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

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

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### laukejasSenior Member

Hi,

I am building a free-standing new mast for a racing dinghy I built last summer. The mast is 5.5m (18 ft.) long, and carries a bermudian sail of 8.6 m^2 (92 sq. ft.). So far, I've been using a windsurfer mast, which didn't work well (video). I plan to build a new round wooden mast with Birdsmouth method, made from 2 pieces (due to transportation and storage issues), with a 6K braided biaxial carbon sleeve.

Up until now, all wooden masts I made were either round or square, single piece, with no carbon or fiberglass coating, which made strength and stiffness estimations very straightforward. For round masts, I used Norman L. Skene's formula (Diameter = ∛(16*P*L*SF/(π*σ), where L = mast length, SF = safety factor, σ = Yield Strength of the mast material). This always worked well.

However, in this instance, I have three different materials to consider - wood core, fiberglass sleeve to join both parts of the mast, and the carbon fiber tubing on top of that. The joint I designed looks like this (proportions exaggerated for clarity):

Green - wood core (birdsmouth with inserts, so it will be solid at this joint)
Red - fiberglass sleeve, glued to the right-side piece of the mast, not glued to the left-side piece)
Black - carbon fiber tubing
White - space between two pieces of the mast.

Now, for the numbers:

Mast length 5.5m (18 ft.)
Diameter at step and partner: 70mm (2 3/4")
Diameter at the top (taper): 45mm (1 3/4")
Width of Birdsmouth staves: 14mm (0.5")
Birdsmouth K ratio: 0.6
Height of two-piece joint from sole: 3.8m (12 1/2')

Birdsmouth section at the step and partner for reference:

(Designed mast diameter is 68mm to account for carbon fiber tubing and paint, so in the end it should come out a little under 70mm).

And the dimensions for the joint:

So, my question is, with such a complicated combination of factors, what is the best way to estimate the strength and stiffness of the mast? Right now, the wall thickness I chose for Birdsmouth (14mm) assumes no carbon fiber tubing. Obviously, this tubing will add a lot of strength and stiffness, meaning I could save considerable weight by making mast walls thinner. Currently my CAD says the mast will weigh 6.6 kg (14.5 lbs)... That is not counting the epoxy and paint.

Question is, how much can I thin it down to get a similar strength and stiffness that I would have if I were to use no carbon fiber tubing?

Also, how do I estimate how thick does that connecting fiberglass sleeve has to be? If it is too thin, then it will break. If it is too thick, then the tapered male insert of the other part of the mast might break too. It has to be balanced just right so that neither the sleeve nor the insert have significant difference in strength.

I am using Solidworks CAD to design all this, and I have access to it's simulation capabilities, but setting up a simulation this complex is a bit beyond my capabilities. Can someone offer any advice from experience?

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### gggGuest...

Biaxial carbon is of very limited use for masts. You need to use unidirectionals other than a single layer out and in to keep all the unidirectionals in line. My understanding is that if you have a serious amount of carbon any stiffness the wood contributes will be nominal. Indeed if you can beg/borrow/steal a suitable mandrel then the wood would be better left out. But if you have a carbon windsurfer mast that works but isn't stiff enough why don't you just stiffen it by adding unidirectional carbon? You can then tune the bend as required.

You might find this article useful. Building Carbon Masts [UK-Cherub Class] http://uk-cherub.org/doku.php/tech/masts

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### laukejasSenior Member

Thanks for your response and that link. The reason I chose biaxial is because if I'd go with unidirectional, I would still need to apply additional layers to provide radial support, or else the unidirectional cloth would be prone to splitting. Biaxial has 45° weave, so it still provides longitudinal strength at 0.707 efficiency factor compared to unidirectional - yes it is significant, but it would remove a lot of complication from the build process. I think it is worth the trade-off.

I have considered full-carbon mast build, and I have consulted with people in my country who do complicated carbon layups. All of them said that this is way beyond the scope of a home builder because of the requirement that this mast be made from 2 pieces like these windsurfer masts. The tolerances required at the joint are just not achievable. Moreover, making a tapered removable mandrel for the mast is also extremely difficult, and the taper is just not enough to allow to remove that mandrel. It will get stuck no matter what. The only way would be to use some foam that could be dissolved afterwards, but this is also complicated to make. Bottom line is, it is just not worth the effort.

