# Bouyancy Force

# Bouyancy Force & Geometric Center

The buoyancy force is the force pushing up on the UUV. This is the same force that applies to any material in a fluid. This buoyancy force will be crucial to our analysis. Since the buoyancy force and gravitational force are the main forces acting in the vertical direction they will be analyzed together, and later analyzed with all of the forces. To understand how the gravitational and buoyancy force interacts with each other a simple diagram can be taken into an illustration with the gravitational force and buoyancy force acting on a ball, thus the center of gravity and geometric volume is at the same point. To calculate the buoyancy, force a simple equation will be used as seen below. The buoyancy force is dependent on the volume of the RV, density of seawater, and gravitational force. As stated previously the gravitational force will be assumed to 9.81 meters per second squared for all cases.

The buoyancy percentage is a central number to determine if the UV will be positively, neutrally, or negatively point. It is a ratio turned into a percentage. The buoyancy percentage follows three rules as listed below

• If BP<100% then ROV will Positively Buoyant and Float

• If BP=100% then ROV will Neutrally Buoyant and neither Float nor Sink

• If BP>100% then ROV will Negatively Buoyant and Sink

We want our vessel to be within 4% positively buoyant. This is because if anything goes wrong then it will float to the surface without any additional proportion, it will not pick up stuff on the sea floor as we dive down, whereas if it were negatively buoyant it would sink to the bottom. To reach the buoyancy percentage, we would like we need to add mass, which is the mass added variable. The beauty of our design is our railing further adding mass and adjusting the center of gravity. We can adjust the center of gravity within a couple of inches and get it to spot on with the center of buoyancy to make sure that there are no torques acting on any axis. The bottom railing is also allowed to have as much weight as needed, well above what we need to make it negatively buoyant.

# Mass Added

Different configurations of mass are available to add to the bottom of this design. To calculate the buoyancy percentage, we need to use the formula below.

Now to calculate the math we need to add to the bottom railing we need to rearrange these equations to find the mass added value. The algebra for this operation is shown below.

Lastly, it is important to note that the buoyancy percentage is not within our optimal design. We can add or take away weight whenever we would like to get it exactly where we need it, and we do not account for the electronics. We will be able to use our railing system to fine-tune the center of gravity just above the center of buoyancy and fine-tune the buoyancy percentage to within our liking.