Estimating strength and stiffness of a carbon-wrapped 2-piece wooden mast

Discussion in 'Sailboats' started by laukejas, Apr 2, 2022.

  1. AlanX
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    AlanX Senior Member

    Hi @TANSL,

    In the initial design (of a mast) you do not know the details of the sail configuration. This is as they say is a "Red Herring".

    The issue is, if you do not know the full design, forces or the material properties accurately, it is rather pointless saying one estimate is better than another.
    I would agree that as you flesh out the design then more complex models can be used. But complexity does not solve uncertainty.

    Put in another way, the reason the Wood/FRP safety factors are so high is that the designer does not know either the loads or the material properties with much certainty.

    On a lighter note:
    I presented a master class to a group on mining engineers, when one bright fellow was not happy with me making low resolution calculations and indicated the calculations should use more decimal places.
    I answered how many weeks are there in a year?
    He answer 52.
    I answer, exactly? No, but does it matter, does the approximation lose it's usefulness!

    Regards AlanX
     
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  2. TANSL
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    TANSL Senior Member

    But that is precisely what the designer is for, to calculate those values.
    The safety coefficients, as I have always understood, can vary according to the precision of the calculation method used but never according to the information that the designer has at the moment of starting his calculations.
    I'm afraid I must apologize because I don't quite understand you and I'm probably responding to things you haven't said. For example, it seemed to me that you, without knowing the sail area and the shape of the sails, you do know the height of the mast. That would be nonsense, so I'm going to stop answering until I can improve my English.
    Thank you for your patience.
     
  3. AlanX
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    AlanX Senior Member

    @TANSL, No problem, Regards AlanX
     
  4. Chuck Losness
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    Chuck Losness Senior Member

    I am not an expert at this by any means. Just interested in the design of free standing masts. I am probably missing this but I have not seen a reference to the righting moment of the boat. It is my understanding that the righting moment determines the load on the mast. And the mast has to be designed to be strong enough to handle that load. Probably using the wrong terminology. I have a spreadsheet for the design of free standing masts. If someone can provide me with the righting moment of the boat I can plug in the rest of the dimensions to compare the different types of mast construction being considered.
     
  5. TANSL
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    TANSL Senior Member

  6. Chuck Losness
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    Chuck Losness Senior Member

    Thanks for the pdf. The pdf references the righting moment as GZ1 which I understand is the righting moment at 1 degree of heel. In the pdf GZ1 is multiplied by 30 to get the righting moment at 30 degrees of heel. Then uses a wind pressure analysis to determine the forces on the mast. This is not new to me. I went back through the posts on this thread and didn't see anything about the righting moment of the boat that this mast is being designed for. Without the the righting moment you can not determine if the designed mast is not strong enough, has sufficient strength or is way over kill. What is the GZ1 for this boat?
     
  7. TANSL
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    TANSL Senior Member

    The GZ30 is not equal to 30 times the GZ1. It is usually something smaller. But that number gives a safety margin. You will have to do some calculation to know the GZ1 of your boat or just calculate the GZ30. I don't know that figure.
    It is assumed that when the boat is in equilibrium the righting moment is equal to the heeling moment. So if you know one, it's easy to know the other. How much do you want your boat to heel before correcting position?
     
  8. messabout
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    messabout Senior Member

    That the mast must be sufficient to withstand whatever righting moment, is not the only criteria. The sail shape is dependent on the bend characteristics of the mast. For a performance mast the bend must be accounted for when the sail is cut. The mast must surely be stronger than the RM of a high performance dinghy would dictate. The OP has a hot rod boat that he is trying to improve by matching the mast to the sail, not visa versa. That is doing it the hard way.
    Carry on.
     
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  9. AlanX
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    AlanX Senior Member

    Hi @TANSL,

    Can you check your beam model equations:
    MastBending.png

    Regards AlanX
     
  10. TANSL
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    TANSL Senior Member

    @AlanX, thank you very much for your comments, I will take them into account for what they are worth by themselves.
    Thanks again.
     
  11. Ad Hoc
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    Ad Hoc Naval Architect

    Inconsistencies have been pointed out before, HERE, and incorrect use of UTS/welded values and grades HERE.
    Thus im unsure why unwelded 5000 series alloys are still even referenced??
     