As for reinforcing windsurfer mast - also not worth the effort. The diameter is just too small. By the time I arrive at what is needed, the mast will be already too heavy. Besides, I can't reinforce the joint, because I would need to add carbon fiber on the inside of the joint walls, and there is no access there. Otherwise the loads will concentrate on that joint and break the mast.

But having a wood core is actually not that bad, because it doesn't have to be removed. Also the joint is simple to make from wood. With carbon reinforcement, wood core can be reasonably thin and light. This is definitively the simplest way to make this new mast. Question is, how much can I rely on carbon for taking up the work of the removed wood. Since I will be adding only one layer of carbon fiber tubing, I need to figure out how much wood I can remove to achieve the same strength that I'd have without carbon.

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### gggGuest...

Well in that case I fear you are going so far from conventional practice in home building spars that there's nothing I can offer to assist, other than to note that a trap to beware off when mixing materials is that if one has lower elasticity than the other then the stiffer material may fail before the more flexible takes up much load.

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### laukejasSenior Member

Interesting point... Well, I haven't realized that I've strayed far from conventional home built spars. I mean, I got the impression that people use fiberglass and presumably carbon on their spars quite often... I even found a video where this guy does pretty much the same as I am planning to do - thin Birdsmouth with biaxial carbon, minus the joint: Hollow 12 sided wooden bird’s mouth sailboat mast covered with a woven biaxial carbon fiber sleeve - YouTube

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### AlanXSenior Member

I have played with self-designed masts using bending moment calculations on variable cross-sections:

I think I know just enough to be dangerous!

First how to analyse:
As an attempt to butt join a wooden mast is doomed to fail (bending strength will always be less than the uncut wood), we are considering the strength of the tube in bending.
As the bending modulus of wood will be much less that the tube material we can ignore the wooden core.
So it is the bending strength (section modulus) of the tube alone.
So based on the strength of the tube material we can calculate the thickness required for the tube diameter. Make it equal to the uncut wood. No issue finding formulas for this.

The next problem it to look at possible failures modes.
I can see the wood failing in shear at the tube ends.
The shear strength of wood is about 15% of the bending strength so that would suggest (ballpark) that the tube length should be at least 6 times the tube diameter.
As we are adding two stressed (shear and bending) to the wood and the tube at the end, then the tube should be longer still. So ballpark I would go for 9x the tube diameter (there are formulas for this but lets not go there).

Question: Does the tube have to be the same outside diameter? It is so much easier if the tube inside diameter is the same as the wood outsided diameter and the tube outside diameter is tapered down at the ends.
Question: What is wrong with using fibreglass cloth for this application?

Anyway, I hope this helps, AlanX

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### laukejasSenior Member

Thank you for a very thorough analysis of the issue, Alan. On your first paragraph, you stressed the point of lack of strength of butt joint - just to be clear, both ends of the mast will NOT be glued to one another. It is a removable joint, like on windsurfer masts. Here is a color pic from my CAD for clarity:

About the tube length - sure enough I can stretch that tube to 6x or 9x of the diameter. For example, this is the drawing with a little over 9x:

For clarity, I hatched the cross section of the joint sleeve. As you can see, it is tapered to a feather edge on the right side of the mast (where it will be glued), and to a 2mm edge on the removable end of the mast, so that it doesn't break or cut flesh when handling. The downside of this much taper is that the wood core will go down to 21mm. Does it really have to be 9x? I don't have my windsurfer mast next to me right now, but the joint on it was somewhere around 100mm long, and it was also around 45mm in diameter at the joint. Meaning it's ratio is 2.2x. Looking at the mechanical property tables of resin-reinforced carbon fiber, I see that it's shear strength is also around 15% of the tensile strength (Mechanical Properties of Carbon Fibre Composite Materials (performance-composites.com)). At yet that joint works at around 2.2x joint. I will be making my joint from fiberglass, which has shear strength at around 9% of the tensile strength, so following that logic and comparing it to known-to-work carbon fiber sleeve, it seems to me that it should be around twice as long as the carbon one, coming out at around 4.5x. With that in mind, isn't 9x an overkill? It adds a lot of weight to the mast...

