Why waterline length sets hull speed
How a hull's own wave caps its speed, why waterline length is the key measurement, and when the 1.34 limit breaks.
The wave a hull makes
A moving displacement hull pushes water aside and generates a wave that peaks at the bow and again near the stern. At low speed several small waves fit along the hull, but as speed climbs the wave stretches out until just one long wave spans the waterline. At that point the boat is effectively sailing uphill out of the trough it has dug, and the power needed to go a fraction faster rises steeply. This wave-making resistance is what the hull speed formula captures.
Why length, and only the waterline part
The speed at which one wave matches the hull depends on that wave's length, and a wave's speed grows with the square root of its length. Because the governing wave spans the waterline, it is the waterline length that sets the limit, which is why the formula takes the square root of LWL. Overhanging bows and sterns that lift clear of the water add nothing, since they make no wave. This is also why heeling a sailboat or loading it deeper, both of which lengthen the waterline, can nudge the hull speed up.
Where the 1.34 comes from
The coefficient 1.34 bundles the physics of a deep-water wave into a single number tuned for feet and knots. It reflects a typical displacement hull whose governing wave travels at roughly the boat's speed when the wavelength equals the waterline. Fuller, heavier hulls behave as if the coefficient is a little lower, around 1.1, because they bury themselves in the wave sooner, while fine, light hulls act nearer 1.5. Fixing the value at 1.34 gives a fair middle estimate that suits most cruising monohulls.
When the limit does not hold
Hull speed is a soft ceiling for boats that stay in the water, but it stops applying once a hull can climb onto its own bow wave and plane. Planing powerboats, dinghies and modern skiffs skim across the surface and shrug off the wave-making penalty entirely. Long slender multihull floats also sidestep the formula because each hull is so narrow that its wave is tiny. For those craft the 1.34 line describes only the awkward transition zone they pass through on the way to much higher speeds.