Question

(a) Explain the use of KN curves. (8)

(b) A ship of 12000 tonne displacement has a rudder 15m2 in area, whose centre is 5m below the waterline. The metacentric height of the ship is 0.3m and the centre of buovancy is 3.3m below the waterline. When travelling at 20 knots the rudder is turned through 30°. Find the initial angle of heel if the force Fn perpendicular to the plane of the rudder is given by: Fn = 577 Av2 sin∝ N

Allow 20% for the race effect. (8)

Answer 1

Part (a)

KN curves are stability curves used in naval architecture. They are created by plotting the righting lever (KN) against the angle of heel (θ) for a given displacement and an assumed KG (height of the centre of gravity above the keel) of 0. The righting lever is the distance between the centre of buoyancy and the centre of gravity, measured along a vertical line through the centre of gravity.

The KN curve is then used to calculate the righting lever (GZ) for any other KG value using the following formula:

GZ = KN - KG * sin θ

Where:

GZ is the righting lever measured from the centre of gravity.
KN is the righting lever measured from the keel (obtained from the KN curve).
KG is the distance of the centre of gravity from the keel.
θ is the angle of heel.

✓ Verified Model Answer (Text Solution)

Where: