Before revision: It is independent of the circle radius; a sine function (over a whole number n of half-periods), which can be calculated by computing the sine curve's arclength on those periods, is Example with 270° angle With similar opposite arcs joints in the same plane, continuously differentiable: Central angle Sinuosity Degrees Radians Exact Decimal 30° 1.0115 60° 1.0472 90° 1.1107 120° 1.2092 150° 1.3552 180° 1.5708 210° 1.8972 240° 2.4184 270° 3.3322 300° 5.2360 330° 11.1267 Rivers In studies of rivers, the sinuosity index is similar but not identical to the general form given above, being given by: The difference from the general form happens because the downvalley path is not perfectly straight.
After revision: It is independent of the circle radius; a sine function (over a whole number n of half-periods), which can be calculated by computing the sine curve's arclength on those periods, is upExample with 270° angle With similar opposite arcs joints in the same plane, continuously differentiable: Central angle Sinuosity Degrees Radians Exact Decimal 30° 1.0115 60° 1.0472 90° 1.1107 120° 1.2092 150° 1.3552 180° 1.5708 210° 1.8972 240° 2.4184 270° 3.3322 300° 5.2360 330° 11.1267 Rivers In studies of rivers, the sinuosity index is similar but not identical to the general form given above, being given by: The difference from the general form happens because the downvalley path is not perfectly straight.