displacement hull catamaran

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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)

Catamaran Hull Speed Calculator For Beginners (Table and Free Spreadsheet)

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Speed is important, it can get you out of harm’s way, and it makes sailing much more fun, but figuring out how fast a catamaran will be able to sail can be tricky. One important aspect is to understand maximum hull speed.

In this article, I have calculated different hull speeds for different lengths of boats; this includes both monohulls and catamarans but focuses on the latter. Here is the catamaran maximum hull speed table:

Table of Contents

Catamaran Max Hull Speed Calculator Table

Length on Water		Displacement Max Hull Speed	Semi Planing Beyond Max Hull Speed
		0%	10%	20%	30%
Feet	Meter	Knots	Knots	Knots	Knots
26	8	6.9	7.5	9.1	11.8
30	9	7.3	8.0	9.6	12.5
33	10	7.7	8.4	10.1	13.2
36	11	8.0	8.8	10.6	13.8
39	12	8.4	9.2	11.1	14.4
43	13	8.7	9.6	11.5	15.0
46	14	9.1	10.0	12.0	15.6
49	15	9.4	10.3	12.4	16.1
52	16	9.7	10.7	12.8	16.6
56	17	10.0	11.0	13.2	17.2
59	18	10.3	11.3	13.6	17.7
62	19	10.6	11.6	14.0	18.1
66	20	10.8	11.9	14.3	18.6
69	21	11.1	12.2	14.7	19.1
72	22	11.4	12.5	15.0	19.5
75	23	11.6	12.8	15.3	20.0
79	24	11.9	13.1	15.7	20.4
82	25	12.1	13.3	16.0	20.8
85	26	12.4	13.6	16.3	21.2

Table Explanation

Length on the waterline (L.W.L.): Length of the boat when measured on the waterline, not to be confused with length overall (L.O.A.), which is the boat’s total length (above the waterline) including bowsprit, etc.
Displacement max hull speed: The max speed of a boat whose L.W.L doesn’t change when underway and where the vessel’s bow wave is the limiting speed factor.
Semi/Light Displacement or Semi planing hulls speed: A boat where the bow waves speed limiting factors can be partially overcome and therefore exceed the displacement hull speed. These hulls usually overcome hull speed by 10-30% .

How to use the Catamaran Hulls Speed Table

Choose your length on waterline in the left-most column, either in feet or meter.
Continue reading to your right and stop either at “Displacement hulls speed” or continue to “10,20, or 30%”, depending on your estimated hull efficiency. This will be your calculated maximum hull speed for a semi-displacement catamaran.

The Formula

First of all, we need to know the maximum hull speed for a displacement hull, and from that number, we will be able to calculate how much faster the semi-planing (or semi-displacement) hull will be. This is the formula for Maximum Hull Speed on a displacement boat:

Now we need to add the increased efficiency (loss of drag) of a semi-displacement hull, usually, this is somewhere between a 10-30% increase.

Note: “1.3” is the increase in efficiency, if you believe you are on the lower end of the scale this would be 1.2 or 1.1.

How to Exceed Hull Speed

This calculator offers a theoretical perspective, but many other factors such as sail plan, weight, and sailor skill, of course, have a profound impact on speed. As we have seen, a semi-displacement hull can exceed maximum hull speed, but we can also see that it isn’t by much. The next step is to reduce drag even further by utilizing a planning hull.

Catamaran Hull Speed Spreadsheet

If you want more info, calculate other lengths, or see the speeds in Km/h or Mph then I suggest you check out this free spreadsheet.

Catamaran Freedom Hull Speed Calculator

Note: If you want your own copy just click, File->make a copy.

Common Questions About Catamaran Hull Design

Below I will answer some of the questions I receive concerning catamaran hull design. The list will be updated as relevant questions come in.

Is a Catamaran a Planing hull?

As we have discussed above, a catamaran can definitely have a semi-planing hull, but can it be designed in a fully planing configuration as well?

Catamarans can be configured as planing hulls, although most sailing catamarans are set up as either semi-planing or hydrofoil. Due to the high speeds needed to get a boat to planing speed, this is only possible on racing sailboats or motor-powered catamarans such as high-speed ferries.

Owner of CatamaranFreedom.com. A minimalist that has lived in a caravan in Sweden, 35ft Monohull in the Bahamas, and right now in his self-built Van. He just started the next adventure, to circumnavigate the world on a Catamaran!

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Calculating power requirements for full displacement hull

Discussion in ' Boat Design ' started by Annode , Sep 2, 2019 .

Annode Previous Member

It seems to take very little power to move even large and heavy full displacement hulls up until about 6-8kts. Then the power curve vs speed seems to go up exponentially after that, and nearly vertical at about 13kts. Assuming that 8kts is sufficient, both in terms of efficiency and speed, what is the nominal (flat water) calculation for power vs weight. After that is known, what is the calculation for additional power for manoevering a heavy steel hull with a lot of inertia, and for wind, sea. Since its not trawling, dont need monster trawler engine, but something extra I imagine. How is this calculation typically made?

DCockey Senior Member

Annode said: ↑ It seems to take very little power to move even large and heavy full displacement hulls up until about 6-8kts. Then the power curve vs speed seems to go up exponentially after that, and nearly vertical at about 13kts. Assuming that 8kts is sufficient, both in terms of efficiency and speed, what is the nominal (flat water) calculation for power vs weight. Click to expand...

to calculate engine power... which for some strange reason is measured in horsepower in boat engines - that only rev to 1500 or 2000 rpm thus disguising the the torque that the engine generates... a more relevant number since a turbo diesel 500hp can generate 2000 ft/lbs of torque

Annode said: ↑ to calculate engine power... which for some strange reason is measure in horsepower in boat engines that only rev to 15 or 200rpm thus disguising the the torque that the engine generates... a more relevant number since turbo diesel 500hp can mean 2000 ft/lbs of torque Click to expand...

JSL Senior Member

how about we get all the facts* about this installation so contributors to the solution find it a bit easier. (* wl length, displacement, power, etc etc. Power, speed, & * etc. also governs propeller size.

Mr Efficiency Senior Member

For practical purposes, rather than strictly theoretical ones, it is the wave making property of the typical displacement hull that causes the rapid rise in resistance, and is related to boat length, the wave system set up that is parallel to the direction of travel, propagates predictably according to speed, in that a given speed gives a given wave length, it is when the crest of the second wave falls behind the stern, that the resistance goes off the chart. Waves on the ocean behave according to similar rules, long wave length equates to speed, short wave lengths slow. Simply, physics.

Ad Hoc Naval Architect

As already noted by JSL, there are far too many variables to consider before attempting to provide any kind of reply. Annode said: ↑ to calculate engine power... which for some strange reason is measured in horsepower in boat engines - that only rev to 1500 or 2000 rpm thus disguising the the torque that the engine generates... a more relevant number since a turbo diesel 500hp can generate 2000 ft/lbs of torque Click to expand...

> boats usually have "reduction gears" between the engine and propeller which reduce rotational speed while increase the torque. yeeeees ... just talking about engine right now. 800 - 2000 rpm for larger boats is normal I am told (with a 3:1 reduction in the gearbox) Specifics... no hab This is a THEORETICAL rough approximation discussion. I am going backwards from the power requirements for reasons that are not relevant right now. answers that are basically "why is that the question?" are not helpful. It is the question. so.. back to the topic...

Chuck Losness Senior Member

Dave Gerr's "The Nature of Boats" discusses power requirements. It might be too basic and not give you what you are looking for. It would be a place to get started. I am sure that this topic has been discussed in the past. Try doing a search for calculating the power for displacement boats.

fredrosse USACE Steam

A rough estimate of horsepower for displacement type hulls is fairly simple: 1. Maximum "hull speed", in knots, is equal to about 1.3 X the square root of the waterline length of the hull in feet. For example, say you have a displacement hull with a waterline length of 25 feet, then the hull speed is 5 x 1.3 = 7 knots. Trying to propel the boat faster than this will result in enormous increasing power requirements. 2. For displacement hulls of reasonable shape (not a square box, which would require more power, and not a rowing shell used for competition, using less power), about 1 horsepower per long ton of displacement will get the boat to hull speed in calm water. This value is based on a propeller of good efficiency, generally a large prop at relatively low RPM. Some additional margin is usually prudent to cope with wind and waves, or non-optimum propeller conditions, but anything over about 2 horsepower per ton of displacement is not required. 3. Much more detail is provided in the FAQ section of thesteamboatingforum.net, as virtually all of the steamboats use displacement type hulls, a general exception to the pleasure boat industry which has much faster boats.

Fred. Thank you. thank you. That was a great answer. These numbers are for flat water and a reasonable shape hull obviously. OK. So the next part of the question is what facto do you use to give you some get out of trouble power. I have been reading on this forum for a while and one thread about a backup 9.9hp outboard and stories of string winds and currents got me wondering how you would calcualte a reasonable margin of "get out of trouble" power on top of the requirement to move at hull speed in clam seas. Obviously you can never have too much power, but these engines go up significantly in price with each step up in power. (for the sake of discussion lets assume a good size boat 25-30m with a steel hull and a weight of 100 - 150 tons. this is out of the category of small fibreglass hulls so things like wind, waves and inertia become significant.

KeithO Senior Member

Take a look at this paper. I think it is on topic for your thread. http://oa.upm.es/14340/2/Documentacion/3_Formas/Savitskyreport_conSemidesplazamiento.pdf

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Hull Hydrodynamics and Design

2.1 Resistance Components on a Hull

Since the main objective of this project involves investigating the resistance of a hull and how it is affected by the introduction of hydrofoils, it is important to understand the components of this hydrodynamic resistance. Additional components will be added with the addition of the lifting foils and the interaction between the hulls and foils will also need to be accounted for. These will be discussed in chapter 3.

2.1.1 Viscous Resistance

The first and most obvious resistance comportent is the visco 3 resistance resulting from the hull skin friction and viscous pressure drag. Viscous resistance is^ç pendent on Reynolds number and so for equivalent scaling of the model we would require Reynolds similaijify.

2.1.2 Form Resistance

Another component is the form resistance. This resistance component results from the shape of the hull as the fluid is forced to change direction (and speed as a result) in order to travel around the hull. This is modelled by simply adding a form factor (1+k) to the viscous resistance, which is roughly equivalent to the average increase in speed required to travel around the hull.

2.1.3 Wave Resistance

The next component is wave resistance. This resistance component results from the additional energy required to create the waves resulting from the hull travelling through the water. These waves may be divided into the following categories - diverging (from bow and stern) and transverse waves. For equivalent scaling, Froude similarity is required. Note: fluctuations in wave resistance are as a result of both interference of the bow and stern wave system (as discussed by Bertram [Ber02]) and the wave interference of the two demi-hulls to be discussed in Chapter 2.1.9)

2.1.4 Spray Resistance

This resistance component is a result of the energy required to produce the spray. It is however expected that since the given hull shape is semi-displacement and the speed range is not very high, this is not expected to be a very large component.

2.1.5 Interference Resistance due to foils

This is the added resistance due to interference of the boundary layers of the hull and foils where they join. This is discussed in section 3.2.4 where the low pressure above the foil creates a downward suction on the hull, which in turn cancels some of the lift generated by the foils. In terms of hull resistance, the reduced pressure and associated increase in flow in the gap between the hull and foils would result in an increase in viscous resistance. This may be factored by a change in the form factor on the hull due to foils. Since only a percentage of the hull is affected and at speeds where the effect is strong, the hull will be elevated from the water substantially, this is not expected to be large, but may account for errors in assuming minimal interference between hull and foils.

The wave interference of the foils and hull niay be pMisidtereo as acting on either the hydrofoils or the hull. It is a function of speed and positioning of foils. Migjiotte [Mig9^] indicates that these effects are both significant but no means of determining them theoretically or empirically are available.

2.1.6 Heel Resistance

This is simply the change in resistance (primarily wave and viscous) due to heel. An empirical equation describing the coefficient of resistance and its corresponding formula is found in Larsson et al. [LE02] however this is for a monohull, which behaves very differently to a catamaran. The main difference is that for a catamaran, the WSA is remarkably reduced with heel as the one hull emerges from the water, thus reducing the viscous resistance. It is however interesting to note that from the formula, the effect of heel resistance increases with the square of the Froude number. It must also be borne in mind that heel has other implications also as the force vector on the sail gains a vertical component with heel. Normally this is assumed to cancel with the upward component on rudders and daggerboards [LE02] but with the addition of lifting foils there is an increase in sideward component due to the heel angle and a righting moment due to the free surface effects.

2.1.7 Induced Resistance

Normally this resistance is associated with hydrofoils and is explained in more detail in chapter 3.2.1. If the hull is thin, it may be thought of as a symmetric hydrofoil of low aspect ratio, operating in the vertical plane. If there is an angle of attack or leeway angle on the hull, there will be a resulting side force and induced resistance. Since the effective aspect ratio and area of the hull are relatively small, the daggerboards and rudders will offer most of the resistance to leeway, and induced resistance on the hull is expected to be very small.

2.1.8 Resistance due to Submerged Transom

Transom sterns have several advantages, the most important being that the wetted area (and hence viscous resistance) is less than that of a hull with a streamlined stern while still producing an equivalent wave pattern. [DD97]

When the transom of the hull is submerged at low speeds, the flow does not separate cleanly off the transom and therefore produces a large stern wave due to the sudden change in flow direction. At higher speeds, the velocity pressure of the flow under the transom is sufficient for separation resulting in 'smooth' flow off the stern and reduced resistance (see figure 2.1 below). This means.that the LCG may be placed further aft for high speeds, but the transom must be preferably in Ii tie with the water level for low speeds.

Doctors et al. [Doc98] quantified the speed at vhich flow off the submerged transom becomes 'cleanly separated' in terms of a Froude number based on depth of the transom below the static waterline (d). This critical Froude number is defined as follows...

2.1.9 Resistance due to Interference between Demihulls

• Induced resistance on hulls due to asymmetric flow around demi-hulls This results from the flow over the two demihulls affecting one another. This effect is a function of Froude number and separation distance. As described by Couser et al. [CWM97] the flow about the demi-hulls centrelines is not symmetric resulting in a relative angle of attack and in turn a side force and induced drag force resulting on each hull (lift and induced drag as described above). The side forces on either hull cancel one another out. However, the induced drag on both demi-hulls acts in the same direction and therefore they add. It is logical to assume (as demonstrated by [CWM97]) that the greater the separation distance and the lower the speed, the less of an effect this has. It was also noted that even for smaller separation distances and narrow hulls (high effective aspect ratio) the resulting induced drag coefficient is much smaller than the drag coefficient for the demi-hulls alone and may therefore be ignored. This is again supported by [CMAP97] who states that the side force on the demihulls decreases rapidly with increasing separation while the drag remains relatively constant. This implies induced drag is not significant. The generation of side force is however significant and may be required for structural calculations. It was also noted that this side force is almost always outwards however for small separations the venturi effect may dominate over the impinging bow wave effect and cause

, suction between the hulls.

Wave and viscous interference between demi-hulls i—

Figure 2.2 a) Graph of interference factor (t) vs Froude (Fr) number taken from IM91

The wave patterns of the two demihulls may also affect each other depending on speed (Fr) and separation distance. A further effect is that asymmetric flow around the demi-hulls effects the viscous flow i.e. boundary layer formation. Referring to [IM91], this type of interference resistance is a function of separation distance and Froude number. The results of [IM91] show that wave interference causes large fluctuations in wave resistance below Fr = 0.5 and a virtually constant and small interference factor above Fr = 0.6. This effect is diminished with increasing separation. Referring ahead to Chapter 2.8, the Froude number (FrL) range of the hull which was ultimately designed as our representative hull (RH1) is 0 -1.06. This corresponds to the range examined by [IM91].

Alternatively Turner et al. [TT68] provide a series of results from model testing to determine parameters affecting interference drag. The dependence on separation distance and Froude number is again shown and the following graph uses the data presented in [TT68]. It shows that at FrL ~ 0.27 and 0.33 there is minimum interference and at (B-2b)/L = 0.266 (same as RH1 - see 2.8) there are large fluctuations in interference with Froude number. These fluctuations are greatly reduced at higher separations.

2.2 Stability

Included in the main objective of this thesis is that the hydrofoil support system that is used in the final result will provide stable support throughout the given speed range. It is therefore important to consider the effect that the introduction of a hydrofoil support system will have on the stability of the sailing catamaran.

2.2.1 Pitch stability (Porpoising and Pitchpole)

As mentioned in chapter 1, pitch stability tends to be a problem for sailing catamarans due to the elevated thrust position and the fine demi-hull bows which offer very little buoyancy and planing effects to resist a forward pitching motion.

With the addition of the lifting foils, the COD would be lowered thus increasing the pitching moment arm between the thrust force and the hydrodynamic resistance. On the other hand the addition of the foils should reduce the resistance so it is unclear whether the pitching moment will be increased or reduced for a particular speed, depending on the positioning of the foils. What is clear is that the higher the hulls are raised by the lifting foils, the greater the angle at which pitchpole occurs. In addition to that the lifting foils should increase the speed of the boat for a given condition so these two factors will increase the severity of the pitchpole if it were to occur on foil support.

The terminal velocity of a conventional sailing catamaran is determined by the speed at which the large pitching moment has lowered the bows sufficiently so that the deck starts to flood. This results in an unstable condition where the bows dig in completely and the boat pitch-poles.

Porpoising is a dynamic instability caused by the combined oscillations of boat pitch and heave, which either remains constant (not a comfortable ride) or increasing in amplitude (Risk of pitch-pole). The general rule for avoiding porpoising is to reduce the trim angle i.e. to move the COG forwards - counter trim by stern. For the case of a hydrofoil-supported boat, the hydrofoils act as natural dampeners for pitch and heave and so this instability may be avoided by careful balancing of the hydrofoils. Given the elevated position of the thrust force which will always tend to trim the bow down, it is unlikely that this will be a problem for sailing catamarans unless excessive lift is being produced on the hydrofoils which 'overpowers' the dampening of the free surface effects.

Since the dagger-boards (to which the main foil is attached) are found amidships the percentage of the lift force created by the aft foils is dependent on how far aft of^ainidships the COG is positioned. Ideally one would desire an even distribution of load on the foils fc jr. good pitch ¡stability. The COG however is fairly dependent on the construction of the boat - particularly wdeffi inboard engines and water and fuel tanks are mounted. Practically it is found to be close to 45%, which implies veiy poor distribution of load.

2.2.2 Yaw Stability

Yaw stability is defined as the ability for an object to remain 'pointing' in the direction in which it is travelling. In terms of boats, it is defined as the tendency to resist rotation about the vertical axis (z-axis, as defined in naval architecture). Another definition [Ber02] is - "the ability to move straight ahead in the absence of external disturbances at one rudder angle"

Yaw stability is achieved by one simple criterion- The COG remains in front of the CLR. This may be illustrated by a dart or arrow. When travelling through the air in the conventional direction, it is easily seen that it remains yaw stable and the reverse can be said about a dart or arrow travelling backwards.

Most sailing catamarans are designed with the daggerboards amidships and rudders near the stern and the COG not far aft of amidships. As a result the CLR is usually well aft of the COG. The only condition where yaw instability is likely is when the boat begins to pitchpole so that the CLR is moved forward significantly. This is a case of pith instability in any case. The effect of hydrofoils of yaw stability is not likely to be significant if the foils are attached to the rudders and daggerboards but a canard foil at the bow would shift the CLR forward, thus increasing the likelihood of yaw instability.

2.2.3 Sudden Loss in Foil Lift

The problem with foils as they near the surface is that of ventilation. This will be discussed in more detail in chapter 3 but in short, results in a sudden loss in lift. This would result in the section of boat supported by the ventilated foil dropping suddenly. This would increase the hull resistance at that point and may result in either yaw or pitch instability, depending on which foil becomes ventilated.

2.2.4 Other Aspects on Stability

Although these three aspects have been identified as the primary concerns with regard to the stability, there are many others. James Wharram [WB91] provides an interesting and insightful discussion on sailing catamaran stability, which stresses the importance of large displacement and that the CE (of the sails) is not too high above the waterline for maintaining good stability. The hydrofoils are expected to increase the displacement due to the added weight (and lower the COG) but also incre^e the height of the CE as the foils lift the hull out of the water. For a more complete evaluation of seawoi;.ihinig& reference should be made to Marchaj [Mar86] and Krushkov [Kru81] For the purpose of future research, guidelines for assessing the Seaworthiness of a similar vessel is laid out by the ITTC in [IT99(ii)]. A me;mis of quantifying stability (stability index or STIX calculations) for a small sailing monohull is given in appendix O. No equivalent was found for sailing catamarans.

2.3 Hullform Development.

Hullforms may be divided broadly into 3 categories; namely displacement, semi-displacement and planing hulls. These describe the range of speeds in which the hull is designed to operate and each will be discussed briefly.

2.3.1 Displacement hulls.

These are hulls designed to operate at relatively low Froude numbers, where the dynamic effects on the running conditions are very small. The hulls are typically 'canoe-like' in shape and they are characterised by large curvature in the aft section to allow for smooth flow that is split at the bow and rejoins at the stern. They also have round bilge station lines (the flow is too slow to separate cleanly off a hard chine hull) and thus vortex shedding at the chines is reduced at low speed. The boundary for this low speed is determined by the Froude number of the boat and these hulls generally operate at below Frv = 0.35 as above this the drag curve is dominated by the hump resistance. [Mig97] Below in figure 2.3 is a typical displacement hull.

