Quote:
Originally Posted by gbmacca
'..., my boat is sitting 1 - 2 inches lower in the water!
...is it the fresh water...?
Gbmacca
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Here is the math: The answer has nothing to do with the prismatic or block coefficient, but just to get an idea of the possible effect of a change in density of the water, I looked at my boat,
Hunter 405, displacement 20,000 lb, with water line length of about 35 feet, max beam of about 12 feet, and average beam of about 8 ft, per eyeball. Just to keep it simple, replace the hull shape with a block with the same WL and average beam. Since we are looking only at small changes in draft at the waterline, the details of hull shape are irrelevant. Then, the draft (depth below the surface of the water), for the block shape, h, is as follows:
h = wt of boat/(density of water X waterline area)
If we have density 1 and density 2, say, 62.4 lb/ft^3 (nominal fresh water) and 64.2 lb/ft^3 (nominal salt water), then the
depth difference due to the change in density is
h2 - h1 = wt of boat/(WLA X density 2) - wt of boat/(WLA X density 1)
A little bit of algebra gets us to:
h2 - h1 = (wt of boat/(WLA X density 1)) X (1 - (density 2)/(density 1))
We can see that a small change in draft due to a change in water density depends only on the ratio of waterline area to the displacement, and has nothing to do with the details of hull shape below the nominal waterline. Using 64.2lb/ft^3 for
salt water and 62.4 lb/ft^3 for fresh water, we get:
h2 - h1 = 20,000 lb/((35 ft X 8 ft) X 62.4 lb/ft^3) X (62.4/64.2 - 1)
h2 - h1 = -0.032 ft = -0.4 in, where the minus sign indicates that the draft got shallower for the transition from fresh to salt.
So, the change from salt to fresh can pretty much be ruled out as the explanation for a change in waterline height of more than about half an inch, at least for boats of modest size and draft. As ship length increases, displacement goes up as the cube of length, whereas the waterline area increases as the square of length. So, change in draft from fresh to salt will be proportional to the length of the ship, all else being equal. Or, more intuitively, the change in draft going from fresh to salt is proportional to the draft.