The eccentric engineer: Froude’s Law and the discoveries of Raven and Swan

William Froude did not intend to be a naval engineer. The son of a Devon archdeacon, he took a first in mathematics before becoming a surveyor for the South Eastern Railway in 1833. This was the great age of railway expansion and Britain suddenly found itself with a pressing need for practical engineers who could find elegant and inexpensive solutions to carving the great railway routes through the country.

Froude was just such a man and in 1837 Isambard Kingdom Brunel, the biggest engineering name of the age, took him on to manage the construction of the last section of the Bristol to Exeter line. Froude applied his mathematical genius to the practical problems of railway building. He devised ‘spiral easements’ to transition between straight and curved track in such a way that the carriages didn’t fly off the rails, as well as drawing up plans for a new type of skew arch.

With a small private income, Froude retired from full-time engineering aged only 36, to look after his ill father. To fill his time, he took on voluntary roles as a magistrate and harbour commissioner as well as applying himself to improving the water supply in Torquay. It was this that first gave Froude the idea of studying friction in water, which in turn perhaps inspired Brunel to hire him to work on another of his great projects – improving ocean travel.

Brunel’s question was simple – how do you find the optimum hull shape to ensure the stability and economy of a ship in seaway? The answer was far from easy. Yet after five years’ work, Froude presented a paper to the Institution of Naval Architects, outlining the first correct theory for the behaviour of a ship in a seaway.

Until this point, ship design had been somewhat haphazard. Ship lines were derived by eye and only tested when the final vessel was launched. Naval architects worked by trial and error, not mathematical planning. Not that the maths was easy – indeed, it took another decade for Froude to perfect his ideas, using modelling where mathematics proved simply too complex, and it was this idea that brought about his next breakthrough.

It was one thing to build a ship by trial and error, another to plan it mathematically, but the actual building of ships required something in between, and Froude realised that was modelling. At the time the idea was considered outlandish. Surely the only way to see how a ship behaved was to build it and sail it? A model would behave differently.

Or would it? Now a Fellow of the Royal Society and a partner in business with Brunel’s son Henry, Froude was asked to join a committee of the British Association charged with creating methods to estimate the power required to drive a ship. Of course, the power was dependent on the shape of the hull and speed of the vessel, and the committee decided the best way to study this would be to build several full-size ships and test them.

Froude disagreed and instead went away and built three models at different scales of each of two radically different hull shapes – the Raven and the Swan.

These were both extensively tested and Froude reported back two astonishing discoveries. First, contrary to centuries of naval understanding, there was no optimum hull shape. Raven sailed better at low speeds, but Swan was better at high speeds. Second, he demonstrated that when tested at corresponding speeds, the resistance per unit immersed volume of his models was the same at all scales; hence, testing a hull model would be just as effective as building a whole ship. This is known today as Froude’s Law.

Of course, engineers of the Royal Navy and the British Association still needed convincing, so in 1871 HMS Greyhound was fitted out as a full-size test vessel, being towed at several speeds and her resistance measured. Much to his delight, this triumphantly proved Froude right.

With the navy now onboard, Froude persuaded them to build the world’s first test tank, near his home in Torquay. At 270 feet (82m) long and with a constant-speed steam pulley system, it allowed the resistance of paraffin wax hull forms to be tested through the water and measured with Froude’s own-​design dynamometers. The machine remained in service until 1938.

Now the toast of the Admiralty, Froude was offered a holiday voyage to South Africa as a guest of the Royal Navy to help him recover from the death of his wife. However, he contracted dysentery onboard and died at Admiralty House, Simonstown in 1879. He was buried with full naval honours.