MARITIME – HULL & NAVAL ARCHITECTURE CALCULATOR
Loll Angle
A precise tool.
What is the Loll Angle & How does it work?
The loll angle is the static heel a vessel adopts when its initial metacentric height (GM) becomes negative, indicating a loss of transverse stability. In this condition the ship will rotate until the righting moment balances the overturning moment, settling at an equilibrium angle known as the loll angle. Mathematically the equilibrium is reached when the net restoring moment about the centre of buoyancy is zero. By resolving the forces in the heeled position, the relationship between the geometry of the vessel (KG and KB) and the negative GM can be expressed in a simple trigonometric form. The resulting formula allows naval architects to estimate the angle of loll from basic hydrostatic parameters, providing a quick check on the severity of instability and informing remedial actions such as ballast redistribution or cargo re‑stowage.
\phi = \arctan\left(\frac{-GM}{KG – KB}\right)
GM = metacentric height (negative for unstable), KG = height of centre of gravity above keel, KB = height of centre of buoyancy above keel
Parameters
Result
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Frequently Asked Questions
What is the loll angle in maritime navigation?
The loll angle is the static heel a ship adopts when its GM (initial metacentric height) is negative, indicating a loss of transverse stability.
How do you determine if a vessel will experience lolling?
A vessel will experience lolling when its initial metacentric height (GM) becomes negative, causing it to rotate until the righting moment balances the overturning moment.
What happens to a ship’s stability when it reaches the loll angle?
When a ship reaches the loll angle, it settles at an equilibrium angle where the net restoring moment about the center of buoyancy is zero.
Can you explain the mathematical concept behind the loll angle?
The loll angle is determined by resolving forces in the heeled position until the net restoring moment about the center of buoyancy equals zero, indicating equilibrium.
Why is it important to calculate the loll angle for a ship?
Calculating the loll angle is crucial for ensuring a vessel’s transverse stability and preventing dangerous situations at sea.
How does the loll angle affect maritime operations?
A high loll angle can reduce a ship’s maneuverability and increase the risk of capsizing, impacting maritime safety and operational efficiency.
What steps should be taken if a ship shows signs of lolling?
If a ship shows signs of lolling, immediate corrective actions such as adjusting ballast or cargo distribution may be necessary to restore stability.
Results are for informational purposes only and do not constitute professional advice.