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If you can use a calculator
you can design a boat…

by Morten Olesen
www.boatplans.dk

Part 3

Hydrostatic

There are many hydrostatic properties that can be calculated for a hull. Within the limits of this article series only the displacement and the longitudinal centre of buoyancy (LCB) is calculated.

From the line drawing it is possible to calculate every station's underwater area. In the example a chine hull is used, so calculating the areas should not be a problem. If you are designing a traditional hull it can be more difficult calculating the area under a curve. One possibility could be to draw the stations on graph paper and then count the squares under the curve. This will give a reasonably accurate result. Remember that your line drawing is only made with a half station, so the area has to be multiplied by two in order to get the entire area of a station.

 Station Area [m2] 0 0 1 0,1584 2 0,3474 3 0,4936 4 0,5952 5 0,6578 6 0,6880 7 0,6920 8 0,6750 9 0,6418 10 0,5972

When you are through calculating the areas you should have a table like the one above. Next step is to use Simpson’s rule for approximating definite integrals. It sounds complicated but it is quite easy to use. Every station area is first multiplied with Simpson’s factor (SF). Then the sum of all the products are divided by 3 and multiplied with the longitudinal distance between the stations.

 Station Area [m2] SF Res. 0 0 1 0 1 0,1584 4 0,6336 2 0,3474 2 0,6948 3 0,4936 4 1,9744 4 0,5952 2 1,1904 5 0,6578 4 2,6312 6 0,6880 2 1,3760 7 0,6920 4 2,7680 8 0,6750 2 1,3500 9 0,6418 4 2,5672 10 0,5972 1 0,5972 15,7828

In the example the longitudinal station distance is: s = 0,648 m.

The displacement for the example hull becomes: 0,648 x 15,7828 / 3 = 3,409 m3

If the boat has to float in freshwater the weight at the construction waterline will be 3409 kg. But since saltwater has a density of approximately 1025 kg/m3 the boat will have a weight of 3,409 x 1,025 = 3495 kg when floating at the construction waterline in saltwater. Thus saltwater has a greater buoyancy than freshwater due to the higher density.

To determine the longitudinal centre of buoyancy (LCB) it is necessary to make some further calculations with the station areas. The next technique introduced is the moment calculation. This technique can be used in various situations. First it is necessary to define a fixed station and in this example the fixed station will be station 10. Then every station contributes to the moment calculation by their area multiplied with the longitudinal distance from station 10.

 Station Area [m2] Arm [m] Moment 0 0 6,480 0 1 0,1584 5,832 0,924 2 0,3474 5,184 1,801 3 0,4936 4,536 2,239 4 0,5952 3,888 2,314 5 0,6578 3,240 2,131 6 0,6880 2,592 1,783 7 0,6920 1,944 1,345 8 0,6750 1,296 0,875 9 0,6418 0,648 0,416 10 0,5972 0 0 5,5464 13,828

The longitudinal distance becomes: 13,828 / 5,5464 = 2,493 m

This means that LCB is laying 2,493 m forward of station 10 i.e. between station 5 and 6. The moment calculation is made from station 10 but the moment calculation can be made from any station desired. Just remember from witch station the calculation is made when evaluating the result.

Weight calculation

The weight calculation is carried out in order to calculate the longitudinal centre of gravity (LCG) for the boat. In principles all elements, even every screw or nail, should be counted in the calculation. But of course it would be a large job to do that, so in practice all major parts should be counted in and then a certain amount added for the small things left out or forgotten.

It is normal to divide the weight into different main areas. You must determine which areas are suitable for your hull, but a minimum must be; hull structure, superstructure, interior, installations, ballast, rig and sail (if a sailboat) and payload.

In order to make the rest of the weight calculation you must make some serious considerations regarding the construction, appearance and layout of your boat. You have to decide how you would construct the hull, what the cockpit and roof should look like, how the interior should be and what engine installation you will have. When these things are decided and drawn you can make a trustworthy weight calculation.

For every area considered, not only must the weight be known, but also the centre of gravity must be known. With many things the centre of gravity is not known precisely so an estimated centre must be used. The centre of gravity for every component is used in a moment calculation similar to the one made in the hydrostatic part. Later on, when the calculation is finished the resulting centre of gravity for the boat is found. Below you can se an example of the weight calculation for the hull structure.

Hull Structure

 Item Weight [kg] LCG [m] Moment Scantlings plywood 431 2,910 1254,21 Scantlings epoxy and glass 312 2,910 907,92 Transom plywood 38 0 0 Transom epoxy and glass 23 0 0 Frames 172 2,490 428,28 976 2590,41

LCGhull = 2590,41 / 976 = 2,654 m forward of station 10

Now it is only a question of finishing the rest of the main areas in the weight calculation. When that is done you can make a new weight and moment calculation that gives the total weight and LCG.

 Item Weight [kg] LCG [m] Moment Hull structure 976 2,654 2590,30 Superstructure 586 2,937 1721,08 Interior 637 3,236 2061,33 Installations 779 1,345 1047,76 Payload 590 2,493 1470,87 3568 8891,34

LCG = 8891,34 / 3568 = 2,492 m forward of station 10

As you can see, the weight is a bit less than the displacement calculated. The difference is thus so small that in practice it is nothing compared to the uncertainty in the calculations. Furthermore it can be seen that the LCG is laying a bit aft of the LCB. This means that the boat will have a small trim, but again it will have no influence in practice.

It is not certain that your first set of hydrostatic and weight calculations will come out like the example above and therefore it may be necessary to go back through the design spiral, each time correcting and refining the drawings and calculations.

Be sure to visit Mr. Olsen's website: www.boatplans.dk

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