Request for collaboration

Sails soft & hard (wingsails), kites, and discussions of aerodynamic theory
Robert Biegler
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Request for collaboration

Postby Robert Biegler » Mon Dec 10, 2018 1:00 am

I think I know how to work out the passive stability of the elevation angle of an airship used as a sail. I had the idea oever a year ago, but I have other projects, both professional and boat related, with higher priority, so nothing has happened. Is anyone interested in a collaboration? The project requires some knowledge of trigonometry, and in case there is no closed form solution, some programming, though that could possibly be done with an Excel spreadsheet.

I did consider buying a small aerostat for practical experiments, but abandoned that idea the moment I checked the price of helium. When I searched for hydrogen, I only found sites about hydrogen fuels, but none telling me where I could get bottles, and at what price. Also, I doubt the cooperative that owns the house which contains my flat would be happy with me storing a bottle of hydrogen.

I also have two new designs for a hapa that should go well with a sailing airship. My employment contract with my university contains a standard clause which states that the university gets a share in anything I might patent. The Office for Technology Transfer was a bit surprised when someone working in the department of psychology came to them with an idea in marine engineering. They concluded that only one of the designs was patentable, and that the potential market was too small for the university to take an interest.

Being an academic, it would be useful for me if this could be published in an academic journal as well as in Catalyst. The International Journal of Small Craft Technology (https://www.rina.org.uk/ijsct.html) seems suitable. Referencing work previously published in Catalyst might also generate a bit of publicity for AYRS, and I could state as affiliation both my university and AYRS. The likely problem is that academic journals take over copyright, and take a dim view of essentially the same stuff being republished elsewhere. One possible solution is to submit the airship part alone to IJSCT, and publish information on both airship and hapa in Catalyst.

Is anyone interested in getting involved?


I also had an idea regarding hull slewing, as instantiated in Jon Montgomery's Quatrefoil (Catalyst 15). Quatrefoil's beams rotate around vertical axes. Instead, rake them aft, a little, perhaps 5 to 10 degrees. As wind pressure tries to lift the windward hull, that rake in the rotation axis means the hull will swing aft until constrained. It would not be necessary to actively slew the hulls, only to stop them from going too far. In case of capsize, some buoyancy in the masts (I assume a biplane rig) will also make the hulls slew. Remove the limit to let the boat fold up until the hulls touch, and it should come up at least on its side. If the hulls then have a step above the waterline, possibly only on the outside, it might even be possible for the boat to right itself without doing anything more.

What would worry me is a sailor getting caught between beam and hull. The best cure for that which I could think of is to put the net between the hulls up high, at the level of the hulls' decks. My other worry is torsion. As I understand it, resistance to torsion comes partly from the distribution of material in each indicvidual beam, as represented by the moment of inertia around the beam's long axis, and partly from the moment of inertia that comes from the distance between beams. Letting the boat fold up to right itself after a capsize means reducing the distance not only between hulls, but also between beams, at a time when waves will twist the structure. How much extra material would be needed to prevent the beams from breaking?

I am an extremely slow builder, and have other projects before this one. Does anyone want to build a (model) cat with raked rotation axes, and report back on how it works?

John Perry
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Re: Request for collaboration

Postby John Perry » Thu Dec 13, 2018 12:46 pm

Presumably you are aware of the work done by Didier Costes and the airships Zeppy 1 (1985) and Zeppy 2 (1992) and Zeppy 3 (2008). Zeppy 2 was an amazing project to cross the Atlantic ocean using an airship connected to a hapa (paravane) with pedal powered airscrew as a second means of propulsion. They did manage to get part way accross the Atlantic but weather conditions were not ideal and after some days they were forced to ditch in the sea. Amazing story which Didier himself told us during one of the AYRS meetings back around year 2000.

