Of sailing ships: Froude numbers

HMS Dreadnought
U.S. Naval History & Heritage Command photo

As an island nation, England has had a long tradition of strong navy ships, but ship casualties at sea were high, not just because of battle and pirates, but because of poor design. The Victorian Age was also the age of the ironclads--massive heavy ships.  One such ship was the "Captain", which turned turtle in 1871 with the loss of almost 500 lives.

A father-son team, William and Robert Froude had been working on ship design and had been conducting experiments with small ships on the River Dart, and later had built their own testing tank at Chelston Cross.**  When the Captain turned turtle, Froude gained support (an enormous sum of 2000 pounds!!) to cover the cost of building a tank in which he could test scale models of ships. This was to revolutionize ship-building, a practice that until then had been done by simple reliance on the experience of shipwrights.

William Froude died in 1879 at the age of 69, and a few years later the original experimental tank (called the Torquay tank) became obsolete.  Robert Froude built a new tank, 475 feet long, 20 feet wide, and 9 feet deep at Haslar. By 1918, over 500 warship models had been tested there, including the "Dreadnought," a revolutionary battleship that rammed and sank the U-29 German submarine during World War I.

Froude was concerned with reducing the drag on ships, and with the problem of applying results obtained from his models to the enormous battleships. There are two sources of drag on ships: viscous resistance from water on the hull, and wave-making resistance, the energy dissipated forming the waves that follow ships (the characteristic V-shaped wake behind ships). At high-speed the wave-making resistance accounts for 50-60% of the resistance.  The drag increased with the speed of the ship, and decreased for larger and larger ships.  A dimensionless parameter, now known as the Froude number, expressed this relation:

Fr = v/((gL)**0.5)

At low Froude numbers (low velocity and/or big long ship) viscous resistance dominates. At Fr=0.4 to 0.5, wave resistance dominates. Most conventional ships operate at Fr<0.4.


**Here's the reference on the two Froudes.
Here's a source of some of the other information that I used here.