Un-stayed mast flexibility

[Inquisitor]

I read several posting that their are benefits of having a certain amount of flexibility in an un-stayed mast. I see from Rob's HarryProa videos, that the flexibility permits the spilling of some air during a gust... thus allowing a multi-hull to be rigged more for the average wind speed versus having to reef for maximum wind speed. Is there a rule of thumb... say the tip can flex 1%, 5% or 10% of the height of the mast? Or is there some more analytical method to give a desirable flexibility?

Thanks All.

[ThomD]

I think it is more an accidental result of early attempts to configure spars.

[Doug Lord]

Originally Posted by Inquisitor

I read several posting that their are benefits of having a certain amount of flexibility in an un-stayed mast. I see from Rob's HarryProa videos, that the flexibility permits the spilling of some air during a gust... thus allowing a multi-hull to be rigged more for the average wind speed versus having to reef for maximum wind speed. Is there a rule of thumb... say the tip can flex 1%, 5% or 10% of the height of the mast? Or is there some more analytical method to give a desirable flexibility?

Thanks All.

========================
You might consider PM'ing Eric Sponberg who is a member here regarding this question. I'm not sure he's ever done an unstayed mast for a multi but he knows the design and engineering of unstayed masts very well.

[rob denney]

Originally Posted by Inquisitor

I read several posting that their are benefits of having a certain amount of flexibility in an un-stayed mast. I see from Rob's HarryProa videos, that the flexibility permits the spilling of some air during a gust... thus allowing a multi-hull to be rigged more for the average wind speed versus having to reef for maximum wind speed. Is there a rule of thumb... say the tip can flex 1%, 5% or 10% of the height of the mast? Or is there some more analytical method to give a desirable flexibility?

Thanks All.

We started out with 10% lay off when the boat flies a hull, but have reduced it to 7%. Adds a little more weight, but the performance is worth it.

As all the boats so far have been cruisers, none have flown a hull so validating this is not possible. However, our engineering package includes a completed weight and flex tests for various weights hung at various positions along the mast. The weights have been within a kg or two and the flex results within a couple of mms, so I am pretty confident that the lay off numbers are pretty accurate as well.

rob

[Inquisitor]

Originally Posted by rob denney

We started out with 10% lay off when the boat flies a hull, but have reduced it to 7%. Adds a little more weight, but the performance is worth it.

As all the boats so far have been cruisers, none have flown a hull so validating this is not possible. However, our engineering package includes a completed weight and flex tests for various weights hung at various positions along the mast. The weights have been within a kg or two and the flex results within a couple of mms, so I am pretty confident that the lay off numbers are pretty accurate as well.

rob

I remember seeing some of your analysis vs actual results (I don't recall where... here, yahoo group or your site) but I recalled the difference being less than 1%. It was very impressive considering material variability... much less fabrication variability.

[rayaldridge]

You might want to look at what Chris White says in his book. He tried unstayed masts in his big tri, Juniper, but eventually converted to a stayed rig. In short, he was not able to adequately control sail shape in heavy air.

[ThomD]

There are some good lessons in Chris' experience, the main one I picked up on was if one has a wide staying base one should use it. In many proa designs one does not have the wide base, or if it is flexible it will not offer great spar support anyway. Another lesson I have heard elsewhere is that the spars with high flexibility and weather dumping "features" can be very expensive to have sails cut for. Lots of trial and error. That is mostly from discussions with sail makers 10 years ago, maybe modeling has progressed... This is often a problem with implementing other cool designs, like older workboat designs. or Lungstrom rigs like White Wings, not limited to unstayed rigs, which are becoming pretty comon.

[rob denney]

Originally Posted by ThomD

There are some good lessons in Chris' experience, the main one I picked up on was if one has a wide staying base one should use it. In many proa designs one does not have the wide base, or if it is flexible it will not offer great spar support anyway. Another lesson I have heard elsewhere is that the spars with high flexibility and weather dumping "features" can be very expensive to have sails cut for. Lots of trial and error. That is mostly from discussions with sail makers 10 years ago, maybe modeling has progressed... This is often a problem with implementing other cool designs, like older workboat designs. or Lungstrom rigs like White Wings, not limited to unstayed rigs, which are becoming pretty comon.

No idea what Chris' problems were, but look at the video at http://www.youtube.com/watch?v=8chR6DAFjGA to see an unstayed mast working on a 50' multi with 18 tonne metres righting moment. Team Phillips had probably the highest righting moment of any cat and her unstayed masts performed flawlessly.

A wide staying base is a handy thing, but still involves over 50 individual parts, any one of which can bring the rig down if it fails and all of which should be replaced every 5 years or so.

Doing an ocean trip with a stayed mast involves being hauled up the mast before you leave to carefully check every component. Then each morning and evening you carefully go round the deck checking to see if anything has come loose or broken. On the unstayed mast, if it is up, there is no problem. A stayed mast should be unstepped and checked each season. An unstayed mast never needs to be removed.

Sailmakers in my experience don't struggle with unstayed masts any more than they do with stayed masts (accurate measurements are needed for both) but the sail will last a lot longer as it does not chafe against the stays and is always hoisted and lowered with the rig pointing into the wind.

rob

[Eric Sponberg]

Originally Posted by Doug Lord

========================
You might consider PM'ing Eric Sponberg who is a member here regarding this question. I'm not sure he's ever done an unstayed mast for a multi but he knows the design and engineering of unstayed masts very well.