I would have thought that the elevation angle of a tether connecting an airship to a paravane would naturally be stabilised by the downward component of the tension in the tether reducing as the height of the airship reduces. So when the wind blows stronger the airship will tend to descend, which might perhaps be good in the sense that wind strength is usually less at lower altitude, so the effect of gusts might be mitigated.

It is not clear from your message what you have in mind, or what problem you are seeking to resolve, if a bit more information were available perhaps you might at least get helpful sugestions from members of this forum.

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Re: Request for collaboration

Postby John Perry » Thu Dec 13, 2018 3:05 pm

and partly from the moment of inertia that comes from the distance between beams.


Robert: Quoting part of a sentence from you message, I think the above is a misconception. Considering two hulls joined by two cross beams, it is true that as the craft as a whole is twisted (i.e. one bow and an opposite hull stern rising relative to the other bow and stern) then each individual beam is subject to torsion producing shear stress in the cross beams that can be calculated from the second moment of area of the cross beam section and the angle of twist per unit length of beam. However, no additional torsion results from the fore and aft spacing between the two beams. After all, the angle of twist along the length of each cross beam is the same and does not change if the beam spacing is changed (assuming that any bending of the hull along its length is negligible). What does happen is that each cross beam bends into an 'S' shape with a point of inflexion at mid length and this causes bending stresses (tension and compression) in the beams that are superimposed on the stresses caused by the torsion of the beams. Both the bending stresses and the torsion stresses in the beams serve to resist twist of the whole structure, buy, unlike the torsion stresses, the bending stresses in the beams do change if beam fore and aft spacing is altered. The regions of the hulls between the beam attachment points are also subjected to both twist and bending, but in many cases the hulls are so ridgid by comparison with the cross beams that the deformation of the hulls can be neglected, at least for an approximate calculation.

It seems to be a common misconception that twisting of a multihull structure is resisted primarily by the torsional stiffness and torsional strength of the cross beams. For many practical designs, indeed I would say most practical designs, it is the bending strength of the cross beams that matters more than the torsional strength. Many multihull cross beams are made from aluminium tube which has a cross sectional form that one would normally select to resist torsion rather then bending, so this selection of material is unlikely to be optimum from a structural point of vew. However, aluminium tubes are readily available, require minimum work to make into a multihull cross beam, they dont have corners to bash your knees on and although they are not wonderful aerodynamically, there could be worse cross sections from that point of view. So I am not saying that it is nessasarily wrong to use aluminium tubes as cross beams, just that it may not be structurally optimum and something like an 'I' beam or channel section beam is likely to be better. An 'I' beam (or channel section beam) with strong top and bottom (the cap-spars in structural terminlolgy) is poor in torsion but makes good use of material in bending.

So far, I have considered only stresses due to twisting of a multihull structure but there are also superimposed stresses due to mast compression load, mainsheet load etc. and since these tend to be mainly bending stresses this again favours a cross beam section that is strong in bending rather than torsion.

An 'I' beam or a channel is not good aerodynamically but a non structural fairing can be added to the front of it which will reduce air drag and, perahaps more importantly, will reduce drag caused by wave tops and spray hitting the beam. That gives a sort of 'D' section with the flat side aft, many modern multihulls do indeed have this kind of cross beam section. Until fairly recently no one seemed to bother much about aerodynamic fairing of the aft side of cross beams, but I note that in the last few years fairing in this area is becoming more common. I am rather surprised that it has taken so long for this step in the evolution, I think I first saw canvas fairings on MOD70 trimarans (forward beam only) and of course on America's cup catamarans.

Robert Biegler
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Re: Request for collaboration

Postby Robert Biegler » Sun Dec 16, 2018 1:41 am

John Perry wrote:Presumably you are aware of the work done by Didier Costes and the airships Zeppy 1 (1985) and Zeppy 2 (1992) and Zeppy 3 (2008).

