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    Re: Wind & Current Navigation
    From: Dave Weilacher
    Date: 2003 Apr 17, 14:24 -0400

    You may have just sorted out a nautical saying that I have often wondered about the arithmetic of.
    "Twice the wind has eight times the force"
    This is probably correct if it is "Twice the wind has eight times the power".
    Do I understand this right?
    -------Original Message-------
    From: George Huxtable 
    Sent: 04/17/03 05:08 PM
    Subject: Re: Wind & Current Navigation
    > 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
    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
    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
    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
    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,
    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
    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
    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
    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.
    contact George Huxtable by email at george@huxtable.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.
    Dave Weilacher
    .US Coast Guard licensed captain
    .    #889968
    .ASA instructor evaluator and celestial
    .    navigation instructor #990800
    .IBM AS400 RPG contract programmer

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