Mast loads for freestanding masts

I have figured the maximum wind loads and was using a tube stress calculator to determine the diameter and wall thickness I will need for my aluminum masts. Problem is that the calculator assumes a tube supported at both ends. At a given length how much more stress does the material endure when cantilevered vs supported at both ends?

What other factors should i consider when deciding how strong to make my masts? This is a catamaran.

 

What is your righting moment?

 

Sigh...where to start...
Yes, free standing mast loads and sections are calculated very differently than shroud supported masts. This is a time where the square/cube law of loads and materials hurts the design. Except for very small masts (think Optimist pram) they are generally heavier overall (including the shroud weight) and require significantly more engineering of the bury section, mast step, and partners (because they are, as you say, effectively Cantilever Beams).

Start here.
https://ericwsponberg.com/wp-content/uploads/state-of-the-art-on-free-standing-masts.pdf

EDIT: X-post with Blueknarr, maybe he already has a spreadsheet of it set-up.

 

Approximately 6000 lbs, 50 ft2 of sail per mast in a biplane setup, masts are 12' high from last support to topmost sail attachment.

 

Forgive me for saying this, but I think stayed masts are one of the dumbest inventions in history, and dangerous. Nothing anyone could say would make me choose to use a stayed mast. Now that that is out of the way...

I understand they are calculated differently, what i really need to know is how to calculate a cantilevered tube using this calculator(Roguefab website, tube calculator). My first impulse is to calculate for the max sail load(~200lbs@40mph per sail) with an even load distribution(battens spaced ~18" apart), but double the actual span of 144" to 288" in the input to account for it only being supported at one end. As above: Approximately 6000 lbs righting moment, 50 ft2 of sail per mast in a biplane setup, masts are 12' high from last support to topmost sail attachment. The masts will slip into tubes integrated into the vertical part of the crossmembers that go down to meet the hulls; I have zero concern about the strength of this part of the sail setup.

 

I found a cantilevered beam calculator: Cantilever Beam Calculator https://calcresource.com/statics-cantilever-beam.html

The calculator assumes uniform wall thickness and diameter. You would save weight by tapering the diameter or decreasing the wall thickness towards the top. That decreasing wall thickness is often approximated by inserting another tube at the bottom, ideally with as tight a fit as lets you still slide it in, and perhaps bonded to the outer tube, and with the wall thickness of the inner tube tapering gradually to zero at its upper end, to avoid creating a hard spot there.

Fatigue. You have to estimate how many load cycles at what load you'll get per hour of sailing, how many hours you expect to sail per year, and how many years you want the masts to last, then make them stronger than your maximum dynamic load by the required factor. Each fatigue curves is, I think, measured for a sinusoidal load of fixed amplitude. The loads on a mast are going to be a spectrum. However, this has to be a standard problem, so it should be possible to find a solution in a textbook.

You should also find out how much extra strength you need to resist local loads, such as compression from your booms, and the load from your halyard blocks.

You didn't say whether the maximum wind load you found is static or dynamic. One source of dynamic loads is a gust hitting, and what resists immediate capsize is not only stability, but also the rotational moment of inertia. Another source of dynamic loads is movement in a seaway.

 

I saw that one too. Some of the outputs are meaningless to me. What would make it simpler for me is to design for the wind load and apply a safety factor to account for fatigue. Is there a standard safety factor or something designers use to account for this?

For masts of this height/size/load it seems overly complicated to use a tapered masts. Each complete rig should come in under 120lbs including battens, mast, sailcloth, hardware, etc. A 12' x 3" diameter x .25" wall 6061 tube weighs just 30lbs, saving even 10 lbs seems not worth the trouble. Also having extra material up top would be good for mounting stuff and probably help minimize mast bend.

The weight of the battens will be balanced relative to the mast and the halyard will be strung right next to the mast, and the halyard load will be small because this sail design will not rely on halyard tension to shape the sail. The halyard will be supporting 60lbs at the most. In other words, bending and compression loads from the halyard will be very small. Basically the only significant loads will be wind loads applied to the mast by the battens that encapsulate it and accelerations from the movement of the boat.

The wind load stated was the maximum wind load I would ever expect, meaning if I chose to sail in 20mph wind with full sail and encountered a gust of double the wind speed. The rig design I have come up with is really all about easy, fast, reliable and safe reefing and trimming.

This is an interesting benefit of the biplane rig, the weight of the rigs is outboard on the hulls, adding even more moment of inertia than a centrally located mast.

Basically I will be using this boat for 6 months to sail to and around the Bahamas and back, then I will probably sell it. This is just a warmup for a larger more seaworthy boat, and to see if the sailing life is really for me. Regardless, I'd like the masts to last indefinitely, along with the rest of the boat. It goes against my ethical structure to build stuff that doesn't last, especially where people's safety is concerned.

I originally planned on using 3" x 1/4" wall 6061 aluminum, I am here to make sure that's an appropriate choice. Probably overkill.

 

Search the forum. Years ago this was discussed in detail. Eric shared a paper he had prepared that describes how to design free standing masts. Free standing masts are a cantilever beam with a force that decreases from the highest at the partners to zero at the mast head. If you are looking for some quickie online calculator it doesn't exist as far as I know. You will need to create a spreadsheet that calculates the load at one foot intervals along the length of the mast.

 

Thank you, that paper was enlightening and shared a simple approach to designing a sufficiently strong mast. I was on the right track originally in a roundabout way.

 

The wind load is irrelevant. Righting moment is what you calculate for. Also, if you want a realistic factor of safety, the maximum force on the mast will be in a rollover.

 

Wind load is not irrelevant, at all. If not, what is the force acting on the mast? What happens is that, since the force of the wind on the sail is very difficult to calculate, it is assumed, simplifying the problem quite a bit, that a force is applied to the mast (at a point that is also approximately calculated) that makes the boat list. 30º. This force can be deduced by calculating the heeling moment at 30º, which is a quantity that does not depend on the force of the wind but on the shape of the boat and its weight. This method is more conservative, gives worse results than the detailed calculation, and is therefore safer and simpler.
It is also assumed that in very strong winds the skipper will order the sail to be reefed. Nobody calculates for the moment of overturning.

 

Wind load is indeed relevant. Can't overcome your righting moment without wind load or wave action.

This is a catamaran, not really worried about what happens to my masts in a rollover.

But you're right, in a way, they use righting moment as a basis for the calculation, but that is representative of potential wind loads, and they factor in fatigue and apply a safety factor. Thats the simple version anyway.

 

For the size of your masts and sail area have you thought about using laser 4.7 sails and masts.

 

You may find this of some assistance, for more quantifiable numbers/methodology.

 

I'm not familiar with that vessel. I really want to design and build my own rig. It is very important to me that it be very simple and reliable in all conditions. I am firmly settled on using a soft wing sail rig. It has all the qualities of a junk rig and can be made even simpler to operate with less lines. For this particular journey windward ability will be very important and it seems that a wing sail is the ticket. It may not be quite as efficient as it could be but it should perform well in a wide variety of circumstances. And it's just safe, shouldn't have to go up and mess with it for any reason. When I have finished the design I am going to post it for people to scrutinize.