1. What is Center of Buoyancy?

The center of buoyancy is the centroid of the displaced volume of fluid by a floating or submerged body. It represents the point through which the buoyant force acts and is crucial for determining the stability of floating objects.

2. How Does the Calculator Work?

The calculator uses the center of buoyancy formula:

Where:

• \( CB_x \) — Center of buoyancy in x-direction (m)
• \( x \) — Coordinate position (m)
• \( dA \) — Differential area element (m²)
• \( A \) — Total area (m²)

Explanation: The formula calculates the centroid of the displaced fluid volume, which determines the point where the buoyant force acts on a submerged or floating body.

3. Importance of Center of Buoyancy Calculation

Details: Accurate calculation of the center of buoyancy is essential for determining the stability of ships, submarines, and other floating structures. It helps predict how an object will behave when floating and ensures proper design for maritime safety.

4. Using the Calculator

Tips: Enter the integral of x dA in m³ and the total area in m². Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between center of buoyancy and center of gravity?
A: The center of buoyancy is the centroid of the displaced fluid volume, while the center of gravity is the point where the weight of the body acts. The relationship between these two centers determines the stability of a floating object.

Q2: How does center of buoyancy affect ship stability?
A: A higher center of buoyancy relative to the center of gravity increases stability. When a ship heels, the center of buoyancy moves, creating a righting moment that returns the ship to its upright position.

Q3: Can this calculator be used for 3D objects?
A: This calculator provides the x-coordinate of the center of buoyancy. For complete 3D analysis, similar calculations would be needed for y and z coordinates.

Q4: What units should be used for input values?
A: Use consistent SI units: meters for coordinates, square meters for area, and cubic meters for the integral of x dA.

Q5: How is the integral ∫ x dA typically calculated?
A: For complex shapes, this integral is typically calculated using numerical integration methods or CAD software that can compute geometric properties of shapes.