3.2.3. Ratio of the Arc Length to the Chord Length (*R*)

The arc length is the invariant of smooth curved motion, and the chord length has similar invariance. The ratio of the arc length to the chord length can roughly reflect the deviation and regression degree of course varying with vessels under the interference of wind and waves, which is similar to the average curvature. The ratio of the arc length to the chord length is defined as follows:

$$R = \frac{l}{d} \tag{26}$$

where *d* is the chord length, and *l* is the arc length.
