Hull Speed

Hull speed = SQRT(LWL)*1.34

This is the theoretical hull speed for a displacement hull (most sailboats). It is a function of the length of the wave created by the boat as it moves through the water. Wave speed is a function of wavelength; longer wavelengths are faster. Longer boats make longer waves. Since longer waves are faster; boats that make longer waves are faster. The hull speed may not be as precise a figure as the formula leads you to believe (1.34 sounds pretty precise doesn't it?). LWL is not static. As the boat heels it can increase. Older racing boats with long overhangs used this to get some extra un-measured LWL to beat the rating rules of the day. As the boat goes faster the bow and stern are immersed deeper in the wave made by the boat. This also increases waterline. In the 19th century sailing ship speeds were often expressed with a hull speed factor. A ship might have a speed factor of 1.17, meaning it can make a speed of 1.17 x sqrt(lwl). There are conditions where you can exceed the theoretical hull speed. Surfing down a wave for example. When surfing or planing the hull is not in a displacement mode. So hull speed may be a bit of a moving target.

Ballast Ratio

BR = Ballast/Disp

The ballast ratio is a measure of the percentage of a boats displacement taken up by ballast. It can give some indication of how stiff or tender a boat may be. Note that it takes no account of the location of the ballast or of the hull shape of the boat. Two boats can have the same ballast ratios with very different righting moments. If the hulls are the same, boat A with all it's ballast in a bulb at the bottom of the keel will be stiffer then boat B with a long shoal draft keel even though they may have the same BR. Racing boats tend to have higher BR's then cruising boats.

Waterline to Beam Ratio

LWL/B = LWL/Beam

This is the waterline length divided by the overall beam. All other factors being equal (of course they never are) the longer boat will be faster (in displacement mode, not planing/surfing). Waterline beam might be interesting to know but it is not a commonly reported figure.

Overhang Ratio


This is the overall length minus the waterline length divided by the overall length. A larger value indicates longer overhangs. A value of 0 would mean no overhangs. Boats with longer overhangs have more reserve buoyancy. Also, as a boat moves faster the bow and stern waves move to the ends of the boat. Longer overhangs let the waves get longer. The overhang ratio has been influenced by rating rules. Under rules that penalize LWL more then LOA longer overhangs developed. The IMS rule has lead to shorter overhangs. Moderate overhangs are considered by some to be good for ocean voyaging boats. The reserve buoyancy helps keep the bow from submerging in waves and helps reduce pitching.

Capsize Screening Formula

CSF = Beam/(Disp/64.2)1/3

The capsize screening formula is a somewhat controversial figure. It came into being after the 1979 Fastnet race in England where a storm shredded the race fleet. The Cruising Club of America (CCA) put together a technical committee that analyzed race boat data. They came up with this formula to compare boats based on readily available data. A lower value is supposed to indicate a boat is less likely to capsize. a value of 2 is taken as a cut off for acceptable to certain race committees. However this is an arbitrary cutoff based on the performance of boats in the '79 Fastnet. The CSF takes no account of hull shape or ballast location. The CCA characterizes the formula as "rough". They go on to say that "While the capsize screening formula places a limit on excess beam, which is important for good stability range, it does not control for another main determinant, ballasting. With only simple data, this is as far as we can go." Naval Architect Robert Perry calls it,"...far too simplistic to be always accurate, but it is one of the currently popular ways of looking at a boat's offshore suitability." (Sailing Magazine, Nov. 2001, p.44).

Prismatic Coefficient

Cp = (displacement / 64) / (midship area x LWL)

The Prismatic Coefficient is the ratio between the actual underwater volume of the boat and an imaginary prism made from the mid-ship section area x the LWL. That's the volume the boat would have if it didn't taper for and aft of the largest cross section area. Displacement hulls require a Cp between .51 and .56 for best efficiency with .54 as the optimum (Gerr). The Cp is a measure of the fineness of the ends of the boat. A block of wood would have a Cp of 1. High speed planing boats have Cp in the 0.72 to 0.78 range because they carry the max mid-ship area all the way aft to provide a large planing surface.

This really isn't a complete list, however the other calculations require a high level understanding of naval architeture or marine engineering. The formulas presented here are a good general set to predict speed with a simple calculator and the spec. sheets for a boat.

Also these most of these formulas only work with displacement craft. Planing craft require computer models to predict speed.

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