I have read what was Costes published in Ultimate Sailing IV (I think), and whatever I could find on the net. I got the impression that Costes now is an advisor, and that the most active person and cotact is Stephane Rousson. I did write to him. The background is that I work at a university, and my contract includes the standard clause that the university shares rights in whatever I may patent while I work there. There is no distinction between stuff that is work-related and stuff that isn't (I am a biologist, I work in psychology, now, and sailing aerostats have nothing to do with either, except as a good platform to study marine life). I don't mind, because the help they can offer is worth it. So when I thought a new hapa design might be patentable, I went to the Office for Technology Transfer. To make their job easier, I contacted Rousson to ask whether the Costes-style hapa he was using both with the latest Zeppy and with kites was based on a more recent patent than the one I already knew. He refused to tell me, on the grounds that I was going to be his commercial competition. I pointed out that, first, a patent granted a temporary monpoly in return for publication, so not even telling me whether there was a patent went rather against the spirit of the thing; and second, that I would happily let him build and market my design if it even turned out to be better than what he had. That didn't change his mind. I found the relevant patent, it just took more work. Costes might think differently about collaboration, but I have no contact details for him, and Rousson seems to think only in terms of competition. I don't think I'll be getting any help there.

John Perry wrote:I would have thought that the elevation angle of a tether connecting an airship to a paravane would naturally be stabilised by the downward component of the tension in the tether reducing as the height of the airship reduces.

That is what I expect for an aerostat straight downwind of the anchor point, whose angle of attack is determined by the attachment point below the envelope, at least once there is enough wind that you can neglect the effect of buoyancy. If the aerostat has a wing attached to the envelope like in Bernard Smith's book, and is at the edge of its flight window, I think it has to be treated more like a kite.

Then there is the question whether the line attaches to a single point, as in an aerostat and in Smith's drawing, or whether you set up a bridle, say to the root and tip of the wing. That changes the caculation of the equilibrium, because now the angle of attack when the aerostat is straight downwind should increase as elevation decreases, like an old-fashioned single line kite. The exact function relating angle of attack to elevation depends on the length of the bridle, and on how lift and drag of the envelope and the elevator surfaces change with angle ot attack. The only way I could do this is by an iterative procedure that calculates these torques for some angle, finds out which way the whole thing would pitch, adjust the angle a bit, and calculates again. Repeat until torque reaches a small enough value. I found a paper on pressure distributions along an airship hull. That would need to be converted first into overall lift and drag, and then into a lookup table for a range of angles of attack. The lookup for elevator surfaces could skip the first step. Still, doing this would take quite a bit of time. Enough that I won't do it this side of retirement, unless my programming and maths skills improve enough that I can speed up the process a lot from the weeks it would take now.

So depending on the configuration, the calculations can be quite tedious. Then I have to describe the case for when the whole thing is at the edge of its flight window. I think I can make the simplifying assumption that the relative contribution to total forces from what happens when the aerostat flies straight downwind versus what happens at the edge of the flight window are proportional to the sine and cosine of the angle between the line to the anchor point and the total horizontal aerodynamic force. So if I can describe each limiting case, I think i can describe what happens anywhere in between. But I am sure the forces at the edge of the flight window are not as simple as you described. Your description applies to one of the possible configurations flying straight downwind.

I don't know how clear that is without drawings, but I won't have time to make any during the next few weeks, which is exam grading time.

Robert Biegler
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Re: Request for collaboration

Postby Robert Biegler » Sun Dec 16, 2018 2:03 am

John Perry wrote:
and partly from the moment of inertia that comes from the distance between beams.


Robert: Quoting part of a sentence from you message, I think the above is a misconception. Considering two hulls joined by two cross beams, it is true that as the craft as a whole is twisted (i.e. one bow and an opposite hull stern rising relative to the other bow and stern) then each individual beam is subject to torsion producing shear stress in the cross beams that can be calculated from the second moment of area of the cross beam section and the angle of twist per unit length of beam. However, no additional torsion results from the fore and aft spacing between the two beams.

