Sail of the century

For those of you with an interest in mechanics, there’s a fascinating project currently going on in Walvis Bay, Namibia, where the Vestas Sailrocket team from England are trying to break the world speed record for a sailing boat — aiming for speeds of 60 knots, or just under 31 m/s.

This isn’t only of interest as an exciting way to risk one’s neck, because pushing the limits of engineering like this depends on understanding some less than obvious aspects of classical mechanics. The first aspect is the simple but surprising fact that it’s possible to sail faster than the wind. This is basically because the force exerted on a sail isn’t just the “drag” force parallel to the relative wind velocity: the sail also experiences a sideways “lift” force like an aeroplane wing, and the water exerts additional forces on the keel, so by clever use of vector addition it’s possible to attain higher speeds than the wind itself. (There’s a detailed discussion on Terence Tao’s blog.)

The other neat piece of physics is the phenomenon of cavitation. Those of you who’ve done a fluid mechanics class will know that, in steady inviscid flow when gravity is neglected, velocity and pressure are related by Bernoulli’s equation,

\displaystyle\frac{1}{2}\rho|\mathbf{u}|^2 + p = p_0,

where p_0 is the pressure where the fluid is still. For flow round the hull of a boat, p_0 is close to atmospheric pressure, p_0 \approx 10^5 Pa, so if the speed of the fluid increases above u_{\mathrm{crit}} = \sqrt{2p_0/\rho} \approx 14 m/s then the pressure can drop locally to very close to zero. What happens if very low pressures are sustained for any length of time is that the liquid boils, forming cavitation bubbles. These directly affect the flow, and also have an even more pernicious effect: when they collapse they can generate localised pressure spikes of several hundred atmospheres and temperatures of several thousand Kelvin — enough to make holes in steel! One of the key design features of the new Sailrocket is that the hydrofoil is shaped to control the cavitation in cunning ways. (Nuclear submarines have similar problems with cavitation on the fast-moving tips of their propellors, but they also have the option of travelling at much greater depths where p_0 is much higher due to hydrostatic pressure. The deeper a sub is, the faster it can travel before cavitation becomes a problem.)

Oh, and if you just want to see things going whizz and splat (well, who doesn’t?), there’s a piece of footage on Youtube. See in particular the run that starts around 3:30 into the video…


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