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Tuesday January 3, 2017 at 11:06am

**Will it float?
(And if so, how deep?)**

Last month, I built a six-metre rowing boat in SOLIDWORKS. I was interested to know just how much I could find out about this boat using Simulation- for example, how many people could fit in here before it sank?

*Render produced in SOLIDWORKS Visualize*

To do this is actually fairly straight forward. All of the values we need are provided by SOLIDWORKS. Thanks to Archimedes, we know that the bouyancy force is equal to the weight of the fluid that is displaced.

**M g = p V g**

*(Mass of
the Boat * Gravity = Fluid Density * Volume of Fluid Displaced * Gravity)*

Gravity can be cancelled as it appears on both sides, giving us :

**M
= p V**

We know the fluid density of Sea Water (1025kg/m3) and Mass Properties within SOLIDWORKS can tell us the mass of the (empty at this point) boat, which I have assigned materials to. The keel and planks are made from Oak, while the interior fittings are made from Teak.

This means that V is the only unknown value, so the equation is rearranged to place it on it’s own:

**V = M / p**

* **(Volume of Fluid Displaced
= Mass of the Boat / Fluid Density)*

**137.144 Kg / 1025 Kg/m3
= 0.1337
m3 **

This means that the empty boat will float at the point where it is displacing 0.1337 m3 of sea water.

I am going to use an iterative Design Study to measure the volume of the boat below a variable plane which will be used to simulate the waterline.

The first thing to do is to remove the unnecessary bodies from the model. This means the Interior fittings, and any passengers. Then I used the Intersect tool to cut the model at the variable plane, keeping only the bodies which lie below the plane.

*Preview window of the
Intersect command*

I added a sensor to measure the volume of these bodies during the setup of the study. It’s quite a simple setup for this Design Study, as shown here.

In each successive scenario, the plane used in the Intersect moves by 100mm, and the volume of the model below is measured by the Sensor “Volume1”.

Once the results have been generated, I can create a graph illustrating how the boat floats-

*Graph produced from the
Design Study in SOLIDWORKS*

This graph shows that the maximum displacement of this boat is 1.16 m3, in Scenario 27, when the waterline was 0.46m above the base of the keel. The sharp decline on the right of the graph is where water flowed over the gunwhals of the boat, filling it with water. In this scenario, the boat would have most likely sank (unless in very shallow water!).

*Ideal waterline- just below
the top plank*

I added a few people into the model, to see how the boat sits in the water and try to work out the ideal number of passengers for this dinghy. I would expect the waterline to come up to somewhere on the middle plank. Lower would be unstable, higher would be at risk of flooding.

*Three 85 Kg dummies in a
boat, bringing the total weight up to 392 Kg*

By putting any weight into our equations, we can easily test which waterline it would be closest to using the graph that SOLIDWORKS produced from our Design Study. Scenario 10 is the highest waterline which doesn’t touch the top plank, so we know that our optimum maximum displacement is 0.45 m3. We can extrapolate this to give a maximum weight of 461 Kg.

If we subtract the initial weight of the boat, this gives us 324 Kg of load that we can stick in our boat, or 3-4 people.

*Some example waterlines: 0
people, 3 people, 6 people*

**Ben Pearson**

**SOLIDWORKS Applications Engineer**

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