[insert_php]
/*
function check_input($data)
{
$data = trim($data);
$data = stripslashes($data);
$data = htmlspecialchars($data);
return $data;
}
$Nh= check_input($_POST[‘Nh’]);
*/

$html=””;

if (isset($_POST[‘Nh’])){
$Shape=$_POST[‘Shape’];
$Nh=$_POST[‘Nh’];
$Lh=$_POST[‘Lh’];
$Lwl=$_POST[‘Lwl’];
$Lbr=$_POST[‘Lbr’];
$Btr=$_POST[‘Btr’];
$Ltr=$_POST[‘Ltr’];
$Cm=$_POST[‘Cm’];
$Cp=$_POST[‘Cp’];
$Cw=$_POST[‘Cw’];
$Lbrc=$_POST[‘Lbrc’];

$kp=$_POST[‘kp’];
$ke=$_POST[‘ke’];
$kj=$_POST[‘kj’];
$Fbi=$_POST[‘Fbi’];
$Bas=$_POST[‘Bas’];
$Vawk=$_POST[‘Vawk’];
$AlphaL=$_POST[AlphaL];
$LambdaA=$_POST[LambdaA];

$engine_power=$_POST[‘engine_power’];
$con=$_POST[‘con’];
$Rm=$_POST[‘Rm’];

//beam of waterline
$Bwl=$Lwl/$Lbr;
$Bwl= round($Bwl, 3);
//—————–
//Tc
$Tc=0;
$tc_html=””;
if (($Btr != ‘-‘) || ($Btr != ‘0’) && is_numeric($Btr) ){
$Tc= $Bwl/$Btr; $Tc= round($Tc, 3);
$Ltr=$Lwl/$Tc; $Ltr=round($Ltr, 3); //If we know Btr, we can calculate Ltr
$tc_html=”Tc = Bwl / Btr = $Tc meters
note: Tc is calculated using Beam to Draft Ratio of hull. Now we can easily calculate Length to Draft Ratio:
Ltr = Lwl / Tc = $Ltr“;
}else{
$Tc= $Lwl/$Ltr; $Tc= round($Tc, 3);
$Btr=$Bwl/$Tc; $Btr=round($Btr, 3); //If we know Ltr, we can calculate Btr
$tc_html=”Tc = Lwl / Ltr = $Tc meters
note: Tc is calculated using Length to Draft Ratio of hull. Now we can easily calculate Beam to Draft Ratio:
Btr = Bwl / Tc = $Btr“;
}
//—————–
//Displacement
$Mldc=2 * $Bwl * $Lwl * $Tc * $Cp * $Cm * 1025; $Mldc=round($Mldc, 2); //fully loaded
$Mlcc=0.7*$Mldc; $Mlcc=round($Mlcc, 2); //empty boat
$Mmoc=0.8*$Mldc; $Mmoc=round($Mmoc, 2); //light loaded
//—————–
//Lrngth to Displacement Ratio
$tmp=1025/$Mldc;
$Ldr=$Lwl*(pow($tmp, 1/3)); $Ldr=round($Ldr,2);
$ldr_note=””;
if ($Ldr>4 &&$Ldr<5.7){$ldr_note="The catamaran is a heavy one and made from solid laminate.";} if ($Ldr>5.65 &&$Ldr<6.2){$ldr_note="The catamaran has a modern sandwich construction.";} if ($Ldr>6.1 &&$Ldr<7.6){$ldr_note="The catamaran is a performance cruiser.";} if ($Ldr>7.5){$ldr_note=”The catamaran is a big racer or super high tech beast.”;}
//—————–
//Beam of Catamaran
$Bcb=$Lh/$Lbrc; $Bcb=round($Bcb,3); //beam of catamaran between center
if ($Shape==’U’){
$Bh1=1.4*$Bwl; $Bh1=round($Bh1,3); //max beam of hull, U shape
}else if($Shape==’Y’){
$Bh1=2.08*$Bwl; $Bh1=round($Bh1,3); //max beam of hull, Y shape
}
$Bh=$Bcb+$Bh1; $Bh=round($Bh,2); //max beam of catamaran
$Bh_pr=$Lh/$Bh; $Bh_pr=100/$Bh_pr; $Bh_pr=round($Bh_pr, 1);
//—————–
//Wet deck clearance
$Zwd=0.06*$Lwl; $Zwd=round($Zwd, 2);
//—————–
//EU Size Factor
$tmp=$Lh*$Bcb;
$Sf=1.75*$Mmoc*(pow($tmp, 1/2)); $Sf1=$Sf/1000; $Sf1=round($Sf1,1); //x10 na 3ta
$eu_category=””;
if($Sf1>15 && $Sf1<40){$eu_category="The catamaran can be certified to a B category.”;}else if($Sf>40){$eu_category=”The catamaran can be certified to a A category.”;}
//—————–
//Powering
$Pm=$engine_power*($Mldc/1025); $Pm=round($Pm, 3);
$Vm=2.44*(pow($Lwl, 1/2)); $Vm=round($Vm, 3);
$Vm_kmh=$Vm/0.539957; $Vm_kmh=round($Vm_kmh, 3);
$Vol=1.2*($Rm/$Vm)*$con*$Pm; $Vol=round($Vol);
//—————–
//Sails————
$P=$kp*$Lwl/100; $P=round($P, 2);
$E=$ke*$Lwl/100; $E=round($E, 2);
$I=0.85*($P+$Bas); $I=round($I, 2);
$J=$kj*$Lwl/100; $J=round($J, 2);

$Lambda_m = $P/$E; $Lambda_m = round($Lambda_m, 1);
$Lambda_f = $I/$J; $Lambda_f = round($Lambda_f, 1);
$Ams = 0.7*$P*$E; $Ams=round($Ams, 2);
$Aft = 0.5*$I*$J; $Aft=round($Aft, 2);
$As = $Ams + $Aft; $As=round($As, 2);
$Ag = 1.65*$I*$J; $Ag=round($Ag, 2);

$Ha = (1.01*$P)+$Bas+$Fbi; $Ha=round($Ha, 2);
$Hlp= 0.04 * (pow($Mldc, 1/3)); $Hlp=round($Hlp, 2);
$Hms= $Fbi + $Bas + (0.4*$P); $Hms=round($Hms, 2);
$Hfs= $Fbi + (0.4*$I); $Hfs=round($Hfs, 2);
$Hce= (($Ams*$Hms)+($Aft*$Hfs))/$As; $Hce=round($Hce, 2);
//—————–
//Righting/heeling moment
$RMd=10*$Mldc*$Bcb/2; $RMd1=$RMd/1000; $RMd1=round($RMd1,1); //x 10 na 3та.
$HMd=0.16*$As*$Vawk*$Vawk*($Hce+$Hlp); $HMd1=$HMd/1000; $HMd1=round($HMd1,1); //x10 na 3ta
$Md=min($RMd, $HMd); $Md1=$Md/1000; $Md1=round($Md1, 1); //x10 na 3ta
//—————–
//Stability on sailing
$FGZmax= atan($Mmoc/(254*$Lwl*2*$Bwl*$Bcb)); $FGZmax_1=$FGZmax*180/3.14; $FGZmax_1=round($FGZmax_1,1);
$LMr= 9.4*$Mmoc*((0.5*$Bcb*cos($FGZmax)) – ($Fbi*sin($FGZmax))); $LMr1=$LMr/1000; $LMr1=round($LMr1,1); //x10 na 3ta
$Awp=2*$Cw*$Lwl*$Bwl; $Awp=round($Awp,2);
$LMp = 2.45*$Mmoc*$Awp/(2*$Bwl); $LMp=$LMp; $LMp1=$LMp/1000; $LMp1=round($LMp1,1); //x10 na 3ta
$tmp=($Lh+$Lwl)/$Bcb;
$LM=0;
if ($tmp >= 4){$LM=$LMr;}else{$LM= min($LMr, $LMp);}
$LM1= $LM/1000; $LM1=round($LM1,1);
$Vw=1.6*(pow(($LM/($As*($Hce+$Hlp))), 1/2)); $Vw=round($Vw, 2);
//—————–
//Appendages
$Fs=$LMr/($Hce+$Hlp); $Fs1=$Fs/1000; $Fs1=round($Fs1,1); //x10 na 3ta
$Vuw=(1.64*pow($Vw, 0.66)*pow($Lwl, 0.3)*pow($As, 0.4)*1852)/(pow($Mldc, 0.3)*3600); $Vuw=round($Vuw,2);
$Clh=(0.1*$AlphaL)/(1+(2*$Lwl/$Tc)); $Clh=round($Clh,3);
$Cpl=$Cp*$Cm/$Cw; $Cpl=round($Cpl, 2);
$Alp=$Cpl*$Tc*$Lwl; $Alp=round($Alp, 2);
$Fh=2*$Clh*0.5*1025*$Alp*pow($Vuw, 2); $Fh1=$Fh/1000; $Fh1=round($Fh1, 2); //x10 na 3ta
$Fsb=0.5*($Fs-$Fh); $Fsb1=$Fsb/1000; $Fsb1=round($Fsb1, 2); //x10 na 3ta
$Cl=(0.1*$AlphaL)/(1+(2/$LambdaA)); $Cl=round($Cl, 3);
$Ab=$Fsb/($Cl*0.5*1025*pow($Vuw, 2)); $Ab=round($Ab, 2);
//Centerboard
$Ad=0.75*$Ab; $Ad=round($Ad, 2);
$Td=pow(($LambdaA*$Ad), 1/2); $Td=round($Td, 2);
$Cd=$Ad/$Td; $Cd=round($Cd, 2);
//Rudder
$Ar=0.25*$Ab; $Ar=round($Ar, 2);
$Tr=pow(($LambdaA*$Ar), 1/2); $Tr=round($Tr, 2);
$Cr=$Ar/$Tr; $Cr=round($Cr, 2);
//—————–
//Performance
$tmp=(1.2454*pow($Cm, 3))-(1.4545*pow($Cm, 2))+(0.6935*$Cm)+0.8614; $tmp=$tmp*$Awp;
$Aws= pow((pow($Bwl, 2)+pow(2*$Tc, 2)), 1/2)*$tmp/$Bwl; $Aws=round($Aws, 2);
$SWR=$As/($Aws + (4*$Ab)); $SWR=round($SWR, 2);
$SDR=$As/pow(($Mldc/1025), 0.667); $SDR=round($SDR, 2);
$BN=pow(10.764*$As, 1/2)/pow(2.2046*$Mldc, 1/3); $BN=round($BN, 2);
//—————–
//Speed
$Vuw1=(1.64*pow($Vw, 0.66)*pow($Lwl, 0.3)*pow($As, 0.4))/pow($Mmoc, 0.3); $Vuw1=round($Vuw1, 2);
$Vuw2=(1.64*pow($Vw, 0.66)*pow($Lwl, 0.3)*pow(($Ams+$Ag), 0.4))/pow($Mmoc, 0.3); $Vuw2=round($Vuw2, 2);
//—————–
//Costs
$Euros=4*$Ldr*$Mlcc; $Euros=$Euros/1000; $Euros=round($Euros, 1); //x10 na 3ta
$Hours=$Ldr*$Mlcc/6; $Hours=$Hours/1000; $Hours=round($Hours, 1); //x10 na 3ta
//—————–
$html=”

Multihull Cruiser Calculations
for $Nh Hulls, $Lh meters long and $Shape-shape hull…

 



1. Beam of waterline:
Bwl = Lwl / Lbr = $Bwl meters


2. Draft (sinking of the hull):
$tc_html


3. Displacement:
Mldc = 2 * Bwl * Lwl * Tc * Cp * Cm * 1025 = $Mldc kg of water [fully loaded]
Mmoc = 0.8 * Mldc = $Mmoc kg of water [light loaded]
Mlcc = 0.7 * Mldc = $Mlcc kg of water [empty]


4. Length/Displacement Ratio:
Ldr = $Ldr
note: $ldr_note


5. Beam of Catamaran:
Maximal Beam of one hull (for $Shape-shape):
Bh1 = $Bh1 meters
Beam of catamaran between hull centers:
Bcb = $Bcb meters
Maximal beam of catamaran:
Bh = $Bhmeters [$Bh_pr% of Length]


6. Minimum Wet-Deck Clearance:
Zwd = $Zwd meters [on fully loaded conditions]


7. EU Size Factor:
Sf= $Sf1 x 103
note: $eu_category


8. Powering:
Required Engine Power:
Pm = $Pm KW
Motoring Speed:
Vm = $Vm knots [$Vm_kmh km/h]
 
Fuel Tank Size (with 20% reserve), for a range of $Rm nautical miles:
Vol = $Vol liters
 


9. Sails Dimensions:
Mainsail Luff:
P = $P meters
Mainsail Base:
E = $E meters
Fore triangle height:
I = $I meters
Fore triangle base:
J = $J meters
 
Mainsail aspect ratio:
Λm = P/E = $Lambda_m
Fore Triangle aspect ratio:
Λf = I/J = $Lambda_f
note: Change the value of kj to change Λf. Keep the value between 2.8 and 3.5 (best is 3.0 – 3.2).
 