Not in either individual beam. And my understanding was that the torsional strength of individual beams makes a negligible contribution to the torsional stiffness of the whole structure.

My memory of what I read also is that if the hulls of a catamaran can be treated as rigid, then the two beams can be thought of like the two sides of a single I beam. I don't know whether that works out the same as your account when quantified. The two accounts have in common that the structure is stiffer in twist the more the two beams are separated.

If the my interpretation of what I read is valid, then the two beams getting closer together when hulls slew should make the whole structure less resistant to twisting. In your account, what happens when supporting the whole boat by one bow and one stern when the beams are at 90 degrees to the longitudinal axis versus some other angle? Do the beams or any other part of the structure need to be stronger to deal with that?

John Perry
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Re: Request for collaboration

Postby John Perry » Wed Dec 19, 2018 11:13 pm

Robert Biegler wrote:Not in either individual beam. And my understanding was that the torsional strength of individual beams makes a negligible contribution to the torsional stiffness of the whole structure.


Robert, I guess that what you meant to say is the the torsional strength of individual beams makes a negligible contribution to the torsional STRENGTH of the whole structure. Strength and stiffness are different properties! (and both are important in boat designing)

But, leaving that quibbling point aside, I do agree with you - both the strength and stiffness of the whole structure under twisting loads are more dependent on the bending properties of the cross beams than on the torsional properties of the cross beams. However, I am not sure I would go as far as to say that the torsion has negligible effect, I think that I would want to include both both bending and torsional effects in a design calculation, at least until I was sure that I could neglect the torsional effects. Another point is that there have been a few multihulls built with only a single cross beam, for example the Hydropterre trimaran and the trimaran that Peter de Savery had built with the America's cup in mind. For a multihull that has only one cross beam, the torsional strength of the cross beam is obviously critical!

The torsional stiffness of a shaft can be calculated from the second moment of area of the shaft cross section, the torsional modulus of the material and the length of the shaft, the relevant forumlae can be found in any textbook on stress analysis. However, any such text book will also tell you that this method of calculation is based on certain assumptions, one of which is usually quoted as 'plain sections remain plane'. That means that if we consider all the molecules of the shaft that lie on some plane transverse to the axis of the shaft when the shaft is not twisted, those molecules must still lie on a flat plane after the shaft is twisted. It is not correct to treat any normal pair of multihull cross beams as a single member under torsion with a combined second moment of inertia for the two beams together since the bending that occurs along the lengths of each beam when the whole structure is twiste, violates the assumption that plain sections remeain plane.

I have made a quick finite element analysis to illustrate these points. The first picture below shows a simplified catamaran structure - I haven't bothered to give it pointy bows or tapered sterns since the details of hull shape are not relevant for this purpose. If the hull centre-line spacing is taken to be 'L' I have made the overall length of each hull '2L' and the cross beam spacing 'L'. As Robert suggests, I have supported the craft on small supports located right at the bow of one hull and the stern of the opposite hull and I have allowed the weight of the craft to twist the structure - not a purely academic load case, I can somehow imagine that inadequate support for a catamaran during on-shore storage could result in this kind of situation.

As you see from the first picture, each cross beam bends into a slight S shape (the picture exaggerates all distortions to make the distorted shape clearer). The colors indicate the level of the Von Mises stresses, red being high, blue low. Clearly the beams are subject to bending stresses wjth highest stresses being towards the top and bottom of the beams in the regions of the beams where the curvature is greatest. At the midpoints of the beams there is no curvature, these being points of inflexion, so there are no bending stresses at the mid-points of the beams, but note that even at these points the Von Mises streess is a bit higher than it is in the main body of the hulls (where it is very low because I made the hulls solid, so they are very ridgid), this being due to the presense of torsional stress which applies uniformly right along the length of each beam.

The second and third picture shows what would happen with the same support/loading arrangement if this were a 'slewable' cat, as Robert describes, with the hulls totally slewed so that the cross beams lie parallel to the hull centrelines. Two pictures, one for supports at the hull ends that are futhest appart and one for supports at the hull ends that are in proximity. You see how the beams still bend into an 'S' shape, but the points of inflexion no longer lie at the beam midpoints and the bending stresses are higher towards one end of each beam, the highest stresses being greater than for when the hulls are not slewed (as in the first picture) - I hope this answers Robert's question, but if actual stress values are needed a lot more detail of the craft would need to be known.

Note that in the second and third pictures the cross beams are not twisted along their length (since the hulls have not rotated about their long axis) so at this slew angle the cross beams are not subjected to any torsional loading, only bending loading. Note that the stress color at the points of inflexion in the second and third pictures are a darker blue than in the first picture, about the same shade of blue as the hulls, indicating no torsional stress at these points as well as no bending stress.

I suppose I could repeat this analysis for an intermediate slew angle, say 45 degrees - this would show a stress situation intermediate between the the two extreme slew angles, zero degrees (first picture) and 90 degrees (second and third pictures)

BTW, if you are wondering what the red arrow pointing downward in each picture is, that represents the force of gravity directed downwards from the centre of gravity of the whole craft.

Slewcat_01.jpg
Hulls not slewed
Slewcat_01.jpg (57.39 KiB) Viewed 320 times
Slewcat_02.jpg
Hulls slewed 90 degrees one way
Slewcat_02.jpg (50.35 KiB) Viewed 320 times
Slewcat_03.jpg
Hulls slewed 90 degrees the other way
Slewcat_03.jpg (61.42 KiB) Viewed 320 times

John Perry
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Re: Request for collaboration

Postby John Perry » Thu Dec 20, 2018 12:53 pm

Rober Biegler wrote:
Is anyone interested in getting involved?


Yes, I am always interested in helping with other members projects and have done on a number of occasions in the past. One that springs to mind is the series of paravanes that I constructed for Slade Penoyre, past Treasurer of AYRS. The limitation on collaborative work is that I do wish to get on with my own AYRS style projects as well, and time seems so short, surprisingly even shorter when retired than when in employment! At the last Devon meeting of the AYRS I presented an idea for applying hydrofoils to a sailing boat in a slightly different way to the ways that others have done it. That presentation was now nearly three years ago and I still have not started any practical work on that potential project. Then, at the beginning of every winter I have been meaning to learn how to use CFD properly, but made no real progress on that. And within the last few days I have been thinking about ways to verify CFD work on sailing boat rigs by measuring the pressure distribution accross a sail using sensors attached to or built into the battens of a fully battened sail. Just the other day I was discussing this with a retired professor of civil engineering who lives locally, between us we came up with a concept for a simple kind of pressure sensor to measure the low pressures involved, say in the range +/- 30Pa gauge. I would really like to make one and see if it might work.

BTW, this discussion seems a bit disjointed, there are bits about a 'slewable' catamaran and bits about an airship/paravane combination, two completely differnent concepts. Perhaps the discussions should be separated.

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Re: Request for collaboration

Postby John Perry » Fri Dec 21, 2018 1:54 pm

Robert Biegler wrote:
That is what I expect for an aerostat straight downwind of the anchor point, whose angle of attack is determined by the attachment point below the envelope, at least once there is enough wind that you can neglect the effect of buoyancy. If the aerostat has a wing attached to the envelope like in Bernard Smith's book, and is at the edge of its flight window, I think it has to be treated more like a kite.


I had to look up the definition of 'aerostat' - apparently it means any aircraft using lighter than air gas foy bouyancy, e.g. powered airship, balloon, hot air or gas. I had not appreciated that you were thinking of wings attached to the tethered aerostat - depending on the size of the wings, that could certainly make it more like a kite than anything else.