Since the Froude number range for displacement hulls is for low Froude numbers, hydrofoils are typically not used for these hull shapes as very large foils (large WSA) are required to generate significant lift. These in turn have large viscous drag components and thus an overall reduction in drag is practically not achievable unless the hull operates at speeds above conventional Froude number ranges for this hull; in which case a semi-displacement hull would have been a more appropriate hull shape.

2.3.2 Planing hulls

Unlike displacement hulls these hulls are designed, to operate at much higher Froude numbers (above the hump speed of displacement hulls) where the dynamic, effects play a major roll in the running conditions of the boat. As a result, the large amount of curvature such as on the affection of displacement hulls would result in large drag due to flow separation and suction. In order to avoid this, planing hulls have less curvature and a 'cut-off' or transom stern. In general, curvature of the buttock lines (a.k.a. rocker) and of the station lines create dynamic suction that induces dynamic sinkage and encourages vortex shedding, thus adding to the drag. Curvature is thus minimised on planing hulls but this will be discussed a bit more in 2.3.4. The WSA and dynamic effects are reduced with the incorporation of hard chines and spray rails. These allow for relatively flat sections in the station lines and the flow to be separated off the hull and create additional lift. The same separating effect is desired from the transom stern. Below in figure 2.4 is a typical planing hull.

Since these hull shapes are associated with operation at high Froude numbers, the use of Hydrofoils is very applicable to these hulls. Most of the lift force on these hulls is derived from dynamic forces and since hydrofoils are approximately twice as efficient as planing surfaces (as will be explained in section 3.3.1), their introduction is likely to reduce drag on the boat significantly.

2.3.3 Semi-displacement hulls

These hulls are a compromise between planing and displacement hulls. They typically have transom sterns, bows similar to displacement hulls and may or may not include hard chines, but seldom include spray rails. (Insufficient speed for spray generation) Sailing boats are almost exclusively in this domain of design, particularly since they operate over a large speed range and are required to perform well in all conditions. All the sailing catamarans produced in South Africa that were found during the internet survey (Chapter 1.9) were round bilge and transom stern in nature and typically had surprisingly large amount of rocker.

Since these hulls are designed to operate at a Froude number range spanning from where buoyancy forces dominate at low speeds to where dynamic forces dominatfe at upper speeds, hydrofoils are applicable to these hull shapes where the performance is red; ed at i<% speed slightly due to increase WSA. As the speed increases the hull is raised out of the water and so the WSA and wave drag will be reduced, thus improving performance.

2.3.4 Rocker (Curvature of the buttock lines)

Rocker or curvature of the buttock lines is an important aspect of hull design and influences the wave-making resistance and seakeeping characteristics of the hull. Typically displacement hulls have lots of rocker while planing hulls have little or no rocker in the stern for planing effects (see following sections). This is because the curvature results in dynamic suction on the wetted surface of the hull, which in turn results in sinkage, increasing the drag on the hull. This effect is a function of free-stream velocity pressure (boat speed) and is therefore small at low speed. Displacement hulls have significant rocker since it reduces the cross-sectional area curve near the bow and stern and therefore reducing the wave making drag at low speed. At higher speed, the resulting sinkage is higher as the dynamic effect becomes significant.

Another aspect of rocker is the effects on seakeeping. Including some rocker in a hull design improves the performance of the hull in waves as it lowers the Centre of Buoyancy (COB) in relation to where the bow and stern enter and leave the water respectively. This allows the boat to respond more smoothly to waves by rocking so as to reduce the slamming and dragging of transom effects that would otherwise be experienced and improve stability. On the other hand, too much rocker can result in hobby-horsing effect in waves which is obviously not desirable in terms of seakeeping. [Shut05 (i)]

Despite dynamic suction effects, rocker may be considered advantageous when a hull supported by hydrofoils is lightly loaded. This combination results in the boat lifting out of the water substantially at relatively low speeds and because of the rocker, the WSA decreases rapidly. If the hulls were compared with foils, they would have very low aspect ratios (since they are slender) and as a result do not produce large dynamic sinkage despite their large area. (Refer to Chapter 3.3.4)

2.3.5 Aspects of bow and stern design

Very fine bows, having deep V shape and narrow angles of entrance are associated with low wave making. This low wave making results in less disturbed flow in the tunnel which is where the foils are found, thus less of an effect on flow over foils. Another advantage is that the wave piercing characteristics of fine bows, results in reduced slamming and heaving of the bows in waves.

