Q6 (16 Marks) Ship Resistance & Propulsion
SC&S • Written Exam

(a) Explain the term angle of loll and state what, if any dangers it poses to a vessel. (6)

(b) A propeller has a pitch ratio of 0.95. When turning at 120 rev/min the real slip is 30%, the wake fraction 0.28 and the ship speed 16 knots. The thrust is found to be 400 KN, the torque 270 KNm and the QPC 0.67.

Calculate: (10)

(i) Propeller diameter

(ii) Shaft Power

(iii) Propeller efficiency

(iv) Thrust Deduction Factor

Appeared In: Jul 2026

Verified Model Answer (Text Solution)

Structured for DG Shipping MEO Class II examination scoring criteria.

Exam Ready
Part (a)

Angle of Loll

The angle of loll is the angle of heel at which a ship with negative initial metacentric height (negative GM) comes to rest in still water, without any external heeling force such as wind, waves, or turning.

When a vessel has negative GM, it is unstable in the upright position because the centre of gravity (G) lies above the metacentre (M). As a result, any small disturbance causes the vessel to heel further instead of returning upright.

As the vessel heels, the centre of buoyancy (B) moves outboard towards the lower side. At a certain angle of heel, the line of action of buoyancy passes vertically through the centre of gravity (G), producing a small positive righting lever. The vessel then comes to rest at this angle, known as the angle of loll.

The ship may remain at this angle on either side and can suddenly loll or flop from one side to the other when disturbed by wind, waves, turning, or other external forces.

Dangers Posed by an Angle of Loll

  1. False sense of stability: Although the vessel appears to be stable because it remains at a constant angle of heel, it is actually in a dangerous condition with negative GM.
  2. Sudden lolling or flopping: The vessel may suddenly and violently swing from the angle of loll on one side to the same angle on the opposite side with little or no warning, especially when affected by beam seas, wind gusts, or turning.
  3. Reduced range of stability: The remaining range of positive righting lever is much smaller than normal. Consequently, even a relatively small additional heeling moment can cause the vessel to capsize.
  4. Risk due to free surface effect: Slack tanks further reduce the effective GM. Incorrect attempts to correct the condition, such as pumping ballast to one side or leaving tanks partially filled, increase the free surface effect and may worsen the angle of loll or even lead to capsize.
  5. Danger of capsize: If the vessel heels beyond the point where the righting arm again becomes zero (the point of vanishing stability), it will capsize.
  6. Oscillation about the angle of loll: Instead of rolling about the upright position, the vessel oscillates about the angle of loll, indicating that it is in an unstable equilibrium.

Corrective Actions

  • Do not attempt to correct the angle of loll by shifting ballast or cargo transversely, as this may cause the vessel to suddenly flop to the opposite side and worsen the condition.
  • The correct method is to lower the centre of gravity (G) and restore positive GM by:
    • Eliminating free surface effects by pressing tanks either completely full or completely empty (avoid slack tanks).
    • Pressing up double-bottom tanks to add weight low down and lower the centre of gravity.
  • Once positive GM is restored, the vessel will return to the upright position and regain true stability.
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