# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Wind & Current Navigation**

**From:**George Huxtable

**Date:**2003 Apr 17, 22:08 +0100

Referring to my comments about wind forces and current forces, which I said would vary as the square of the velocity, Dan Allen responded- >On Thursday, April 17, 2003, at 07:16 AM, George Huxtable wrote: > >> The force will vary as the square of the velocity > >Why the square? and Marvin Sebourn commented- I may misunderstand something though--I thought that the power or force of the wind is proportional to the cube of the velocity, not the square. and Dave Weilacher asked- ...so would a 2 knot current be the sqrt((2^2) * 830) = 58kt wind? It's gratifying to find such an interest in the science of hydrodynamics. Dave's question first. The answer is yes (other things being equal, which they usually are not, exactly: see below). Now for Dan's fair question: why the square? Let's consider something like a dustbin-lid on a long bridle, towed far behind an immersed submarine. It makes no difference whether it's the bin-lid moving through the water, or a water-current impinging on the lid. If the speed doubles, then in a given time twice as much water impinges on the lid. And with the speed doubled, every drop (or every molecule or every gram) of that water has twice as much momentum (which is mass x velocity) which it gives up to the lid when it's brought to a stop. Force is given by the rate of transfer of momentum, so we get the force increased by 2 x 2 = 4. Is that good enough to satisfy Dan, or does he wish to get more fundamental? Now for Marvin's statement- I thought that the power or force of the wind is proportional to the cube of the velocity, not the square. Well, power and force are NOT the same thing. Power is a measure of the rate at which work is done, which is the product of force and speed. If, as we said above, force goes as the square of speed, then power, being force multiplied by the speed again, goes as the cube of speed. All this is rather an oversimplification. At very low speeds the forces get so low that the viscosity of water has an appreciable effect, and that component of force doesn't follow a square-law (but don't ask me what law it DOES follow!) There's an additional effect, a really important one. A displacement vessel floating on the surface is supported by displacing a pit in the water into which the hull nestles. As the vessel moves, that pit has to move with it, and it has to elbow water out of the way to do so. This process feeds energy into surface waves, and at certain higher speeds this wavemaking becomes the dominant energy-loss mechanism, contributing greatly to the drag. That component of drag doesn't follow a square-law either (which is why we specified our bin-lid as being towed by a submarine, to avoid making surface waves). These effects were spelled out by a fellow called William Froude in the mid-1800s in order to interpret the data from model ships towed in test-tanks, and to decide what speeds to tow them at. George. ================================================================ contact George Huxtable by email at george---.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================