A model of a ship is built to a scale of 1 / 20. If the ship...

A model of a ship is built to a scale of $1 / 20$. If the ship is to be designed to travel at $4 \mathrm{~m} / \mathrm{s}$, determine the speed of the model in order to maintain the same Froude number.

Key Concepts

Froude Number

The Froude number is a dimensionless parameter that represents the ratio of a body's inertia to gravitational forces. It is typically defined as the speed of the body divided by the square root of the product of gravitational acceleration and a characteristic length (v/?(gL)). This number is central in the analysis of ship hydrodynamics because it helps compare the similarity in wave-making phenomena between different scales, ensuring that the forces acting on the model accurately represent those on the full-sized ship when dynamic similarity is maintained.

Dynamic Similarity

Dynamic similarity is the condition under which two systems, such as a full-sized ship and its scale model, behave in a substantially identical manner when appropriately scaled. To achieve dynamic similarity, key dimensionless numbers—like the Froude number in the context of marine vessels—must be equal in both systems. This ensures that the physics governing their motions and interactions, such as wave patterns and resistance, are correctly replicated in the model.

Scaling Laws

Scaling laws in engineering allow predictions of a system’s performance based on a reduced-size model. These laws dictate how various physical quantities, such as length, time, and speed, transform between the model and the real ship. Specifically, for maintaining Froude number similarity, the speeds of the model and the real ship are scaled in accordance with the square root of the scale ratio, ensuring that the model accurately mimics the dynamic behavior of the full-scale ship.

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