Anonymous wrote:

Hi Len,

I like your raised question: what do we build for? Promoting is one thing, for sure. But it might not be the main reason for everyone converting to junk rig. For more experimental minded ones, it might be a calculated risk to lose a mast if knowledge can be gained during that process. For others, a reliable cruising rig is priority #1.

It may be interesting that as I continued to do research on free standing masts, I came across an article by a naval architect with some history of why free standing masts have not been adopted. One story was of a boat with free standing masts caught in a storm violent enough that the boat pitch poled and sank after which many people decided free standing masts were not a good thing... thing is, even though the boat pitch poled and sank, it was found that the masts remained intact. So maybe promoting is a lost cause, people want to have a sailboat like they drew in grade school.

For my boat, I have decided that because the stronger of the two masts I can realistically build is still only about 3% of my displacement anyway, That is the size I should go with. I don't expect we will cross the Pacific (even half way to Hawaii) or travel the coast to Mexico. Nor do I see us still sailing when I am 100 plus years old. On the other hand, my sailing area (Georgia Strait) does have short cycle, choppy waves.... besides it will impress my girl  ;)   She is new to sailing, things that look strong are good.

Hi Len,

Very interesting thoughts of you!

If I (very roughly) divide 500 million cycles by the average wave period in the baltic (3s), an aluminium mast should not fail in 48 years - if the mast only has to withstand loads up to 40% of its ultimate tensile strength. What an abstract, theoretical number! Are we able to draw any practical advice from it, except from that life is not endless?

I like your raised question: what do we build for? Promoting is one thing, for sure. But it might not be the main reason for everyone converting to junk rig. For more experimental minded ones, it might be a calculated risk to lose a mast if knowledge can be gained during that process. For others, a reliable cruising rig is priority #1.

Maybe I am stating the obvious here: I think it is important to separate the calculation process from the judging process (sorry for my bad english):

From an engineers view, it is pretty standard to calculate the strength of a free standing mast. No big deal. So, you calculate by material and geometry, you get a number, and if you do it properly, you also get the percentage of unsafety of that number. Also, you don't need to restrict to statical cases, you could also determine dynamic bearable loads, using Woehler line, fatique limits, etc. This I would call the calculation process. Nothing really to discuss here, as it is standard procedure. Again, this number tells you about the bearable loads.

Now it gets interesting, the judging process: how do you judge that number? What do you expect for actual working loads? How does hull shape, sea state, etc. affect the expected working loads? What sailing behaviour, reefing early or late? etc. All this summed up find its way into the "safety factor", or "sea margin".

IMHO, if you want to compare the actual strength of masts to each other, you just compare the calculated bearable loads from the calculation process. This can give you the required base on which to think about in the second step, discussing and deciding on safety factor, sea margins, etc.

Only in this judging process, personal preference should be a factor. One likes it lighter but more wobbly, one likes a sturdy pole. It is all okay, no good or bad here, just a personal decision. However, this should not be blurred into the calculation process!

It would be nice to have a data base of failed masts...

I totally agree! Not only of failed masts, but of working masts, too. Ideally including material properties, all relevant mast scantlings, amount and kind of sailing, hull shape, ship data, etc... And then find someone who wants to do his phd on this data, and share the results :-)

But, if the same manufacture builds in a safety factor of two or three, then it makes sense even if a weaker alloy is used.

I would be very (!) hesitating to transfer the safety factor from my jobs project example to any other material specification. I would find it very optimistic and unrealistic to directly transfer a one-time experience with CRP to general aluminium applications. I only mentioned this example to give a hint about how accurate material properties might (!) be listed.

Cheers,

Paul

In an earlier post Arne wrote: "My calculations may well be on the conservatives side. The mast of my IF appears to take no strain at all, even when we are heeled down to 30degrees."

I have often wondered about the veracity of calculations based on a boat's righting moment.

I would have thought the greatest strain on a mast would be when running down-wind, possibly under too much sail, and being  stopped by a wave.

I must say I am a little "out of my depth" when it comes to doing these calculations, I am impressed by people who can do that, and not knocking it - but perhaps for this reason I do think it is quite important, and convenient, also to simply look at the mast scantlings of comparable boats, and take it from there.

According to this Gabrian Chart the 170MPa is for T5 (AKA T52 etc.) and T6 is 214MPa. In my case, I can only get 6063 T5 but I can 6061 T6 at 275MPa. I will note that these numbers seem to vary a bit from supplier to supplier's documentation but generally in the last digit. It seems T52 is similar in strength to T5 but age hardened.

Okay now that is a significant deviation for the same material - or at least material declaration! Didn't expect that. I took my values directly from Nedal, as both german subsuppliers kindly let me have the original technical drawings including material numbers from Nedal.

Sure, if I insert 214 MPa for yield strength of 6063 T6, the mast strength will be exactly the same as of Ingeborg. But, hm, I don't like to calculate myself happy, especially as I am not used to aluminium too much... However, I should not be surprised by the deviaton of material properties: in my job I designed several underwater acoustic domes from CRP. Due to own inhouse material tests, we found the suppliers material property values to be conservative by factor 3 (and it wasn't a cheap supplier)!

It would be interesting to know why they choose 6063 and not 6062 or the more common 6061. Like what the engineer's reasoning is for material choice.

As far as I understand, 6063 is the most common (beside 6060, which is even worth regarding strength). I guess it is less an engineers reason rather than a matter of price.

