What is the Froude number?

Hull model being tested in a test tank.

The Froude number is used in naval architecture to:

  • predict the boat-created wave system that moves along with the boat as it makes its way through the water;
  • determine the resistance to boat progress generated by that wave system;
  • infer the wave resistance of full-scale boats based on the results obtained with models tested in facilities such as test tanks.

It was named after the English Engineer Willian Froude (1810-1879). In the 1860s he proposed to build what is considered today the first true test tank for ship models. Based on the results obtained testing, he observed that the resistance of models and full-sized ships were related through what was called later the Froude Number. This law of similitude has been paramount in the advancement of hull design and naval architecture.

The Froude number is a dimensionless number used to quantify the influence of gravity on the motion of a fluid. It is the ratio of the inertia forces to the gravitational forces related to the mass of water displaced by a floating boat.

The Froude Number formula

As a boat moves through the water, it must put aside a mass of water equal to its volume displacement times the density of the water. The forces required to move aside this volume of water are called the inertia forces. The Froude number relates these inertia forces to the gravitational forces that would act to the same mass of water if it was situated at a relative height equal to the length of the hull (length of the waterline or LWL).

The Froude number is not only used in naval architecture to predict or compare the wake making resistance between hulls of various sizes and shapes. For example, it also finds application in hydraulics in flow free-surface situations, like water flowing in an open channel, and particularly in describing the surface wave behavior and the flow pattern over an obstacle (hydraulic jump). In these cases, instead of Lwl, the characteristic length used to calculate the Froude number is the depth of the flow. When the Froude number is equal or bigger than 1, the flow is called supercritical. When the Froude number is less than 1, the flow is called subcritical.

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