Mast bend charasteristics ( dynamic gust response)

Hello All,

I am planning on building a carbon wing mast for a catamaran, the section shape will be a 5% mast according to the method presented by Tom Speer in the paper:
http://www.tspeer.com/Wingmasts/teardropPaper.htm
The question I have concerns mast bend. I've read about dynamic/automatic gust response, in Frank Bethwaite's High persformance sailing and on homepages from various spar manufacturers. However none of these sources offer anything more substancial in the way of furmulae or numbers.

The taper on a a-cat mast (marström), was from a circumference of 17,5 cm to at the hounds to 14cm at the masttip. This would (with same laminate stack) result in a reduction in stiffnes to 64% of the stiffnes at the hounds.

I don't know if this is at all representative, and I don't know how it scales.( I plan to have a 27sqm unarig on a 4m wide doubletrapping cat) Could anyone please give me some hints??

Regards
Patrik Elfving

 

Anyone have some sort of clue???
Would be very good with ballpark guesses, somthing to put me a bit in the game.

I don't really grasp if the mast bend works the same way for skiff masts as for catamaran masts ( the former should be much "softer" in the fore aft plan).

Any input greatly appriciated.

Patrik

 

hi patrik111,

You will not get very much flex in the for and aft direction of a wingmast, so bending to gusts will happen from the mast bending sideways. If you have a comparable standard rig that has the right bend characteristics in the for and aft direction, your ballpark sideways dimensions for the wingmast can come from the for and aft dimensions of the standard rig. Of course, since the inertia of the wingmast section will be greater, (since it is a comparitively longer section), you can make the wingmast's athwartships dimensions smaller. By how much and where, is a project in finite element analysis, or equivalent calculations.

One option is to look around for comparable cats with wingsails and copy.

hope this helps.

 

Patrik,

In my free-standing mast designs, I calculate mast bend to a certain amount, based on a fraction of the overall righting moment of the boat. This works well for monohulls, but on multihulls I am still waiting for some of my designs to be built so that I can get some feedback on mast bend in gusts.

On a monohull with a free-standing mast, I design the structure of the mast to the maximum righting moment of the boat x 3 factor of safety. This covers strength. For stiffness, I take 2% of the righting moment (assuming a triangular load distribution, maximum at the gooseneck and partners, tapering to zero at the tip) and design for 2% tip deflection. On monohulls, I usually have to add carbon fiber to make this work. In the end, the mast bends normally in winds up to 15-18 knots (onset of white caps on the sea). Then gusts bend the mast tip to leeward, and the hull remains at heel, without going over further. Usually, the boat speeds up through the gusts, and the whole action is very comfortable and not threatening. And, as the masts recover from the gust bend, this action causes a pulse in boat speed. That is, as the mast comes back to shape, the hull accelerates forward--you can feel it.

On multihulls, it is a different story. The same design criteria applies, 3 x max. righting moment. But on a multihull, the max. righting moment is extremely high--it occurs as soon as the windward hull leaves the water, a very real situation on lightweight multihulls. As a result, the mast is very heavily built, so it becomes impossible to design for optimum deflection because overall strength is such an important, overiding criteria.

For wingmasts, I generally design to a chord-to-width ratio of 2 to 1, sometimes 2.5 to 1, and the mast section is an ellipse. An elliptical shape is very easy to engineer, much less cumbersome than an aerofoil shape, and airflow enjoys the elliptical nose shape for good, prolonged boundary layer attachment. To go thinner on the section, such as 3 to 1 or 4 to 1, the foil would become so thin as to be hard to trim, and it would bend uncontrollably. By keeping the section shape at 2 to 1, the mast bends both athwartships and aft, and is relatively easy to control and trim.

Again, I have more experience of this behavior on monohulls. I have two mast designs on the board now for large catamarans. One is for a 51' cat that has been in construction for 7-8 years, and is only now starting to go together on the rig. It will likely be another year or two before that owner has the boat out and sailing so that I can get some feedback on its rig. The other cat that I am working on is a 58'er being professionally built in Hungary. I just finished its mast design (the boom design is yet to happen) and again, it may be a year or two before that boat is sailing back across the Atlantic. Both of these rigs have balustrade booms that support both the main and the jib. The mast and boom both rotate independently of each other, so they are quite interesting rigs. But I have to wait until they are launched to get any more feedback. I expect that the masts will be very stiff, and that they will bend some, but perhaps not as much as would be ideal in moderate wind conditions. Their optimum gust bend will likely occur at higher wind speeds.

Eric

 

Eric -

So for stiffness, you essentially design for 2% tip deflection (in relation length of cantilever portion of mast) at a righting moment equivalent to only 2-3 degrees of heel? (2-3 degrees heel looked to be +/-2% of max righting moment when I interpolated from stability curves of several monohull cruiser/racers).

What kind of tip deflections do you end up with at 15-20 degrees of heel?

Chris Krumm

 

Chris,

The rule I described is one I derived empirically from my previous designs that allows a decent amount of deflection in moderate wind speeds. Yes, 2% deflection is in relation to the cantilever portion of the mast. If 2% of the righting moment occurs at 2-3 degrees of heel, so be it--of course, a lot depends on the shape of the hullform. At 15-20 degrees of heel, it is nearly impossible to predict what the mast bend will be, because the load on the sail necessarily decreases as the wind speed and heel increase (the mast and sail fall away from the wind, and the angle of attack is all over the place--these are not steady state conditions). In fact, the mast will pump a little in gusts, and the amount of travel is really pretty gross, on the order of inches and feet, rather than fractions of an inch or a few inches. Suffice to say that a mast will typically bend up to 2-3', depending on its engineered characteristics.

Too much bend is worse than not enough bend. The rig and the boat go out of control, and of course, sail shape goes to hell. I had one mast design that was built in fiberglass (the last fiberglass mast I ever designed) and its tip deflection was about 8' in about 12 to 15 knots of wind--the top of the mast was overhanging the deck edge, way off side. We had to stiffen the mast with double diamond wires to bring it back to something reasonable. Fiberglass is a lot more flexible than carbon fiber, and that is why it is not a good material for masts--they act too much like fishing poles.

I suppose that one could figure out some kind of extrapolation to design mast bend for more realistic conditions--say at 10 or 15 degrees of heel, with some desired amount of bend. How much is enough??? 10%, 15%, 20%? Again, one would have to study a bunch of different boats to find out what makes sense, and unfortunately, there really aren't that many free-standing rigs out there whose owners are willing to give me data. And you need to know the specifics of the mast design--inside/outside diameters, laminate schedule, etc., all normalized to a uniform engineering basis. Also, data collected by owners/amateurs is usually totally unreliable--you cannot depend on it, no matter how clear your instructions are. You have to be there. And, it would cost a lot of money to go around the country setting up test sails in unpredictable wind conditions in order to collect the necessary data on the masts, boats, and mast bend.

My rule of thumb, as I say, was easily derived on inspection of a large set of mast designs that I had done previously. In particular, I designed the masts for the Herreshoff cat-ketches (28', 31', 38', and 45'). The 28'er masts were too stiff, the 31'er masts were just right, the 38'er masts were too flexible, and the 45'er masts were way too flexible. All these masts were built on the same mandrel, so engineering and design were fairly uniform with minimal variation in design parameters. Knowing these things, my derivation became a convenient measure and check on my work which evolved into my deflection criteria.

Eric