Mainsail Area:
Ams = 0.7 * P * E = $Ams m2
Fore Triangle Area:
Aft = 0.5 * I * J = $Aft m2
Gennaker area:
Ag = 1.65 * I * J = $Ag m2
note: For calculating the sails area, a coefficient of 0.7 has chosen for high roach on the main sail; 0.5 is standard.
 
Total sail area:
As = Ams + Aft = $As m2
 
Air Draft:
Ha = 1.01*P + Bas + Fbi = $Ha meters
 
Height of underwater lateral center:
Hlp = $Hlp meters
Height of mainsail center:
Hms = $Hms meters
Height of fore triangle center:
Hfs = $Hfs meters
Height of center of effort:
Hce = (Ams*Hms + Aft*Hfs)/As = $Hce meters


 
10. Righting / heeling moment (ISO 12215-9):
Righting moment:
RMd = 10*Mldc*Bcb/2 = $RMd1 x 10 3 Nm
Heeling Moment:
HMd = 0.16*As*Vawk*Vawk*(Hce+Hlp) = $HMd1 x 10 3 Nm
note: The righting moment of catamaran is caused by the boat size. For the heeling moment is using the design wind speed, which for cruising catamaran <=18m is typically Vawk=32 knots. With the bigger catamarans can be lower, so you are able to adjust Vawk in the initial input of the calculator, to get the right Hmd.
 
Design moment of mast:
Md = min(RMd, HMd) = $Md1 x 10 3 Nm
note: On small catamarans the righting moment RMd is bigger than the heeling moment HMd and then the design moment is the righting moment. On bigger cat’s the opposite is true and so their design moment is the heeling moment. In general the smaller moment will be chosen.


11. Stability on sailing (ISO 12217-2)
note: For the safety sake a sailor need to know when it is the time to reef. In a catamaran this is indicated with the reefing wind speed, Vw (apparent wind).
 
Heel angle of maximum righting arm:
ΦGZmax = atan(Mmoc/(254*Lwl*2*Bwl*Bcb)); ΦGZmax=ΦGZmax*180/3.14 = $FGZmax_1 deg
 
Limiting moment in roll for a catamaran:
LMr = 9.4*Mmoc*((0.5*Bcb*cos(ΦGZmax)) – (Fbi*sin(ΦGZmax)))= $LMr1 x 10 3 Nm
 
Water Plane Area:
$Awp = 2*Cw*Lwl*Bwl = $Awp m2
 
Limiting Moment in pitch for catamaran:
LMp = 2.45*Mmoc*Awp/(2*Bwl) = $LMp1 x 10 3 Nm
 
Limiting Moment chosen to be used:
LM = $LM1 x 10 3 Nm
note: If the calculation of the estimated hull size (Lh+Lwh)/Bcb is >= 4, LMr will be used to calculate Vw. If the result is < 4, the lower value of (LMr, LMp) will be used
 
Reefing wind speed (apparent wind) will be:
Vw = 1.6*(square_root((LM/(As*(Hce+Hlp))))) = $Vw knots
note: If the reefing wind speed is unnecessarily high, simply increase the mainsail luff ratio kp, and if reefing wind speed is too low, decrease it.
 


12. Appendages
Builders of keel cats often add daggerboards to their designs, with the objective to market increased performance and safety. This usually results in a compromise when considering the hydrodynamic hull requirements of both types, which might differ substantially; proper integration, engineering, and construction become crucial factors.
The appendages as a hulls and/or boards need to create lift enough to have acceptable leeway.
 

