Rotating Wing Mast – theoretical discussion

Is telescopic best? must be hard to organise sail track etc? 11m to 3m means three pieces?What about a fwd mast pole that integrates with mast and is used as a king post so it can be dropped entirely and raised entirely? like a tabernacle? Just a thought. If you have to see then bringing main to deck no good. For gust response like skiffs use ( so called auotmatic tops) no. If you have other ideas happy to discuss. Do you have a layout of the boat? Cheers Peter S

 

http://www.onesails.com/design.php

http://www.wb-sails.fi/en/services/vpp-analytics/

some sailmakers near you with CFD capability Cheers Peter S

 

Re the comment about molding: In my mast designs, I have designed one-off masts that have the molding framework built in. It's made of lightweight wood-epoxy and although it adds some weight to the mast, it is easy to build and not expensive. It makes building a one-off mast possible without building expensive and wasteful tooling.

Re deflection: I design my masts to have the right amount of deflection so that you don't need any other rigging or devices to assist in deflection. You want some deflection, but not too much. It is better to err on the side of being too stiff than being too flexible, and it is possible to engineer the mast just right for the correct amount of stiffness and strength.

Re section size: Any mast, no matter what type, stayed or unstayed, is going to have form drag in and of itself, so it is beneficial to have a mast that is only as big as you need, consistent with strength and stiffness, and no bigger. Masts need a certain amount of wall thickness as a percentage of diameter to guard against thin-wall buckling, t/D ratio. This means that for every rig, there is an ideal size of mast section that is just big enough for strength and stiffness with just enough wall thickness and no more. If you go bigger in mast section than the ideal with a very thin wall, you have too much form drag and the real possibility of buckling failure. If you go smaller than the ideal, you have too much wall thickness which is actually heavier than the ideal, and it also means that you have spent too much money on the materials. You will also likely have too much deflection. The single biggest controlling factor in tip deflection is mast diameter, and diameter, together with wall thickness determines strength and stiffness.

In my free-standing mast, flagpole/lightpole, and windmill blade designs over 35 years, I have found that for carbon fiber tubular structures with laminates made with unidirectional and off-axis fibers, that the essential minimum t/D ratio is 0.03. That is, the wall thickness should be at least 3% of the diameter at any given section. For round section masts, generally the laminate is should be a mix of 80/20 unidirectional fiber to off-axis fiber, and the off-axis fiber should be split evenly between 0°/90° fibers and ±45° fibers. These off-axis fibers should be on the very inside and outside layers, with the ±45° layers being the extreme outside surfaces, with the 0°/90° directly underneath, sandwiching all the unidirectional fibers in between these surface layers. For fairly thick laminates, it is OK to put more layers of the off-axis fibers spaced evenly throughout the laminate thickness. As laminates tend to more non-round shapes, like wings, then this split of unidirectional fibers to off-axis fibers changes to more of a 60/40 split, with the laminating principles being the same for the order of layers. Incidentaly, laminates should be mirror images of each other through the middle plane of the laminate so that you don't build in shear torsion as the mast is loaded. You have to engineer the total strength and modulus of the laminate to whatever split you choose because strength and stiffness is highly dependent on the mix of fiber orientations. An 80/20 laminate will have a higher strength and modulus than a 60/40 laminate.

I hope that helps. I have discussed this topic before a number of times in other places on this forum, so this is a good place to review it again.

Eric

 

Hi peter, thanks. Yes there is just two pieces, because when I go under the bridge it needs to be taken all the way down. It's in the hatch so can be tilted to windward then pulled out of the bottom bearing when it is more horizontal. Or tabernacle as you say. More later everyone.

 

One point I have not seen discussed is the sail control with regards to the mast chord.
With a bigger mast chord, the sail gets a higher aspect ratio, so it should get more difficult to control the camber over its span. But also, the shape gets less important, because so much camber comes from the mast rotation.

The ideal mast bend will change with how much ballast one has. This should be important in a pac proa. Mast needs to be strong and preferably stiff enough for several crew, but it is meant to be sailed alone as well.

