The secrets of a catamaran’s performance: the Length on Water Line
|17 May 2017||Posted by Caroline under Technical world|
To challenge conventional wisdom about sailing yachts’ performance, but also to stop endless bar talks about them, we would like to share a series of technical articles with you to provide key elements to compare catamarans with each other.
For the first topic, let us start with a simple but crucial element: the length of the hull or Length on Water Line (LWL).
What is the Length on Water Line?
The Length on Water Line or waterline length is an objective criterion to gage the speed performance of a boat. This is the maximum length of the underwater hull of a boat.
On a multihull, the Length on Water Line is measured on the hull starting from the end of the bow to the tip of the stern. Be careful not to mix up the LWL with the Length Over All or LOA, which is the maximum length of the boat taking into account all the parts even the above-water ones, like a bowsprit.
How can the Length on Water Line determine the speed performance of a boat?
When a boat hull moves on the surface of the water, it forms a wave system composed first of the bow wave, followed by the trough, and then another wave, called the stern wave.
The bow wave is circled on the below photos of the 52 F.
The 52 F’s bow wave
The horizontal distance between the crests of two waves is called the wavelength.
This wavelength increases with the speed of the boat, as shown in the drawing below.
Bertrand, C., 2014: Comment marchent les voiliers ? In Voiles et Voiliers
Given that a moving boat is trapped between her bow and stern wave, it becomes clear that a sailboat will reach her maximum speed when her wavelength is equal to her Length on Water Line. This speed is referred to as the hull speed.
Indeed, the faster the boat, the greater the bow wave will be, implying pitching and preventing her from going faster. This phenomenon is easily seen on a motorboat: at low speed, the trim is horizontal, and when accelerating, the boat rears up under the effect of her bow wave. She will then need a lot of energy to overcome this wave, which a motor boat does easily by speeding up. We will come back to this in an up-coming article.
Could we say that big sailing boats go faster than small ones?
We have just demonstrated above that the maximum speed of a boat is a function of her wavelength, and hence her Length on Water Line.
This correlation is expressed in the following formula* and will be used to determine the maximum speed of a boat:
Max hull speed= √((Length on Water Line x g) /( 2 x pi)) x 3600/1852
* Gerr, D., 1999: The Elements of Boat Strength: For Builders, Designers, and Owners, McGraw Hill Edition
Where g = 9.81m / s² is the universal gravitation number.
And Pi = 3.1416 …. Pi, sometimes called the Archimedean constant, is a number represented by the Greek letter of the same name (lowercase and italic): π.
This mathematical formula gives the following results:
Thus, it allows us to conclude that the longer the Length on Water Line, the better the speed performance of the boat.
Therefore, with this formula, one can objectively have a first measure to compare two catamarans with each other.
While a standard boat’s performances are limited by her maximum hull speed, multihulls and racing yachts are able to go beyond this speed. The famous victory of the Americans with their “small” 60-foot catamaran facing the New Zealanders and their “big” 90-foot monohull at the America’s Cup in 1988 is a good example. Indeed, beyond the size, there are also other elements that need to be considered in assessing the performance of a yacht such as the different forms of a hull, the ratio sail area/ displacement, width…
To be continued, in the next article.