Free Standing Mast Loading

Discussion in 'Boat Design' started by Chuck Losness, Dec 24, 2015.

  1. Chuck Losness
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    Chuck Losness Senior Member

    I really like cat ketches and wish that I could have a high performance cat ketch. Since my finances don't allow that all I can do is study and dream. I would like to thank Eric Sponberg and all the rest of the forum members for sharing their knowledge of freestanding mast design. There are two things that I have not been able to figure out.
    First when dealing with a freestanding rotating mast set on a stub mast I have not been able to figure out what loads are born by the stub mast verses the rotating mast. I can think of two different scenarios and have attached a drawing showing how I think the loads might be distributed between the stub mast and the rotating mast.
    My other question concerns the balance of a cat ketch. Specifically how much the center of effort of the sailplan should lead the center of lateral resistance. I have a vague recollection of reading one time that the lead should be zero with the center of effort directly over the center of lateral resistance. But I have never been able to find where I read that.
    Thanks for any help you guys can provide.
    Chuck
     

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  2. PAR
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    PAR Yacht Designer/Builder

    Well Chuck, it depends on a lot of factors, many having little to do with the rig, such has entry type and half angle, hull form, performance expectations and of course rig proportions and layout, etc. As a rule, net zero lead isn't practical underway, so some lead is factored in, so the helm offers responsiveness and the hull tends to want to point rather than fall off. As a matter of course, I've never seen a yacht that went well to windward with too little lead. You need the turning moment to keep the bow "engauged" so you can claw upwind. Too little or no lead and it'll just blow away and piss you off. On the yachts you're in love with (my assumption) the lead is relatively modest, as it is in most divided rigs, but 8% to 14% would be the range. This range can be refined by clipping the corners with the other portions of the equation, such as rig and appendage aspect ratio, hull form efficiency, form, etc. For example you'll need more lead with a bluffer than usual bow, less with a finer one, more lead if the sail aspect ratio is higher than typical, less if lower, etc., etc., etc. Your boat is in the 10% - 12% range, probably closer to 10%.

    As to the stub loading, well (again) it depends. If this is a frictional thing, with no bearings, load or thrust accommodation (in their simplest form - washers), then look toward B (tube in a tube), but if the design is more refined and load transmission and dispersal is addressed, you could get localized loading like that in A, but the bearings and thrust accommodation is partly or wholly handled (dispersed).
     
  3. Chuck Losness
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    Chuck Losness Senior Member

    Par
    I agree with everything you said about balancing the rig. I asked the question about balance because I remember reading somewhere that the lead should be zero with a cat ketch rig and I was just looking for input on that.
    I probably didn't ask the right question regarding the loading on the stub mast verses the rotating mast. It is my understanding that with a free standing mast the max load is the righting moment at 30 degree heel. This max load is at the partners/deck and at the gooseneck/wishbone. It tapers to zero at the mast head and at the base of the stub mast.
    The better question is how is this load apportioned between the stub mast and rotating mast at the deck and the boom. My intuition suggests that since the stub mast is rigidly attached at the deck then the surrounding deck structure shares this load and therefore the stub mast does not take the max load at the deck. The loads at the boom are different. The rotating mast has to be able to withstand the max load here all by itself because otherwise it would fail just above the stub mast. The stub mast at the boom provides support for the rotating mast but how much of the load does the stub mast bear. I don't know the answer to that question.
     
  4. PAR
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    PAR Yacht Designer/Builder

    Only on a very small boat can you get away with a net zero lead. I call this the asymmetric butt cheek computation. Ever notice your boat sails better on one tack, compared to the other? Bingo, just like a well presented set of boobs, your butt cheeks aren't symmetrical and the fat side rules the day, buddy. You think I jest? Think of this as the Darth Vader and Jedi side of things with small sailboats. Once your boat gets big enough,that a good fart isn't going to cause an accidental jibe, the lead needs to be dialed in better or you'll suck on some points of sail.

    If this is a tube in a tube, you have to consider the modulus of the stub and the point loading at the tip of the stub. What this usually brings on are estimates of how much bend you're willing to kiss off in light air, knowing it's stiff enough in heavy. On a racer (which brings the rig type into question), I'd set the stub modulus at twice the boat's displacement, knowing it'll be too stiff in zephyrs, but will likely get you back to shore when it's bending a lot more than you feel comfortable with (welcome to free standers) in SCA conditions. Personally, I'm not a fan of the stub arrangement and would prefer (on a boat like yours) to capture the heel and use the purchase depth to control things. How much purchase depth do you have or invision?

    Why don't you give me a call (my number is on my site) and in 5 minutes we can get an handle on this puppy. Tomorrow is "cackling hens day" (the ladies come over and play cards and it's cluck, cluck, frigging cluck all damn day, so I need the excuse). Help a buddy out man . . .
     
  5. Chuck Losness
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    Chuck Losness Senior Member

    Been thinking about how to determine the load at the upper end of the stub mast. It is my understanding that the design load at the partners is the righting moment at 30 degree heel. The stub mast is a cantilever beam and the formula for determining the bending moment at the base from a point loading along the beam is Mb=L*P where Mb is the bending moment. L is the length of the beam and P is the load. Since we know what the Mb is can the formula be rewritten to solve for P? P=Mb/L. If the formula can be rewritten then the maximum load at the end of the stub mast can be calculated. For example, if the righting moment is 6000 lbs and the length of the stub mast above the deck is 4 feet then the maximum load at the end of the stub mast should be 1500 lbs. (6000/4=1500). Is this correct.
    This then got me to thinking why couldn't you use this same process to determine the maximum load at any place along the length of the freestanding mast?
     