On the boats I have sailed, the sails could be effectively twisted out by letting the clew up. For mainsails it is usually held down by a kick and a sheet. If one uses the sheet for AoA only, then the kick could be designed to be overcome by sail pressure, with some sort of flexible design. That is one of the alternatives to a flexible mast as a gust response/automatic trimming device that I was thinking of.

 

Hi Eric - Just a point of difference. If you build laminates with the 45s on the outside they perform worse in buckling then if you put them on the inside. I shall do a little FE model to explain this, this week. But for the engineers out there. The bending stiffness of the 45s on the outside is less then the bending (flexural) stiffness is if they are on the inside. The initial in plane stiffnes is the same (plus the flexural strength is less so when it does buckle it breaks earlier vs "snapping back"). With high in plane compression the onset of buckling is determined by the lesser of the in plane stiffness or the flexural stiffness. So it is better to have the 45s (no hoop plies as well, as the 90deg or hoop plies always fail first so better not to have them) on the inside and yes it is better to have the laminate to be symmetric. Your min D/t ratio is 33 I'm happy at 45-50 so perhaps having 45s on inside explains that. My FE model will enlighten this better. Re comment about making one off masts with timber is valid, all depends on what weight mast you want to acheive & at what cost. I'd expect an infused E glass mast to be lighter then a timber/carbon mast but then you still need to make the mould. All a time/quality/weight/cost tradeoff. If you have a typical lamainte spec you want me to run to explore this happy to use it if you spec it here. Over the yaers I have had many tubes made and tested and this difference does show up in practice. Cheers Peter S

 

I wonder about that. From my experience on free-standing masts, if you do not have some kind of off-axis wrap around the unidirectional laminates on the very outside and inside surfaces, the unidirectional fibers themselves can buckle out of the laminate. The UDR has to be sandwiched in between other layers. You can use a 0°/90° cloth on the outside and inside if you wish.

Also, you do need torsional strength and stiffness in the laminate and the ±45° fibers give you that.

Finally, you do need 90° fibers in the laminate for section shape stability. As a free-standing mast bends, the mast section wants to ovalize, so diameter transverse to the direction of bend tends to get smaller. That is really critical because diameter is everything for strength and stiffness, and if you lose even a little bit of diameter, you are losing a tremendous amount of strength and stiffness. However, if you put 90° fibers on the very outside of the laminate, they will lead to cracking in the surface which can later penetrate into the laminate beneath. This phenomenon is the bane of a lot of Freedom Yacht masts built by TPI that had circumferential windings on the outside surface and they have terrible cracking problems--not fatal to the masts--but bad enough that if the cracking gets too extensive, then the mast should be repaired. I have written a standard repair procedure for Freedom Yacht owners who might have experienced this problem (virtually all have). An alternative, as stated above, would be to use a carbon fiber cloth on the inside and outside surfaces, and the fibers in each direction can be included in the necessary mix of fibers in the 0° and 90° directions.

I would be interested in what your FEA model shows. You say that you should not have 90° fibers, yet I wonder if your modeling shows this section shape collapse if you don't have them. I know from full-scale testing of composite poles that 90° adds essential stiffness to section shape stability.

I can't give you a typical laminate right now--it's the weekend and I am off on Monday for the IBEX conference for a week and I have a lot of things to take care of before I go. But when I get back I may be able to pull out a laminate from one of my designs for you to study. I'd prefer to send that to you privately.

I have found that E-glass masts just don't have the stiffness necessary for a good free-standing mast. An infused one would be a lot better than a vacuum bagged one, but still, it can't beat carbon for weight, strength, and stiffness efficiency.

Eric

 

Hi Eric - Like you I have been designing and building masts from sabots to superyachts over the last 20 years plus.

