Mast loads for freestanding masts

@Ad Hoc attached a PDF for GL rig design rules in post #14. It is from 2002. I was aware of Germanischer Lloyd, but not being a naval architect/marine engineer, I never dug into it. GL was bought by DNV in 2013 and became DNV/GL. Now it is just DNV.

DNV has more online resources than you can shake stick at, and the principal references don't have a fee. You have to go to Veracity Home https://www.veracity.com/about to set up an account with DNV, after which you can use the 'DNV Explorer' to access all of the ship and boat design resources online. You can download any of the documents as PDF's. You can get the 2024 version of Ad Hoc's PDF plus a whole lot more! Awesome resource!

I don't see one place where they consolidate tables for materials and properties. As an example, you have to dig down into the chapter on composite scantlings before you find their values for raw material. Maybe I'm missing something?

It's nice to have all terms defined and criteria for when you can design without testing vs. having to submit test samples. Even with the digging, it nice to have 'standards' to compare with all the numbers one sees in research papers and manufacturer's specs.

 

In these times when everything moves so quickly, it is very easy to become obsolete. Nobody can rest on their laurels.

 

I'm putting together a spreadsheet comparing values between DNV, Eric Sponberg, and Martin Hollman (@rxcomposite - met and spoke with him at an EAA convention in the 80's - have 3 of his books) for uni-d, single-ply, composite laminates. This table is from DNV-RU-Pt.3 Ch.5:


I was really surprised at the E value for E-Glass perpendicular to the fiber as compared to other fibers. I assume the value is correct. I'd never really thought about glass as being isotropic vs. anisotropic before, since composite laminates are dominantly controlled by longitudinal fiber orientations.

Years ago I remeber a rule of thumb that 'shear modulus is ~1/3 tensile modulus.' About right for steel or aluminum...and glass. Not with anisotropic fibers!

 

@tropostudio- I bought most of Eric's books when he retired. I too was searching for design guidelines on composite mast but there was none so I developed my own spreadsheet.

Eric did mention that there are three fabric wounds/Fabric types applied to composite mast and briefly mentioned the proportions. The answer lies in the book Filament Winding Composite Structure. I bought it in SAMPE show and should be available in your library. Along with it I have Composite Pro software which automate most of what the book says. I use it to validate my work. It runs only on 32 bit computers. The latest version is so expensive. There is an Excel version of the CLT which I posted sometime ago. I also use M Hollmann books. I have all of his books as he was our mentor during the early composite aircraft design. The last I used is the Combined Loadings lecture in YT. As there are several versions, there is some discrepancy in the answers.

The problem with CFRP is there are at least 6 commercially available version of the fabric from Low Modulus to High Strength/High Modulus carbon fiber, and Standard Carbon fiber. Properties varies with the resin used and the type of manufacture from hand layup to Autoclave. The standard formula based on resin content used by LR and ISO is out of range or skewed. You will have to formulate strength/modulus/Poisson's ratio/Influence factor using engineering constant described in Filament winding and early BV Rules. In short, it is matrix algebra and calculus.

Right now what I have is a working collection of rules and method comparison. Rather large and complex spreadsheet. I will try to recover the original algorithm I used in the design.

 

Thanks much for the additional info @rxcomposite. I might take some of Hollman's BASIC code from his books and push it into Excel with VBA. Is Composite Pro the Helius program bought out by AutoDesk? If so, they Autodesk pulled it off the market in 2022. Think Composites has articles and spreadsheets for Stephen Tsai's recent 'Double-Double' method for engineering composite laminates. Very cool method - still advancing the field in his 90's!

I figured for my spreadsheet exercise it'd be worth seeing how the method contained in DNV, using their standard properties, compared to uni-d laminate samples from a couple of designers back in the 1980's. Hollmans numbers look to be from actual samples, and so do Sponberg's. Understood that OEM material spec, F/R ratio, and layup method all matter. DNV has the math for their calc, so we'll see what numbers that comes up with.

