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    Speed and waterline length. was: Revisiting hull pressure wave
    From: George Huxtable
    Date: 2005 Jan 27, 10:40 +0000

    Bill wrote-
    >First, is "draught" the same as US "draft?  (She draws 3 feet, her draft is
    >3 feet?)
    Yes, it's the same word. Just another example of two nations divided by a
    common language.
    Somehow (perhaps erroneously) I equated the downward pressure wave
    >with speed and length at waterline.  The longer the hull (at waterline) the
    >bigger the bow wave and bigger waves can move faster than smaller waves (1.3
    >sqrt).  So I *assumed* a larger vessel (draft being equal) would also create
    >a greater "downward* pressure wave.
    >If I understand the below only the draught/draft (probably ignoring thin
    >"blades") and speed is of importance relative to the depth.
    >Thinking it through, we are trying to maximize our speed--sail at hull
    >speed.  A 34'craft might have a hull speed of 7.6 knots, while a similar 50'
    >craft may have a hull speed of 9.2 knots.  If both had the same draft and
    >were moving at hull speed, and depths were equal, the larger craft would
    >reach the critical number before the smaller craft because of her higher
    >speed.  In the real world, the larger craft may well have a deeper draft
    >than the smaller craft, further hampering her speed at the same depth the
    >34' boat experiences.
    >So the length-at-waterline issue may be folded into the equation you
    Hydrodynamics isn't my subject (though that won't stop me having my say).
    Bill's question about "downward pressure wave" is one I have avoided
    answering, because I don't understand the concepts involved, and I'm not
    answering his question now.
    But he also raises the old question of the "hull speed" of a vessel, in
    relation to its waterline length, and that's a matter that might benefit
    from some discussion on Nav-l.
    It's (wrongly) called the "speed / length ratio" though it should really
    known as the "speed / root length ratio". If you take the maximum speed of
    a vessel in knots and divide it by the square root of the waterline length
    in feet, the answer will come out somewhere near 1. Perhaps 1.4 for a fast
    displacement yacht; considerably more for a sailboard. Apologies to metric
    It's a concept that has some limited use, but those limitations need to be
    kept in mind. It's one of those "rules", honoured as much in the breach as
    in the observance.
    First, a bit of history. The rule came from William Froude's tests to find
    the shape of ships which would slip though the sea with minimum resistance.
    This work was done using scale-model hulls in a long test tank. Although,
    at low ship speeds, the resistance was largely surface friction with the
    water, as speed increased the energy lost in creating surface waves became
    dominant. Froude found that if he made a model at say 1/10 scale, and then
    tried towing it at 1/10 speed, there was little wavemaking from the model,
    and the pattern of wave generation was quite unlike that from the vessel.
    Instead of reducing the model's speed to 1/10, if it was reduced to 0.316
    of the speed of the speed of the real (that is, dividing it by root-10)
    then the wave pattern around the model would match closely that from the
    real ship.
    So this rule was devised as a way of comparing two vessels of exactly the
    same shape but
    quite different dimensions. And Froude found that the power required to
    drive the tenth-scale model, at a speed scaled down to 0.316, was down by a
    factor of 1000 on that of the real ship at full speed: in other words, the
    horse-power required per ton was the same in the two cases. I have
    simplified matters somewhat.
    It's true that for any displacement hull, the power that's lost to making
    waves rises rapidly as speed increases. At the speed where the wave pattern
    is such that the bow is raised on the bow-wave and the stern is sunk in the
    following trough, there's a particularly sharp increase. That wave-pattern
    occurs when hull speeds in knots are somewhere near the square-root of the
    waterline length in feet. It's not an actual block on higher speed, but it
    implies that providing sufficient power to achieve it may be impracticable
    or uneconomic. If money is no object, as in the case of a destroyer making
    a sprint, it's overcome simply by supplying extra power using lightweight
    gas-turbines. For a merchant vessel, fuel and money are saved by keeping
    well below such a speed.
    In the case of a displacement yacht, reaching it's "maximum hull speed" at
    which the stern is getting into a wave-trough, if you could supply
    sufficient extra power, or push, on the sails, you could certainly get some
    extra speed. Not much, it's true, being in the region of diminishing
    returns, but more speed for more power is always the rule. However, other
    considerations apply. When the force on the sails gets great enough, you
    start to worry about its effect on stability, or about something carrying
    away aloft, and take in canvas accordingly. There's always a practical
    So this concept of a maximum hull speed and its relation to waterline
    length has some validity, especially when comparing craft of similar shape
    but different size, but it shouldn't be taken too religiously. That's my
    opinion, as a non-expert, for what it's worth.
    In my dinghy-sailing days I remember a keen experimentalist who attached a
    long flat fin behind the transom of his boat, shifting his rudder to its
    rear end, arguing that he was increasing the waterline length, and
    therefore the maximum speed. Didn't work, of course.
    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.

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