Question

(a) Explain the use of KN curves. (6)

(b) The 1/2 breadths of the load waterplane of a ship 150 m long commencing from aft, are 0.3, 3.8, 6.0, 7.7, 8.3, 9.0, 8.4, 7.8, 6.9, 4.7 and O m respectively. Calculate:

(i) Area of waterplane

(ii) Distance of centroid from amidships

(iii) Second moment of area about a transverse axis through centroid.

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: