Part 2: With 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.
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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.
LH = 12.20 LWL = 12.00
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.
|B WL= LWL/ LBR||In this example LBR = 11.0 and beam waterline B WL will be:|
|BWL= 1.09||A narrow beam, of under 1 meter, will be impractical in designing accommodations in a hull. |
|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).|
|Midship coefficient – C m|
|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 mdepends 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|
|Prismatic coefficient – Cp|
|Cp=D / A m× LWL||where D is the displacement volume (m 3) of the boat. Prismatic coefficient has an influence on boat resistance. Cp 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|
|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 |
|We can now estimate our empty boat displacement (kg): This value must be checked after weight calculation or prototype building of the boat.|
|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 .|
|Length/beam ratio of the catamaran – L BRC|
|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.|
|B CB = LH / LBRC B CB = 5.55||Beam between hull centers (m) – B CB|
|BM T = 2[(BWL3 × LWL x Cw2 / 12) +( LWL × BWL × Cw x (0.5BCB )2 )] × (1025 / mLDC )|
BMT = 20.7
|Transversal height from the center of buoyancy to metacenter, BMT can be estimated|
BML = (2 × 0.92 x L WL3 × B WL x C w2 ) / 12 x (1025 / m LDC )
BML = 20.9
|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|
|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:|
|B H = BH1 + BCBB H = 7.07||Now we can calculate the beam of our catamaran B H (Figure 4):|
|Z WD = 0.06 × L WL |
Z WD = 0.72
|Minimum wet deck clearance at fully loaded condition is defined here to be 6 % of L WL :|
|EU Size factor|
|SF=1.75 x m mocSF = 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.
|Engine Power Requirements|
|P m = 4 x (mLDC /1025)P m = 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 m = 2.44V m = 8.5||Motoring speed (knots)|
|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|
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.
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)