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  6. gonzo
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    gonzo Senior Member

    The load will depend on the type of rig. For example, a marconi rig will have a distributed load. A boomless balanced lug will have a point load at the parrel.
     
  7. Eric Sponberg
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    Eric Sponberg Senior Member

    Hi Chuck,

    I have been away from BD.N for some time and have only just now stumbled on your post. You're close in your reasoning. First, you consider the combination of wingmast/stubmast as one unit. The maximum bending moment is at the deck, and it is a live load that should be equal to the maximum righting moment of the boat. We'll use the designation of this moment as Mbs. Divide Mbs by the depth of bury of the stubmast between the deck and the heel, and that equals the reaction at the heel of the stubmast. Divide Mb by the distance from the deck to the top bearing and that equals the load at the top of the stub. The sum of all transverse loads on the stubmast must be equal to zero, so the reactions at the top of the stub and at the heel, added together, equal the reaction in the opposite direction at the deck on the stubmast.

    Now for the wingmast. Divide Mbs by the height of the top of the wingmast above the deck, and that equals the equivalent transverse load at the masthead. Multiply that top transverse load by the distance from the masthead to the level of the top bearing on the stubmast, and that equals the maximum bending moment on the wing--we'll call that Mbw. Divide Mbw by the distance between the top bearing and the deck, and that equals the reaction of the bottom of the wingmast at the deck bearing. Again, the sum of forces on the wingmast have to be zero, so if you add the load at the top of the wing to the load at the bottom of the wing, you get the wingmast load at the level of the bearing at the top of the stub. Ideally, it should be equal and opposite to the transverse load in the other direction that you calculated for the stubmast.

    For illustration, I attach a PDF excerpt of the mast calculcations that I did for the wingmasts/stubmasts on the Globetrotter 66.

    I hope that helps.

    Eric
     

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  8. PAR
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    PAR Yacht Designer/Builder

    Eric are you fully retired now or still puttering about? Most of us find retirement just proves that, your golf game can't justify all the extra time on your hands, so you're back to doing something pretty quickly.
     
  9. Eric Sponberg
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    Eric Sponberg Senior Member

    Hi Paul,

    I am fully retired as of 1 January (last week). I have been meaning to make an official posting here on BD.N but have been too busy--with making last minute repairs on my boat and the myriad things that happen when you have a change of course in life--like what to do with 40+ years of office stuff and professional output. There will be an announcement in the next Professional Boatbuilder magazine in Dan Spurr's Rovings column. Sponberg Yacht Design Inc. no longer exists--it shut down officially on 31 December 2015. I can still consult, but I am being very picky about taking on any new work. Certainly, I am not going to be designing boats and masts any more--my wife and I are going to become full-time sailors again. We have purchased my very first commissioned design, Corroboree, back from the original owners, and we are outfitting her for world cruising. I will try to make a more informative posting in due course.

    Thanks for asking.

    Eric
     
  10. PAR
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    PAR Yacht Designer/Builder

    Well, have fun. I'll bet we'll read about your voyages soon enough, on that nice little sloop. How well have the 30 year old sticks held up over the years?
     
  11. Eric Sponberg
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    Eric Sponberg Senior Member

    I'll probably be reporting on our activities through our Facebook pages.

    The mast is the second mast for the boat. The first one burned in a fire in 1995. The whole deck burned in the fire, so the boat was rebuilt after the fire and a new mast was made and installed. It's in good shape.

    Eric
     
  12. Chuck Losness
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    Chuck Losness Senior Member

    Eric,
    Congrats on being retired. Your life will now become busier then you can imagine and you will wonder how you found the time to work in the past. Your day planner will quickly become your most important tool.
    My only advice on going cruising is to not get obsessed with upgrades, changes, etc. to your boat. Just do the absolute bare minimum to be safe and leave the dock. I mean get out of dodge as soon as you can. Cut those dock lines. After a year or two you will discover what you really need. It will be very different from what you thought you just had to have before you left.
    I would like to thank you for all of your knowledge that you have freely shared over the years. I have spend literally hundreds of hours studying freestanding masts. The starting point in my studies was the paper that you shared several years ago that you authored back in the 80's on the design of freestanding masts. I am just a sailor who likes to understand how things work and I enjoy intellectual challenges. Roark's Stress and Strain has put me to sleep more times than I care to remember.
    Time for me to redo my spreadsheets yet again.
    Fair winds and calm seas.
    Chuck
     
  13. LP
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    LP Flying Boatman

    Any chance that paper is floating around here on BD.net? I'm working some freestanding masts and have been dredging up mostly forgotten engineering fundamentals to dimension them. The design books I've read deal mostly with stayed rigs or base freestanding dimensions on the length of the stick Some free standing theory would be a nice read with the bonus of a little application too. :D

    And congrats to Eric. Thanks for all of your contributions over the years.
     
  14. Chuck Losness
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    Chuck Losness Senior Member

    LP
    Eric did post it here on BD.n 5 or so years ago as I recall. I have a copy but since it is not my work I will not repost it. Search through Eric's postings and you should find it. If you can't find it then pm Eric and ask for a copy.
     

  15. Eric Sponberg
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    Eric Sponberg Senior Member

    LP, the paper is attached. This was presented at the 6th Chesapeake Sailing Yacht Symposium in 1983. Pay particular attention to the Addendum at the end of the paper, it has some corrections and additional advice. You may circulate this paper to anyone who is interested. A few years ago, I gave copies to The Landing School and to Westlawn so that all their students could study it.

    Good luck,

    Eric
     

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