As long as I'm hijacking the thread, could I get your thoughts on these assumptions?:

1) Wood and carbon fiber generally work well together. Granted, E and T-yield differ greatly, but ratio of E-par/E-perp are similar. Elongation-to-failure of both are close - on order 0f ~1.5% . In contrast, Kevlar 49 has an elongation to failure of ~2.4%, and E-glass of ~4.5%

2) Kevlar is a poor material choice for structures that are compression-critical. Kevlar 49's Compressive Strength/Tensile Strength is ~0.2; E-glass is ~2.0 (seems crazy, but looks to be true); CF is ~0.5 (ballpark, knowing there are so many types).

3) If you are designing a new structure for your own use, much less for anyone else: Run your numbers. Make samples and test them to failure. Proof load the finished structure before using it. Goes for a freestanding mast, a one-off stayed mast, an airplane wing, etc.

 

Composite is one of the material choice. Could be Alloy or Stainless Steel and needs to be designed properly. That is in line with the OP's original question.

Some design the mast so that it fails before capsizing the boat, others want it intact even after the boat capsizes. There is a solution for that.

 

Gotcha. Fair enough.

 

The design process I use:
The righting moment is used as the basis. Windward hull weight x centreline beam to centreline beam for a Harryproa. 0.5 centreline beam x total weight for a cat or tri. 30 degrees for a mono as a) it is usually available, b) it is unlikely wind force will heel the boat more than this.
Sail area and mast height are not included as they affect the wind strength required to heel the boat, not the force.
A rig with headsails is treated a little differently (cantilever with a point load), but the same basic method.

The heeling moment is increased to allow for the vector of the fore and aft component of the drive as the rig is pitching as well as heeling the boat. ie, it is depressing the bow as well as lifting the hull/heeling the boat

A safety factor is applied to allow for:
Loading not considered in the rm analysis such as point loads from attachments, etc. eg boom, mast mounted radar, etc
Degradation of the material properties with age and exposure to heat, humidity and solar radiation. This is not an issue with a white painted mast in normal locations.
Deviation from expected material properties and expected manufacture quality: Testing of samples and using a controlled process (infusion, vac bag or autoclave) alleviates this.
Any damage that may be sustained by the mast in it’s lifetime: This is more likely to be while the mast is out and it's dropped or something is dropped on it , although a Harryproa had a mast broken when a ship ran into it in the Atlantic.
To ensure the product has a long fatigue life. Easily calculated for the standard pole once the life span and use are known.

The weighting of each of these is done on a per boat basis after discussion with the owner.

On cost dependant projects (most of them) we use fibreglass for the off axis reinforcement (about 10% of the total laminate) and carbon uni for the lengthwise and 90 degree laminate. Building in female half moulds allows for minimal wastage, less difficulty keeping count of what is placed where and less work than the Sponbeg method which uses 25mm/1" wide tapes over a male mandrel.
When Eric retired, he forwarded his enquiries to me. When he visited Aus on his cruise, he dropped in and we went through his design spreadsheet. He maintains a minimum wall thickness of 3% of the diameter is required to prevent buckling which is another variable towards the top of most masts.

I disagree with Eric about unstayed masts for cruising multihulls, have been specifying them for 25 years on Harryproas and several cats. His concerns are performance oriented (and overstated, imo), mine are ease of use and minimal maintenance. On a 15m/50' Harryproa with unstayed ballestron rig, the righting moment is about the same as a 12m/40' 6 ton catamaran. Mast diameter at the deck is 300mm/12", tapering to 100mm/4" at the top. Tube weight is 120 kgs/246 lbs with about 10 kgs extra due to it having a headsail, and another 5 for the glass off axis.

For a cruising catamaran, the "debate" on which is better ended with post #87. The posts on the subject since barely addressed these, certainly did not come up with any valid logic to use a stayed mast on a cruiser.

 

You may, or may not find THIS of interest to you.

 

@rob denney - the outline of your process and guidelines are appreciated. I figured test coupons would be in order to 1) verify an analysis and 2) verify process. Earlier I mentioned proof loading the finished structure before putting into use. @rxcomposite mentioned testing to an entire structure to failure would be impractical and expensive. I was considering 'proof loading' in terms of loading to perhaps 1.25- 1.5x your Safety Factor to check deflections against your calcs and to verify recovery.

