Trying to work out unstayed wooden mast scantlings

[Peter Vella]

I have been trying to work out scantlings for hollow wooden masts for a two masted centreboard lugger of 21ft LOA. The main is a dipping lug and the mizzen is a standing lug, therefore the sails are only attached to the mast at the parrel. I got a reference from Skenes for an 'unstayed jib headed cat' solid mast which recommends the mast diameter at the partners is length * 0.0165. Converting the dimensions of a solid spar to a hollow one of equal strength is not a problem, but I am assuming that this type of mast is designed to have the luff of the sail laced onto it and would therefore not be a reliable rule for my application.

I have worked out a reasonable estimate of VCG and from that have got the righting moment for 34° heel which is going to be getting very near the downflooding angle, the boat being a half-decked daysailer. I have worked out the load at the parrel for each mast as being:

Load = RM / Length of mast (partners to parrel) * ratio of sail area carried by mast to total sail area.

I know this is not the true arm for the heeling moment, but is it good enough?

 

[Doug Lord]

Have you seen this article? Free-Standing Mast Designs https://www.ericwsponberg.com/free-standing-mast-designs/

Eric is a pioneer of wood-epoxy and carbon fiber unstayed mast design and construction....

 

[Peter Vella]

Thanks, Doug. There is a lot of good information there.

 

[Chuck Losness]

Eric has freely shared his expertise on free standing mast design on this forum. There are several threads on this. Most of the threads deal with carbon fiber masts but you could substitute wood strengths for carbon fiber and work out the design details for your proposed wooden masts. The critical number you need is the righting moment at 30 degrees. This is the number that masts are designed to. This is not an easy, quick study. I have spent hundreds of hours studying this.
Eric occasionally still checks in here. He might chime in.
Doug thanks for the link to Eric's new website.

 

[gonzo]

If you are making wooden masts, there are simple rules of thumb that have worked for centuries

 

[Peter Vella]

@gonzo That excerpt from Skene's is the rule of thumb I mentioned in the OP - 'Jib headed Cat Mast'. I have read the first formula somewhere but can't recall where. The problem I have is with 'cantilever uniformly loaded' which would be a different breaking stress to a cantilever beam that is point loaded surely? A 'jib headed'/bermudan cat mast could be considered uniformly loaded as the sail's luff is laced on the mast, whereas a dipping lug sail is attached to the mast only at the parrel.

 

[gonzo]

For a point loaded cantilever this link can help. Is kind of heavy on the math, but only pay attention to the solved equations, where you can simply plug in the dimensions of your mast. Look at equations 39 to 60 , for point load.
https://www.researchgate.net/file.P...58e&assetKey=AS:329079610986497@1455470101705

 

[TANSL]

But a mast is not a beam loaded at a single point, it is not even a beam loaded evenly. What formulas should be applied, Gonzo?

 

[Ad Hoc]

Is kind of heavy on the math, but only pay attention to the solved equations, where you can simply plug in the dimensions of your mast.

The maths is just showing the basic derivation of the theory - that's all.

However, as the author even notes:

"...The stresses and deflections of tapered logs are usually computed by analyzing an "equivalent" prismatic beam. However, the greater the taper, the less accurate are such approximations...."

Thus, without understanding the derivation of these formula one can easily use the wrong one. and not know why!

What formulas should be applied, Gonzo?

None...all...that's your choice. But, it is not about plugging in a one liner formula.

One must analyse the mast for all the loads on it and apply basic structural theory to analyse it. If you can't then get someone who can...otherwise, you'll fall into the same trap as many do trying to find a one line equation to fit all - even which the authors recognise leads to errors, hence their opening statement, cited above.

Structural analysis is not difficult - except to those that have not done it before and hence plugging in a one line formula without understanding what it is for and its limitations is a recipe for disaster.

 

[TANSL]

Although the question was not addressed to you but to someone who has kindly provided us with a link that is not valid for the case we are dealing with, I will analyze your answer.

Structural analysis is not difficult

I see now. That's why in another thread related to unstayed masts you were talking about the need to calculate the stays too. It seems that structural analysis, even for those who imply that they do it with ease, is not easy.
Whether or not it is easy, that is not the question, in the end it almost always reduces the issue to apply a formula. Not the formula that one wants, as some expert advises, but the correct formula for the case that is being studied. And for that, even if you do not say it, you have to make a correct analysis of the situation. To know the loads that act on the mast, which is the first and most important thing to analyze, you do not have to "apply basic structural theory to analyze", that will come later, if we could know what you mean by such a phrase, apparently, full of knowledge

 

[Ad Hoc]

I see now. That's why in another thread related to unstayed masts you were talking about the need to calculate the stays too. ..

Indeed. As I noted my stupid mistake, once highlighted, for not reading the whole thread properly. That was all - your point being?

To know the loads that act on the mast, which is the first and most important thing to analyze, ..

Indeed.
Just as you posted your little guide to mast design - but was also riddled with errors as many pointed out. Here and here and just confusing.

Thus, as stated, you need to understand the theory to apply the said loads and derive your own formula based upon the loading scenario for analysis, assuming said loads are correct to begin with.

 

[TANSL]

Thanks Ad Hoc, your comments are always worthy of analysis. I do not say that they are correct, because sometimes they are not, I say that it is worth studying them. Some are even funny.
You say you screwed up "for not reading the whole thread properly" or maybe you read it but you did not understand it. You will never confess it and we will never know.
I am glad that you have indicated exactly where my mistakes were, enormous in quality and quantity, because thus, if someone wants to waste time checking how you deform the facts, you will see clearly what in that thread was said incorrectly and the explanations that each one gave. And, please, get in your head that making mistakes is human, it is not bad, the bad thing is not recognizing that one has made a mistake.

and derive your own formula

Wow, this is important. In all my professional life I have never been able to establish my own formula to solve any problem. I have always had to resort to the formulas that others established. There, then, I have to recognize my different level with respect to what, apparently, is yours.

 

[Ad Hoc]

In all my professional life I have never been able to establish my own formula to solve any problem. I have always had to resort to the formulas that others established. .....

Really????????????!!!!!!!!!!!!!!!!!!!!

Well here are a few basic quick calc's to show you how I do it....

Unstayed mast on a motor monohull:

Just first few pages shown of each..

and now on a catamaran, stayed:

And another just establishing the effects on the decks below:

So, you have never established a formula yourself based upon known theories to calculate the structure of something that is unknown and not part of any simple plug and play formulae, whether a mast, a deck beam, a propeller shaft etc etc...

My my....

 

[TANSL]

Yours yours ..... but how obsolete are you Ad Hoc!. That is, I suppose, the exercises that your teacher put at your school. Did you do them well or did you mess up calculating the stays and the shrouds, with your own formulas?
And do you expect me to believe that the formulas you use are your invention? Let's go Ad Hoc that I do not suck my finger. What arrogance and what a way of distorting reality!
My my.....

 

[Ad Hoc]

I have never been able to establish my own formula to solve any problem. I have always had to resort to the formulas that others established.

Your inability to do anything beyond a simple plug and play from a given formula and your response to those that can, which explains your polemic, emotive and subjective comment, is thus:

That is, I suppose, the exercises that your teacher put at your school.....

and

You say you screwed up "for not reading the whole thread properly" or maybe you read it but you did not understand it. You will never confess it and we will never know...

Your disingenuous failed rhetoric far outweighs (which is not an easy task even for you) your own ignorance on the subject(s) and the ability to engage in any intellectual rigour. Google translate not working again too?

Just a waste of bandwidth....