What the 1.34 is
A hull moving through water makes a wave at the bow and another at the stern. The length of a surface wave is tied to its speed, and as the boat speeds up, its own bow wave lengthens. At a speed of about 1.34 times the square root of the waterline length in feet, the wave is as long as the boat, so the hull sits in a trough of its own making with the bow wave at the bow and the stern wave at the stern. Going faster means climbing the back of that bow wave, and the power to do it rises steeply — steeply enough that on most displacement hulls the throttle stops buying speed and starts buying noise, wake and fuel burn.
On a thirty foot waterline that lands at 7.34 knots. Not 7.34 as a ceiling enforced by physics, but 7.34 as the speed past which each additional tenth of a knot costs a disproportionate amount.
Why it is a rule of thumb and not a law
The 1.34 coefficient describes a typical hull of moderate beam and displacement. Change the hull and the number moves. A long slender hull with little wave-making — a rowing shell, a catamaran hull, a fine-ended displacement powerboat — exceeds it comfortably, and designers routinely work at 1.5 or higher without anything unusual happening. A short, beamy, heavily laden hull with blunt ends may never get there at all, because it runs out of practical power first.
What survives across all of them is the shape of the curve rather than the exact number. Resistance rises gently, then very sharply, and the sharp part starts near the speed-length ratio the boat was designed around. Knowing where your boat sits on that curve is worth more than the single figure at the top of the page.
Planing is a different problem entirely
A planing hull does not solve the wave-making problem, it leaves it. Past a speed-length ratio somewhere around two to three, a hull with the right shape — flat or vee bottom, hard chines, a sharp transom that lets water separate cleanly — generates enough dynamic lift to rise and skim rather than push through. Once it does, waterline length stops governing speed and weight-to-power does. That is why hull speed says nothing useful about a bass boat and everything about a trawler.
The transition itself is the awkward zone. Between hull speed and full planing, the boat is bow-up, dragging, burning fuel at a rate that buys very little speed, and running with poor visibility over the bow. Semi-displacement hulls are designed to live there and do it acceptably. Displacement hulls pushed there just make an enormous wake.
The Crouch formula, and what it is worth
For planing boats the traditional estimate is Crouch: speed in miles per hour equals a constant divided by the square root of displacement in pounds per shaft horsepower. The constant encodes the type of boat — around 150 for an average runabout or light cruiser, 190 for a racing catamaran. A three thousand pound boat with two hundred horsepower at the prop is fifteen pounds per horsepower, square root 3.87, so 150 divided by 3.87 gives about 39 mph.
Treat that as an order-of-magnitude figure. It knows nothing about your hull bottom, your propeller, your trim, your bottom condition or the load distribution, and every one of those is worth several miles per hour. It is genuinely useful for a sanity check when someone tells you what a repower will do. Whether the engine is actually able to deliver its power to the water is a propping question, covered on the propeller pitch and slip calculator, and the displacement you should be feeding into it is the loaded one from the boat weight and capacity planner, not the dry weight in the brochure.
Waterline length is not length overall
Two boats of the same advertised length can have very different waterlines, and the waterline is what goes into the formula. A traditional hull with long overhangs at bow and stern has a short waterline at rest and a longer one when heeled or settled, which is one reason such boats sail faster than their static numbers suggest. A modern plumb-ended hull of the same overall length has nearly all of it in the water and a correspondingly higher hull speed. If you are comparing boats, compare waterlines. And measure it loaded, because a cruising boat with a season of stores aboard sits deeper and floats on more length than the drawing shows.
Questions people ask
What is the hull speed formula?
Hull speed in knots is about 1.34 times the square root of the waterline length in feet. A 25 foot waterline gives 1.34 times 5, or 6.7 knots. A 36 foot waterline gives 1.34 times 6, or 8.04 knots. The square root is what makes long boats so much faster in displacement mode: doubling the waterline only multiplies the speed by about 1.41, but that is still a very large gain for a hull that was never going to plane. Note the units are knots and feet as a pair — the coefficient changes if you work in other units.
Can a boat go faster than its hull speed?
Yes, and many do. The figure describes where wave-making resistance climbs sharply, not a wall. Long slender hulls, multihulls and fine-ended displacement powerboats regularly work at speed-length ratios of 1.5 and above, and any planing hull leaves the whole concept behind once it is up. What is true is that pushing a conventional displacement hull past its hull speed costs power out of all proportion to the speed gained, and produces a large stern wave and a bow-up attitude while it does. That is a real effect even though the number is a rule of thumb.
Does hull speed apply to my planing boat?
Only below planing speed, which for most planing boats means at idle, in a no-wake zone, or when the boat is too heavily loaded or underpowered to get up. In that condition it behaves like a displacement hull and the same wave-making limit applies, which is why an overloaded planing boat feels like it has hit a wall around six or seven knots. Once the hull is on plane, waterline length stops setting the speed and the ratio of weight to power takes over. The two regimes are genuinely different problems with different arithmetic.
What waterline length should I use?
The length the hull actually touches water for, with the boat loaded the way you use it. That is not length overall, which includes overhangs, bow pulpits, swim platforms and outboard brackets. On boats with significant overhangs the difference can be several feet, and several feet on a thirty foot boat is a meaningful change to the square root. If you cannot measure it, look for the designed waterline in the specifications rather than the marketing length, and remember that adding weight lengthens the waterline slightly on an overhanging hull and does nothing but slow a plumb-ended one.
How accurate is the Crouch formula?
It is a first approximation and should be treated as one. It uses only weight, power and a single constant for hull type, and it therefore cannot know about bottom shape, deadrise, running surface, propeller efficiency, trim, appendage drag or bottom fouling — all of which move the answer, sometimes by ten percent or more each. What it is good for is scale: telling you whether a proposed repower is likely to yield five more miles per hour or fifteen, and catching claims that are obviously implausible. It is not a substitute for a sea trial with the load you actually carry.