Hull Efficiency (η_H)

Hull Efficiency (η_H) in Ship Propulsion

Hull efficiency, denoted as η_H, quantifies the hydrodynamic interaction between the ship hull and the propeller. Unlike propeller open-water efficiency, which evaluates the propeller in isolation, hull efficiency accounts for how the hull modifies the flow into the propeller and how the propeller’s thrust interacts with the hull.

η_H is a central component of the classical propulsion efficiency chain and plays a critical role in translating propeller performance into effective thrust at the ship.

Definition and physical meaning

Hull efficiency is commonly defined as the ratio between the effective power required to tow the hull and the thrust power delivered by the propeller:

η_H = (R_T · V_s) / (T · V_a)

In practical engineering formulations, this expression is often rearranged or simplified using wake fraction and thrust deduction coefficients, which capture the dominant hull– propeller interaction effects.

Wake fraction (w)

The wake fraction w represents the reduction in axial flow velocity at the propeller plane due to the presence of the hull. Because the hull slows the flow, the propeller typically experiences a lower inflow velocity than the ship’s forward speed.

V_a = V_s(1 − w)

Wake fraction depends on hull form, propeller location, loading condition, and speed, and is usually obtained from model tests, CFD, or empirical experience.

Thrust deduction (t)

Thrust deduction t represents the increase in hull resistance caused by the propeller’s action. When the propeller operates behind the hull, its induced flow and pressure field increase the resistance compared to the bare-hull condition.

t = 1 − R_T / T

A higher thrust deduction indicates stronger adverse interaction between propeller and hull, which reduces hull efficiency.

Coefficient-based formulation

Using wake fraction and thrust deduction, hull efficiency can be written in a compact and widely used form:

η_H = (1 − t) / (1 − w)

This expression is particularly useful when w and t are available from towing-tank tests or empirical data, and it provides a clear interpretation of how hull–propeller interaction improves or degrades propulsion performance.

Force- and speed-based formulation

When thrust, resistance, and velocities are known directly, hull efficiency can be computed without explicit use of w and t:

η_H = (T · V_a) / (R_T · V_s)

This formulation is often used in full-scale trials, CFD-based propulsion analysis, or diagnostic studies where forces and speeds are directly available.

Typical values and interpretation

• η_H < 1.0 — unfavorable interaction; propeller increases hull resistance significantly.
• η_H ≈ 1.0 — neutral interaction.
• η_H > 1.0 — favorable interaction; wake recovery outweighs thrust deduction.
• η_H ≈ 0.95–1.30 — typical range for merchant ships.

Values above unity are common and physically meaningful, indicating that the propeller benefits from operating in the hull wake.

Limitations and correct usage

• η_H depends strongly on loading condition and speed.
• Wake fraction and thrust deduction are not constants across the operating envelope.
• Hull efficiency alone does not represent overall propulsion efficiency.
• Consistent definitions of T, R_T, V_a, and V_s are essential.

Related propulsion & power calculators

Hull efficiency forms one link in the propulsion efficiency chain:

• Propeller Efficiency (η₀) – open-water performance of the propeller.
• Relative Rotative Efficiency (η_R) – torque interaction between hull and propeller.
• Delivered Power (PD) – power required at the propeller.
• Brake Power (PB) – engine brake power including drivetrain losses.

Tip: Hull efficiency should always be evaluated together with propeller efficiency and relative rotative efficiency. A favorable η_H cannot compensate for poor propeller design or excessive drivetrain losses.