1) generally I spec a plain weave glass or carbon cloth on the outside of the laminate. This is usually described as a dress layer but it will stop bursting. But in a well built laminate without the dress if the laminate is bursting then it would have done so much earlier with 45s on the outside.
2) Generally if the 45s are on the inside or the outside the torsional difference is very little
3) The hoop ply is definitley not needed in a mast. I have yet to design one that it is needed. The hoop does present a problem in that it is the most likely layer to bridge and make a poorly consolidated laminate reducing mechanical and geometric quality
5) infused Eglass laminates have an E=35GPa plus and make much lighter masts then timber, obviously they can't compete with carbon. Using S2 or H glass we can get 45GPa which is quite attractive
But they still need a mould. Masts are always a compromise with cost/materials/required weight/manufacturing process etc etc. All these things have to be considered and mastered to make a good one.
6) The FE can predict all the buckling modes global & local. But it does require accurate mechanical properties. I always request clients commit to testing their laminate before we design. They generally save the dollars in the project due to the accurate mechanicals.
7) When you have time send me an email and I'll set up a small experiment. I'll do a simulated coupon test on some of my figures & publish when done here.
8) I may even do a quick mast for sigurd if he has the right info. Cheers Peter S

 

I recently did a review project for Mike Waters at small trimaran design for one of his masts. The section is about 190x66mm speced by him. The panel length is 3m. Although not a free standing mast I did a full buckling analysis on it for Eglass and CF. The results are as follows: 1) 1.9mm thick Eglass section 1.61kg/m 2) 1.2mm thick CF 0.81kg/m. The target weight for the mast was 2kg/m and the timber version was heavier then this. The design compression load was 1900kgf (sf=2.5) The Eglass version could have been made lighter if the section was made wider but the width was a given. The glass version would be quite a bit cheaper and easier to do then the CF version and fulfilled the weight target easily. Cheers peter S

 

Those are expected results, in my view, with a stayed rig where the mast is in pure compression, and the buckling is an in-plane phenomenon. My design comments are based on free-standing masts where the mast experiences pure bending, which puts one side of the mast in compression, the other side in tension, and shear across the leading and trailing sides. The critical concern is to make sure that the mast section does not ovalize under load--it needs enough wall thicknes and fibers oriented properly to handle the shear load and prevent the mast section from ovalizing--the sides of the mast move closer together, making the mast section narrower. This assumes that the mast is bending primarily toward the narrow side (transversely) although there is also some fore-aft bend.

When I get back from my trip, I'll try to pull out a mast design for you to check. I'll be interested to know if your program can predict how much section shape ovalizing occurs. The trouble with ovalizing is that once the mast section starts to ovalize, the moment of inertia and section modulus of the section both change--they are not constant--so that the strains in the laminate change accordingly by a large amount.

Packking for my trip, so I'll be available only intermittently for this coming week.

Eric

 

Hi Eric - yes initial buckling is an in plane mechanism. Its due to the compression of the material into a shorter space (not by a stress level as can be commonly described) . The geometry/material cannot exist at that length so it has to buckle to accomodate the shortening. There is no difference in a free standing rig to a wire rigged mast in terms of the local buckling mechanics. Ovalising is called lozenging whereas a local buckle is called a cripple. I can predict lozenging and crippling and global buckling. Buckling is the structures desire to reduce local strain. But to explain something. A normal mast section is designed to be elastically stable at some load factor above the maximum service load, say 2 or 3 times. This is usually determined by linear static buckling analysis. eg we require that the section first buckles globally (called Eulers buckling) at say 2x the service load, then after that it buckles locally say 3 or 4 x the max service load. So these local effects should theoretically never be seen in the mast. In the case of a free standing mast the first global buckling case is the mast deflecting sideways. Then it will lozenge or cripple depending on the geometry and the deflection. Just because a mast cripples or lozenges does not mean it fails. This is called strain stiffening or strain softening. If the section is strain stiffening when it buckles it unloads, snaps back and reloads. If it is strain softening it buckles, continues to deform and may end up with the mast failing. In thin aluminium dingy masts its common to see small wrinkles in the mast base. These are cripples but are stable. In composite masts that have no plastic capability buckles tend to occur, snap back lifes good or buckles, become unstable mast fails lifes bad, for a short period. To determine if a buckle is stable or not rquires a non linear buckling analysis to be done. These I do regularly either to investigate the post stability of a buckle, to check that the linear assumption is correct or some other factor. In designing racing nmasts where the client wants a reall y lightone I have to agree to designing say at SF=1.5 or 1.25. In this case I have to usually flip the failure chain to loacl the global. So its hard to get the local failures occur before the first global buckle occurs. This is the tradoff to lightweight design. Potential mast instable buckles are close to the working loads and these occur before the Euler buckle. So we are closer to elastic failure vs a normal mast. Will work through this soon.... Cheers Peter s

 

Peter, Eric,

Very interesting insights on mast technology. I am very ignorant with structural analysis & FEA.

