Part 3
Part 1 - Part 2
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.
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