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    Hull Speed & Froude Number
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    Hull Speed & Froude Number

    Definitions

    Hull speed, sometimes referred to as displacement speed, is a common rule of thumb based on the speed/length ratio of a displacement hull, used to provide the approximate speed potential (i.e. maximum speed possible) of the hull.

    The Froude number is a dimensionless number comparing inertial and gravitational forces. It may be used to quantify the resistance of an object moving through water, and compare objects of different sizes.

    Topics of Interest

    Hull speed, sometimes referred to as displacement speed, is a common rule of thumb based on the speed/length ratio of a displacement hull, used to provide the approximate speed potential (i.e. maximum speed possible) of the hull. It is the speed of a deep water wave whose wavelength is equal to the waterline length of the hull. The most commonly used hull speed constant is the wave propagation speed for the hull length, and it serves well for traditional sailing hulls. In English units, it is expressed as:

    \mbox{knots} \approx 1.34 \times \sqrt{l \mbox{ft}}

    Or, in metric units:

    \mbox{knots} \approx 2.43 \times \sqrt{l \mbox{m}}

    where "l" is the length of the waterline (LWL) in feet or meters.

    Hull speed is typically not a term used by naval architects (they use, instead, a specific speed/length ratio for the hull in question) but is often used by amateur builders of displacement hulls, such as small sailboats and rowboats.

    The concept has to do with the effect of drag from the water on the hull. With all else being equal, a longer boat will have a higher hull speed. In yacht racing this is demonstrated by looking at handicap ratings such as PHRF; generally speaking longer boats have higher handicap, although there are other factors.

    The quantification of the speed/length ratio is generally credited to William Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. Froude's observations led him to derive the Froude number, which allows experimental observations performed on scale models to be applied to full-scale vessels.

    The speed-to-length ratio is traditionally expressed in knots of speed (V) and feet of waterline length (LWL):

     \textrm{Speed Length Ratio} =\frac {V}{\sqrt \textrm{LWL} }

    The speed/length ratio is strictly only useful when comparing different scalings of otherwise identical hulls whose drag is dominated by wave drag. However, for many hulls, a generic speed/length ratio will provide a good general estimate of the speed potential of the hull when it is operating in displacement mode. This is commonly called the hull speed, and this term is commonly found in the boating community and among amateur builders, though it is not used by naval architects or engineers.

    The hull speed limit does not readily apply to certain types of hull which are not primarily limited by wave drag. Examples of these craft are:

    • Very long, narrow hulls such as rowing shells, flatwater racing canoes and kayaks, and multihulls such as catamarans and proas. In these hulls, skin drag is often far greater at the normal operating speeds than the wave drag.
    • Boats which operate in a semi-displacement mode where the hull shape provides some lift. In these hulls, the lift reduces the displacement, providing a reduction in the quantity of water moved and a corresponding reduction in wave drag.
    • Small, highly powered boats such as sailing dinghies and personal watercraft, which can easily plane. These hulls quickly and easily surmount their bow waves, and rely entirely on dynamic lift when planing.

    The Froude number is a dimensionless number comparing inertial and gravitational forces. It may be used to quantify the resistance of an object moving through water, and compare objects of different sizes. Named after William Froude, the Froude number is based on his speed/length ratio.

    The quantification of the resistance of floating objects is generally credited to Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. Froude's observations led him to derive the Wave-Line Theory which first described the resistance of a shape as being a function of the waves caused by varying pressures around the hull as it moves through the water. The Naval Constructor Ferdinand Reech had put forward the concept in 1832 but had not demonstrated how it could be applied to practical problems in ship resistance. Speed/length ratio was originally defined by Froude in his Law of Comparison in 1868 in dimensional terms as:

    \mathrm{Speed Length Ratio} =\frac {V}{\sqrt \mathrm{LWL} }

    where:

      v = speed in knots
      LWL = length of waterline in feet

    The term was converted into non-dimensional terms and was given Froude's name in recognition of the work he did. It is sometimes called Reech-Froude number after Ferdinand Reech.

    The Froude number is used to compare the wave making resistance between bodies of various sizes and shapes.

    In free-surface flow, the nature of the flow (supercritical or subcritical) depends upon whether the Froude number is greater than or less than unity.

    Source: Wikipedia (All text is available under the terms of the GNU Free Documentation License and Creative Commons Attribution-ShareAlike License.)

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