Wood Mast, Rectangle vs Oval
I have been trying to find a rectangle mast chart online and have come up with nothing. Skenes has a chart for oval wood masts, but nothing for rectangles. I am wondering if the difference between "oval" and rectangle is enough to worry about or can i just use the numbers from the oval chart and leave the mast a little more boxy?
Also I am intending to build the mast out of D-fir instead of Spruce. Fir having less compressive strength, does anyone know a rule of thumb number to increase the scantlings?
It's possible to calculate the moments of inertia exactly if you have the algebra skills to tackle it--it's not hard.
To calculate the moments of inertia for a rectangular section exactly, you follow the basic formula for a rectangle: I = (A x B^3)/12 where A and B are the length and breadth of mast cross section respectively. Using the dimensions as in the Skene's figure, A = outside length, B = outside width, then we'll call the inside dimensions with small letters: a = inside length, b = inside width. We see that the wall thickness, according to the figure in Skene's, is 20% of the overall dimensions. Then, the moments of inertia are:
Ill = (B x A^3 - b x a^3)/12
Itt = (A x B^3 - a x b^3)/12
Barring that, if you pick a size out of the Oval Chart in Skene's, and simply make it rectangular in shape to the same overall dimensions, your mast will be slightly stiffer and stronger, and probably with not enough difference to worry about.
As for switching from Spruce to Douglas fir, and assuming the same dimensions of the mast section: The moment of inertia calculation above is a stiffness criteria that is related to the modulus of elasticity of the material. Overall stiffness of a mast (or any structure) is proportional to ExI where E is the modulus of elasticity, and I is the moment of inertia, as calculated above. Douglas Fir, according to the wood properties chart in the back of the WEST System manual, has an E = 1.95 x 10^6 psi, and Sitka Spruce has an E = 1.57 x 19^6 psi. So for stiffness, the Douglas Fir mast will be stiffer and be able to resist buckling better than Sitka Spruce for the same size section and load. If you want to have equivalent stiffness, the same ExI, then for the mast with the lower E, you have to increase I in direct proportion so that the product ExI is the same.
For compression strength, Douglas Fir strength parallel to the grain = 7,240 psi, and Sitka Spruce = 5,610 psi. So again, Douglas Fir is stronger. Your Douglas Fir mast will be stronger than the Sitka Spruce mast for the same mast section and load. If you want to have the same strength in compression between two different types of wood in a mast, which for a stayed mast is always under compression, then the equivalency is with area of the section. That is, Load P divided by cross section area A, P/A, = compression stress, and so you want to match the stress to the strength of the wood. If one wood is weaker, its cross-section area will go up for the same load P. So, P = compression stress x A. The higher the compression stress, the smaller the A, and vice versa.
You have to consider both strength and stiffness in any mast situation, and stiffness, related to moment of inertia, usually prevails.
I hope that helps.
Eric W. Sponberg
Sponberg Yacht Design Inc.
St. Augustine, Florida
Eric has done his kind and charitable thing once again. LTD you can put his advice in the bank.
One more small item is that the C fir is likely to be a bit heavier than sitka spruce. Aloft weight will matter particularly if the mast is tall.
The stiffness of the mast is an important consideration for the sail maker. If you already have sails, then marrying them perfectly to the mast can be problematic. The sails might need to be reshaped a bit unless they are lug sails.
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