Delivered Power (P_D)

Effective Power (P_E) in Ship Resistance & Propulsion

Effective Power, denoted as P_E, represents the net power required to overcome the hydrodynamic resistance of a vessel at a given speed through water. It is the most fundamental power component in ship propulsion analysis and forms the starting point of the propulsion efficiency chain.

Unlike Delivered Power or Brake Power, effective power is purely hydrodynamic and does not include losses related to hull–propeller interaction, propeller efficiency, or mechanical transmission.

Definition and physical meaning

Effective power is defined as the product of total ship resistance and ship speed through water:

P_E = R_T · V_s

Here, R_T is the total resistance acting on the hull, and V_s is the ship’s speed relative to the surrounding water. The resulting power represents the ideal towing power required to maintain steady motion.

Total resistance R_T

Total resistance includes all hydrodynamic forces opposing the ship’s motion, such as frictional resistance, wave-making resistance, viscous pressure resistance, and appendage resistance.

In practice, R_T is obtained from towing-tank experiments, empirical prediction methods (e.g. Holtrop–Mennen), CFD simulations, or full-scale trial measurements.

Ship speed V_s

The ship speed used in effective power calculations must be the speed through water, not speed over ground. Currents, wind, and environmental effects should therefore be excluded when evaluating P_E.

Consistent units are essential. Resistance is typically expressed in kilonewtons (kN) and speed in meters per second (m/s), yielding power in kilowatts (kW).

Role in the propulsion efficiency chain

Effective power represents the lowest level of power demand in the propulsion chain. To obtain higher power levels, efficiency losses must be accounted for:

P_D = P_E / η_H

P_B = P_E / (η_H · η_R · η₀)

Where η_H is hull efficiency, η_R is relative rotative efficiency, and η₀ is propeller open-water efficiency.

Typical applications

• Resistance prediction and hull-form optimization
• Speed–power curve generation
• Comparison of alternative hull designs
• Baseline input for propulsion and engine sizing
• Performance monitoring and model–ship correlation

Limitations and correct usage

• P_E does not include propeller or mechanical losses.
• Accuracy depends directly on the quality of resistance prediction.
• Environmental effects must be excluded from speed measurements.
• Effective power alone is insufficient for engine selection.

Related propulsion & power calculators

Effective power is the foundation of propulsion power estimation:

• Hull Efficiency (η_H) – hull–propeller interaction effects.
• Delivered Power (P_D) – power available at the propeller shaft.
• Relative Rotative Efficiency (η_R) – rotational interaction effects.
• Brake Power (P_B) – engine power including drivetrain losses.

Tip: Always treat effective power as the starting point of propulsion analysis. All subsequent power levels must be derived using consistent efficiency definitions and operating conditions.