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)

Statistics: Posted by John Perry — Wed Jan 16, 2019 10:44 am

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QUOTE

I volunteered to organise this year’s AGM in the UK, it has been held in New Zealand for the last two years and I would be thrilled to have a good turnout.

This will be during May Spring Bank Holiday (Sat 25th - Mon 27).

It is most likely to be held in Brixham (during Brixham Heritage Regatta).

Please keep this date in your diary for JR sailing and AGM. I know that for many of you this is not just round a corner and to get there requires planning and time.

The Honorary Secretary will send his official AGM announcement as soon as the details have been finalised and I will be in touch with all the logistic afterwards.

Hope to see many of you for the AGM and even more so on JRA boats! Blossom (Pete Hill’s new boat should be ready for this too!).

May the seas be kind and the winds favourable for you in 2019!

Please help me to make this a great event for us all.

Linda Crew-Gee

Membership Secretary

UNQUOTE

Their AGM of course is only for JRA members, but the boats will be there for all to see.

Statistics: Posted by AYRSWebAdmin — Sun Jan 13, 2019 11:15 am

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Paid-up members can download an open copy through the Forum, see https://www.ayrs.org/phpbb/viewtopic.php?f=37&t=3231

Statistics: Posted by AYRS Editor — Wed Jan 09, 2019 11:44 am

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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)

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.

Statistics: Posted by Robert Biegler — Sun Dec 23, 2018 7:41 pm

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

Statistics: Posted by John Perry — Fri Dec 21, 2018 6:47 pm

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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.

Statistics: Posted by John Perry — Fri Dec 21, 2018 1:54 pm

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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.

Statistics: Posted by John Perry — Thu Dec 20, 2018 12:53 pm

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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.

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.

Statistics: Posted by John Perry — Wed Dec 19, 2018 11:13 pm

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The paragraph in the post above is the paragraph I have edited.

John

Statistics: Posted by John Perry — Wed Dec 19, 2018 8:37 pm

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