Mast loads for freestanding masts

I make no claims of credentials here; my aim is understanding.

Is this a correct view of the math, at a high level and conceptually?

F = force (design failure)
RM = max righting moment
k = safety factor

F = RM • k

or RM = F/k, so the higher the safety factor the higher the (design) force; all things equal

And then, the F is used to size the alloy.

And so, the righting moment is not necessarily the failure unless you design close to zero safety factor or 1, I suppose. Anyhow, this was how I read it before the thread went onto sailing arguments.

Anyhow, I’m no sailor, just find this interesting.

I think the problem occurs here when you forget the design is factored to 3 times for a safety factor of 3. Anyhow, hope this makes sense and is somewhat correct. I did not apply units and probably should have.

I’ve learned quite a lot paying attention to @rxcomposite.

 

In Post #3, @jhardiman recommended starting with Eric Sponberg's 'State of the Art on Freestanding Masts.'

In Post #26, @rxcomposite linked to Eric Sponberg's 1983 paper 'Design and Engineering Aspects of Free-standing Masts and Wingmasts.' See page 78 for the intro to how he figures his design conditions and safety factors factors.

These articles and many more can be found here:
Articles https://ericwsponberg.com/articles/

In Post #29, @rxcomposite linked to a spreadsheet with diagrams of a force analysis at a freestanding mast with boom. Nice work - but I was looking for the calculator part, too!

The MIT spreadsheets I linked to in Post#105 do calculations, with graphs, and all formulas exposed. The first spreadsheet they list will let you play around with distributed loads, point loads, and an additional end moment at the tip of a freestanding mast. It's a 2D model, but helps with a general understanding.

Here's a short article by Ted Van Dusen on engineering composite freestanding masts:

https://composite-eng.com/custom-carbon-spars/solution-carbon-spars/

An insight into their design method:

"The first step in designing a mast is to determine the stability of the boat. We use the maximum righting moment to determine the highest loads the mast can experience and then use the righting moment at the heel angle for optimal beating in a good breeze to determine the luff curve which the sailmaker then uses to design the sails."

The maximum load is figured the same way that Eric Sponberg does. Sponberg uses 1/4 - 1/3 max righting moment as his design condition in his 1983 paper. Van Dusen uses righting moment at a particular point of sail as his design condition. Improvements in modeling the behavior and production of composites since the1980's could be a factor in their selection of a design condition, along with differences in their skillsets.

 

The part that keeps adding to the confusion is a higher safety factor does not result in a weaker design! The design condition where k is the safety factor is not

F = RM max / k

I speed read a paper of Spongberg’s and he designs at the max moment of righting, not one third or one fourth of it.

I encourage more learned replies from rx or tansl.

This notion of a safety factor reducing the design is silly.

 

Here is the link for the particular spreadsheet I posted. There is a part A and several other variations including stayed pipe. Just search 'combined loads'.



And Calculating mast and rigging (1).pdf by Tansl and another one originally posted by Alik Почему ломаются балки катамаранов https://boatportal.ru/master/290/ Not sure if the site is still being maintained as it is in Russian.

Using the particular example I developed this into a spreadsheet so that it reads triangular sail, elliptical sail, alloy mast, composite mast (tapered and non tapered, alloy and composites) and weight analysis. I used other published articles/textbook for deck support and deflection by area moment loading by M Hollman, Composite Aircraft Design.

 

It can be used but that is not the proper way (k being a decimal). Righting moment (or maximum righting moment at an angle of heel) is normally used to define the maximum allowable force needed to heel a boat. That equation needs Displacement and Second Moment of Inertia.

Safety factor is normally used to define how much force is needed for a material to break. A safety factor of 1 means you are applying a force enough to break the material. A SF of 2 means you are applying only 1/2 of the force to ensure the material don't break being that most material begin to yield at 5/8 of the force. Design for <5/8 or something below that. A SF of 3 means you are applying only 1/3 of the force.

This is called Design Load or Allowable Stress. By design, you ensure that that the material will not 'deform' (breaking is still way much higher) with the intended force/load. So in short, define the Ultimate Stress of of the material first, divide by the safety factor, and you have it.

The difference between that 'yield' and designed force is called the Margin of Safety (MS) and it is always more than 1 because it is the difference +1. But that is another topic.

