3.2.2. Average Curvature (*k*)

Curvature is the rate of change of the angle between the tangent of a point on the curve and the x axis relative to the arc length, which is defined by differentiation to indicate the degree of deviation of the curve from a straight line. The average curvature represents the deviation and regression degree of the course, which reflects the course correction ability varying with vessels under the interference of wind and waves. The average curvature (*k*) is defined as follows:

$$\overline{k} = \frac{\sum\_{i=0}^{n} \frac{\|l\_i""\|}{\left[1 + \left(l\_i"\right)^2\right]^{3/2}}}{n} \tag{25}$$

where *li* is the first derivative of the arc length, and *li* is the second derivative of the arc length.
