Catamaran Design Formulas
with permission fromTerho Halme  Naval Architech
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.
LH = 12.20 LWL = 12.00
Figure 1  
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: 
Figure 2 

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 deepV 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 m depends on the shape of the midship section: a deepVsection 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  
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 glasssandwich 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. 



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 pitchpoling 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 



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 ) 
Transversal height from the center of buoyancy to metacenter, BMT can be estimated 



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 hobbyhorsing 


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


Z WD = 0.06 × L WL 
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 moc 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. 



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 = 2.44 V 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 
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