To clarify terms:
Design Stress or Strain = Ultimate (Yield) Stress or Strain/ Safety Factor
Proof Stress or Strain = ~Proof Factor x (Ultimate (Yield) Stress or Strain/ Safety Factor.
Proof Factor for non-destructive testing on order of 1.25-1.5 (that's a guess).

Sandbagging a mast similar to what one does proof load an experimental/homebuilt airplane wing won't match in-use loading exactly, but it ought to at least be a check on your math and fabrication process. For a homebuilder or one-off I'd want to check my work!

@ adhoc - Interesting. I wonder how much someone like Van Dusen can rely on math to spec a sail for one of his spars in advance? I bet a lot of analysis modified by a lot of fabrication experience!

 

Thank you! This is very helpful for me!

 

No more or less than any other structure.
It is a combo of calculations and testing to gain the confidence in the response required.

 

For sure, but test coupons are flat and short, masts long and round, so it is not a great verification of process.
There's little need to test anywhere near breaking. If the weight is correct and qc has been observed with the laminate, resin and additional reinforcing, the only required testing is deflection. This can be done by supporting the ends and hanging a weight from the middle or by supporting it at the bearings and hanging a weight off the end or evenly along the mast.

Unstayed masts are simple structures. They have simple loads. Designing and testing them is a simple process.

The easiest way to test to (actual, not theoretical) ultimate is to put it in the boat and sail with the hull just clear of the water. If it survives this, you can be pretty sure it will not break for the rest of it's life, due to the excellent fatigue properties of carbon and the aforementioned simplicity of the loads. Use the same test to prove that your anticapsize device works.

Adhoc,
Thanks. Interesting, but way more detail than required for a cruising rig.
What it does show is how complicated stayed rigs are to design (not copy), relative to unstayed. And that, even with all that high tech build, standardisation, knowledge, experience and maintenance, the IMOCA's dropped (and are still dropping) a lot of rigs.
This may be because there are so many more 'difficult to analyse' loads on a stayed mast. eg flogging headsails, stretchy rigging, different running rigging tensions, etc.
Also interesting that their coupon samples were not balanced. I have several rules of thumb for composite laminates.
1) Balance the laminate around the centre.
2) Minimise angle changes between layers.
3) Inside and outside laminates of tubes in compression (all of a stayed mast, the lee side of an unstayed mast) should not be lengthwise.
4) No more than 2 mms (this number varies a lot between engineers and structures, I have been advised of up to 6mm) of solid laminate in any single direction. 2mms is conservative for masts, so I use it.
Assuming the first term is the orientation (±45, 0 or 90), the number in brackets is the number of layers and the layers are .15mm thick so 7 layers is 2.05mm thick:
The coupons: ±45(2), 0(20), 90(2), 0 (10)
My laminate: ±45(1), 90(1), 0(8), ±45(1), 0(7), ±45(1), 0(7), ±45(1), 0(8), 90(1) ±45(1)]

We have found excellent flex results between theory based on samples and practice, but have not rechecked these after use. Will do so when the circumstances allow it. When we ask a sailmaker how stiff to make it, they all say 'as stiff as possible'.
The best solution in my experience is to build the mast, then ask the sailmaker to design and fit the sail. Good ones ask for measured deflections under given loads at various points along the mast. Their software generates great pictures of how the sail 'will' look (draft and camber depth and position in various breeze strengths). I advise clients not to pay the final instalment until these have been achieved. It is an easy process to photograph draft stripes and calculate draft and camber using a boom mounted camera. Good sailmakers will show you how to obtain these ideal shapes and/or recut the sails until they are correct.

 

@rob denney - seems like very reasonable and sound advice.

Maybe more useful than test coupons to failure in a UTM for me would be more on order of what Gougeon did making laminate samples on order of 0.5m x 0.5m to test for deflection and breakage against other commonly accepted materials for a similar use. I believe they would vary edge support from 2 sides to 4 sides in those tests. Marine ply was often used as a 'control' sample for comparison.

I'm a decent hand laminator and can set up a vacuum bag, but it would be good to know if my calculations and workmanship stack up before diving into the final product.