calculating hull displacement

any info on calculating hull displacement using sipmpsons rule would be much appreciated. I have measurements filling out a form for NMMA but having trouble getting the same totals they give. Thanks

 

Are you looking for real or legal displacement? Real displacement is the weight of the boat.

 

http://www.nmma.org/index.asp?bhcp=1

I don't see the "nmma" will deal with precise hydrostatic inf.
Like Gonzo said "do you mean weight".

Often, you need to quote the lightweight and full displacement.
Lightweight can be weighed, using one to three load cells.
Loaded displacement can be calculated, as you intended to do.

If you know the section shape, get the area with either Simpson rule, trapezoidal rule or by a planimeter (see the next posting).

Plot the sectional area along the length and calculate the area plot to get the displacement. Using a graphic method, you can easily apply the trapezoidal rule, commonly used in Europe in the past, while the British use the polynomial integration with Simpsons rule.

Simpson's rule for three ordinates at equal spacing. Multipliers are 1, 4, 1. Apply these to ordinates of a 2nd degree polynomial (i.e. parabola). Sum the product and divide by the sum of the multipliers to get the mean value. Area = Length x mean ordinate.

Simpson's rule for four ordinates at equal spacing. Multipliers are 1, 3, 3, 1. Apply these to ordinates of a 3rd degree polynomial. Sum the product and divide by the sum of the multipliers to get the mean value. Area = Length x mean ordinate.

Sometimes, you need to enter an intermediate ordinate in the bilge location. The Simpson's rule for this case, can apply a mixed multipliers in two steps: 1, 4. 1 then 0.5, 2, 0.5 to generate a common set of multiplier 1, 4, 1.5, 2, 0.5 or reverse as 0.5, 2, 1.5, 4, 1. Continue to do the same process to get the mean ordinate.

Lets look at the Trapezodial rule. It is very simple, but get a small error due to missing the segmental elements. It is only a mather of 1% to 2%. You can add more ordinates to close the error up.
This method allow any number of ordinates equally spaced. Multipliers are 0.5, 1, 1, 1, 1, .........1, 0.5. Complete the process.

If you have pc system in naval architecture series, you don't want to go back to the above manual numerical process.

For reference, see the current domestic tonnage rule. They still use the Simpson's rule.

Here is a web page on Simpson's and Trapezoidal Rule:
http://130.39.236.59/redlingdir/2307/classtopics/area/trapsimpclass.pdf


Peter

 

Calculating displacement

One of the simplest explainations and examples of the process I have found in texts, is located in Dave Gerrs book "The Nature of Boats".

You might try your local library or bookstore for a copy. I have compared the results from Dave Gerrs method, using a planimeter and Simpsons rule, and using AutoCad. The results have been so close it has not been worth worrying over.

While accuracy is important, I sometimes feel that technology has us blindly splitting hairs. Ten to fifteen years ago if you were within 1/8" on some measurements you were doing good. Now thanks to various computer programs we can become obsessed because our numbers are out 1/100 th of an inch. I have caught myself doing this many times.

Good luck.

Ray