Inquisitor,

Thanks for Doug's comment. I always calculate deflection in my mast designs. It is better for a free-standing mast to be too stiff rather than too flexible. It is always going to bend some, but will it bend enough or too much? My deflection checkpoints have changed slightly over the years, but what I am lately settled on is this for monohulls: Calculate the boat's maximum righting moment, take 5% of this for the deflection moment load at the deck and tapering in a straight line to zero at the tip, and the mast tip should deflect 2% of the height of the mast above deck. For multihulls, the deflection moment is 10% of the boat's maximum righting moment and should result in the same 2% tip deflection of the height of the mast above deck. If the mast passes this criteria as an engineering checkpoint, it will have suitable deflection in most wind and weather conditions. The mast should be spilling the wind by the time you want to start reefing--this is usually around 15-20 knots of wind. If the mast bends too much, the sail will invert--curve in the opposite direction from a normal sail camber--Obviously, multihulls have huge righting moments, and a linear relationship does not necessarily exist between equal length monos and multihull boats. But there you are, this checkpoint works for me.

The actual deflection calculation is a double intergration (calculus) of the factor (M/EI)dx^2 along the length of the mast. The mast is tapered, and it has a varying wall thickness, so E and I both vary along the mast. The bending moment, M, is also varying. So M/EI is different everywhere along the mast,generally at maximum at deck level, and tapering to zero at the masthead. I do the double integration in a spreadsheet, and the result is the full deflection curve of the mast from heel to truck. You have to calculate the deflection between the deck and the heel, too. If the deflection does not come out right, then I have to reshape the mast (different size or shape sections, or different wall thickness, which means a different laminate), recalculate strength again, and then recalculate deflection. I give this final deflection curve to the sailmaker who can then use it to make a first pass at the shape of the luff of the sail. This is double-checked once on board the boat and the mast bend can be measured at the dock, and then assessed again when sailing.

Engineers reading this will recognize that this is a cantilever beam calculation, but because the "beam" (the mast) has a varying cross-section and the load also is varying, that is why calculus is required for the double integration of deflection. Boundary conditions also have to be applied (fixed points at mast heel and mast partners) to make the calculation come out correctly in inches (or millimeters) of deflection that can actually be measured.

For a lot of the rest of you, the above has probably caused your eyes glaze over, but you engineers reading this will know what it means. The point is, I do use a specific criteria to calculate mast deflection in the normal course of engineering the mast, and this has direct use for the sailmaker. The above engineering method works well for me.

Eric

[cavalier mk2]

Sew (ha!) the amount of anticipated deflection can be presented to the sailmaker who then allows for bend similar to allowing for headstay sag, though more at the top instead of the middle.

[Inquisitor]

Eric,

Thank you for your reply. It has been very helpful. I have been working on just such a spreadsheet which minimizes the use of Carbon for the zero degree plies (and total weight). It does account for variable E, I and M. Moment is variable from moment diagram (peak at base) and variable loading from a irregular shaped sail. It also does the cursory check of My/I stress along the length to confirm the S.F. stays above a certain value (say 4.0). Even with (or because of) all that, it doesn't constrain the problem.

The rules of thumb from yours and Rob's experience nicely cap that off.

Thanks.

[Eric Sponberg]

Peak bending moment will be at the deck partners, not the base. As a result, the shear loads are very high between the partners and the base, and the laminate should be checked for sufficient shear strength in this area. Also, I have found a factor of safety of 3.0 is plenty sufficient for a maximum moment at the partners equal to the maximum righting moment of the boat. A FoS of 4.0 uses up a little too much carbon unnecessarily if you are using the same moment.

Eric

[junk2lee]

Originally Posted by Inquisitor

I read several posting that their are benefits of having a certain amount of flexibility in an un-stayed mast. I see from Rob's HarryProa videos, that the flexibility permits the spilling of some air during a gust... thus allowing a multi-hull to be rigged more for the average wind speed versus having to reef for maximum wind speed. Is there a rule of thumb... say the tip can flex 1%, 5% or 10% of the height of the mast? Or is there some more analytical method to give a desirable flexibility?

Thanks All.

I have an unstayed mast and the first thing that came to mind per flexibility is that were it attempted to closely DESIGN it to spill wind,it might be very irritating as sail flogs on every boat-roll in a breeze...ie:the same apparent wind as a "gust".

[Inquisitor]

Eric,

I have many simplifying assumptions... off axis plies are not accounted for in the EI (conservative). The stress concentrations (nice crack tip initiators) where the carbon tows end along the mast are ignored (non-conservative). So, I only consider the spread sheet as a far-field (away from the actual boat joint). Its good to know that a S.F. of 3 can handle those. As far as the joint, I'll do an FEA model of the region and use the far-field loads.

One run of the spreadsheet, I got the Carbon fiber portion down to 42 lbs for a 45' mast, with 85K ft-lb moment at the base. That was using Rob's 7% tip deflection criteria. I'll also incorporate you're information. I'm concerned about that designs validity... with the wall thicknesses and local buckling. I use to have some closed form equations for orthrotropic shell buckling prediction, but seem to have lost that box from the old days.

[cavalier mk2]

Aren't commercial s.f./FoS 5? Would you need the higher amount if the boat was to be used for charter?
Junktolee, it is true that modern cloths such as Dacron, Mylar etc...are of a fairly rigid shape and won't conform to deflection. I suppose the old cotton sails stretching with the spars would luff less. Of course we can say the sail was designed to spill the wind in such a manner, if it was designed to set well with deflection it would look pretty awful when the spar was straight! Maybe there is a market for sail cloth that mimics the natural fiber stretch, though that might be hard on the manufacturers after all these years!