Franklin
Don't miss the key word THEORETICALLY.Hull speed is theoretically 1.34 times the square root of your waterline. The key word is "theoretically." The formula needs to be adjusted according to the hull design and displacement of your boat. The formula is only a general guide to how fast your boat will sail.Among other things, the formula doesn't consider hull shape. A modern, light-weight, beamy, fin-keeled hull is certainly faster than a narrow, traditional full-keeled hull.In any scientific discussion of hull speed, reference is often made to Froude’s Law. Froude was a scientist who worked in the second half of the 19th Century doing much research work for the British Admiralty. The work was for warships so any references to sailing and Froude are probably distortions even though he did like yachting.He did his basic research on models of 3 ft, 6 ft and 12 ft for two different hull forms. He observed that when models were run at speeds in proportion to the square of their length they created similar wave patterns. In 1876 he gave his famous Law of Comparison which states that the resistances of similar ships are in the ratio of the cubes of their linear dimensions when their speeds are in the ratio of the square roots of those dimensions. This is equivalent to saying that the resistances vary as the cube of the scale when the speeds vary as the square root of the scale.Nowhere did Froude make reference to a maximum speed or an unattainable speed based on the waterline length. The hull speed is only a guide to a speed that should not be exceeded in the interest of fuel economy but then it might as well be 1.3 or maybe 1.4 or 1.2.When a vessel proceeds through the water it creates a wave train at the bow and another at the stern depending on the speed and the length on the waterline. If there is an interaction the resistance is higher than the smooth line ignoring all the interferences. If there is no interaction the resistance is less than the smooth “average” line so there is a series of humps and hollows. Although the LWL is the usual length used in resistance calculations the length actually depends on the pressure variation at the ends and it varies so that LWL is a kind of average used to simplify the problems.Hull speed is not an absolute limit. It is the approximate speed where a significant increase in power is needed to lift a vessel out of the bow wave that has lengthened with increasing speed until it is the same length as the waterline.The actual formula, as popularised by a book on Yacht design published in the early sixties, is:Hull speed in knots = C x sqrroot(waterline length in feet)where C is a constant varying with form. Yachtsman usually take it as 1.34 but it varies from about 1.42 for fine hulls to 1.18 for chunkier ones. It only pertains to displacement hulls and gives an approximation of the maximum speed a hull can achieve before the bow wave combines with the stern wave to dig a trough out of which the vessel would not be able to climb without using inordinate amounts of power. The formula needs to be used circumspectly and applied to hulls within reasonable limits. It cannot be used indiscriminately to prove absolute values for any hulls.The absurdity becomes apparent when a hull of infinte length is inserted into the formula. It is not self limiting. Thus a hull of a few millimetres could almost not move while an infinte one could move infintely fast. In fact the formula is not much use above about 200 feet and is in fact best utilised on small sailing dinghies. In fact the ocean literally teems with vessels exceeding their "hull speed" according to this formula.