displacement catamaran speed

Hull Speed Calculator

Table of contents

Welcome to the hull speed calculator . If you've ever seen a boat go so fast that its nose started rising, then you've seen the concept of hull speed in action. In this article, we'll explain what hull speed is and what it means for a ship's design. Later, we'll show you how to calculate hull speed with the hull speed formula, so that you can work out how to calculate hull speed for your own boat.

What is hull speed?

Hull speed is the speed at which a vessel with a displacement hull must travel for its waterline to be equal to its bow wave's wavelength. A displacement hull travels through water, instead of on top of it as a planing hull (like a kiteboard ) would, thereby displacing water with its buoyancy as it sails. The pressure that this displacement exerts on the water creates a wave; this wave is known as the vessel's bow wave . A slow-moving boat's bow wave might make small waves, but, as the boat sails faster, the bow wave's wavelength λ \lambda λ grows. When the wavelength meets the waterline length (that's also when the bow wave's first and second crests are at opposite tips of the waterline), the boat is said to be traveling at hull speed. Take a look at the picture below to see what we mean:

A diagram of a boat's waterline versus the bow wave's wavelength.

Why does hull speed matter?

Although it's not perfect, hull speed remains a useful concept that can help us answer questions about how fast a sailboat can go, and the optimal amount of thrust you need to keep a boat moving forward.

A boat's hull speed limits how fast it can travel efficiently. When traveling at hull speed, the boat's bow wave and stern wave have synchronized and constructive interference occurs, which allows the boat to move very efficiently. However, at speeds greater than hull speed, a vessel's nose automatically starts rising as the vessel tries to climb its bow wave. This process is called planing , and it wastes lots of energy. Trying to move faster than the hull speed will therefore require more and more thrust (whether that comes from sails, rowing, or engines) in exchange for smaller and smaller gains in speed as more energy is wasted angling the boat upwards. Hull speed can therefore be said to impose a flat limit on how fast a sailboat can go.

Shortcomings of hull speed

Although the physics behind hull speed is sound, it is heavily dependent on the hull's shape. Long and thin hulls with piercing designs can easily break their hull speed without planing. Such hulls are found on:

Catamarans; and
Competitive kayaks.

A hull's design can enable it to circumvent the workings of hull speed. It is for this reason that hull speed is not used in present-day ship design; naval institutions nowadays favor more modern measurements of speed-to-length ratio, such as the Froude number .

How to calculate hull speed

The formula for hull speed only needs the length of the vessel's waterline in feet, denoted as L waterline L_\text{waterline} L waterline . With this length, the vessel's hull speed in knots can be calculated with

If you want to instead work out exactly how long your new boat's waterline must be for it to have a certain hull speed, you can invert the formula to obtain

How to use the hull speed calculator

The hull speed calculator is just as easy to use as the formula.

Enter your vessel's waterline length into the first field. This is the length of your boat's hull at the height of the waterline. Your vessel's hull speed will then be calculated and presented in the second field.

You can also use the hull speed calculator backward to work out how long a vessel's waterline must be if you know its hull speed.

You can freely change the units of your measurements without interfering with the hull speed formula.

How can I increase my boat's hull speed without changing its hull?

Load your boat heavier! If you think about a normal displacement hull, it's usually narrower near the bottom than at the deck. So pushing it down with some weight will lengthen the boat's waterline, and so its hull speed is increased. Of course, heavier boats are harder to move, so while your loaded boat now has a higher hull speed, you would need more power to move it.

Waterline length

The length of the ship at its waterline.

The speed at which the ship's waterline length equals its bow wave's wavelength.

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Catamaran Design Formulas

Post author By Rick
Post date June 29, 2010
10 Comments on Catamaran Design Formulas

Part 2: W ith permission from Terho Halme – Naval Architect

While Part 1 showcased design comments from Richard Woods , this second webpage on catamaran design is from a paper on “How to dimension a sailing catamaran”, written by the Finnish boat designer, Terho Halme. I found his paper easy to follow and all the Catamaran hull design equations were in one place. Terho was kind enough to grant permission to reproduce his work here.

