Solid wood mast vs hollow wood mast

[Bruce46]

Perhaps I'm having a senior moment, however, I can't seem to find a reference on how to convert a solid mast to a hollow mast. The masts in question are to be free standing on a 23' cat ketch. According to Skene's, my main mast is 4.58" dia. x 24' and my mizzen is 3.85" dia x 22'
Main SA =135, Mizz SA = 88 sq. ft. I'm probally wasting time, however, I wanted to see how much weight I could save by making birdsmouth masts, and comparing them to masts of almuinum.

[Eric Sponberg]

You have two options:

First, in Hasler and MacLeod's book "Practical Junk Rig," there is a procedure for determining the section size and wall thickness for hollow wood free-standing masts.

Second, once you know the diameter of the solid wood mast, you can calculate the equivalent moment of inertia, I, and section modulus, SM, of a hollow mast.

For the solid mast, I = PI(OD^4)/64, and SM = 2I/OD

For a hollow mast, I = PI(OD^4 - ID^4)/64, and SM = 2I/OD

For equal strength, SM for each mast should be the same. For equal stiffness, I for each mast should be the same. Vary OD and ID until you get equivalency. For a wood mast, the wall thickness should be no less than 20% of the outside diameter.

I hope that helps.

Eric

[Bruce46]

Eric
Thanks very much, I should know that but the gray hair got in the way.

[ancient kayaker]

Originally Posted by Eric Sponberg

... For a wood mast, the wall thickness should be no less than 20% of the outside diameter ...

Eric, what is the underlying consideration for that rule? I ask because I built a couple of masts with thinner walls - down to 12.5%. Based on my long-ago experience with thin-wall tubular structures subject to Euler buckling I concluded that the ultimate limitation was the maximum number of staves one was prepared to use. With walls at 20% of OD there is a max weight saving of only 36% compared with a solid mast of the same OD.

I am assuming that OD of the hollow mast is increased compared to the solid mast it is replacing. Does the rule apply for the same OD - cantilever strength and stiffness would hardly be effected - or perhaps the thick walls are to retain fasteners ...

[Eric Sponberg]

Hi Terry,

I quote that 20% guideline only from what "Practical Junk Rig" stipulates (and the authors admit to not being engineers), and it is also used in "Skene's Elements of Yacht Design" by Francis Kinney for hollow wood stayed rigs. I dare say that with proper engineering and testing, you could reduce that guideline considerably for free-standing masts, as you apparently have done with your experience.

If I were to do such a study for free-standing masts, my consideration would be to determine the required thickness to prevent buckling during bending, which is not an Euler phenomenon since the mast is not under pure compression. Nevertheless, if the wall thickness is too thin, the section will collapse by buckling before the full strength of the wood is reached. For composite masts and tubes made of primarily unidirectional fiber with some off-axis fiber, for both fiberglass and carbon fiber, I have found that the minimum thickness-to-diameter ratio (using inside diameter) is 3%. If the t/ID ratio is less than that, premature buckling will occur. If it is more than that, usually the material will fail in compression before buckling collapse. Wood, therefore, having less modulus than carbon fiber certainly, would require a bigger t/ID ratio.

Eric

[ancient kayaker]

Thanks Eric. They seem to stand up OK but I wondered if there was a specific theory behind the rule. I suspect there is a max weight-saving of around 50% when designing a hollow mast to match the strength of a solid one (using the same material) but I haven't done the math.