# Hydrostatics

Hydrostatics refer to water at rest. Displacement and initial stability are the issues addressed by
hydrostatics. A basic activity in this area is the Golf Ball Challenge.

For a boat to float, it must generate a buoyant force equal to its weight. The buoyant force is
generated by displacing water and can be determined using Archimedes' principle.

*A body fully or partially immersed in a fluid is buoyed up by a force equal to the weight of fluid displaced.*

To determine the displacement, first calculate the underwater volume of the hull. This may be done by measuring the submerged area of each section and then integrating over the length of the boat using Simpson's rule. Multiply the underwater volume of the hull by the specific weight of
water (rg or "rho-gee") which is 64 ft^{3 }/ 2240 lbs for salt water and 62.4 ft^{3 }/ 2240 lbs for fresh water. For smaller boats use 0.577 ounces per cubic inch. The product of the volume and the specific weight will be the weight of water displaced. By Archimedes' principle, this is also the buoyant force.

The designers job is to match the weight of the boat with the displacement, and still leave enough
freeboard so that water will not splash over the deck while the boat is operating.

In order for your boat to stay upright, the meta-center (M) must be above the center of gravity.

### To find the center of gravity

Divide the weight into 3 groups

For the Radio-controlled Sailboat that would be:

- Rigging and Sails
- Hull and radio controls
- Keel bulb

For each group, multiply the weight of the group by the height of the center of gravity of the group (above the keel). Add up the products and divide by the displacement (D).

KG = {wKg + wKg + wKg} / D

### To find the center of buoyancy

KB estimate or paper cutout

### To find the metacentric radius (BM)

BM = I / underwater volume

### To find the metacentric height (GM)

- KB + BM = KM
- KM - KG = GM

### The boat will be initially stable if the GM is positive.

- A good radio-controlled sailboat design will have a GM upwards of 10 inches.
- The canal barge should have a GM of at least 0.5 inches.
- The Comet Cup boat needs to have a positive GM.