Arne Kverneland wrote:
Stavanger, Sunday
Scaling up or down a mast section using the cube rule
Peter
Finding the right scantlings for a JR mast, sloop or schooner will always involve some guesswork. One method is to start with a known boat with a mast from the same material as you want. The thing to remember is that the breaking strength of a mast varies with the cube of the masts diameter. If you want a mast that is twice as strong as another one, just multiply it with the cube root of 2 (=1.260). Likewise, if you want a 3 times as strong mast, the cube root scale factor gets 1.442.
Now if we start with David’s "Tystie" at 8tons, your 20tons boat is likely to need a main mast that is 2-3 times stronger than Tystie’s main mast, at 8 5/8" (=21.9cm)
Then your mast should be between...
21.9cm x 1.260=27.6cm (=10.86") and...
21.9cm x 1.442=31.6cm (=12.43")
Note: I don’t know the wall thickness of Tystie’s mast. This must be scaled up too if the cube rule shall be correct. The 12" pole you mention sounds therefore reasonable if the wall thickness is not too thin.
Arne
Yes, I'd agree with that, Arne, so long as the "stiffness" of the boats compared is not too different. Tystie is of shoal draft, and not particularly stiff.
The strength of a tube is dependent on its section modulus, which is given by:
0.098(D
4 - d
4)÷D
In inches, the section modulus of Tystie's mainmast tube is 10.24.
The section modulus of a 12" x 1/4" tube is 26.5
Thus, the 12" tube is 2.6 times stronger than my mast, and ought to be suitable for a boat whose righting moment is 2.6 times greater than Tystie's. I'd still like to measure that righting moment, though. It's quite easy to do, and if a new unstayed mast was found to be not strong enough it would be an expensive failure.