That is why I reason using analogy.

Regarding the mast wall thickness/ mast diameter ratio I saw 3% figure above, probably for a classic mast fitted with a classic sail with a lot of load on the leech
and therefore compression loads well above compression due to righting moment only
(It is my intuitive analysis).

Somewhere on this forum or SA, I remenber Steve Clark mentionnning Cogito's main spar with 200mm diameter and 2mm wall thickness so a 1% ratio.

For such "wing-tubes" , filament winding seems to be the road to go.
As long I have the good inputs, I think I could perform calculations for flexion, torsion, and buckling.
But for instance how to account when some UD fiber is @ 10° ?

Could it be wise to have the most external & internal layer @ 45° or around (I saw somewhere the optimum angle would be 51°)in order to address torsion.
And could these 45° layers play the role of the 90° layers used to coupound the whole stuff in order to save weight ?

In fact I know a filament winding boutique making spinnaker poles using T700 and post-cured at hight temp, but no autoclave, their mandrin's section would be perfect for my A-Cat wing.

Does anybody know any workpaper addressing structural engineering calculations for carbon/epoxy filament winding technology?

Thanks for writing these long comments, very enlightings for my SE understandings.

Best regards

EK

 

Hi Erwan - Filament winders put the 45s on the outside to control and consolidate the 0-5deg fibres on the inside. So this is a procesing issue not the best answer. Due to the slight pretension a winder produces the laminate realises a very good properties. But it is better to have the 0deg fibres on the outside if possible (as a geneeral statement)The ratio of D/t is very dependant on the geometry (local radius) and loading. 100/1 or 1% wall thickness is common in many applications. As I do all of my design via FEA I don't get caught up in the ratios. The model either works or it doesn't. The other reason winders produce such a great tube is that the geomerty is very accurate as they have to use high spec machining and finishing to produce the mandrel so the tube istherefore very accurate. I often have to do models to test if the manufacturing variables are OK/. eg most parts change shape as they cure, especially thin ones. So we estimate the worst shape the part could eb and run the buckling on that. Not on the theoreticl shape. eg if we build a perfect round tube (as a CAD system would) then apply loads to it perfectly as a FE system would we get a perfect answer. So the buckling loads will be higher then we see in practice due to all the real world imperfections. I have to be aware of these relative to the project. There is stuff around on pultrusions and winding if you dig around.

laminates are designed using classic ply laminate theory. It accounts for the change of axis direction of the fibres. I'lll try and find a simplified approach paper I was given when I started on this stuff. But to paraphrase it. You design the UD component to resist the bending and direct tension/compression. Then you design the 45/45 to resist the torsion, then you combine them together as an interleaved laminate in the knowledge that the combination is better then the component. So its a conservative approach. The +/-60 winding (or 51 as you say) optimised laminate that has no UD is a nice theory but puts a lot of load on the resin. So is rarely used. Some UD is beneficial to reduce the resin strain. Cheers Peter S

Cheers Peter S

 

Thanks Peter,

Intuitivly I was thinking as you said, calculate the UD for bending compression, calculate the 45° for torsion, wrap everything with a 90° inside and outside, and you get it. But I am always very cautious with my intuitions.

If everything works fine, next week I should be able to make some pictures at the ICCC, in Falmouth, you know the C-Cat regattas.

If anybody is looking for some detailled picture of something on C-Cat, just let me know, I ll try to do my best.

Best regards

EK

 

For a general purpose tube don't use 90deg fibres. Only need 0deg and 45deg. Hoop plies fail early and first plus they bridge. Try a 70%UD and 30% DB works great. Put the 45s on the inside if the process will allow 35% UD then 30%DB then 35% UD . Eg if you make it using infusion this is easy. If you having it wound the 0deg will be say +/-5deg and the DB will be outside. Peter