Ship Hull Resistance Simulator: Froude Number & Power Prediction

simulator beginner ~9 min
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R_T = 285 kN — 100m vessel at 15 knots

A 100m vessel with 15m beam and 6m draft at 15 knots (Fn = 0.25) experiences approximately 285 kN total resistance, requiring about 2.2 MW effective power. Frictional resistance accounts for roughly 65% at this speed.

Formula

Fn = V / √(g × L) (Froude number)
R_F = 0.5 × ρ × S × V² × C_F (ITTC friction)
P_E = R_T × V (effective power)

The Drag of Moving Through Water

A ship moving through water must overcome resistance — the force opposing its forward motion. This resistance determines how much engine power is needed to achieve a given speed, and thus fuel consumption, emissions, and operating costs. Naval architects have studied ship resistance for over 150 years, beginning with William Froude's pioneering towing tank experiments in the 1870s that established the principles still used today.

Components of Resistance

Total hull resistance has three main components. Frictional resistance arises from the viscous boundary layer along the hull surface — water molecules near the hull are dragged along, creating shear stress. Wave-making resistance is the energy lost to the ship's wave system — the characteristic bow wave and stern wake. Form resistance (viscous pressure drag) comes from flow separation and eddies, particularly at the stern. Air resistance on the above-water hull adds a small contribution at high speeds.

The Froude Number & Hull Speed

William Froude showed that wave-making resistance depends on the ratio of speed to the square root of length — the Froude number. At low Fn (< 0.2), waves are small and friction dominates. At Fn ≈ 0.35-0.40, wave resistance rises sharply as the bow and stern wave systems interact. At Fn ≈ 0.5, the ship sits in a single transverse wave as long as the hull — the famous 'hull speed' where further acceleration requires enormous power. Fast ships must be long relative to their speed.

Power & Efficiency

Effective power (P_E = R_T × V) is the minimum power to move the hull. Actual engine power must be higher to account for propulsive efficiency, appendage drag, and sea margin. The propulsive coefficient (P_E/P_brake) is typically 0.55-0.70. At current fuel prices, a 1% reduction in resistance saves millions of dollars per year for large container ships. This drives intense optimization of hull forms using CFD, model testing, and operational measures like slow steaming.

FAQ

What is the Froude number in naval architecture?

The Froude number Fn = V/√(gL) is the most important dimensionless parameter in ship hydrodynamics. It relates ship speed to hull length and governs wave-making behavior. Ships with the same Froude number produce geometrically similar wave patterns regardless of size — this is Froude's law of comparison, the basis of model testing.

What causes wave-making resistance?

As a ship moves, it creates a wave system: bow and stern waves that propagate outward. Energy put into these waves is lost as resistance. At Fn ≈ 0.5, the bow and stern wave systems interact constructively to create a single large transverse wave as long as the hull — the 'hull speed' barrier where wave resistance increases sharply.

What is frictional resistance?

Frictional resistance arises from the viscous shear stress of water flowing along the hull surface. It depends on wetted surface area, speed, water viscosity, and surface roughness. For large slow ships (tankers, bulk carriers), friction accounts for 70-80% of total resistance. Smooth, clean hulls are essential for fuel efficiency.

How is ship resistance measured?

Scale model testing in towing tanks remains the gold standard. A geometrically similar model (1:20 to 1:100 scale) is towed at the corresponding Froude number. Frictional resistance is calculated using the ITTC 1957 friction line and subtracted from total model resistance to isolate residuary (mainly wave) resistance, which scales directly to full size.

Sources

Embed

<iframe src="https://homo-deus.com/lab/ocean-engineering/ship-resistance/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub