Initial Stability of a Boat

The diagram illustrates the initial stability of a boat at small angles of heel and highlights the key concepts:

1. Metacentric Height (GM)
   The vertical distance between the center of gravity (G) and the metacenter (M). The metacenter determines the restoring force when the boat heels slightly. A positive GM indicates a restoring moment, causing the boat to return upright.
2. Center of Gravity (G) and Center of Buoyancy (B)
   B represents the point around which buoyant forces act when the boat heels. As the boat tilts, the center of buoyancy shifts, creating a restoring moment (GZ line).
3. Righting Arm (GZ)
   The horizontal distance between gravity and buoyancy lines during heel. The GZ curve vs. heel angle shows that for small angles (up to 5–10°), GZ is nearly linear and proportional to GM.
4. Initial Stability
   Determined by the slope of the GZ curve at small heel angles. Larger GM → greater stability. At small heel angles, a positive restoring moment returns the boat upright.
5. Summary of Interactions
   Gravity at G acts downward, buoyancy at B acts upward. When the boat heels, the center of buoyancy shifts, creating a horizontal distance (GZ) that generates a restoring moment. Positive moment at small angles demonstrates initial stability, with GM as the key indicator.