Open-water propeller efficiency computed either from KT–KQ–J coefficients or directly from thrust & torque measurements.
η₀ (open-water efficiency): —
Advance ratio J: —
Advance speed Va: — kn
Rotational speed n: — rev/s
Propeller open-water efficiency, commonly denoted as η₀, measures how effectively a propeller converts rotational shaft power into useful thrust power under idealized open-water conditions. It is defined independently of hull interaction effects such as wake, thrust deduction, and hull efficiency, and therefore represents the intrinsic hydrodynamic performance of the propeller itself.
η₀ is a key parameter in propulsion analysis, propeller selection, and performance diagnostics, and forms one of the core efficiency components in the classical propulsion power chain used in naval architecture.
In its most general form, propeller efficiency is defined as the ratio of useful thrust power to delivered rotational power:
η₀ = (Thrust power) / (Shaft power at the propeller)
In open-water analysis, this becomes a purely hydrodynamic quantity, evaluated either from non-dimensional propeller coefficients or directly from measured thrust and torque.
In propeller open-water tests, thrust and torque are typically expressed using non-dimensional coefficients: KT and KQ, plotted as functions of the advance ratio J.
Using these coefficients, open-water efficiency is computed as:
η₀ = (J · KT) / (2π · KQ)
This approach is standard when propeller series data, open-water diagrams, or CFD-derived KT–KQ curves are available. It allows rapid comparison of propeller designs across operating points without direct dependence on absolute thrust or torque values.
The advance ratio J represents the ratio between axial inflow speed and propeller rotational speed:
J = Va / (n · D)
where Va is the advance speed at the propeller plane, n is the rotational speed in revolutions per second, and D is the propeller diameter. J strongly governs propeller loading and efficiency and is the primary independent variable in open-water propeller series.
In behind-hull operation, the flow arriving at the propeller is reduced by the hull wake. The advance speed is commonly approximated as:
Va = Vs(1 − w)
where Vs is the ship speed and w is the wake fraction. This calculator allows Va to be entered directly or derived from ship speed and wake fraction for convenience and transparency.
When thrust and torque are known directly—such as from full-scale measurements, CFD results, or dynamometer data—open-water efficiency can be computed without using KT–KQ coefficients:
η₀ = (T · Va) / (2π · n · Q)
where T is thrust, Q is torque, and n is rotational speed. This method is particularly useful for validating propeller performance against measured data or numerical simulations.
Typical open-water efficiency values depend on propeller type, loading, and operating point:
Maximum η₀ typically occurs near the design advance ratio and decreases rapidly outside that range.
Propeller open-water efficiency is one component of the full propulsion efficiency chain:
Tip: Always interpret η₀ together with slip, wake fraction, and hull efficiency. A high open-water efficiency does not guarantee good overall propulsion performance if hull–propeller interaction is unfavorable.