Catamaran Hull Design

[BluWtrSail]

Hello all:

I have an amateur designed catamaran hull which I just completed in Carlsons software. I have a question that I hope the more knowledgable and experienced can clear up for me.

When I do the statics...I did it at 3K, 3.5K and 4k pounds, obviously I get different results for draft, lwl, d/L ,L/b etc...but, the CG remains the same. I know that the CB is suppossed to shift over to the CG when the hull trims out. To find this magical CG, all I did was place a little heel in the program and whala. The CG is different from the CB when the hull is static without heel. That was the first part.

I then took off all heel, inputed the displacement and started to play with pitch until the CB = CG. In all cases, the bow came up and it came up different degrees of pitch for the displacement. That was the second part.

My confusion is this. When I decide to design the bridgedeck and all other "weights" am I supposed to design it so that:

weight on the hull maintains the distance between the CG and the CB or,

am I suppossed to design it so that the hull trims out first and then the weight on the hull keeps the CG and the CB equal or,

am I suppossed to design the weight so that I "force" the CB to move to an empirical specific position or distance from the CG?

I ask because it seems that if I keep them apart, I will have to place a substantial amount of weight forward in order to keep them "forced" either where they are or where the CB should be empirically.

I am enclosing the results for one of the displacements in static and the same displacement with the appropriate amount of pitch to place the CB over the CG for analysis and comment. Please ask any questions that will help you to help me put this in perspective. Measurements are in inches and pounds...I guess I can convert if requested.

1 Hull
LOA 408" (33')
Beam Max 72" (6')
Displ. 3000#'s:
CG = 225.7" (18.80') Aft.

Static:
CB (x): 211.8"
CB (y): 10.2"
Draft: 15.7"
LWL: 373"
CP: .57
D/L: 45
S/L: 2.53
D/L Max Hull Speed: 14.13Kn.
LWLBm: 31.44"
L/B: 11.86

Pitched: .99 Degrees
CB (x): 225.7"
CB (y): 9.9"
Draft: 16"
LWL: 384"
CP: .54
D/L: 41
S/L: 2.61
D/L Max Hull Speed: 14.76Kn.
LWLBm: 31.28"
L/B: 12.27

Well, there it is...I hope that someone can analyze this and offer some advise and clarity on how to read into this. Hopefully, I will be able to move on to the next stage. I'm not sure how I can place the picture of the hull in this thread, but if someone would tell me how I would be happy to, or I can give the x,y,z coordinates for plotting if you get or have Carlsons software.

Thank's again to all:

John

[mackid068]

I would think you'd try to keep the CG and CB as low as you can while making the bridge deck. So, attempt to keep them the same but don't worry about a bit higher...I think. Just my 2 cents.

[tspeer]

The center of gravity is pretty much fixed, and is a function of where you put stuff on the boat. You mention a bridgedeck, so this is evidently a cruising catamaran, not a beach cat where crew placement has a big effect on the c.g. So you can either calculate the cg location and design the hull shape until the Cb is in the right place, or you can move structure, equipment and cargo around until you get the cg to correspond to the Cb. In practice, you have to do a bit of both to get everything to balance the way you'd like.

If there's a difference between the Cb and the cg, then there's a moment (torque) applied to the hull. This can only be the case (assuming steady conditons) if there's some kind of external load (besides gravity) acting on the boat. For a sailboat, the sail rig applies this kind of load.

You can account for the external moments by using a virtual cg. In otherwords, if the heeling moment from the sail would make the boat trim at a certain heel angle, the Cb will be displaced to the side from the cg. If you were to remove the moment from the sail, you could get the same heel angle by moving the cg to the side so that it corresponded to the heeled Cb. This is the virtual cg location corresponding to the heeling moment from the sail rig.


You can then map out the X-Y location of the Cb as a function of the heel and trim angles. There will be some external load that can be applied that will result in the boat achieving any given heel and trim angle, and the virtual cg for that load will correspond to the Cb for that heel and trim.