The disadvantage of fine bows (as discussed in 2.2.1) is their inability to resist pitchpole and the sharp bows mean the CLR moves forward rapidly as the boa* pi':clies forward, reducing yaw stability. Fortunately for sailing cats, most of the lateral resistance comes from the rudders and daggerboards, diluting this effect.

Bulbous bows have been incorporated into some power cat designs, to reduce wave making resistance. The reduction in wave making drag is small on cats as it's already fairly small due to the narrow demihulls. [Mig97] They also tend to move the CLR forward, thus reducing yaw stability while also dampening pitching motion. Bulbous bows are almost never evident on sailing catamarans, and with therefore not be considered as part of the hull design.

The aft sections of power cats are usually designed in terms of stability and high speed performance. Stability is controlled more by the large rudders and daggerboards on sailing cats, and the high speeds achieved on power boats are only achieved in strong wind conditions. These aspects are therefore of less concern in the design of aft sections on sailing boats.

Since the sterns are generally broader and flatter, the effect of rocker is more significant on the mid to aft section. As a result rocker tends to result in natural trimming by stern which increases dynamically. This is to an extent desirable as it tends to counter the pitching moment but excessive rocker results in excessive induced and separation drag and sinkage as mentioned in 2.3.4.

2.3.6 Planing Effects

This dynamic effect acting on the hull is as a result of trim angle. It is not to be confused with planing speed but both are associated with relatively high speed (Froude number). As a result of trim angle, the hull rises out of the water. An analogy may be drawn between the hull and a flat plate at an angle of attack (See figure 2.5) where the effective downwash (as in a hydrofoil) results in a lift force on the hull. To ensure this trim angle, the LCG should be aft of zero trim position but this generally results in the transom dragging at low. (See 2.1.8)

Planing effects and dynamic suction resulting from hull shape (rocker and soft chines) will combine and result in the running conditions (trim and rise) which will vary with speed.

2.4 Hull Selection

After the size of the yacht was determined in Chapter 1.5, two possible means of hull selection were determined. An existing hull shape of a sailing catamaran currently being produced in South Africa could be used, or a standard hull shape of suitable characteristics could be used. In either case, a representative hull shape would need to be found in order to determine these characteristics.

2.4.1 Finding a Hull

The first thing noted about sailing catamarans produced in South Africa is that the demihulls are symmetric. This is owed to the large separation between demihulls resulting in relatively small interference.

After consulting with local sailing yacht manufacturers, a hull was found but some concerns were expressed regarding the large amount of rocker this boat displayed. The associated dynamic suction on the hull would need to be overcome by a lifting foil system if employed on this hull shape. Nonetheless, the characteristics of the hull were determined so that they could be compared to standard hull shapes. The hull characteristics were compared to the NPL [Bai76] and Series 64 [Yeh65] however no suitable match was found.

It was noted by the student that through his experience as a sailor, a fair amount of rocker is common in many sailing catamaran designs. As a result it was decided that the original hull shape would be used and if the problem of excessive rocker was overcome, this could be treated as a worst case scenario and even better results could be expected for applications to hull shapes with less rocker. Since the boat is fairly lightly loaded, this rocker may prove to be advantageous as discussed in 2.3.4.

Since no lines drawings were provided by the manufacturer, only 2D drawings and photos were provided, it was decided that demihulls based on the representative cat would be designed as part of this study. For the purposes of modelling the thrust force on the sails, details of the rig from the original hull are used. Since the hull generated by the student is aimed at being a representative hull of sailing catamarans produced in South Africa it was named Representative Hull 1 or RH1. (See figure 2.6)

2.4.2 Discussing hull shape

According to Tom Speer [BD99], an expert in the field of sailing boat design, "Since minimum wetted area and not form stability is the driving influence on multihull shapes, you can pretty well determine the lines yourself by taking the product of the profile and typical section shape." As a result it was decided that this method of determining the representative hull, although not accurate, should yield a suitably representative hull.

After referring to a discussion by Shuttleworth [Shut05(ii)] which explained how the buoyancy can be placed as a function of heave, so as to effect the trim of the boat, it was concluded that the bows were a little fine and should have been flared slightly above the waterline. This would however only affect upper speed conditions when the boat tended to nose-dive as only flat water model testing would be conducted.