Then there is the question whether the line attaches to a single point, as in an aerostat and in Smith's drawing, or whether you set up a bridle, say to the root and tip of the wing. That changes the caculation of the equilibrium, because now the angle of attack when the aerostat is straight downwind should increase as elevation decreases, like an old-fashioned single line kite. The exact function relating angle of attack to elevation depends on the length of the bridle, and on how lift and drag of the envelope and the elevator surfaces change with angle ot attack. The only way I could do this is by an iterative procedure that calculates these torques for some angle, finds out which way the whole thing would pitch, adjust the angle a bit, and calculates again. Repeat until torque reaches a small enough value.


Re. the attachment of the bridal, do you mean to the leading edge and trailing edge? - wing root and wing tip does not seem right.
If you neglect any curvature of the kite string and a bridle arrangement is used to fix the angle between the kite string and some datum line on the aerostat then surely the function relating angle of attack of the aerostat to elevation of the aerostat is very simple and not dependent on lift and drag. However, I wonder if that is really what you want to know. I am guessing this is to do with a kite and paravane combination as so often discussed within AYRS circles. If so, then you ultimately need to know the overal lift and drag of both the airborne and water borne components, all resolved to a horizontal plane, in order to predict performance. Would also be nice to know whether the kite will be stable in elevation rather than zooming down into the sea/land as kites sometimes do!

You haven't mentioned aerodynamic and gravitational forces on the kite string which would considerably complicate the calculation if you intend to include them. The kite string will be curved in a plane that may not be vertical, due to both gravitational and aerodynamic effects and this curve will change the gradient of the string at the kite end and hence if the kite is connected through a bridal its angle of attack will be directly affected. The aerodynamic lift (downforce actually) and the drag of the kite string will also come into the lift and drag calculation for the airborne system as a whole, and this may be quite significant.

I found a paper on pressure distributions along an airship hull. That would need to be converted first into overall lift and drag, and then into a lookup table for a range of angles of attack. The lookup for elevator surfaces could skip the first step. Still, doing this would take quite a bit of time. Enough that I won't do it this side of retirement, unless my programming and maths skills improve enough that I can speed up the process a lot from the weeks it would take now.


I could take a look at this to at least see what would be involved in those calculations. I take it you have the pressure distribution along the airship hull for a range of angles of attack, not just for zero angle of attack? Of course the pressure distribution on its own does not give you the total drag, there is also skin friction. I dont know about airships, but for seaships, both surface pressure and skin friction are significant in determining drag. Do you also have lift and drag curves for the wings that you are thinking of attaching to the airship?

I do wonder where this kind of investigation is intended to lead. I can see that a kite and paravane combination, or aiship and paravane combination, or glyder and paravane combination, could be a contender for the world sailing speed record. All these combinations actually have some similarity to Paul Larsen's Sailrocket - Sailrocket replaces the kite string with a streamlined carbon fibre pole, but the principle is much the same. So is a kite sting going to be better than a streamlined pole - I think that is quite an interesting question.

A kite string can probably be made a lot longer than it is really practical to make the pole and that does have a big advantage in that it raises the wing (or whatever aerodynamic object is taking energy from the wind) to a greater height where wind velociy is higher and wind turbulence is less. Against that, replacing the pole with a string means that a human located in one of two objects, that are linked only by a string, has to maintain control over both objects, and for it to be a sailing craft I would say this control has to be maintained without stored energy and powered actuators. Surely that is likely to complicate the control problem and it is actually control difficulties that seem to have been the limiting factor for at least some of the record contenders, Sailrocket may be no exception. The aerodynamic properties of a string versus a pole are probably a bit less important but, depending on its length, a string may have less aerodynamic drag than a pole, however, if the pole is well streamlined the string does not need to get all that long before it becomes aerodynamically inferior to a streamlined pole.

