catamaran hull design, catamaran design, catamaran designers, displacement catamaran, catamaran hulls, catamaran hull shape
There's been a lot of recent interest in catamaran performance and the catamaran designs that define performance. This page contains notes on boat hull design goals and the mathematical formulas used in catamaran hull design. The content of this page was taken from two impeccable sources. The first section was reproduced from the maestro of Catamaran designs, renown British maval architect, Richard Woods, who has a lot to say on the subject of catamaran hull design. jump directly to this section The 2nd section from a paper on "How to dimension a sailing catamaran", written by a Finnish boat designer by the name of 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. jump directly to this section |
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When it's all said and done, the performance of a sailing catamaran is dependent on three primary specs: length, sail area and weight. If the boat is longer it generally means it's a faster boat. If she has more sail area, it means she's a faster boat and if she's light it means she's a faster boat. Of course, there are limits: Too much sail area capsizes the boat in brisk winds. If the boat is designed too light, she will not take any kind of punishment. Too slim a hull design and the boat becomes a large Hobie Cat capable of only carrying your lunch. Of course, too long and large and you'd have to be Bill Gates to afford one. Then there are lot of additional and very important factors like underwater hull shape, aspect ratios of boards and sails, wet deck clearance, rotating or fixed rigging and so on. |
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| Catalac 8M Performance Specs |
| All Catamarans are not equal, but all boats have two things in common: They travel on
water and they're wind powered, so the Catamaran design equations in the 2nd section of this page should apply
to every catamaran from a heavy cruising Cat to a true ocean racer. |
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Richard Wood's comments on catamaran design: |
| We all know that multihulls can be made faster by making them longer or
lighter or by adding more sail. Those factors are the most important and why they are used as
the basis of most rating rules. However using just those figures is a bit like determining a
cars performance just by its hp and curbside weight. It would also imply that a Tornado would
sail as fast forwards as backwards (OK, I know I just wrote that a Catalac went faster
backwards than forwards) So what next?? Weight and length can be combined into the Slenderness Ratio (SLR). But since most multihulls have similar Depth/WL beam ratios you can pretty much say the SLR equates to the LWL/BWL ratio. Typically this will be 8-10:1 for a slow cruising catamaran (or the main hull of most trimarans), 12-14:1 for a performance cruiser and 20:1 for an extreme racer. So by and large faster boats have finer hulls. But the wetted surface area (WSA) increases proportionately as fineness increases (for a given displacement the half orange shape gives the least WSA) so fine hulls tend to be slower in low wind speeds. The most important catamaran design hull shape factor, is the Prismatic Coefficient (Cp). This is a measure of the fullness of the ends of the hull. Instinctively you might think that fine ends would be faster as they would “cut through the water better”. But in fact you want a high Cp for high speeds. However everything is interrelated. If you have fine hulls you can use a lower Cp. Most monohulls have a Cp of 0.55- 0.57. And that is about right for displacement speeds. However the key to Catamaran design is you need a higher Cp if you want to sail fast. So a multihull should be at least 0.61 and a heavy displacement multihull a bit higher still. It is difficult to get much over 0.67 without a very distorted hull shape or one with excessive WSA. So all multihulls should have a Cp between 0.61 and 0.65. None of this is very special or new. It has been well known by naval architects for at least 50 years. There are various ways of achieving a high Cp. You could fit bulb bows (as Lock Crowther did). Note this bow is a bit different from those seen on ships (which work at very specific hull speeds - which are very low for their LOA). But one problem with them is that these tend to slam in a seaway. Another way is to have a very wide planing aft section. But that can increase WSA and leads to other problems I’ll mention in a minute. Finally you can flatten out the hull rocker (the keel shape seen from the side) and add a bustle aft. That is the approach I use, in part because that adds displacement aft, just where it is most needed. I agree that a high Cp increases drag at low speeds. But at speeds over hull speed drag decreases dramatically on a high Cp boat relative to one with a low Cp. With the correct Cp drag can be reduced by over 10%. In other words you will go 10% faster (and that is a lot!) in the same wind and with the same sails as a boat with a unfavorable Cp. In light winds it is easy to overcome the extra drag because you have lots of stability and so can fly extra light weather sails. The time you really need a high Cp boat is when beating to windward in a big sea. Then you don’t have the stability and really want to get to your destination fast. At least I do, I don’t mind slowly drifting along in a calm. But I hate “windward bashing” But when you sail to windward the boat pitches. The sea isn’t like a test tank or a computer program. And here I agree with Evan. Immersed transoms will slow you down (that is why I use a narrower transom than most designers). I also agree with Evan (and why not, he knows more about Volvo 60 design than nearly anyone else on the planet) in that I don’t think you should compare a catamaran hull to a monohull, even a racing one. Why chose a Volvo 60/Vendee boat with an immersed transom? Why not chose a 60ft Americas Cup boat with a narrow out of the water transom?? To be honest I haven’t use Michelet so cannot really comment. But I have tested model catamarans in a big test tank and I know how inaccurate tank test results can be. I cannot believe that a computer program will be better. It would be easy to prove one way or the other though. A catamaran hull is much like a frigate hull (similar SLR, L/B ratios and Froude numbers) and there is plenty of data available for those. There is also a lot of data for the round bilge narrow non planing motorboats popular in the 1930’-50’s which again are similar to a single multihull hull. One of the key findings I discovered with my tank test work was just how great the drag was due to wave interference between the hulls. Even a catamaran with a modern wide hull spacing had a drag increase of up to 20 % when compared to hulls at infinite spacing. One reason why just flying a hull is fast (the Cp increases when you do as well, which also helps). So you cannot just double the drag of a single hull and expect to get accurate results. And any speed prediction formula must include a windage factor if it is to give meaningful results. About 25 years ago we sailed two identical 24ft Striders next to each other. They were the same speed. Then we moved the crew of one boat to the bow. That boat IMMEDIATELY went ½ knot faster. That is why I now arrange the deck layout of my racing boats so that the crew can stay in front of the mast at all times, even when tacking or using the spinnaker. I once raced against a bridge deck cabined catamaran whose skipper kept the 5 crew on the forward netting beam the whole race. He won. Richard Woods of Woods Designs www.sailingcatamarans.com |
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Catalac 8M design specs |
| Catamaran design formulas
from Terho Halme's Paper
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| This next section has the 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. |
| Length, Draft and Beam |
| There are two major dimensions of a boat hull: The length of the hull LH
and length of waterline LWL
. The following consist of arbitrary values to illustrate a calculated example.