As for the outside diameter - yes, the tube absolutely has to be the same diameter as the mast. It must be flush with the surface. Sail will be raised and lowered with velcro straps lashed around the mast, and if there is a thicker section at the joint, there will always be trouble with straps getting stuck on that tube, even if it is tapered down. Later I may even make a sock at the luff of the sail, which makes it even more important that the mast is smooth and doesn't have sudden changes in diameter.

EDIT: Forgot to answer your second question. I will be using fiberglass cloth for this joint. The carbon tubing I mentioned in my first post will be added on top of this joint and the whole mast, and then slit at the joint opening so that both sides of the mast can be removed again.

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### AlanXSenior Member

The butt joint for wood comment was made as this would not necessarily be understood by other people, that it would not work. If it was steel or aluminium then it is possible. Unfortunately, I need to cover my bases.

Also when I say "butt joint", I mean joining the wood end to end, not the butt joint with a backing plate. Yes, this would have been confusing.

No. It depends on the percentage strength (section modulus) of an uncut mast you want. Think of a scarf joint (which is a pretty good approximation of what you are trying to do):
• 1:5 60%
• 1:8 75%
• 1:10 80%
• 1:12 85%
As far as a 45 mm carbon fiber tube on a wind-surfer mast and a 2.2x joint (100mm) joint length. I suspect that bending strength would not have been an important criteria here.

Now that we know that is a wind-surfer mast then a strong join as a percentage of the uncut mast is not important and anything length coupling you use within reason will be okay.
AlanX

Last edited: Apr 4, 2022
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### laukejasSenior Member

Okay, thanks a lot for that clarification. In that case, I will probably go for 6x.

Then one more question remains: if I add a biaxial 6K carbon fiber tubing on this wooden mast (like in that video), how much strength and stiffness can I expect it to add? How much can I thin down the Birdsmouth walls to save weight by using this carbon fiber tubing? How do I put it to numbers? Let's disregard that fiberglass joint for now, and consider this case as if it were just a regular Birdsmouth mast with carbon fiber tubing along it's entire length.

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### AlanXSenior Member

You need to know the strength(s) (MPA), specific weight of your material.
For "normal" epoxy fibreglass I use 120kPa (working stress) and 1/16 mm per Oz/yd^2.

AlanX

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### AlanXSenior Member

If you are using carbon fiber then you could use a paper tube as a base it you want to.
AlanX

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### laukejasSenior Member

Yes, I have that info. For the wood (Baltic pine) that I will be using, the Elastic Modulus is 13500 MPa, and the tensile strength is 94 MPA. These values I got from my own tests with various samples I got at hand.

For carbon fiber composite that I will be using, the elastic modulus is 196000 MPa, and tensile strength is 3450 MPa. These are theoretical values from datasheets. I am not sure if I should multiply that by a factor of 0.707 to account for 45°/-45° weave compared to the load direction.

So yes, I have these numbers, but I have no idea how to combine them when calculating mast strength and stiffness. It is easy enough with single material, but I have no idea how loads would be distributed when the Elastic Modulus differs so wildly between wood and carbon fiber.

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### laukejasSenior Member

Well, since I am using only one layer of carbon fiber tubing, I don't think it would be strong enough on it's own... Which is why I am using that birdsmouth construction as a base. I expect the loads to be distributed 50:50 between wood and carbon fiber. But I don't know how to calculate it to check what the real proportion would be like.

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### AlanXSenior Member

You have migrated a long way from "butt" joining two wooden spars!
I can't keep up.

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### laukejasSenior Member

Sorry about that! The info you provided on the joint is good and I consider that issue solved for now. The mast would probably work as it is in that configuration. But now I want to add carbon fiber sleeve in order to be able to use thinner staves on the birdsmouth and thus save weight. I think we can disregard that fiberglass joint for now, and from here on consider this a regular birdsmouth mast. I'll work out how to combine these two things afterwards. Right now, I just need to understand how to calculate the combined strength and stiffness of wooden mast and carbon fiber sleeve on top of it.

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