The Froude number is a dimensionless number used to compare how ships, submarines, and scale models move through water. It relates a vessel's speed to its length and to gravity, which controls how surface waves form. This matters because waves affect drag, fuel use, stability, and the accuracy of model testing.
When a model ship and a full-size ship have the same Froude number, their wave patterns are similar in shape.
Key Facts
- Froude number: Fr = V / sqrt(gL)
- V is vessel speed in m/s, g is gravitational acceleration in m/s^2, and L is a characteristic length in m.
- For ships, L is often the waterline length because it sets the scale of the wave system.
- Equal Froude numbers mean model and full-size vessels have dynamically similar wave patterns.
- If Fr_model = Fr_ship, then V_model / sqrt(gL_model) = V_ship / sqrt(gL_ship).
- Model speed scaling: V_model = V_ship sqrt(L_model / L_ship).
Vocabulary
- Froude number
- A dimensionless ratio comparing a vessel's speed to the speed scale set by gravity and length.
- Dynamic similarity
- A condition where two systems behave in matching ways because important dimensionless numbers are the same.
- Waterline length
- The length of a vessel measured along the surface of the water from bow to stern.
- Wave resistance
- The part of drag caused by the energy a vessel uses to create waves.
- Scale model
- A smaller physical version of a vessel used for testing and prediction.
Common Mistakes to Avoid
- Using length in centimeters while speed is in meters per second. This is wrong because the Froude number formula requires consistent units, usually SI units.
- Forgetting the square root in Fr = V / sqrt(gL). This is wrong because gravity and length combine as a speed scale, not as a simple product.
- Assuming equal model and ship speeds give similar behavior. This is wrong because a smaller model must usually move much slower to match the full-size vessel's Froude number.
- Using total vessel length when waterline length is required. This can be wrong because surface wave behavior is mainly controlled by the length of the hull in contact with the water surface.
Practice Questions
- 1 A ship has a waterline length of 100 m and travels at 10 m/s. Using g = 9.8 m/s^2, calculate its Froude number.
- 2 A full-size ship is 64 m long and travels at 8 m/s. A scale model is 1 m long. What model speed gives the same Froude number? Use V_model = V_ship sqrt(L_model / L_ship).
- 3 Two vessels have the same speed, but one has twice the waterline length of the other. Explain which vessel has the smaller Froude number and what that means for comparing their wave patterns.