Will My Boat Float?

This is a fundamental question that requires a fundamental understanding about objects in water! What makes something float? Simply put, an object will float on water whenever the volume of water it displaces is less than its own volume. Practically speaking that means the average density of a floating object is less than that of water.

Weight speeks volumes about floating!

For example, in the Raingutter Regatta, your boat can not weigh less than one or two ounces (see your local rules). How much water is displaced by a boat that weighs two ounces?

Let's figure it out. Water weighs 0.554 ounces per cubic inch (oz/in3). Then 2 ounces (oz) of water occupies 2 oz / 0.554 oz/in3 = 3.6 cubic inches (in3) of space.

The volume of water displaced by a two ounce boat is

3.6 cubic inches.

How much pine wood weighs 2 ounces? First we have to look up or measure the density of the wood. It is about 0.28 ounces per cubic inch, about half that of water. Then two ounces of wood occupies 2oz / 0.28 oz/in3 = 7.1 cubic inches of space.

That's why it floats! The wood takes up more space than the water for the same weight, so it floats.

Knowing this, we can say that if your boat's hull has a volume greater than 7.1 cubic inches, it will be heavier than two ounces!

What's more, the rules dictate that your boat must be 6 inches or less in length and 2.5 inches or less in width (check for your own race limits). For reasons of stability, you will always want your boat to have the most length and width allowable

That means your boat could have a surface of 6 in x 2.5 in = 15 square inches (in2). If it also weighs 2 oz, your hull will have a volume of 7.1 cubic inches. How thick is the hull? Divide the hull volume by the hull surface, 7.1 in3 / 15 in2 = 0.48 inches. Just about half an inch.

Where will the water line be on your hull? Divide the volume of water displaced by the hull surface, 3.6 in3 / 15 in2 = 0.24 inches. That's about a quarter of an inch, half way up your hull.

What is the most your boat can weigh? The rules allow your boat's hull to sink 1.25 inches below the water line. This is the maximum draft your boat can have. The most water your boat can displace is 6 in x 2.5 in x 1.25 in = 18.75 cubic inches of water. How much does that much water weigh? 18.75 in3 x 0.554 oz/in3 = 10.4 ounces.

That's a hull of 18.75 in3 / 0.28 oz/in3 = 39.3 cubic inches of pine wood. Divide by a 15 square inch surface and we get a hull that is 2.6 inches tall. That's the largest that would be allowed!

Just from the very basics of water displacement and buoyancy we already know about how large your hull can be and how high it can ride on the water!

Plan your hull so it floats

Remember everything you add to your hull, the mast, the sail, bumpers, paint, sealer, it all adds weight. If you cut your hull to make it two ounces, when you are done your boat will weigh more. If possible, weigh everything that will be attached to your hull first, then cut your hull to be that much less than two ounces.

In order to cut a rectangular hull to a specific weight, you can:

1. Divide the desired weight of your hull in ounces (w) by the density of your wood in ounces per cubic inch (d) (pine is about 0.28 oz/in3, balsa is about 0.1 oz/in3) to get the volume of wood in cubic inches (v) at the desired weight. In symbols this is v = w/d.
2. If the volume is less than 3.6 cubic inches, your boat will sink! See if you can put less on your hull or use a lighter wood. If not, you will need to increase the desired weight of your boat. Repeat steps 1 and 2 until your boat will float with the weight you specified.
3. Divide the volume of wood in cubic inches (v) by the surface area of the rectangular hull in square inches (s) (usually 6 in x 2.5 in = 15 in2) to get the height of the hull in inches (h). In symbols this is h = v/s.
4. Cut your hull from your piece of wood.

Note, this procedure can be modified for other shapes. For a general shape,

1. Do steps 1 and 2 above.
2. Draw the top view of your hull on a piece of graph paper.
3. Count the squares in the contour of your deck and estimate for those on the edges of your deck.
4. Multiply the number of squares on your deck by the size of a square in square inches (0.01 in2 for ten lines per inch or 0.0625 in2 for four lines per inch) to get the surface area (s) for use in step 3.
5. If you intend to contour the depth of your hull, the height (h) will be the average height of your hull. Now draw a rectangle with the same length as your deck and height h on graph paper.
6. Using this rectangle as a reference, draw your hull and make sure there are the same number of squares inside the rectangle that are NOT part of your hull as there are squares outside the rectangle that ARE a part of your hull.
7. Proceed with step 4 above.