volume
LWL is the waterline length​
Principles of Naval Architecture, Vol 2, 1988 p73 and other references.

For a vessel with the submerged portion a hemisphere (provided I did the math correctly) Cs = (3/2*Pi)^1/2 = 2.17

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### DCockeySenior Member

kvsgkvng's coefficient which I'll refer to here as Ckvsgkvng can be reduced to:

Ckvsgkvng = (18*Pi)^1/3 * Del^2/3 / S

Ckvsgkvng = 3.838 * Del^2/3 / S

and in terms of more commonly used ratios:

Ckvsgkvng = (18*Pi)^1/3 / (Cs * (L/Del^1/3)^1/2)

Ckvsgkvng = 3.838 / (Cs * (L/Del^1/3)^1/2)

Cs = S / (Del * LWL)^1/2
S is the wetted surface area
Del is the displacement volume
LWL is the waterline length​

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### kvsgkvngSenior Member

Thank you for pointing me in the right direction. I didn’t realize that that name was already taken. I don’t even know what to call this new parameter and if it has any significant use. Perhaps it does, as the “compactness” or “roundness” of the hull directly connects with the wetted surface.

The only thing is that I was not able to arrive at the 3.838 coefficient. I have the math here; please correct me if I was wrong because my coefficient is 0.23962 or approximately 0.24

I think that this coefficient may be just dropped because it is just a ratio; and the formula would be "cleaner":

Cc= (D)^0.667 / S

#### Attached Files:

• ###### Cc_s.jpg
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### DCockeySenior Member

The reason for the difference in coefficients is your forumla uses D as the displacment in lbs and the resulting coefficient
Cc= (D)^0.667 / S​
has dimensions of lbs^2/3 / ft^2.

I used the Del, the volumetric displacement, ie the volume of the water displaced, which has units of length cubed, and as long as the same units of length are used for Del and S then

Del^2/3 / S​

is dimensionless.

Divide 3.8 by (64 lbs / cubic foot)^2/3 and .24 is obtained.

I have a strong preference for non-dimensional ratios which work in any system of units as long as the units are consistent.

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### kvsgkvngSenior Member

Thnaks for explanations. You are absolutely right about volumetric parameter. Again, not knowing the exact semantic nomenclature I used a simple mathematical handle "D" instead of "Del"

My estimates refer to volumetric properties as well. Thanks again and best holidays wishes!

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