Since the main parameters of RH1 were based on the original boat, these are expected to be accurate and suitable. Since all other aspect were fairly well defined by the 2D drawings, the hull was deemed suitable.

As can be seen in figure 2.8, there is significant rocker all along the keel line of RH1. From the discussion in 2.3.4 and 2.3.5, we therefore expect a reasonable amount of dynamic sinkage at high speed and due to the large rocker (giving low effective trim angles on the aft section of the boat - where the hull is broad and flat) and narrow demi-hulls, we expect very little planing effects.

2.4.3 Evaluating performance

Larsson et al. [LE02] provides a few ratios for the evaluation of monohull sailing boat performance. Although we expect the performance ratios to be a bit higher for catamarans given their reduced displacement for a given sail area, these are nonetheless used as a yardstick.

The sail area to wetted area (Where the viscous 'force's are being compared to thrust force on sail) should be above 2 for reasonable performance and 2.5 is considered good. The waterline length- displacement ratio needs to be above 5.7 to ensure that the boat will r< ch semi-planing conditions. The sail area - displacement ratio (Where the wave drag is being compared to the Hirust ftwce on sail) should be between 20 and 22 for good performance. As can be seen in the table below, RH1 should have a veiy good performance based on these.

Ratio	Good performance range	RH1
Sa / Sw	2 - 2.5	2.86
LWL / V1/3	> 5.7	7.4
Sa / V2/3	20 - 22	32

Table 2.1 - Evaluating performance ratios of RH1

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COMMENTS

Catamaran Design Formulas – CatamaranSite
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
DISPLACEMENT POWER CATAMARANS
The power needed to do 30 knots is about (2) 450 hp or 900 hp. One live example of a displacement catamaran is the HoloHolo on Kauai. See www.holoholocharters.com Its 62’ long, weighs about 25,000 lbs, has a pair of 440 hp engines and operates in some of the most severe waters in the US.
A Case for Displacement Power Catamarans
We have now designed a large number of displacement power cats exemplifying the “long and slim” approach of powerboat design. The Zenith-47 displaces 13 tons fully loaded, and motors at 20 knots maximum much more economically at 16 knots with only two 122 kw (160 HP) pushing hulls with a 24.5 knot hull speed.
Catamaran Hull Speed Calculator For Beginners (Table and Free ...
Choose your length on waterline in the left-most column, either in feet or meter. Continue reading to your right and stop either at “Displacement hulls speed” or continue to “10,20, or 30%”, depending on your estimated hull efficiency. This will be your calculated maximum hull speed for a semi-displacement catamaran.
Comparing Boat Hulls in Rough Water (Displacement vs. Planing ...
A displacement hull’s round bilges, upswept buttocks and emerged transom create very little form, or wave-making, drag at these low speeds. All those molecules of water being displaced by the hull separate and then regather gently and gradually, so wave-making resistance is very low.
Calculating power requirements for full displacement hull
A rough estimate of horsepower for displacement type hulls is fairly simple: 1. Maximum "hull speed", in knots, is equal to about 1.3 X the square root of the waterline length of the hull in feet. For example, say you have a displacement hull with a waterline length of 25 feet, then the hull speed is 5 x 1.3 = 7 knots.
Displacement vs Planing Hull Yachts: what you need to know
Whether you are planning an extended oceanic cruise or a leisurely one in coastal waters, a displacement hull yacht promises a serene and luxurious experience. In contrast, planing hull yachts are designed to rise up and offer an exhilarating ride on the water’s surface as they gather speed.
Hull Hydrodynamics and Design - Catamaran Sailing - SchoonerMan
Hullforms may be divided broadly into 3 categories; namely displacement, semi-displacement and planing hulls. These describe the range of speeds in which the hull is designed to operate and each will be discussed briefly.
Prowler Series Power Catamaran - SDI Schionning Designs ...
The Prowlers use semi-displacement hull shapes, which means if you want to potter around comfortably at 10 - 12 knots or if you prefer flying along at 20+ knots, this boat will do it all in comfort.
Argus Boats - E35 Cruising Power Catamaran
Roger Hills' evolutionary displacement catamaran design fine tunes a boat with acknowledged outstanding performance for the Australian environment. At 10.2 metre waterline length, the displacement hull technology provides an extraordinary smooth ride.