Froude number and wave ship resistance

William Froude(1810- 1878) English engineer and naval architect

creator of the first Towing tank for testing models

Essential in the hydrodynamics study, the Froude Number (Fr) is a dimensionless number linking gravity(g), velocity(v), and boat Length (L) :

Fr= v/(g.L)

Froude number waves ship resistance

While the architects of the time argued that only the experience of the real, could give applicable results, and considered experiments on models, such as " nice little fun experience" , William Froude developed laws of similarity and practiced work on friction.

William Froude expressed the fundamental hypothesis, stating that the resistance to the advancement of vessels is the sum of:

  • direct resistance mainly due to waves

This resistance is a function of nombre de Froude

  • resistance to friction

This resistance is a function of Reynolds number and roughness coefficient of the hull

Although this division of the resistance in distinct parts, is theoretically questionable, thus separating these two components and assuming them independent, it is possible to determine the rules of similarity between resistance to the advancement of scale models and prototypes of actual size.


Predictions he made on models, Verified by towing a ship in sea, (the Greyhound) were successful, giving ship resistance, only 10% below the actual observations.

The method models, then entered the era of practical applications.

ship resistance waves hull froude

W.Froude sketch representing the wave train due to the bow

Despite advances in theory and computer means, this method is still valid, and it is still practiced nowadays in the design of modern ships:

effects of friction measured experimentally basins hulls

voir hydrodynamic naval :testing model Towing tank