Is There a Formula for Determining Wetted Surface Area ?

[fstbttms]

Is there a formula for determining wetted surface area?

[Blue Stocking]

Some CAD programs can reduce a compound shape to a development form plane, and give area.
Or you could measure the linear length of every station line on a set half-breadth hull lines, average the total length by the number of stations, and multiply by the WaterLine length.
Wheres Robert Perry when you need him?

[ewsponberg]

Originally Posted by fstbttms

Is there a formula for determining wetted surface area?

Fstbttms,

No, there is no simple formula for determining wetted surface because each boat has a unique geometry, and the results vary widely from boat design to boat design. As we design boats on the computer, the computer will tell us pretty much instantaneously what the wetted surface is by using very complicated and advanced mathematics, and that's pretty accurate, but without a computer model, we have to estimate it in pieces.

For example, for most sailboats, the wetted surface is made up of the canoe body of the hull, the keel, and the rudder, at least in most modern designs. So we can estimate the parts. The Area of the canoe body (Acb let's say) can be estimated by: Acb = Lwl x B x 0.7.

The Area of the keel: Ak = 2 x (root chord length + tip chord length)/2 x span. The 2's cancel out, so the wetted area would be Ak = (root chord length + tip chord length) x span. root chord is the fore-aft length of the top of the keel where it joins the hull, the tip chord is the fore-aft length of the deep end of the keel, and the span is the vertical distance between the two, i.e. the depth of the keel.

The Area of the rudder is calculated the same way as the keel: Ar = (root chord length + tip chord length) x span.

Then, the total wetted surface area is the sum of all three, typically called WS = Acb + Ak + Ar.

On a boat with a less distinct keel, say a Bristol Channel Cutter, it will be harder to define the keel because it is more integral with the hull. So you kind of have to fudge estimating the area as best you can. Same thing applies to rudders that are not barn-door shaped, you have to make an educated guess as to the proper dimensions or area.

For a powerboat such as a trawler, the same applies--you have to make educated guesses based on length, beam and draft. Break the hull down into parts that can be easily estimated, and then add the results together to get the final result.

I hope that helps.

Eric

[fstbttms]

Thanks for the responses. I am trying to poke holes in a study of copper contribution from anti fouling paint in Marina del Rey. The study used the following formula with the assumption that the average LOA was 40':

Wetted hull surface area = (Overall length) * (Beam height) * (0.85)

I'm just trying to figure out if the formula would give a reasonable approximation of actual total wetted surface for all the boats in MDR.

[Ziggy]

Originally Posted by fstbttms

Thanks for the responses. I am trying to poke holes in a study of copper contribution from anti fouling paint in Marina del Rey. The study used the following formula with the assumption that the average LOA was 40':

Wetted hull surface area = (Overall length) * (Beam height) * (0.85)

I'm just trying to figure out if the formula would give a reasonable approximation of actual total wetted surface for all the boats in MDR.

The wetted surface area is listed on the IMS certificate. You could try to get hold of certificates for a few boats, and check the formula for reasonableness.

[fstbttms]

Originally Posted by Ziggy

The wetted surface area is listed on the IMS certificate. You could try to get hold of certificates for a few boats, and check the formula for reasonableness.

Not interested in going to that much trouble. Just want to know how accurate the number given in the study for copper contribution may, or may not, be.

[ewsponberg]

Originally Posted by fstbttms

Not interested in going to that much trouble. Just want to know how accurate the number given in the study for copper contribution may, or may not, be.

That may not be too far off. If I were to offer a modification, a coefficient of 0.85 seems a touch too high, and I would suggest maybe 0.80 as being a little more realistic. I don't think it would be any greater than what you suggest, though.

Eric

[pbmaise]

I found a good graphic that defines the terms Root Cord and Tip Cord that are mentioned by Eric.

I want to add a few cents.

Eric's equation does not yield the actual wetted surface of a keel or rudder. Instead it is a reasonable estimate. Root cord and tip cord are in the centerline of the hydrofoil. The outer surface of a hydrofoil, the surface that actually touches water, is curved. The wetted surface of the rudder is greater.

Note: Do not use "wetted" surface area when calculating the lift and drag force of a keel and rudder.

Instead they use the average cord length ((root cord + tip cord)/2) times the span. This figure is 1/2 the value of the wetted surface equation provided by Eric. This area is sometimes called the wing area. A better way to describe this area is the reference area.

The word reference...means in reference to the drag and lift coefficients. I.E. what area was the researcher talking about when determining these coefficients. When talking about a car, the reference area is typically the projected frontal area of the vehicle. The length of the car doesn't factor into it.

The terms projected area or planform area should not be confused with wing and wetted area. Think of a bright light shining on the object that comes from the same direction of the current flow. The area of a shadow on a wall immediately behind the object is the projected and planform area.