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  12. rnlock
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    rnlock Senior Member

    I'll admit I don't have the patience to sit down and calculate and specifically go through all the details that have been discussed here. However:
    -In at least one spot, the ultimate strength values were used, rather than yield. This might be ok if you were only going to face one big gust, and you didn't care if the mast was starting to get damaged after.
    -The quality of the layup matters quite a bit. Not just the resin to fiber ratio, but the straightness of the fibers. This affects both stiffness and strength. If you can use pre-cured, pultruded strips, you'll get MUCH better results, especially for strength. But that might be kind of expensive. Hand laid up tow or good uni cloth will be much stiffer and stronger than woven cloth. "Uni" with cross stitching on it turns out to be a lot floppier than uni that's actually straight. I've seen the results on a hydrofoil that was much bendier than hoped.
    -The lower the quality of the layup, the less the mismatch between wood and carbon fiber. Let's consider wood that has an elastic modulus of 2,000,000 psi, and a yield strength of 5,000 psi. Elongation at yield will be about 0.25 percent. Maybe you have a lousy carbon layup that's kinked, and fails at 50,000 psi, with an elastic modulus of only 15,000,000 (guessing here). Elongation at failure would be 0.33 percent. So the mismatch isn't TOO bad. You still get to use 3/4 of the strength of the layup before the wood fails, creating a stress riser or point for buckling and the whole mast fails. Let's say you do a really good hand layup with tow. Maybe you have an elastic modulus of 19,000, 000 and yield at 100,000. Now, your elongation at failure is 0.53 percent, and you're using less than half the strength of the layup. If you're using pultruded carbon strips, they might not fail until 200,000, and the elastic modulus might be 20,000,000, for elongation at failure of 1 percent. At that point, you're only using a quarter of the available strength. This mismatch may be alleviated somewhat by using higher modulus carbon fiber. I wouldn't be surprised, also, if some kinds of wood have a higher elongation at failure. Or, maybe the wood core could be cross-grained. It's probably too much trouble to make a core of little wedge shaped pieces of end-grain balsa, but that would be ideal. Some builders of human powered airplanes used to lay up over aluminum tubing, and then dissolve the aluminum with acid. Maybe the thing to do is use a foam core that you don't count for anything, and work with it in a long piece of angle iron to keep it straight until it has reinforcements on all sides.
    -I had a friend who reinforced his wood mast with carbon fiber and epoxy. It failed at the partners. After that, he had a top-heavy aluminum mast, but at least it didn't break. Carbon epoxy isn't terribly strong perpendicular to the fibers, so it's probably important to protect the fibers from point loads, and also from buckling that might result from point loads. So something tough over the composite, and maybe some extra layup, with off-axis fibers inside would help. Or a heavy wood plug. Point loads would also be things like boom or gaff jaws, halyard attachments, etc.
    -The bending moment at any point will taper off quite a bit faster than linearly. Even with a perfectly rectangular sail, with a huge end plate to prevent an inevitable drop off in lift at the end, the moment will be proportional to the remaining height squared. Real sails are tapered, and real loads will likely taper faster. One could do worse than estimate the loads with Schrenk's approximation, which can be done graphically. You can pretend that the sail and mast are equivalent to a wing starting at the deck, because the first few feet aren't particularly important. Schrenk's approximation is probably good enough, considering all the other unknowns. Basically, you draw out equivalent area shapes, one's an ellipse and the other's the chord (width) of the sail at different heights. Hmm.. at least if you're using a vang. Still, I don't know typical values for wind shear over height, so maybe we should toss it all out the window. Maybe, at least in cases where there's a known good example with a wooden mast, the moment of inertial of the mast section can be matched at any given point, while making sure that the strength is at least as good. I expect, with limitations on minimum wall thickness to prevent buckling an local damage, such a mast might be narrower than a wooden one.

    -Come to think of it, while the righting moment of the boat is a pretty good guide to the load on the mast as long as it's not in the water, the biggest load might be when the mast goes into the water when it's rough. Ouch.

    -Some of the discussion was about torsional loads. What would put a significant torsional load on the mast?

    There's probably other relevant stuff I was thinking about, but I have a strong forgetory. (Other people may have strong memories.)
     

  13. TANSL
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    TANSL Senior Member

    There are also stupidities of enormous size (do not forget that we are talking about a self standing mast, which does not have, by definition, stays) :
     
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