Question

The dynamics of a 90 m long ship are governed by the non-dimensional Nomoto equation. The magnitude of Nomoto gain \( |K'| = \frac{72}{35\pi} \) and that of Nomoto time constant \( |T'| = \frac{288}{35\pi} \). The steady turning radius of the ship for a 35° turning circle maneuver is ________ m (answer in integer).

Hint:

For turning radius calculations, always ensure the angle is in the correct unit (degrees or radians) and use accurate trigonometric values.

Answer 1

Step 1: Use the relation between steady turning radius and Nomoto gain. \[ R = \frac{L}{K' \delta} \] Where: \( L = 90 \, {m} \) \( K' = \frac{72}{35\pi} \) \( \delta = 35^\circ = \frac{35\pi}{180} \, {rad} \)
Step 2: Substitute values. \[ R = \frac{90}{\left(\dfrac{72}{35\pi}\right) \cdot \dfrac{35\pi}{180}} = \frac{90}{\dfrac{72}{180}} = \frac{90 \cdot 180}{72} = \frac{16200}{72} = 225 \, {m} \]