Below are basic equations and parameters of catamaran design, courtesy of Terho Halme. There are also a few references from ISO boat standards. The first step of catamaran design is to decide the length of the boat and her purpose. Then we’ll try to optimize other dimensions, to give her decent performance. All dimensions on this page are metric, linear dimensions are in meters (m), areas are in square meters (m2), displacement volumes in cubic meters (m3), masses (displacement, weight) are in kilograms (kg), forces in Newton’s (N), powers in kilowatts (kW) and speeds in knots.

Please see our catamarans for sale by owner page if you are looking for great deals on affordable catamarans sold directly by their owners.

Length, Draft and Beam

There are two major dimensions of a boat hull: The length of the hull L H and length of waterline L WL . The following consist of arbitrary values to illustrate a calculated example.

L H = 12.20 L WL = 12.00

After deciding how big a boat we want we next enter the length/beam ratio of each hull, L BR . Heavy boats have low value and light racers high value. L BR below “8” leads to increased wave making and this should be avoided. Lower values increase loading capacity. Normal L BR for a cruiser is somewhere between 9 and 12. L BR has a definitive effect on boat displacement estimate.

B L / L	In this example L = 11.0 and beam waterline B will be:
Figure 2
B = 1.09	A narrow beam, of under 1 meter, will be impractical in designing accommodations in a hull.
B = B / T	A value near 2 minimizes friction resistance and slightly lower values minimize wave making. Reasonable values are from 1.5 to 2.8. Higher values increase load capacity. The deep-V bottomed boats have typically B between 1.1 and 1.4. B has also effect on boat displacement estimation.

T = B / B T = 0.57	Here we put B = 1.9 to minimize boat resistance (for her size) and get the draft calculation for a canoe body T (Figure 1).
	Midship coefficient – C
C = A / T (x) B	We need to estimate a few coefficients of the canoe body. where A is the maximum cross section area of the hull (Figure 3). C depends on the shape of the midship section: a deep-V-section has C = 0.5 while an ellipse section has C = 0.785. Midship coefficient has a linear relation to displacement. In this example we use ellipse hull shape to minimize wetted surface, so C = 0.785
Figure 3


C =D / A × L	where D is the displacement volume (m ) of the boat. Prismatic coefficient has an influence on boat resistance. C is typically between 0.55 and 0.64. Lower values (< 0.57) are optimized to displacement speeds, and higher values (>0.60) to speeds over the hull speed (hull speed ). In this example we are seeking for an all round performance cat and set C := 0.59


C = A / B × L	where A is water plane (horizontal) area. Typical value for water plane coefficient is C = 0.69 – 0.72. In our example C = 0.71


m = 2 × B x L × T × C × C × 1025 m = 7136	At last we can do our displacement estimation. In the next formula, 2 is for two hulls and 1025 is the density of sea water (kg/m3). Loaded displacement mass in kg’s


L = 6.3	L near five, the catamaran is a heavy one and made from solid laminate. Near six, the catamaran has a modern sandwich construction. In a performance cruiser L is usually between 6.0 and 7.0. Higher values than seven are reserved for big racers and super high tech beasts. Use 6.0 to 6.5 as a target for L in a glass-sandwich built cruising catamaran. To adjust L and fully loaded displacement m , change the length/beam ratio of hull, L .


m = 0.7 × m m = 4995	We can now estimate our empty boat displacement (kg): This value must be checked after weight calculation or prototype building of the boat.


m = 0.8 × m m = 5709	The light loaded displacement mass (kg); this is the mass we will use in stability and performance prediction:


	The beam of a sailing catamaran is a fundamental thing. Make it too narrow, and she can’t carry sails enough to be a decent sailboat. Make it too wide and you end up pitch-poling with too much sails on. The commonly accepted way is to design longitudinal and transversal metacenter heights equal. Here we use the height from buoyancy to metacenter (commonly named B ). The beam between hull centers is named B (Figure 4) and remember that the overall length of the hull is L .

