Vessel Displacement Calcs

Hello all!

I’m back, 2 weeks in a row. A record!

Okay, so this weekend, as I mentioned in my last post, I’ve calculated the displacement of my vessel and I’m pleasantly surprised.

The displacement of the vessel is the amount determined as the amount of water it will displace, or move, when sat in the water with a certain load.

If you think of putting a bowl in a full tank of water. The bowl will sit on the surface of the water, floating, after it has dropped so far down. At the point when its vertical movement has stopped, the force it is exerted on the water is equal to the force the water is exerting upon it. The water it has displaced from the tank will equal the amount of volume of the bowl that sits below the water line. Therefore, the volume of the vessel below the water line multiplied by the density of seawater equals the weight of the boat plus its load. I believe this is known as Archimedes’ principle.

So what I have done, is using a very rough version of Simpson’s/Trapezoidal rule is to make a calculation of the volume of my vessel. I am not very accurate as I do not have formulae for the curvature on the hull, I have taken the difference between the area of 2 bulkheads, divided it into steps and worked out the volume of the vessel over 10mm intervals.

So, for the entire volume of the vessel, I worked out the volume of the sections of the vessel like this (section A-B is only 275mm long, hence no last interval):

Volume	Bulkhead x to y	Step	1	2	3	---	27	28	29
5741781	A-B		0	1518.99	3037.979	---	39493.73	41012.72
16922035	B-C		44050.7	45072.21	46093.72	---	70609.97	71631.48	72652.99
24852949	C-D		73674.5	74533.45	75392.4	---	96007.24	96866.2	97725.15
28050694	D-E		94992.8	95116.64	95240.48	---	98212.59	98336.42	98460.26
23191072	E-F		65947.2	66948.77	67950.34	---	91988.08	92989.66	93991.23
13637687	F-G		29367.19	30628.57	31889.95	---	62163.06	63424.44	64685.82

For the entire volume of the vessel:

Total Volume	1.12E+08	mm^3
Total Volume	0.112396	m^3
Density Seawater	1020	kg/m^3
Density Fresh water	1000	kg/m^4
Displacement in Saltwater	114.6441	kg
Displacement in Fresh Water	112.3962	kg

So, if we ignore the weight of the vessel, that volume displacement should take my entire weight and I won’t sink it? Hardcore!

So, I’ll look at a more sensible displacement value now. I’ll calculate the displacement of the vessel with the waterline 120mm from the deck:

Total Volume	44243653	mm^3
Total Volume	0.044244	m^3
Density Seawater	1020	kg/m^3
Density Fresh water	1000	kg/m^4
Displacement in Saltwater	45.12853	kg
Displacement in Fresh Water	44.24365	kg

This is pretty good. If I can keep the entire weight of the vessel with all ancillaries onboard below 45kg, it’ll have 120mm between the deck and the waterline. Although this would be brilliant if it comes out like this, I expect it to sit lower in the water than that.

I’ll calculate the weights of the vessel components and keep a running total as accurately as I can during the build.

This has been a good weekend of work! It proves that the design will work, I have a maximum weight figure to work with and the vessel shouldn’t sink due to overloading. Shouldn’t, not won’t. :)

Next Steps

•  Finalise the carbon fibre mast size to use and bring into model.
• Keel bulb size and shape.
• Keel thickness review.

Until next weekend! Enjoy your week!