# Mast and Rigging calculations

Discussion in 'Software' started by TANSL, Feb 11, 2016.

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### TANSLSenior Member

LP, I think, with this discussion, I can also clarify a lot my ideas, so thanks for your answers.
In my opinion, if the force on the sail is reduced to a single force applied by the CE, we are considering the bending moment between the masthead and CE is zero, which does not reflect reality (imo). Therefore, it is better to decompose the total force in two, Ftp in the masthead and Fp in the pintle (no more contact points of sail with mast). The problem and, I think, that's one of my differences with E. Spomberg, is how this load is distributed.
I have more questions on how to make the model in the area between the deck and the base but I do not have an answer I can give as correct.

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### LPFlying Boatman

Re: free standing masts.

The forces between the masthead and CE are definitely not zero. For developing forces at the foot and deck, a single force vector can be substituted with validity. If you are evaluating internal forces in the mast between the head and the tack, then you do have to look at the distributed load. Since the sail load is essentially zero at the head of the mast, theoretically, a mast mast cross-section of zero could be used, but his is unrealistic and other forces also come into play. By taking the deck moment and dividing it by the mast height above deck, you create a pseudo-force, applied to the masthead, that can be used to solve for internal forces at intermedia locations down the mast. The forces are not true internal forces, but err on the conservative side, add the the stoutness of the mast and account many of the "other" forces that are playing with the masthead.

I have developed a set of "luff-stations" that I am using for checking internal mast forces at intermediate locations down the mast in way of the sail. Mostly, I think I'm having fun with numbers. I take the luff length and divide to by ten to create 10 luff-stations to evaluate the mast. Eleven actually with luff station zero at the head and luff station 10 at the tack. (((Luff x luff-station/10) x (foot x luff-station/10))/2/sail area) gives me a sail area percentage that I can use to apply a percentage of sailforce to the mast at the luff-station plus 33%. This is being applied to a trangular sail and would need to be modified if used with different sail shapes. The forces in the upper parts of the mast due to the sail are insubstantially small and other means need to be used to develope strength requirements in the upper portion of the mast. Skene uses an inscribed circle that defines an elliptical taper that mimics the stress profile in the mast caused by sail forces.

I think that the area between the deck and the foot/heel/base is staight forward. You have two points of contact only. At the step, you only have sheer forces and compressive loads. At the deck, bending and compression. Size each according and taper if and as necessary per the construction material. Maybe, I'm being too simple.

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Er quite right, thanks for spotting that very large error. To be honest i didn't even read/look at the text/ document, just saw replies posted. I was rushing off out to attended grandma's funeral on saturday, so mind was on other things. No excuses though, my bad. Sorry for the confusion.

However, the only masts I design are without sails, thus how much tension is there in a typical stay for a FSM; is it enough to make allowances for it and the BM it imposes as an in-plane load, or is it always deemed negligible? Or are there simply no rigging lines attached to the mast at all? (not my forte).

EDIT...out of curiosity, I did a bit of background reading on FSM. (as this isn't my field). And yup...no loads from rigging, like stays
Ive not sailed since I was a teenager, it's all new to me

No, the yield point and proof stress are not that close at all, which is why proof stress is quoted. See below:

Yield should never be used with ally, only its proof stress.

If you're going to suggest a FoS then you need to clarify the assumptions and why. Otherwise it is far too arbitrary and provides little confidence to the designer if they need to make changes, for whatever reason. The designer can then elect to to either increase or decrease said FoS based upon their own assumptions.

Last edited: Feb 14, 2016
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### philSweetSenior Member

I am having some difficulty getting my head around the way TANSL has solved for the forces on the rigging elements. He has sent me some docs, all derived works in several different languages none of which I read, but which also show a similar calculation philosophy. My issue with it is that it is physically wrong and also more complex than the natural method. I have found that google gives a preview of some of the NBS method, but with gaps. I am wondering if those gaps haven't been filled in by some guesswork. Does anyone have a list of the formulas that NBS method uses to calculate the loads on the shrouds and spreaders of, say, a two spreader rig from a reputable source? This is a question only about the specific NBS method. I know how to solve a statics problem. I'm trying to figure if the NBS method is being perpetually misrepresented, or if it is just really that weird.

It is the formula list for D3, V2, C2, D2, V1, C1, D1 that I am looking for.
Where explicitly listed, every document I found has them wrong (each in their own way), but they share a common wrong assumption. The error due to the faulty assumption is smallish, but it makes the calculation harder than doing it the right way.