Likewise, you can map out the X-Y location of the virtual cg for different combinations of apparent wind speed and apparent wind angle. This tells you where the Cb has to be to trim out these loads. The location of the virtual cg will depend on the size and shape of the sail rig.

When you superimpose these two maps, you get the multihull footprint for that design. It allows you to quickly see what the heel and trim angles will be for different wind conditions for that hull design and that rig design. Here's an example:

The blue lines are the Cb as a function of heel and trim. The black lines are the virtual cg corresponding to a given apparent wind speed. The red line shows the point at which the deck of the lee bow is at the water surface - you wouldn't want to carry the spinnaker and full sail in 30 kt of wind!

[BluWtrSail]

Hawdy...

I'm not sure what you mean by as low as possible? Do you mean vertically or as a percentage from the bow? Thank's.

John

[BluWtrSail]

Hello Tom:

Thought you should know I read your articles quite a bit. Very technical, takes a lot for us laymen to finally get it...Thank's for the response.

I know that you already know it, but, I was talking about the longitudinal trim instead of athwartships. Because heel will be minimal, I'm not too worried about that right now.

Yes, it is a racer/cruiser, but not too racy. Anyway, you state that I can move the CG around, I would think you mean aft or forward, but I have been unable to get it to go further than maybe 12 inches forward. What do you mean that I can manipulate hull and structure to get the CG to move to the CB? I thought that it was the CB which moves to the CG?

What would the hull have to look like for me to move the CG forward? Where is it suppossed to be for a cat? Wouldn't I always want to keep the CB forward of the CG so that there is always a moment creating a bow up attitude?

Okay, thank's.
John

[Skippy]

I think Tom just means that you can move the weight around in the design of the boat if that improves the performance of hulls that you've already designed. Even without heeling, cat hulls tend to have a V-shaped section forward and be squarer aft. When the leeward hull is pushed down farther into the water, the CB naturally moves forward as the wide upper part of the V bow is more immersed. All you have to do is make sure the CG is far enough aft of the CB to resist the pitching moment of the sails without the hulls nosing in too much.

[BluWtrSail]

Hello...

I think I understand. If I let the CB=CG by letting the hull trim out and then design the weight so that they remain equal, then the CB will move forward when the hull has negative pitch and aft when the hull has positive pitch.

This amount however can be negligible...right? So I should design the weight so that the hull does not trim out and the CB is maintained a certain distance forward of the CG...does that sound right? That distance would of course have a moment equal to the arm (CB to CG) x weight of the entire design wouldn't it?

This leads me to the next question...if I do that, then when the boat heels or pitches forward, the CB will move forward at a much concentrated but controlled velocity...right? Wouldn't the oppossite be true if the boat (for whatever reason) pitches or heels aft? If she squats, the CB will want to move over the CG and it will do it at a maximum uncontrolled velocity...right?

Should these observations, if correct, make me want to put the CB as close as possible to amidship with the CG nearby? I'm thinking of a teeter totter with something at either end or in the middle...is that right?

Thank's again...

John

[BluWtrSail]

Hello Tom:

I'm going to try to do the footprint graph that you have explained. Can you tell me if it applies to the cat hulls? Also, and if it's not too much trouble, if you could go through one example instead of just producing the result, I would appreciate it since I'm not sure what variables I need to manipulate in order to obtain a correct answer.

Thank's again for your help.

John

[Skippy]

"the CB will move forward when the hull has negative pitch and aft when the hull has positive pitch. This amount however can be negligible...right?"
No, definately not. If the change in CB were very small, the boat wouldn't be nearly stable enough. The ends of the hulls will move in & out of the water quickly with small pitch angles, moving the CB something like a quarter of a hull length with a few degrees of pitch. The angle required to do that (in radians) is something like the vertical height of the hull divided by its length. (multiply by 180/pi to get degrees)

"when the boat heels or pitches forward, the CB will move forward at a much concentrated but controlled velocity...right?"
I'm not sure what you mean. The boat will pitch forward under sail until the counter-pitching moment generated by the boat's weight and bouyancy just balances that of the sails. Or the boat pitchpoles.

The teeter-totter analogy isn't too bad. The whole question is the totter angle , and the pitching moments that lead to it.

[BluWtrSail]

Pitchpole? The thought of it makes me go numb from the hair down.

It sounds like that would take a horrible design or an incredibly negligent skipper...I guess that there is always the freak day for mother nature. That has to be a most frightening event. Are there survivors from those catastrophies that have written on this? Can it happen in both directions?

What I meant to say, contolled velocity, is that if there is a moment from the CB and CG not being lined up, then the speed of recovery towards the CG should be faster than further increasing the moment by moving away from the CG. Does that make sense or is it just as fast in both directions regardless of moment and where it is? Is that a lot like the period of the boat?

I come up with 10.95 degrees based on your formula. I didn't use the windage height or the LWL...I used the entire height of the hull 78" and the LOA 408". What does the 10.95 Degrees represent? Is that the angle to move the CB 25% of the hull or does it mean something else? That seems like a hell of a lot of pitch...at 3k pounds, the moment works out to 25,175#'s for negative pitch and 16,925#'s for positive pitch...and thats just one hull. Does that mean that it will pitchpole at those points?

I'm starting to think that it may be better if I just design the rest of the structure after I let the hull CB =CG. It will take 21.7" of negative pitch to get it to midship, that works out to 5425#'s per hull. I'm just not sure if the CG and CB being 10% aft of midship is a bad scene waiting to happen. Like the pitchpole thing.

Thank's for all your help.

John

[nero]

Looking at it from a non numerical point. Maybe you could just draw the cat with the deck house. When you get it drawn out, then run your calculations.

CG is for the all of the cat ... not just the hulls. So getting them equal to each other after all the boat is drawn, means that your boat will float close to the dwl.

You probably have a preference for battery and tank locations. Add them into the design. Then it is the time to start sliding weights around to get it to balance out.

There are a couple of theories on catamaran hull shapes. I kinda like
Shuttleworth's way of going about it. The flat stern section (according to him) does not illiminate pitchpoling.

When you build your test model you will see how your hull moves. Until then it is just guideance from the numbers. smile

[BluWtrSail]

Hello Nero...

This throws a wrench into the equation. I was under the impression that the CB and CG of the hulls were the important issue because regardless of where they are on the cathouse, the cathouse sits on the hull, so the weights and distances for the cathouse would have to be placed in a position where the CG and CG of the hulls were wanted. Is that right?

The way I see it is like this. If you build the hulls and float them with some way to keep them from spreading out and with the cathouse structure already built, you can have the cathouse craned onto the top of the hulls and shift it back and forth until the CB and CG is exactly where you may want it (which may be in line or not). In my mind, the CB and CG of the cathouse is null and void once it becomes part of the hulls. Am I wrong in assuming this or do I have to rethink the cathouse?

I did draw out the cat with the deckhouse in CAD! Great guess. It "looks" correct, but I'm just not that brave and need to know that the CB and CG for the hull will be in the right place or close to it. Right now, it has a bow up attitude and the CB is always forward of the CG in all displacements...guess I got lucky.

I didn't pancake the hull. I have a nice deep v entry and it gets shallower going all the way back to the stern...only the stern is horizontal. I just don't see too much benefit in all the slammin in a cruiser or suppossed planing. I say suppossed because those flat shapes "promote" planing but it has to be a lightship with lots of sail and heavy duty wind for it to happen consistently. A cruiser in my mind with those attributes sounds tiring.

Once again you are correct. The tankage, batteries and engines would definitely be utilized for making sure that everything is distributed correctly, but I'm still not sure where correctly is yet. Noone has really said...the CB should be so and so from the CG or midship or etc...I guess there isn't any hard and fast rule and it just takes a little naked eye science.

I'm beginning to lean towards building the model and then looking at the way it sits...but this worries me because of all the unknown weight differences that can manifest in the model since a frame-out for the cathouse may weigh a lot more in reality than the little sticks I might use to get the model made and this would give me an erroneous point of placement of the cathouse on the hull. I also don't think that the wind can be "scaled" for the model in order to get real pitch and heel figures and if there is a way, it must be extremely difficult to do or calculate.

Thank's again.

John

[tspeer]

The principle is just as applicable to catamarans. Most trimarans are functionally catamarans most of the time because one hull is typically out of the water and the other two immersed at any given time. What makes things complicated for a multihull is you can't just consider sideways stability and pitch stability separately. Probably the most dangerous case is when the boat is broad reaching in a high wind, and is subject to a combination of heeling and pitching loads. This calls for stability on a diagonal direction, which the footprint plot makes clear.

You may be right that the freedom you have to pick the c.g. is limited. A good way to start is to look at a lot of other designs to see where their c.g. is, and use that as a starting point. As the design becomes more refined, you can update your initial guess with better estimates. The way a designer looks at a boat and the way a sailor looks at a boat are a bit different. The sailor takes the boat as it is, and adjusts the way the boat is operated to suit. The designer assumes an operating condition, and changes the boat to match. For example, a designer may move the motor fore or aft to help balance the boat, or add material to make the forward beam very strong while making the aft beam lighter and still counter the same design loads. Maybe relocate where the cargo is stored. That's all part of the art of design.

Naturally, the center of buoyancy will correspond to the center of gravity when the boat is sitting at the dock. If you haven't arranged things that way in your design, then the boat won't be floating on her lines!

In addition to the center of buoyancy, another key parameter is the center of flotation (LCF). This is the centroid of the waterplane. As the buoyancy changes, the change will be added or subtracted at the center of flotation. John Shuttle worth has some excellent advice on this in his article, Multihull Design Considerations for Seaworthiness. He says the center of buoyancy should move forward on the hull that is being immersed more fully, and aft on the hull that is lifting. That means the center of flotation should be ahead of the center of buoyancy when the hulls are evenly loaded.

In "Sailing Yacht Design - Practice" (edited by Claughton, Wellicome & Shenoi) Alexander Simonis presents a case study for the design of a cruising cat. He presents a table of the design parameters for 17 of his charter cat designs. The LCB for his designs varied from 53.1% to 56.43%, and the center of flotation varied from 53.53% to 58.42% of the waterline length. In contrast to Shuttleworth, he places the LCF a little behind the LCB. In the paper he discusses the evolution of these parameters, and their relation to the rig center of effort, as his designs evolved over time. He says of his latest design "It is considered that the fine entry combined with the LCF positioned as far back as possigle would reduce the pitching motion as long as the LCB moved rapidly foward when the bows went down. This is also partly why the bows have a slight angle forward instead of being plumb as seen on earlier cruising designs." For this design (the Moorings 4500), the LCB is at 55.23%, the LCF at 56.36%, the CE at 55.95%, and the center of lateral resistance (CLR) at 56.03%.

Shuttleworth also presents a stability factor,
SF = K * sqrt( (0.5*B*D)/(SA*CE) )
B = beam, measured between hull centerlines (0.5*B is distance from c.g. to lee hull)
D = displacement
SA = sail area
CE = height of the center of effort of the sail rig above the c.g.
K = 9.48 in English units (ft, lb, mph)
K = 0.202 in SI units (m, kg, m/sec)
where SF is the limiting wind speed for the design with full sail. This is the point at which the crew should begin to reef. Shuttleworth also recommends that the forward pitchpole stability be 81% of SF and the diagonal stability (combined heeling and pitching) be 115% of SF for a trimaran. I can't find his recommendations right now for a catamaran, but the pitchpole and diagonal stability ratios were a bit different.

Here's what Shuttleworth's stability criteria look like when transformed into a footprint plot for the design above:

You'll notice they are in pretty good agreement with the sail moments I calculated based on the Hazen model in Larsson & Eliasson's "Principles of Yacht Design" and plotted as the black lines in the previous figure.

Calculating the virtual c.g. is easy - you just divide the moment by the displacement and add it to the c.g. location. Taking your original figures as an example, I'll assume the c.g. is at 211.8", since that's where your static Cb is. Total displacement is 6000 lb. If boat were sailing dead downwind and the sail rig were to apply a moment of 83,400 in-lb, that would move the virtual c.g. forward by 13.9 inches, locating the LCB at 197.9" That would pitch the boat forward by a degree (-1), based on the numbers you presented (assuming the pitching is reasonably symmetric for small changes). This moment could be produced by 417 lb of sail force acting on a center of effort that is 200 inches up.

[nero]

"He says the center of buoyancy should move forward on the hull that is being immersed more fully, and aft on the hull that is lifting."

What ever Tom said is correct. He is the professional. Tom quoted Shuttleworth Somewhere else on the Shuttleworth websight, there was a statement that said the way to get this was to have the bow flairing more than the stern. ( at least that is what I understood)

The effect of this is that as a wave passes the bow flair will hold the front up but when that same wave passes the bow that it is allowed to climb the hull so as not to throw the stern up and the bow down. This was the argument against a fat wide stern section.

When I went thru my hull designing, I stressed over the front not being to pointy. Lots of reserve boyancy. When cats sail the wind force is pushing down on the bow. The way cats flip is normally over the bows. A high .64 coefficient helps.

And by carring the 'light bulb' flair up to the front and then sweeping it around for the bow profile, it also helped air dynamics ( another very important monkey wrench to add to the collections) Also standing the bow profile straight up could make the boat wet from spray from the bow. For my second model, I went back into TouchCad and trimmed down the side profile in front to get less of a wall for the wind to push on. Shuttleworth wrote that cats sail at 30 degrees off wind and that air resistance is greater than water resistance.

Aren't you glad you are learning all this fun stuff?

I guess what I was suggesting earlier is just design the boat like you imagine it ... and then go back and engineer it to be as close to what you wanted it to look like.
A few times thru the loop and you will be more confident, or tired and it will probably be fine once built. smile

[BluWtrSail]

Hello Tom...

Holy mackerel... you know that this is going to take a little time for me to consume. I can't say that you're being easy on me, but hey, ask a question and get ready for target practice. I will definitely look at all the references and I will work out some more calculations to see where all those LCF's, LCB's, LCG's, xyz's, abc's etc. are located and then I will come back with some answers since I'm a gluton for punishment.

I haven't started to think too much about the stability formula yet because I haven't yet given too much thought to the sail area yet. I know that I want it to be lively..maybe an SDR that I can manipulate between 25 to 30 or 35. This of course assumes the vessel can handle it, but knowing me and my super safe, overbuild and then reef down mentality, I don't think that a mast of 1.2 x LOA with an ama c/c spacing of 20 feet will have too much trouble keeping her right side up, unless I get a brain fart out there and decide on a beam reach in 80 knots of wind with all her clothing on.

Nah...I'll stick to the old rule of thumb, "Force 4 = whitecaps = reef it or lose it. For me it's easy to quickly calculate the loads on the sails at force 4 because it puts about a pound per square foot on the sails, so I definitely believe I can maintain way safely. I would even tend to think that little heel will probably give a false sense of security, so I would be at panic stations most urgently with a multihull. I can sail some, mono's, designing is a little harder...getting harder all the time...that's why I'm here.

I really want to design her to be aero and hydro dynamic as possible...more quality than quantity. Shoot, I saw some cats that have windage of 25% and greater of their LOA. I don't have standing headroom in the house, but at least I have excellent sitting room at 20% LOA( I was shooting for 16% but then I would have to either go too long or lose the house) and the bridgedeck clearance is 7% of LOA. I saw one design a "blue-water" mansion with 24% windage and 5.5% clearance, seven feet of headroom in the house!!!! Insane!!! I don't want to call names, but I don't want to build that. I think it's the selling hype that designed that. I bet that Blue Water cruiser never leaves the dock.

Well, thank's again and I'll study up and come back with some more questions.

John