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Re: Request for collaboration

Postby John Perry » Fri Dec 21, 2018 6:47 pm

Just one further point: I recall that when Didier Costes last attended a meeting of the AYRS, which was quite a few years ago now, I clearly remember him saying that the best lift to drag ratio of an airship hull used as an aerofoil is about 4:1. Perhaps this one piece of information might enable you to do some rough calculations to see whether whatever it is that you have in mind is worth persuing in more detail? Does anyone know if Didier is still contactable? My impression was that he was very ready to share information and help others with projects.

Well I had better leave this topic now so that others here can get a word in edgeways!

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Re: Request for collaboration

Postby Robert Biegler » Sun Dec 23, 2018 7:41 pm

John Perry wrote:Robert, I guess that what you meant to say is the the torsional strength of individual beams makes a negligible contribution to the torsional STRENGTH of the whole structure. Strength and stiffness are different properties! (and both are important in boat designing)

Probably. I had assumed that if the structure is designed to impose greater stress on an element, say by closer spacing of the beams, there would be more strain.

John Perry wrote:The second and third picture shows what would happen with the same support/loading arrangement if this were a 'slewable' cat, as Robert describes, with the hulls totally slewed so that the cross beams lie parallel to the hull centrelines. Two pictures, one for supports at the hull ends that are futhest appart and one for supports at the hull ends that are in proximity. You see how the beams still bend into an 'S' shape, but the points of inflexion no longer lie at the beam midpoints and the bending stresses are higher towards one end of each beam, the highest stresses being greater than for when the hulls are not slewed (as in the first picture) - I hope this answers Robert's question, but if actual stress values are needed a lot more detail of the craft would need to be known.

This is exactly what I had hoped to see. Am I correct in interpreting the larger red areas as representing greater stressed when slewed? Such that a slewing catamaran would need stronger beams?

I don't think we need to separate the thread for his. For the time being, that is all I want. The only innovation in this is to rake the rotation axes back a little, so that sail pressure will slew the hulls. I still don't know whether it is worth trying out. My three worries are crew getting caught between moving parts, that highly loaded moving parts might wear more than non-moving parts, and that the noise when wear makes them sloppy would take all the fun out of sailing. Mostly, having the whole sructure held together by hinges, each of them critical to the integrity of the whole structure, makes me a bit uneasy. But I admit that worry is not based on any actual engineering knowledge that tells me whether moving parts really do wear more, and if yes, whether the amount of extra material needed to compensate is enough to matter.

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Re: Request for collaboration

Postby Robert Biegler » Sun Dec 23, 2018 10:21 pm

I just lost two hopurs of typing a reply, because the system logged me out before I clicked on "Preview", then didn't take me backl to what I had written after I logged in again. I have to see when I have time to write this again. Probably a week or so.

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Re: Request for collaboration

Postby John Perry » Wed Jan 16, 2019 10:44 am

Hi Robert, Sorry you lost your typing, this reminds me that when writing more than a few words to an internet forum it is best to first enter the text into a separate app then copy and past it to the forum website! I like to use the free Notepad++ app for that kind of thing, I find it much better than a full word processing app when you just want to put text together and are not worried about the layout of the text on a printed page.

Anyway, you asked:
Am I correct in interpreting the larger red areas as representing greater stressed when slewed? Such that a slewing catamaran would need stronger beams?


Yes, with the loading arrangements we are considering the peak bending momeent in the beams - and hence stress in the beams if we are neglecting torsional effects - is indeed greater when the catamaran is slewed. And this is indeed shown by the larger red areas for the fully slewed diagram compared with the non-slewed diagram.

