A KN curve is a specific type of stability curve used in naval architecture to represent a vessel's righting lever, with the unique characteristic that it is constructed assuming the vessel's vertical center of gravity (KG) is located at the keel (KG=0).
Understanding the KN Curve
In simple terms, a KN curve plots the value of the righting lever (KN) against various angles of heel for a ship, but specifically under the hypothetical condition that the ship's weight is concentrated at the very bottom, at the keel.
According to the provided reference, when stability curves are constructed with an assumed KG of zero, they are known as KN curves. KN represents the righting lever measured from the keel.
Why KG is Assumed to be Zero
Assuming KG=0 simplifies the initial stability calculations. While a ship's actual KG is never zero, using KN curves allows naval architects to determine the righting lever (GZ) for any actual KG value through a simple calculation. The righting lever GZ, which is crucial for stability analysis, can be derived from the KN value using the formula:
- GZ = KN - KG * sin(angle of heel)
Where:
- GZ is the actual righting lever (measured from the vessel's true center of gravity, G).
- KN is the righting lever measured from the keel (K), as obtained from the KN curve for a given heel angle.
- KG is the actual vertical distance of the vessel's center of gravity (G) above the keel (K).
- sin(angle of heel) is the sine of the angle at which the vessel is heeled.
Practical Applications
KN curves are essential tools for naval architects and marine engineers for several reasons:
- Simplified Stability Assessment: They provide a standardized basis for assessing stability without needing to calculate GZ for every potential loading condition (which would involve different KG values).
- Ease of GZ Calculation: As shown in the formula above, once KN curves are available, determining the actual righting lever GZ for any loading condition is straightforward.
- Comparison: They allow easy comparison of the inherent stability characteristics of different vessel designs, independent of the actual weight distribution of cargo or ballast.
- Verification: They are used to verify that a vessel meets required stability criteria under various operational scenarios (e.g., loading, ballasting, damage).
Structure of a KN Curve
A typical KN curve is a graph where:
- The horizontal axis represents the angle of heel (usually in degrees).
- The vertical axis represents the KN value (the righting lever measured from the keel, typically in meters or feet).
Multiple curves may be plotted on the same graph, representing different displacements (total weight) of the vessel. As displacement changes, the shape and values of the KN curve will also change.
| Angle of Heel | KN Value (approximate) |
|---|---|
| 0 degrees | 0.0 m |
| 10 degrees | 0.5 m |
| 20 degrees | 1.2 m |
| 30 degrees | 1.8 m |
| 40 degrees | 2.1 m |
| 50 degrees | 2.0 m |
Note: Values are illustrative and vary greatly depending on the ship's design and displacement.
In summary, a KN curve is a fundamental stability diagram that depicts the righting lever measured from the keel against the angle of heel, assuming the vessel's center of gravity is at the keel (KG=0). It serves as a baseline from which the actual righting lever (GZ) can be easily calculated for any given loading condition and KG.