Figure 4


	Length/beam ratio of the catamaran – L
L = L / B	If we set L = 2.2 , the longitudinal and transversal stability will come very near to the same value. You can design a sailing catamaran wider or narrower, if you like. Wider construction makes her heavier, narrower means that she carries less sail.

B = L / L B = 5.55	Beam between hull centers (m) – B

BM = 2[(B × L x C / 12) +( L × B × C x (0.5B ) )] × (1025 / m ) BM = 20.7	Transversal height from the center of buoyancy to metacenter, BM can be estimated

BM = (2 × 0.92 x L × B x C ) / 12 x (1025 / m ) BM = 20.9	Longitudinal height from the center of buoyancy to metacenter, BM can be estimated. Too low value of BM (well under 10) will make her sensitive to hobby-horsing

B = 1.4 × B	We still need to determine the beam of one hull B (Figure 4). If the hulls are asymmetric above waterline this is a sum of outer hull halves. B must be bigger than B of the hull. We’ll put here in our example:

B = B B B = 7.07	Now we can calculate the beam of our catamaran B (Figure 4):

Z = 0.06 × L Z = 0.72	Minimum wet deck clearance at fully loaded condition is defined here to be 6 % of L :

	EU Size factor
SF=1.75 x m SF = 82 x 10	While the length/beam ratio of catamaran, L is between 2.2 and 3.2, a catamaran can be certified to A category if SF > 40 000 and to B category if SF > 15 000.

	Engine Power Requirements
P = 4 x (m /1025)P = 28	The engine power needed for the catamaran is typically 4 kW/tonne and the motoring speed is near the hull speed. Installed power total in Kw
V = 2.44 V = 8.5	Motoring speed (knots)
Vol = 1.2(R / V )(con x P ) Vol = 356	motoring range in nautical miles R = 600, A diesel engine consume on half throttle approximately: con := 0.15 kg/kWh. The fuel tank of diesel with 20% of reserve is then

Tags Buying Advice , Catamaran Designers

Owner of a Catalac 8M and Catamaransite webmaster.

10 replies on “Catamaran Design Formulas”

Im working though these formuals to help in the conversion of a cat from diesel to electric. Range, Speed, effect of extra weight on the boat….. Im having a bit of trouble with the B_TR. First off what is it? You don’t call it out as to what it is anywhere that i could find. Second its listed as B TR = B WL / T c but then directly after that you have T c = B WL / B TR. these two equasion are circular….

Yes, I noted the same thing. I guess that TR means resistance.

I am new here and very intetested to continue the discussion! I believe that TR had to be looked at as in Btr (small letter = underscore). B = beam, t= draft and r (I believe) = ratio! As in Lbr, here it is Btr = Beam to draft ratio! This goes along with the further elaboration on the subject! Let me know if I am wrong! Regards PETER

I posted the author’s contact info. You have to contact him as he’s not going to answer here. – Rick

Thank you these formulas as I am planning a catamaran hull/ house boat. The planned length will be about thirty six ft. In length. This will help me in this new venture.

You have to ask the author. His link was above. https://www.facebook.com/terho.halme

I understood everything, accept nothing makes sense from Cm=Am/Tc*Bwl. Almost all equations from here on after is basically the answer to the dividend being divided into itself, which gives a constant answer of “1”. What am I missing? I contacted the original author on Facebook, but due to Facebook regulations, he’s bound never to receive it.

Hi Brian, B WL is the maximum hull breadth at the waterline and Tc is the maximum draft.

The equation B TW = B WL/Tc can be rearranged by multiplying both sides of the equation by Tc:

B TW * Tc = Tc * B WL / Tc

On the right hand side the Tc on the top is divided by the Tc on the bottom so the equal 1 and can both be crossed out.

Then divide both sides by B TW:

Cross out that B TW when it is on the top and the bottom and you get the new equation:

Tc = B WL/ B TW

Thank you all for this very useful article

Parfait j aimerais participer à une formation en ligne (perfect I would like to participate in an online training)