Trimaran crossbeam calculations

As Ad Hoc says, defining the load is the main issue. Once you have the forces and vectors, there are several formulas or methods available to plug the numbers in and get a solution. Engineering is based on experience and experimentation. It makes sense to look at successful designs and see if what you come up with is close.

 

I agree, designing the structure is the hard bit. Calculating it is easy.

Multihull cross beams must never break and are also a significant percentage of the weight. So their design should be considered from day 1, not at a late stage.

I write more about crossbeam design on the FAQs page of my website

Richard Woods of Woods Designs

www.sailingcatamarans.com

 

Twiggy Mk2

Gary I can try and scan the plans in sections so you can have a look. Considering Brett is not interested and Lock isn't around I think it should be safe to publish them.

The problem with designing these things is that you can't get good load data. I spent over a year asking some very clever Australian people about the load conditions on tri beams. The more clever the person I asked the less they knew. If designers really knew every parameter of the load condition on a tri then they would not have had the beam and hull failures in the 2002 Rhut du Rhum. Cleverer people that us designed and built those boats. I prefer the seat of the pants along with a calculator. That is why reverse engineering is the safer option than starting from scratch. No one has made available accelerometer data on lots of sailing tris, or beam load cell data either. So it is very hard to make sensible assumptions about loads unless you start with those projects that have worked and go from there. And be very wary of changing materials or shapes. One reason for the carnage in the 2002 RdR was that the Carbon cored boats were not very good at crack stopping. Crack stopping? No one had had to think of that before. So the next gen of Irens tris had a very different laminate schedule.

cheers

Phil

 

It is not so much knowing every load.

The loads imposed upon the boat are not that difficult to estimate/calculate within around a 90%-ish certainty. Since the loads are directly proportional the weight of the boat. And the force from the sails is directly proportional to the sail area and the arrangement of the rig, from a known or assumed wind speed.

The difficultly is two fold.

1 The hull has mass, ie weight. So what?...well, this mass when subjected to accelerations creates forces on that mass, primarily the instantaneous velocity in the direction of motion (ie parallel) and then the force towards the centre of the axis of rotation. We can define this as the moment of inertia (about an axis) related to its length. This is length is often “k” in the equation and is referred to as the radius of gyration.

So how do we calculate the k?...it is basically calculated by taking into account the total weight of the boat as the sum of many small weights (distrusted around the entire boat- like from a detail weight breakdown) and then adding the products of each weight and the square of its distance from the axis of rotation.

Again, so what? Well, when the boat is subjected to waves, what occurs, the boat moves. The motion is in 6 degrees, where 3 are rotational motions, roll, pitch and yaw. So we now have a mass with rotational motion an axis of rotation and thus forces imposed upon that mass.

If we know what seas the boat shall encounter, we can use RAOs (statistical analysis) of a sea spectrum to calculate the loads. This is not 100% accurate, but very close to it.

So, we now have a boat, with a known weight and forces from the rotational motion in a sea way.

The difficultly here is where is the exact centre of rotation of pitch, roll and yaw. Secondly calculating the radius of gyration for each axis is not so straight forward, as the known LCG/KG is required (which can only be known once built and launched).

2 The loads once imposed upon the boat requires structure and structural continuity. With composite boat building this can never be 100% guaranteed, as the quality of the structure/lay-up is directly related to the competency and skill of the laminator. There is still too much of a “human error” in composite boat building to say for 100% certainty that structure is “sound”. Two identical boats subjected to the same forces/loads, one can fail the other not, owing to poor QA. Reducing this human error aspect is paramount and the cost of this QA can be exorbitant.

Now, when you take racing boats such as in the RdR, these are like F1 cars, built to the limits. The performance is related to their weight, the lighter the better. Being lighter also reduces the direct loads. But their radius of gyration changes and constantly. Since the weight of the crew is now a much larger %’age of the total weight. Their movements around the boat changes the radius of gyration and hence the response in a given sea way.

These changes coupled with establishing the exact location of the centre of rotation for each and then superimposing that on a given seaway to yield the correct response, ie the centre of rotation is not necessary static, is a very time consuming task. Suffice to say it is rarely done for every scenario.

So “fudge factors” are used, or some would like to say “experience”, based upon previous designs. But this is ostensibly a trial and error situation. If is aint broke, don’t change it. But knowing what the factor of safety is, is generally unknown until something fails and is reversed engineered.

That 10%-ish I quoted at the beginning, is their window of winning and losing and hence pushing that envelope. This shouldn’t apply to the average sailor. Since, for a normal cruising cat the factor of safety would be significantly different to that of an ultimate racer where weight is everything, ergo reduce the scantlings from those over heavy cross beams that is slowing the boat down by 0.1 or 0.5knots etc and reducing the hull weight by ever increasing exotic materials.

The loading scenarios are very different too, since they race to win, ie don’t stop or slow down, unless absolutely necessary which also means encountering conditions which are beyond the 10% range, but how often and how much…unknown. Whereas you, I doubt you’ll want to keep pushing at full chat for 24hours in extremes seas just to get to the pub at the quayside 5mins earlier, where after just 24mins you may have had enough!

 

Very eloquent, Ad Hoc - you even take into account the shifty natures boat building characters add to the equations.
A point about the '02 Route du Rhum, I heard a (maybe apocryphal) story that some of the racing ORMA tris were considered by their crews to be overbuilt and overweight and therefore not fast enough ... and so the laminates were ground down in a pile of carbon dust (and you're welcome to that job). Now I don't know if they attacked the beams as well as the hulls (but I bet they did) ... so some very valuable reverse engineering could be ascertained from those shifty fellows ... but I doubt we'll get the information.
Catsketcher Phil - I didn't mean for you to go to too much trouble; just thought you might have Lock's figures close to hand.

 

Crossbeam calculations

Well, a big thank you to everyone - great discussion. Several points raised I want to address:-

Daiquiri - Agree with Ad Hoc, your summary clarifies things. Euler and buckling, thanks for that. I've gone through that now and due to the slenderness ratio of my possible tubes (31.8) calculated by Johnson formula and the results look fine, though, not finding the maths particularly easy I am wondering about the combined effect of deflection caused by bending moment and the buckling force on the tubes. Designing the beams to be within fatique stress levels is where I started from and have been taking the fatique stress of 6061 T6 as 96 Mpa. I have seen figures to suggest that 6082 T6 has slightly higher fatigue stress around 120 Mpa, but I'm not sure if 6082 is really viable in the marine environment. You mention "inertial relief" how do you calculate for that? How do you calculate for an impact into seawater?

 

Hi, Catsketcher Phil,

I've read, with great interest, your posts elsewhere about your tri/cat deliberations. I imagine your tri plans would be very interesting to see...

Thanks for the FT reference. I even have the book..just been so long since I read it I'd clean forgotten all that stuff about the beams, so have now read and re-read it again. And for general historical perspective here are two pages from the book.


Reverse engineering - precedent. Yep, been doing lots of that, looking everywhere for data. Going out with tape and camera has got to be worthwhile and pleasant, too. Just hope the marina security people don't get too agitated....

I do admire the Buccaneers and Lock Crowther's tris in general and have some info on the Bucc 24 and 33:

Buccaneer 24: LOA 24' 3" LWL 23' BOA 19' Displ 2000 lbs
Crossbeams specified as 4 3/4" by 0.104" wall extruded 6061 T6
aluminium tube.
Unsupported beam length approx 3'6" between edge of wing
and float inner gunn'l.

Buccaneer 33 LOA 33' LWL 31' 6" BOA 23' 6" displ. 6000 lbs

Crossbeams elliptical 8" x 5 3/4" x 3/16" wall
203.2 x 146.1 x 4.8 mm 6061 T6
aluminium tube.
Unsupported beam length between wing edge and inner float gunn'l
= approx 4' 10"

I really like the Bucc 33, wish I'd built one back then...however, she is also the most interesting example for me because she's so close to my design as far as basic measurements go - 24' BOA / 6000 lbs displacement and similar measurements on beam unsupported length, main hull beam at crossbeams etc. Lock Crowther's specified beams are smaller than what I've come up with for my boat - 12" / 1/4" wall tube 304.8/ 6.35mm BUT the Buccaneers have waterstays and shrouds out to the floats. I read one description of a Bucc 24's floats pretty much being held up by the mast... As of right now I don't know how to calculate the difference that triangulation of beam, waterstay and shroud affects the beam scantlings. And my boat won't have rigging out to the floats anyway.

You mention Chris White's Explorer 34 - another good example, big ally tubes, no waterstays, but I've no info on her exact dimensions. Nice boat, though.

Oh, and lastly, I am fixed on this being a tri not a cat. I just have to accept that an amateur designed and built trimaran will be worth firewood money at the end of it all. But I'm in it for the designing and the making and the sailing and the going and that's that. Cheers!
(And no, that doesn't mean I have bucketsfull of banker-bonus scale money .)

 

The Euler formula is propedeutic to the beam buckling, and what you have in this case requires a step further into a slender-beam buckling theory.

