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Why are longer boats faster?

2009 December 1

Why are longer boats faster?
Dear Boat Doctor,
I have a lot of interest in sailing and really want to learn more. I went to the Annapolis Boat Show this year and saw a lot of cool boats. I noticed that the performance boats seem to have different hull shapes than cruising boats. A friend told me all about hull shape and mentioned waterline length. He explained that a longer waterline makes for a faster boat. I don't completely understand this and would really like to. Can you explain how this works? Thanks.

Kristine Olstrom
Denver, Colorado

Dear Kristine,
Waterline length is an important factor but is not the ultimate controlling factor of hull speed, but your friend is correct, all things being equal a boat with a longer waterline will be faster.

It is first important to understand that a sailboat is essentially a displacement hull, meaning that it does not ride on top of the water, but needs to push water out of the way to flow through it. This is not absolutely true as almost any hull will surf on top of the water to some degree, given enough speed and a little help from some following seas, but the approximation is good enough for our purposes. As the hull moves through the water it acts as a piston and pushes a wave of water up at the bow. The bow wave crest forms a short distance in front of the boat, has a trough amidships, and another crest under the stern. The length of this wave is a function of the speed of the boat and the length of the waterline.

The theoretical hull speed of a boat is the maximum speed it can travel without surfing, it is commonly calculated by the formula 1.34 x ?LWL, where LWL is the waterline length in feet. For example, a boat with a 20-foot waterline length would have a hull speed of 6 knots, and a boat with a 40-foot waterline would have a hull speed of 8.5 knots.

When a boat reaches its hull speed, it gets practically trapped between its bow and stern crests. Regardless of the power applied with the sails or engine it cannot climb over the bow wave. You can see this readily when attempting to motor at a high speed. At moderate speeds a boat will motor just fine, but if you apply more and more power, the boat will not go much faster but will start to climb its bow wave a bit and will squat down in the stern.

Given this behavior, a boat will only go the speed of the wave it produces. The length of this wave is a function of the waterline length, thus a longer waterline will produce a longer wave.

A good next question is "Why are longer waves faster?" This answer is a bit more academic, but I'll attempt an answer. Given the basic physics motion formula, the velocity of a wave is equal to its wavelength times its frequency. Translating this to a water wave, the wavelength is the length of the wave, its velocity is the speed at which it moves, and the frequency is the number of crests per unit time. Keeping frequency constant, if we increase the length of the wave the velocity must increase because the longer distance (wavelength) must pass the distance in the same time. As I said, this is a little academic, you just need to accept that longer waves travel faster.