Exam Question

### (a) Admiralty Coefficient
The Admiralty Coefficient (C) is a dimensionless constant used for the preliminary estimation of the required shaft power for a ship of a given displacement at a specific speed. It is an empirical method derived from historical data of similar ships and provides a quick approximation without the need for detailed hull form analysis or model tank testing.
**Concept and Use:**
- **Basis:** The coefficient is based on the assumption that for small variations in speed, the total resistance of a ship is proportional to the wetted surface area and the square of the speed ($$ R_T \propto S V^2 $$), and that power is resistance multiplied by speed ($$ P \propto R_T V $$). The wetted surface area (S) is assumed to be proportional to the displacement to the power of two-thirds ($$ S \propto \Delta^{2/3} $$). Combining these leads to the relationship $$ P \propto \Delta^{2/3} V^3 $$.