The combined effect of the axial force and bending moment is accounted for by the so-called "eccentricity" (of the applied axial force). In other words, you have to consider the axial force applied not at the centerline of the beam (like Euler formula does), but at some distance y from the centreline. When you know the eccentricity you can calculate the maximum allowed stress with, for example, the secant formula.

You can find the explanation of the method here, for example: http://www.mitcalc.com/doc/buckling/help/en/buckling.htm , with the clarification of the variables involved.

Another website where column buckling is very well explained, and which I really reccomend reading, is this one: http://www.efunda.com/formulae/solid_mechanics/columns/eccentric.cfm

The inertial relief accounts for local acceleration of the rigid or elastic body. For example, I've prepared this drawing which shows how the inertia force affects the calculation of the bending moment along the cross beam (supposed rigid):

The case n.1 shows the calculation of the bending moment (Mb,1) if there were just static forces, like buoyancy Fh and ama's weight.
The case n.2 shows the same calulation, but with inclusion of the inertia force acting on the ama's mass. As you can see, the bending moment (Mb,2) equals Mb,a minus a moment due to inertial force. In other words, there is a relieving effect on the bending moment due to body inertia.
The inertia force points downwards because, in the boat's reference frame, the ama will tend to accelerate upwards pushed by the hydrodynamic force - and hence the inertia will act downwards.

So it clearly plays in favour of safety to ignore the inertial relief and do just the static-case bending moment calculations.

Otherwise, a proper calculation of the accelerations requires the inclusion of crossbeam's elasticity - and is not trivial. It is usually done with combined structural FEM and CFD - where CFD gives the hydrodynamic loads due to ama's impact with water, which is then fed to a FEM software for the calculation of the structure's response. And that's done for incremental time steps form the moment of impact with water surface.

It can also be done manually, but is an incredibly tedious task - not worth doing for a small boat. It is done by considering a quasi-static case where the water acts on the ama through the hydrostatic buoyancy only. At every time step the vertical force due to the buoyancy, and it's effect on the boat's dynamics, is calculated through time-wise numerical integration. A titanic job indeed, if done manually.

You can find attached here a pdf file with guidelines for FEM calculations for container ships, made available by DNV classification society. Just for the sake of our general culture.

Cheers!

 

Daiquri - hells' bells ! But thank you, I shall try and get through that - I have a feeling it's going to take me a few hours...at least. Empirical methods suddenly get very attractive!

 

crossbeam calcs

Richard, thank you, I'll look at waterstays and see if I can use them to reduce the scantlings on the tubes. Interesting sidelight on the Wolfson unit suspending FT with her floats filled with water. Makes me wonder what the float total bouyancy was and hence what weight of water they got in there.

Gary -According to David Palmer's book, FT's design displacement was 5,300lbs on a LWL of 27'9". It went up to nearly 7000 lbs and, as she now floated bows down,the WL stayed the same.

Gonzo - Ama shapes - I've tried to design for a gentle take up of displacement by the amas. They are single chine v bottom, but not too tall at 3' 3" total midsection height, bouyancy 170%. So at 6" draught each would displace 140 lbs, at 1' - 665lbs, at 1.5' - 1866lbs and so on. I'm hoping this will smooth out the ride and have a damping effect on the rolling / heeling forces as well as smoothing out the forces delivered to the beams.


Ad Hoc - thank you for a masterly exposition of the problem. Nothing else I've read has put it so clearly, so succinctly and yet in such detail. You're quite right, there is much in there that I have never considered before.

 

Dacquiri

I like the idea of catering for the shock waves due to the impact of the float hitting the water surface. One of the interesting things about this is that similar size and weight tris can have huge differences in slaming due to float design. Some designs (Langdon's sounds a bit like this) have 90 degree or less vee to reduce slamming. Some of the racier designs have pretty flat bottoms. The very seaworthy Cirrostratus designs by Chamberlin have 60 degree float bottoms.

If you get on board a few different tris even on anchor you can feel the different shock loads these designs put on their beam structures. The worst one I felt was the Grainger Spoon Bay 10.6. It did get a bit slammy even at anchor.

Without trying to be nasty or anything I have to say - how did early designers start off? - Nicol was a policeman (and some floats fell off - three I think) Piver was a publisher (and most boats stayed together een when built from terrible materials) Crowther was an electrical engineer (did the same first years as a mech eng in the 60s) Chamberlin was a school drop out, Newick never learned calculus and wasn't actually an naval architect although it is in some books that he is, Brown worked for Piver but was mostly a boat bum when he started designing, Grainger was a surfer ( and a few floats fell off at first when he tried to be tricky).

So before FEA and computers these guys were designing safe boats that worked well. (There must be thousands of good Pivers and Searunners) They must have used a pretty simple model. Maybe I should just ask Jim Brown what he did as it obviously worked well.

cheers

Phil

 

Well, we could be even more nasty by saying that egyptian pyramids and greek temples were made with no help from computers, FEM or even just pencils more than 5000 yrs ago and they are still here, while our finest ultra-modern tall buildings will hardly last more than 200-300 years before they become shaky and get dismantled.

The biggest contribution of the modern technologies and computer-assisted design is that it has allowed us to use the materials and their strength in a more rational way than ever.
Piramids, for example, are essentially just a huge pile of stone blocks with a regular geometric shape, containing a couple of tiny chambers inside. An egiptian pyramid can weigh up to around 6e9 kg, is 140 m tall and contains only a solid mass of limestone blocks inside, plus a couple of tiny little chambers. On the other side, the ultra-modern Khalifa Tower in Dubai is 640 m tall, weighs 1/6th of a pyramid and contains - a lots of useful space.

Guess that's how it goes in human history. We start by grossly putting stones on top of each other, until we're sure they won't fall down. But then we start thinking it over and creating math, physics and theories... Until one day we become confident that we can build a sci-fi particle accelerator and create the antimatter and similar stuff. And all that just to understand the nature of the force which makes those stones always want to fall down instead of going up. So the next time, thanks to this and other knowledge, we'll be able to do that damned pyramid with 1/10th or less of the materials our ancestors needed.

Cheers!

 

Langdon2, I have huge respect for Derek Kelsall; a famous, courageous and open minded pioneer with a huge list of race winning designs to his name ... but FT was a design that seemed to be off in another direction to his usual trimarans (an aside: note the full length floats, one of the earliest) - like Three Legs of Mann, Trifle, Trumpeter, Great Britain 4 and many others; maybe there was some arm twisting by the FT crew for the boat to be a light weather flyer, anyway, the boat had very deep rocker and a very fine, acutely angled bow profile with a V cross section - and the original small section box beams were all that was available at the time and were a make-do situation ... and although cleverly drawn geometrically for strength and stiffness, fittings loosened or failed and gave the already mentioned trouble.
The new beams seem to be overkill (maybe Kelsall was being overly conservative knowing Wolfson and others were hotly breathing down his neck) and the boat weight went up 1600 or so lbs, a very large increase ... and your mentioning that the fine bow went down yet waterline stayed the same ... does not ring true if you look at photographs published, before and after beam changes ... because the stern is dragging horribly and deeply immersed, as is the bow. It is no wonder that the Newick Third Turtle (similar WL length, less sail area, but much lighter) ran away from poor overloaded FT.

 

Langdon2

Firstly, the Euler-strut theory requires additional aspects that require further analysis as Daquiri has already eluded too. One of them being torsional buckling. As you can see from this graph, (from BS8118) depending upon the factors of your strut/column the “design allowable” can be as low as 30-40MPa, when taking torsional into consideration.

As for fatigue….hmmm..how long have you got??

This figure of 96MPa, and 120MPa must be treated like it is radioactive. Those figures, you quote, are for virgin untouched unaffected by any manufacturing process, ie, “idealised” values. They do not reflect the real environment post manufacture. This is a "simple" illustration of various alloys:



This graph here of 6061 alloy indicates how much loss can be expected from minor imperfections and details, significant!!!. So, you really need to draw up (design) your arrangement then perhaps post here, and I can advise further, since there is so much in manufacturing that seriously affects the joints. Even more so when welded!

Finally, I’d strongly recommend 6082-T6, not 6061. The alloy 6061 hasn’t been used commercially in the aluminium high speed boat industry for some 20 years. Only the Americans continue to use it, simple because their Mills pump out lots of this grade for the Aero industry and wont do a “little run” of 6082. This may change now they are building big Tri’s down south. 6061 has 3 times as much copper content than 6082, and thus should not be used unless you have no other choice. I haven’t used it since the early 90s.

Not so fast. You won’t read about all the failures these guys have had before their “successes”!!

This is because they didn’t fully know what was going on, and thus over engineered. If you ask one of them for their rationale (mathematically that is) behind their conclusions for the structure, you’d be very surprised by their reply!!. It is only with today’s technology and advances in science and mathematics that allows us to reduce these high FoS in over engineering to a more rational science based approach, that’s all.

 

You beat me too it

Nicely said