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### TANSLSenior Member

I want, first of all, thank you for your participation and comments. In second place I'd like to insist that is not my method (I have not the skills to devise a new method) that I have outlined but the NBS method. One can ask many questions about it because, indeed, some assumptions seem totally wrong. However, even today, it is accepted and used by many designers. Probably because when it was created, the calculation tools were much lower than today.
I think that many things may be incorrect, starting from the very begining of NBS method :
• Calculating the effect of each sail separately.
• Forget the interaction between both sails
• Assume that main sail is refeered and with only 60% of its actual height. Why?
• decomposition of forces on main sail in two forces. Why they are given the value of 0.4T and 0,33T ?. The sum of the two is not equal to T.
• NBS uses safety factors that are different for cargo C, V and D and between charges of the same type vary with height. Why?
• The safety factors for stays equal to unity. why?
PhilSweet, find the components of a force in two directions is very easy and I think there are more important things to clarify now. Supposing spreaders in a horizontal position makes the load on it is of the order of 5% (10% if you like, it doesn't matter) higher than if we consider it as the angle bisector of the shrouds. Most important is accurately calculate the sails loads and their distribution on boom and top mast. I believe that's one of the first questions we should ask in relation to NBS method.
This was not the intention of my thread but it might be a good opportunity, if anyone is interested, to analyze a method that, until now, had been apparently accepted without any objection.

Ad Hoc, thanks for your help, as always and my condolences on the death of grandma.
Going on with the thread, I'm not going to Suggest a FoS. I just copied the coefficients NBS uses in its method.
About proportional limit versus yield point what I mean is not worth differentiating between points 1 and 2 shown in the curve:
1 proportional limit
2 yield point.
I thought those were the points that Gonzo meant. I hope I have not misinterpreted. He can say what points he meant.

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### TANSLSenior Member

After reading your comments, do some thinking about it and trying to get something simple but valid and useful, I have written the following method that I would like to discuss with you. Thank you

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Last edited: Feb 15, 2016
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### HJSMember

The bending moment in the deck for a freestanding mast must be related to the boat's righting moment. Next, the bending resistance is adjusted to how you want the mast should bend under different loads.
See more on:

http://www.boatdesign.net/forums/sailboats/elipetical-birds-mouth-mast-55061.html
entry 4 and 10

js

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### TANSLSenior Member

I think this is exactly what I'm doing. Perhaps you mean that the bending moment on deck must equal the righting moment. What do you think about adding crew heeling moment?
I'm afraid I have no clear physical concept of "bending resistance" and therefore how to calculate it. You mean the modulus of the cross section?. And, sorry, but I do not understand what can be done to "how you want the mast should bend" in a FSM.
I read the post of the thread indicated and I have not managed to clarify anything. Perhaps you are talking about very small single-handed boats or wind surf tables, which is not at all what I'm trying. Thanks for your help.

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I think you need to be clear which metal you are referring to. Since the blue line is aluminium and clearly exhibits a very different stress-strain curve. Steel the red, technically has a lower and upper yield point.

The proportional aspect is where the load v extension is linear, i.,e. remove the load and the extension returns to zero.

For metals which do not exhibit a clearly defined proportional limit with 'yielding' before the onset of plasticity, like aluminium, a 0.2% offset to the stress-strain line is used. The intersection becomes the "yield" point or more correctly the 0.2% Proof stress limit.

As for a FoS, you should make note that it is advisable to use one and give guidance or suggestions and the assumptions. Since not everyone shall know what FoS to use or why. This then allows the reader/designer to select their own.

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### TANSLSenior Member

Ad Hoc, now is clear the issue of proportional limit and elastic limit. Speaking of metal masts there are not many options for the metal to be used.
According to all that, for an aluminium mast, what would be the answer to Gonzo's question?
Regarding the FOS my opinion is: NBS makes a number of assumptions trying to simplify and make available a calculation that otherwise, 30 years ago, it would be very laborious. It is a set of things that, as a whole, may be correct but used one by one might not be. So I guess if this method is chosen must be followed to the end. You can not use a part and then put the safety factor you want because, as I say, the whole may be correct but the mix of things with different criteria surely it will not be. That's my opinion and therefore I would not give freedom for the designer to apply safety factors to his own taste.
As for explanations of why these safety factors are used and not others, the truth is that neither this nor any other calculation assumptions I have found explanations from NBS. But I did not want to investigate but simply implement this method in my application for small boats design.
Thanks, again, for your enlightening response.

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Always use the correct published proof stress or accepted 'yield stress'. Whether proportional or not makes little point since what is one designing? Do not use data from mills/suppliers. Since these are generally 'sales' figures and also not to any particular standard. Always use internationally published and accepted values. The best/easiest to use are those from Class. Noted below for ref, with unwelded and then as welded properties:

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### TANSLSenior Member

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### gonzoSenior Member

HJS:
I think that what you use as maximum bending moment will largely depend on the use of the boat. For a daysailor or triangle racer, that would be adequate. A cruiser should probably need the maximum moment calculated for a rollover.

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### TANSLSenior Member

MyR, software for calculating mast and rig, can now be downloaded from my website.
Your feedback will be greatly appreciated. Thank you.

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### jarmo.hakkinenJunior Member

Good morning,
I just downloaded the application from your site, extracted and installed it. For some reason nothing happens, when I click to open it. I mean, no program interface appears, but it does start three processes named MyR.exe. When installing, no error messages appeared, so I think it was installed correctly. Any ideas how to fix this? I was planning to check the results against some of my spreadsheets.

Greetings,
Jarmo

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