What is actually happening is that the beams are bending rather differently in those two diagrams. For the non-slewed diagram, if we consider each beam individually, one end of the beam is going up and the other end is going down, relative to the middle of the beam, but the topsides of the hulls remain parallel to each other so there is no rotation of the ends of the beam about a horizontal axis transverse to the beam. This means that each beam bends into a symmetrical 'S' curve with the same curvature and the same bending moment at each end of the each beam. Compare this with the second of the two diagrams. Again, relative to the middle of the beam, one end of each beam is going up and the other end is going down and if it were still the case that there were no relative rotations between the beam ends then the bending moments and bending stresses in the beams would be exactly the same as for the first diagram. However, in the case of the second diagram, the longitudinal tilting of the hulls is causing a relative rotation of the beam ends about horizontal axis transverse to each beam. This modifies the symmetrical 'S' shape bending seen in the first diagram by adding bending moment to one end of each beam and taking it off the other end. The result is still an 'S' shape bending of each beam, but one end of each beam is now carrying greater bending moment than the other end, so the maximum bending stress in the structure is increased.

So would a slewing catamaran need stronger beams? Based on my three diagrams it would seem so, but I think you also need to consider the situation(s) under which the boat would be significantly slewed. For normal sailing you probably dont want to use large slew angles because if you do you will significantly reduce lateral stability and hence sail carrying ability. If you intend to use large slew angles primarily to aid in righting the boat after a capsize this is a special situation which probably has quite different loading on the structure compared with normal sailing, so I dont think you would necessarily need stronger beams for that situation. I think you would need to analyze the sailing situation and the capsize situation separately.

Although this is a digression from the topic of 'slewable' catamarans, I think the loading situation for the non-slewed catamaran shown in the first of my three diagrams may be worth some further consideration. As I said before, this loading situation could result from uneven supports when the boat is laid up on shore. It also has some similarity to the situation when the bow of one hull and the stern of the opposite hull are both on wave crests. It is quite a simple matter to determine the maximum bending moment in the cross beams under this loading condition. If, to begin with at least, we ignore the torsional stiffness of the beams, then each end of each beam transmits only a vertical force to the attached hull. From the symmetry of the situation these four vertical forces are equal in magnitude but one diagonal pair is upwards and the other downwards. So let the magnitude of these four forces each be 'F'. We can then consider momnents about the mid length of one of the hulls. For one hull, half the total weight of the boat is applied upwards at the point of support which we assumed to be right at the end of the hull, so if the length of the hull is 'L' and the boat weight is 'W' that gives a moment about the hull midlength point of L*W/4. For our assumed loading condition this moment is resisted only by a couple generated by the two forces, magnitude 'F' applied to the hull from the two beam ends, so if the fore and aft spacing of the cross beams is 'a' this couple is F*a. Equating F*a to L*W/4 gives F = (L*W)/(4*a). If we are interested in the hull being supported by wave crests rather than by supports at the extremity of bow and stern then we need to make some estimate of the effective length between supports - as an initial rough guess perhaps about two thirds of L would be not too far wrong? Now that we have the magnitude of F we can consider the bending moment in the beams. F is applied vertically upwards to one end of the beam and vertically downwards to the other end, and there is no rotation at the beam ends so, if the length of the beam is 'b', the maximum bending moment is F*b/2, i.e. (L*W*b)/(8*a). From this we can select an appropriate beam cross section to provide adequate strength and stiffness. This is not a complete analysis of the beam loading, but a good start, for a more complete analysis you would also need to add in bending moment resulting from things like the mast foot load and the mainsheet load.

Coming back to slewable catamarans, the 'Dragonfly' range of trimarans has hinges that carry the full beam bending moment so yes, it could be done, but it would certainly add weight and cost to the boat. I can see that it would offer better resistance to a 'leebow capsize' since it would move the bouyancy of the leeward hull forward relative to the centre of gravity of the boat. As for capsize recovery, various schemes have been proposed by AYRS members and others but I know of no cases where such a scheme has been successful with a multihull larger than a beach cat and with an unaided crew in conditions severe enough to cause a capsize in the first place. Maybe this is simply because multihull capsizes are quite rare anyway. (Leaving aside the big racing trimarans which do capsize but are usually righted with the aid of large rescue boats)


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