What Is the Ship Hydrostatic Metacentric Height (GM) Stability Calculator?
Metacentric height (GM) is the vertical distance between a ship's center of gravity (G) and its transverse metacenter (M).
It dictates the initial stiffness and natural roll period of the vessel.
How Does the Ship Hydrostatic Metacentric Height (GM) Stability Calculator Work?
Estimates vertical center of buoyancy KB from draft and form coefficients using Morrish formula.
Calculates metacentric radius BM from second moment of waterplane area divided by submerged displacement volume.
Computes height of metacenter KM = KB + BM and subtracts center of gravity KG to get GM.
Ship Hydrostatic Metacentric Height (GM) Stability Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Hydrostatic balance of centers of buoyancy and gravity determining transverse metacentric stability.
How to Use the Ship Hydrostatic Metacentric Height (GM) Stability Calculator
- Enter molded beam and draft in meters.
- Enter ship vertical center of gravity KG from loading computer or inclining experiment.
- Optionally adjust hull waterplane and block coefficients.
Step-by-Step Example Calculation
Panamax Container Ship Stability
Input Values:
Understanding Your Result
GM > 0 indicates stable equilibrium; IMO rules typically require GM >= 0.15 m for cargo ships.
Very high GM (>3 m) produces a "stiff" vessel with violent, jerky roll motions uncomfortable for crew.
Low GM (<0.5 m) results in a "tender" sluggish vessel vulnerable to dynamic capsize.
Factors That Affect the Result
- Deck cargo loading: High container stacks raise KG, reducing GM and compromising stability.
- Free surface effect: Slack liquid tanks create virtual rise in G, directly lowering effective GM.
When Should You Use This Calculator?
- Naval architecture hull design and cargo loading plan verification.
- Analyzing results of mandatory shipyard inclining tests.
Assumptions & Limitations
- Valid for small heel angles (theta < 10-15 degrees) where metacentric point M remains stationary.
- Uses standard empirical form coefficients for commercial displacement hulls.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard naval architecture hydrostatic formulation aligned with IMO A.749 code.