 

In my reading of Sponberg, he clearly states he designs near the maximum moment of righting, not 1/3 or 1/4. I copied it here. If it it copyrighted, I will delete, but I believe he has been misquoted above @tropostudio. Sponberg’s work on free standing masts is fascinating stuff.

I just like math. If I’m botching it badly; very sorry.

 

I have a hard time reading it. It is blurry to me.

He is correct in his explanation. Notice that he is designing below the Maximum Righting Moment of 30 degree and designs around 15 to 20. He also stated that max load (to the mast) is to be 3 to 4X this value. That means the designed load/"working load"/applied load or whatever is used so that the boat heels to no more than 30 degree.

That means the load he applies is only 1/3 or 1/4 of max load (SF of 3 or 4). In short, he is reducing the applied load to the mast. He is conservative as always.

 

It is just so important to be clear on terms.

The masts are designed to be able to basically pick up the entire boat from an almost complete knockdown. No?

The sails are designed to only provide so much load. This gives the safety factor. So, when Gonzo asked..

The answer is no, but Gonzo’s intuition is not wrong. His query would have been the sails are designed to provide 1/3rd the masts righting moment.

The sails are what load the masts and the loads are designed at 1/3rd the Mr?

So, unless I am horribly mistaken (playing the idiot well here), the masts are designed to essentially pickup the entire vessel without failing, and the sails are designed to provide only a fraction of that. Then there would be a safety factor in both the mast design exceeding Mr and a safety factor in anticipated sail loads.

Is this close?

I think the confusion is this thread is about masts and has been conflated with sail design.

 

@fallguy - I think your interpretation is correct.

from page 78 the same paper you grabbed your screenshot from:


The above is Sponberg's failure condition. Reference 12 = Skene's.

A little further down on page 78:


This paragraph explains why his design working condition is set to 1/4-1/3 of maximum righting moment. 3-4x safety factor to cover 1) unexpected mast loading beyond the design stress calculated with the boat at 15-20 degrees heel - i,e. up to the max righting moment of the boat and 2) gradual degradation of the composite matrix over time (fatigue). This corresponds to the specific design example you photographed and to @rxcomposite response in post #112. Sponberg assumes maximum righting moment at 30 degrees heel for the boat in his example. That seems super conservative, but he knows the hull in his head better than we ever will from his sketch.

Ted Van Dusen is in the same league as Sponberg in this stuff. He uses the same failure condition as Sponberg - maximum righting moment. Van Dusen chooses his design working condition to be the "righting moment at the heel angle for optimal beating in a good breeze." And he must have confidence in his ability to predetermine mast bend because he uses that info "to determine the luff curve which the sailmaker then uses to design the sails." Sponberg mentions building the mast first and then having the sailmaker adjust the cut of the sail to work with the mast bend. Van Dusen now has a lot more experience and data to work with than either he or Sponberg did in 1983.

 

While all this discussion of righting moment is going on,has anybody looked at the pitching moment when running?Since I have little interest in catamarans,I've never considered the values involved and I wonder if anybody contributing to this thread might have some insights that relate to the differences.

 

thanks .. I posted on the edge of sleep and your post is far more articulate.. Hopefully, Mr. Sponberg will appreciate us getting this correct versus telling people to design masts at 25% of the righting moment!

 

Straight from Wikipedia:

" Factor of safety = yield stress/working stress

• The design load is the maximum load the part should ever see in service. By this definition, a structure with an FOS of exactly 1 will support only the design load and no more. Any additional load will cause the structure to fail. A structure with an FOS of 2 will fail at twice the design load."

A question for those who routinely encounter this sort of thing in their work: Do you typically calculate your factor of safety using yield stress (in the numerator) or ultimate stress?

Metals tend toward behavior in tension or bending where they hit yield strength, but can continue to carry load past that from strain hardening up until they hit ultimate strength. Interestingly, many wood species exhibit similar behavior. Most composites don't behave that way. The stress/strain rises quite linearly until 'Bang!' and the fail catastrophically. From a practical standpoint, yield strength is ultimate strength. Is it common with brittle materials (most composites) to use some percentage of of the ultimate strength and designate that as the yield strength, thereby gaining another factor of safety?

Seems like the best bet for anything you are concerned about trusting your life to is to test material samples and small parts to failure, and proof load bigger structures to the design load and verify your deflection calcs. That's pretty much standard for experimental aircraft.

