Froude Number
Ratio of inertia to gravity waves; governs hull resistance.
Formula
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Example
v=5 m/s, L=10 m: Fr = 5/√98.1 ≈ 0.50
How it works
The Froude number compares a vessel’s speed to the speed at which gravity waves can travel relative to a length scale such as the waterline length. Because wave-making resistance depends strongly on how the hull’s disturbance interacts with its own bow and stern wave system, Fr is a key similarity parameter in ship hydrodynamics. It works by nondimensionalizing speed with \sqrt{gL}, which is the natural gravity-wave speed scale for a body of length L on a free surface.
When to use it
Use this when analyzing ship resistance, hull testing, model-to-full-scale similarity, or estimating whether a craft is operating in displacement, semi-displacement, or planing-like regimes. It is especially useful in naval architecture and towing-tank studies where wave effects dominate drag behavior.
Worked example, step by step
Given: v = 12 m/s, L = 36 m, g = 9.81 m/s^2 Step 1: Compute gL = 9.81 × 36 = 353.16 Step 2: Take the square root: √353.16 ≈ 18.79 Step 3: Divide speed by this value: Fr = 12 / 18.79 ≈ 0.64 Final answer: Fr ≈ 0.64
Common mistakes to avoid
- Using boat length overall instead of the waterline length specified by the formula
- Forgetting that g must be in m/s^2 and L in meters so the units are consistent
- Interpreting a higher Froude number as "more efficient" without considering wave drag and hull type
Did You Know?
Naval architects match the Froude number to test small models that behave like full-size ships.
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