I will note that Poppy, a 31 foot, 4300kg longbow, with a ballast to displacement ratio of 44.68 has a 150mm mast (6inch). When I do the calculation for my smaller 3500kg Cal29 using 6061 T6 at 275KPa, I seem to need a full half inch in a 6inch tube (13mm thick) which means the bottom 20 feet alone would weigh 91kg. But a move to 8inchx.25 tube at 21ft only weighs 68Kg and is stronger too. So I wonder how thick the tube wall on Poppy is and what alloy too.

Now, if you just look closely at the formula of the maximum bearable moment of a tube, regardless of how it is used or abused...

...it becomes quite obvious that at least three values are needed to compare masts: yield strength, diameter and wall thickness. If only the diameter of a mast is given, the strength comparison to another mast can be easily off by 50% if not even more. In my eyes, such a blurry comparison would be close to useless...

One of the things Arne's calculations do not account for is mast mass. Another is mast flexibility. All of these calculations go back to wooden masts with generally much thicker walls, greater overall mass and a less uniform strength. I would also note that the original JR would have had wood battens and canvas sails which would also increase the effective mass of the mast. In many ways, looking at what has worked for other people is a good measure too.

Even for my 29ft yacht. I keep wondering if I am doing something wrong in my calculations  :) I am beginning to think this is all guesses.

I am very grateful for Arne's calculation scheme, as it helps to give an close idea and kind of takes you by the hand for a good part of the path during the design process. But I am sure he would not call it "the end of the flagpole" (directly translated from german, sry). Shipbuilding designs always follow a very conservative philosophie, compared to other fields of engineering. While this might appear frustrating from time to time, it is just natural if you look at the lack of available test data and the cost of testing - which in this case would be losing your rig several times until you find the sweet spot. 

Thus, I would not call it guessing, but rather carefully approaching the optimum mast scantlings from the safe side of the available spectrum - strictly avoiding the other side, the crash side.

Anonymous wrote:

Now for the mast, I can only get 6063T6 aluminium, for 12 m conical poles as well as cylindrical 6 m pieces...Unfortunately, the yield strength of 6063T6 is only 170 MPa compared to 6082T6 with 250 MPa (thus, 6082T6 is about 50% stronger than 6063T6).

According to this Gabrian Chart the 170MPa is for T5 (AKA T52 etc.) and T6 is 214MPa. In my case, I can only get 6063 T5 but I can 6061 T6 at 275MPa. I will note that these numbers seem to vary a bit from supplier to supplier's documentation but generally in the last digit. It seems T52 is similar in strength to T5 but age hardened.

However, lucky me, I thought, as I am offered two conical masts:

• 222 mm/ 5 mm tapered to 90 mm/ 7,5 mm, with the lowest 5 m being cylindrical
  
• 177 mm/ 4 mm tapered to 76 mm/ 4 mm, with the lowest 4 m being cylindrical

Did the manufacture say what they thought the yield strength of the alloy was? 222 (over 8inches) does seem high. I have the funny thing that I live in Canada, a metrified country and all the aluminum tube I can find is in inches. If I look in the US... where they use the kings units (well sort of, the gallon seems to be the taxed size not 10 pounds) are in sway, the tube sizes are all in mm. Go figure.

From a geometric view, the 177/4 profile would be even stronger than the 150/5 profile you suggested: Its section modulus is about 15% higher. Unfortunately, the strongly differing material properties crash it: The 177/4@6063T6 is 22% weaker than your suggested 150/5@6082T6.

Retry with the 214KPa for your T6. It would be interesting to know why they choose 6063 and not 6062 or the more common 6061. Like what the engineer's reasoning is for material choice. Maybe we could learn something. It may be that they use a cold forming process starting from tube and going to tapered and 6063 works better for that.

I will note that Poppy, a 31 foot, 4300kg longbow, with a ballast to displacement ratio of 44.68 has a 150mm mast (6inch). When I do the calculation for my smaller 3500kg Cal29 using 6061 T6 at 275KPa, I seem to need a full half inch in a 6inch tube (13mm thick) which means the bottom 20 feet alone would weigh 91kg. But a move to 8inchx.25 tube at 21ft only weighs 68Kg and is stronger too. So I wonder how thick the tube wall on Poppy is and what alloy too. I wonder how much the flex in the pole has to do with things.

One of the things Arne's calculations do not account for is mast mass. Another is mast flexibility. All of these calculations go back to wooden masts with generally much thicker walls, greater overall mass and a less uniform strength. I would also note that the original JR would have had wood battens and canvas sails which would also increase the effective mass of the mast. In many ways, looking at what has worked for other people is a good measure too.

The 222 mm would weigh 72 kg at the length I aim at. The 177 mm one would weigh 55 kg.

When I calculate the ratio of M_b,yield/M_r,max, the following (rounded) figures appear:

• 222ish mast: Mb/Mr = 2,6
  
• 177ish mast: Mb/Mr = 1,5
  

Now, given only these two options, if I want to stick to the guidelines from your chapter 6b, the decision appears to be pretty clear, doesn't it?

However, a 222 mm Alu mast appears really oversized to me, considering a 25 ft yacht. But this is merely a gut feeling, according to the numbers it would fit just fine. Any thoughts on this?

Even for my 29ft yacht. I keep wondering if I am doing something wrong in my calculations  :) I am beginning to think this is all guesses.