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| LH
= 12.20 LWL
= 12.00 |
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| Figure 1 |
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| After deciding how big a boat we want we next enter the
length/beam ratio of each hull, LBR. Heavy boats have
low value and light racers high value. LBR
below "8" leads to increased wave making and this should be avoided. Lower values increase
loading capacity. Normal LBR
for a cruiser is somewhere between 9 and 12. LBR
has a definitive effect on boat displacement estimate. |
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| B WL= LWL/ LBR | In this example LBR = 11.0 and beam waterline B WL will be: |
| Figure 2 |
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| BWL= 1.09 | A narrow beam, of under 1 meter, will be impractical
in designing accommodations in a hull.
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| B TR = B WL / T c | 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 TR between 1.1 and 1.4. B TR has also effect on boat displacement estimation. |
| T
c = B
WL / B
TR T c = 0.57 |
Here we put B
TR = 1.9 to minimize boat resistance (for her size)
and get the draft calculation for a canoe body T c
(Figure 1).
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Midship coefficient - C m |
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| C m = A m / T c (x) B WL | We need to estimate a few coefficients of the canoe body. where A m is the maximum cross section area of the hull (Figure 3). C m depends on the shape of the midship section: a deep-V-section has C m = 0.5 while an ellipse section has C m = 0.785. Midship coefficient has a linear relation to displacement. In this example we use ellipse hull shape to minimize wetted surface, so C m = 0.785 |
| Figure 3 |
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| Prismatic coefficient - Cp | |
| Cp= D/ Am× LWL | where D is the displacement volume (m
3
) of the boat. Prismatic coefficient has an influence on boat resistance. C
p 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
p := 0.59
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| Water plane coefficient - Cw | |
| Cw = Aw / BWL× LWL | where Aw is water plane (horizontal) area. Typical value for water plane coefficient is Cw = 0.69 - 0.72. In our example Cw = 0.71 |
| Fully loaded displacement - mLDC | |
| mLDC
= 2 × BWL x LWL×
T c × C
p × C
m × 1025 mLDC = 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 |
| Length/displacement -ratio - LDR | |
LDR = 6.3 |
LDR 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 LDR 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 LDR in a glass-sandwich built cruising catamaran. To adjust LDR and fully loaded displacement mLDC , change the length/beam ratio of hull, LBR . |
| Empty boat displacement - m LCC | |
| mLCC=
0.7 × mLDC mLCC= 4995 |
We can now estimate our empty boat displacement (kg): This value must be checked after weight calculation or prototype building of the boat. |
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Light loaded displacement - m moc |
| mmoc=
0.8 × m LDC mmoc = 5709 |
The light loaded displacement mass (kg); this is the mass we will use in stability and performance prediction: |
| Beam of sailing catamaran | |
| 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 M ). The beam between hull centers is named B CB (Figure 4) and remember that the overall length of the hull is L H . | |
| Figure 4 |
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Length/beam ratio of the catamaran - L BRC |
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LBRC = LH / BCB |
If we set L BRC = 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. |
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BCB = LH / LBRC BCB = 5.55 |
Beam between hull centers (m) - B CB |
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BMT
= 2[(BWL3
× LWL x Cw2
/ 12) +( LWL × BWL
× Cw x (0.5BCB
)2 )] × (1025 / mLDC
) |
Transversal height from the center of buoyancy to metacenter, BMT can be estimated |
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Longitudinal height from the center of buoyancy to metacenter, BML can be estimated. Too low value of BML (well under 10) will make her sensitive to hobby-horsing |
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BH1 = 1.4 × BWL |
We still need to determine the beam of one hull BH1 (Figure 4). If the hulls are asymmetric above waterline this is a sum of outer hull halves. BH1 must be bigger than BWL of the hull. We'll put here in our example: |
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BH = BH1 + BCB BH = 7.07 |
Now we can calculate the beam of our catamaran B H (Figure 4): |
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ZWD
= 0.06 × L
WL |
Minimum wet deck clearance at fully loaded condition is defined here to be 6 % of L WL : |
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EU Size factor |
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SF=1.75 x mmoc
SF = 82 x 103 |
While the length/beam ratio of catamaran, L
BRC 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. |
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Engine Power Requirements |
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Pm = 4 x (mLDC /1025) Pm = 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 |
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Vm
= 2.44 Vm = 8.5 |
Motoring speed (knots) |
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Vol = 1.2(Rm / Vm )(con x Pm ) Vol = 356 |
motoring range in nautical miles R m = 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 |
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