Maximum Side Force of the catamaran:
Fs = LMr/(Hce+Hlp) = $Fs1 x 10 3 N
 
Maximum Boat Speed, using nominal sail area, fully loaded:
Vuw = (1.64*Vw0.66*Lwl0.3*As0.4*1852)/(Mldc0.3*3600) = $Vuw m/s
 
Next we’ll estimate how much side force is taken by the hulls. It will be handled by the hulls without using boards.
Lift coefficient of the hull:
Clh = (0.1*αL)/(1+(2*Lwl/Tc)) = $Clh
Longitudal prismatic coefficient of the hull:
Cpl = Cp*Cm/Cw = $Cpl
Lateral area of the hull:
Alp = Cpl*Tc*Lwl = $Alp m2
Lateral force (side force) of the hulls:
Fh = 2*Clh*0.5*1025*Alp*Vuw2 = $Fh1 x 10 3 N
 
The rest of the side force must be handled by the boards (daggerboards).
Lateral force (side force) of one board:
Fsb = 0.5*(Fs-Fh) = $Fsb1 x 10 3 N
Lift coefficient of boards:
Cl = (0.1*αL)/(1+(2/ΛA)) = $Cl
Lateral area of the boards in one hull:
Ab = Fsb/(Cl*0.5*1025*Vuw2) = $Ab m2
 
Centerboard
Centerboard must be around 75% of the board area.
Area of the centerboard:
Ad = 0.75*Ab = $Ad m2
Draft of the centerboard:
Td = (ΛA*Ad)1/2 = $Td m
Chord of the centerboard:
Cd = Ad/Td = $Cd m
 
Rudder
Rubber must be around 25% of the board area.
Area of the rudder:
Ar = 0.25*Ab = $Ar m2
Draft of the rudder:
Tr = (ΛA*Ar)1/2 = $Tr m
Chord of the rudder:
Cr = Ar/Tr = $Cr m


13. Performance
The performance of cruising catamaran is the actual reason for all calculations. It is the most important indicator is the input data will give us the fastest, the most economical and most secured vessel.
 
Wetted surface of catamaran:
Aws = … = $Aws m2
Sail area / wetted surface ratio (included boards):
SWR = As/(Aws+4*Ab) = $SWR
note:The sail area to wetted surface area ratio should be more than 2.5, to show a fast boat in light wind.
Sail area / displacement ratio:
SDR = … = $SDR
note:If SDR is grater than 20, in general means good performance.
Bruce Number:
BN = pow((10.764*$As), 2)/pow((2.2046*$Mldc), 3) = $BN imperial units
 
Boat speed
Average boat speed potential with jib or genoa:
Vuw1 = … = $Vuw1 knots
 
Average boat speed potential with gennaker:
Vuw2 = … = $Vuw2 knots


14. Cost estimation
Material cost:
Euros = 4*dr*Mlcc = $Euros x 103 EUR
 
Hours of work:
Hours = Ldr*Mlcc/6 = $Hours x 103 hours
note:Ldr (length/displacement ratio) is included in estimation, because building a lighter boat needs more time and the materials are more expensive. In general the building of time and cost are proportional to the mass of the empty boat Mlcc.

 

 


<<-- CORRECT YOUR INPUT    |   START NEW CALCULATION


“;
}else{
//=============================================================
$html=”

Multihull Cruiser Calculator

 

1. Size:

Number of Hulls:
Lh [Overall Length, meters]:
Lwl [Length of Waterline, meters]:
Hull Shape:
U – Shape   |   Y – Shape


2. Shape Coefficients:

Lbr [Length to Beam Ratio]:
Btr [Beam to Draft Ratio]:
Ltr [Length to Draft Ratio]:
Cm [Midship Coefficient]:
Cp [Prismatic Coefficient]:
Cw [Water plane Coefficient]:
Lbrc [Length/beam ratio of cat.]:

3. Powering:

con [Fuel Consumption, kg/KWh]:
Engine Power, KW/T:
Motoring Range, miles:
 

5. Appendages:

αL [Leeway angle, deg]:
ΛA [Geometric aspect ratio of boards]:

4. Sails:

kp [Mainsail Luff P ratio, %]:
ke [Mainsail Luff E ratio, %]:
kj [Mainsail Luff J ratio, %]:
Fbi [Freeboard at mast]:
Bas [Mainsail above mast foot]:
Vawk [Design wind speed, knots]:

 

“;
}
echo $html;

[/insert_php]