Froude Estimator — Resistance Prediction

What Is the Froude Resistance Estimator?

The Froude resistance estimator is a simplified empirical method used to approximate the calm-water resistance of displacement and semi-displacement vessels based on classical hydrodynamic scaling laws. It combines frictional resistance, evaluated using the ITTC-1957 line, with a Froude-number-based residuary resistance correlation.

This approach is intended for rapid, early-stage resistance and power estimation when detailed hull-form data is unavailable or when more complex regression-based methods are not yet justified.

Background and hydrodynamic basis

The method is rooted in classical naval architecture theory, where total resistance is decomposed into viscous (frictional) and wave-making (residuary) components. While frictional resistance can be estimated reliably using Reynolds-number-based formulations, residuary resistance is primarily governed by the vessel’s Froude number.

The Froude estimator leverages this relationship by expressing the non-viscous component as a function of the Froude number, allowing resistance trends to be captured without explicit geometric detail.

Role of the Froude number

The Froude number is a dimensionless parameter defined as:

F_n = V / √(g · L)

where V is vessel speed, g is gravitational acceleration, and L is the characteristic length, typically the waterline length.

It represents the ratio between inertial and gravitational forces and governs the formation of the vessel’s wave system. As the Froude number increases, wave-making resistance grows rapidly and eventually dominates total resistance.

Resistance components

• Frictional resistance – calculated using the ITTC-1957 friction line and evaluated over the wetted surface area.
• Residuary resistance – an empirical term that accounts for wave-making and pressure-related effects as a function of Froude number.
• Total resistance – the sum of frictional and residuary components acting on the hull in calm water.

Wetted surface area estimation

If the wetted surface area is not known, the estimator uses a common preliminary approximation:

S ≈ 1.7 · L · B

where L is waterline length and B is beam. This approximation is widely used during conceptual design stages and provides reasonable accuracy for conventional displacement hull forms.

Applicability range

The Froude estimator is most suitable for:

• Displacement and semi-displacement vessels
• Early-stage design and feasibility studies
• Trend analysis and comparative performance evaluation
• Typical Froude numbers up to approximately 0.4–0.5

Outside this range, particularly near or beyond planing conditions, more specialized methods should be used.

Engineering use cases

Naval architects and marine engineers commonly use Froude-based estimators to:

• Estimate resistance and power demand during concept design
• Check plausibility of results from more complex methods
• Develop speed–power curves for preliminary studies
• Support feasibility assessments when limited data is available

Limitations

• The method is empirical and does not account for detailed hull geometry.
• It assumes calm-water conditions and neglects added resistance effects.
• Accuracy decreases for very full, very fine, or unconventional hull forms.
• Results should not be used as final design values.

Related calculators

• Holtrop–Mennen Resistance – for detailed displacement hull prediction.
• Telfer Method – for semi-displacement vessels in the transitional regime.
• Savitsky Planing Method – for high-speed planing craft.
• Effective Power (PE) – converts resistance to power demand.