 

When working trying to comply with a standard, the designer does not choose the design stresses but must comply with the values that the standard indicates. Adopting a higher or lower value does not make sense.
For example, ISO 12215-7 says that the tensile/compressive design stress for steel should be taken equal to 0.8 of the yield point.
For other materials, other values are given.
A structure, regardless of the FOS used, must never support a stress greater than the design stress.

 

Thanks @TANSL - that makes sense. Professional guidelines or standards are developed to be be sure an industry follows accepted best-practices, minimizes risk to users, and limits liability.

When not being required to comply to an industry or professional standard, I assume a designers and engineers do as they see fit based on accumulated knowledge and experience, correct? I'm thinking along the lines of projects such as Vestas Sailrocket, Burt Rutan's Voyager, or Gougeon's trimaran Adagio.

I ask because Eric Sponberg's 1983 paper 'Design and Engineering Aspects of Free-standing Masts and Wingmasts' is a SNAME document prepared for a sailing yacht symposium. Sponberg's paper, including a look at the references, doesn't imply he was adhering to any particular 'standard.' Not that that concerns me - his FOS are conservative, and he he understands his materials and engineering principles. Perhaps at the time, or maybe even now, the method and materials were new territory?

 

Dog does NOT have a point. He has no right to throw childish abuse around because he doesn't like the degree of detail I provided.

1- I have explained how I reef my main on a square run. I sometimes pull on a bit of sheet, then I lower the halyard and wind on the reefing lines. It's simple. It's easy. Any experienced sailor should be able to work out from that simple description what happens. I am NOT a liar and I am NOT leaving out any significant detail.

You didn't have the grace to admit that sailors who are far more experienced than you and I say that it is better to reef stayed rigs downwind than upwind, which shows that downwind reefing is not the problem you imply that it is.

2- It is weird for you to demand me to you how Kankama's main is reefed. I did NOT mention her until YOU decided to. It is dishonest to criticise me because I will not discuss someone else's boat that YOU brought into the conversation.

3- Yes, reefing an unstayed rig downwind may be easier. That is one factor in a multitude of factors determining rig choice.

4- I have sailed many unstayed dinghies and boards. Yes, I have not sailed an unstayed yacht as far as I can remember, but my experience shows that some claims made by some advocates of unstayed rigs are wrong. For example, I didn't write "screeds" on Lasers - I used Laser experience to show that the claim that an unstayed rig has a speed advantage on a square run because it can be sheeted to about 140 degrees and keep the flow attached is wrong.

My extensive experience and ownership of unstayed rigs proves that it's beyond silly for anyone to imply that I am biased against them. It also indicates that the claims that an unstayed rig gains an effective first reef because of mast bend are unfair since stayed rigs can also depower with bending, and much of the time they can do it better since the bend characteristics of the rig can be controlled independently by the backstay, the stay tension, etc.

I regularly "tune" my rig with the backstay, since it has a significant depowering the rig. Pulling on that one string straightens the forestay, therefore flattening the headsail. It also bends the mast, therefore flattening the main and twisting it off. This allows me to carry full sail upwind and then have the advantage of full sail downwind without messing around.

5- I haven't said whether or not unstayed rigs are easier to sail with since I don't believe that either stayed or unstayed has an overall advantage. It depends on how one wants to sail, what one wants to sail, and how one wants to sail - and then there's the factor that simple ease is not always the main factor in sailing.

6- It is silly for you to criticise my responses because you use such loose terms as "bangs off a wave". On the one hand you use such loose terms and then you hypocritically demand that I give a more detailed step-by-step response about how I reef downwind.

7 - It is silly for you to make grossly incorrect claims such as the one that stayed rigs are pulled out every year, and then complain about others "nitpicking".

8 - A well sailed mono of many designs could tack up that channel, or in a similar situation, with no problems. Yes, it may be an unlikely scenario, but you missed the point that anyone can make up a particular scenario and use it to "prove" the superiority of some feature. That is a classic case of cherry picking.

What is important is not how a rig handles a particular scenario - it is how it handles a wide range of them.

9- You keep on complaining that my examples are not specific to cruising cats but you ignore the point I have already made - the OP threw global insults at stayed rigs as a concept. He did not restrict his criticism to cruising cats and therefore I did not restrict my defence to cruising cats.

It's really not worth dealing with you any longer.