What is Angle of Contraflexure?

In this Article,we will learn What is the Angle of Contraflexure ?

What is angle of Contraflexure ?

This is the angle at which the curve goes / moves from concave to convex.

Angle of Contraflexure


It is the angle of heel up to which the rate of righting lever ( GZ ) With the heel is changes I.e Before this point rate of righting lever with heel is increasing but after this point rate of righting lever will decrease.

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What is it’s significance ?

The physical Significance of this point is that ,it is the point or angle at which Deck just touches the surface of sea.

The below figure is the Curve of Statical stability for a ship in Particular condition of loading.

Angle of Contraflexure

How this Curve Obtained ?

This curve is obtained by plotting the Righting Lever against the angle of the heel.

Angle of Contraflexure

The above curve is for Positive Metacentric Height

Angle of Contraflexure

The above curve is for negative Metacentric Height.

From the above figure we can get following information:-

  1. Range of Stability :-The range in which the ship has positive Righting lever (GZ ) i.e 0 – 86 in figure 3. & 18- 9 in figure 4.
  2. Angle of vanishing stability:-It is the angle of heel when the righting lever (GZ ) returns to zero,or the angle at which the sign of righting lever changes from positive to Negative I.e 86 degree in the figure 3.
  3. Maximum GZ :-It is obtained by plotting a tangent to the highest point of the Curve. i.e 0.63 meters which occurs at 42 degree.
  4. Initial GM :-It is found by Drawing a tangent to the curve through the origin and then erecting a perpendicular through the angle of her log 57.3 degree.The two lines are allowed to intersect and the value of GZ is noted which is initial GM.
  5. Point of Inflection/Contraflexture :-It is the angle at which the curve goes / moves from concave to convex.
angle of contraflexure

The above figure is for Negative Metacentric Height.

In the above figure,we can see that ,at an angle less than 18° the the righting arm / lever are negative and beyond 18° to 90° the righting lever is positive.

Hence, 18 degree is the angle of look or point of loll.

Note :- Initial GM of ship is plotted at 57.3°.

Now the Question come in mind that why we take Initial GM of ship at 57.3° ?

The answer of this Question is that 57.3 °= 180÷ 3.14 57.3°.


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Ship stability wikipedia

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