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We can now calculate the stress at the partners (S) and also see what Safety Factor (sf) this gives us. A sf of less than one would mean that the mast broke. And we can calculate the deflection (Y) – we will calculate it at the height of the CE. Here are the formulae:

S = RM*y/I N/mm^2
Y = FL^3/3EI mm
sf = R/S

So, working this for 30º we have:

S30 = RM30*1000*y/I = 4049•1000*75/21629865 = 14.04 N/mm^2
sf30 = R/S30 = 69/14.04 = 4.91
Y30 = F30*L^3/3EI = 1093*3.705^3•1000^3/3*13400*21629865 = 64 mm

Note:
Because the RM is in Nm, we multiply it by 1000 to bring it to Nmm.
Because L is in metres we multiply it by 1000 (cubed in this instance) to bring it to mm.

And for a knockdown, we have:

Smax = RMmax*1000*y/I = 7031•1000*75/21629865 = 24.38 N/mm^2
sfmax = R/Smax = 69/24.38 = 2.83
Ymax = Fmax*L^3/3EI = 1898*3.705^3•1000^3/3*13400*21629865 = 111 mm

So our first stab at a mast diameter looks a bit on the high side because it gives a safety factor of 4.91 and we really do not need more than 3. And even with a knockdown, the safety factor is 2.83 and we only need something like 1.8. Deflections are all within reasonable numbers. Remember though, that deflections are at the CE height – they will be proportionally more at the masthead.

The nice thing about this calculation is that it doesn't matter what sails you have up (on the mainmast). A main and a genoa will produce much the same result – as long as their combined CE is not higher (and it usually isn't). This is because we are not considering sail area as such – simply the Righting Moments needed to heel the vessel.

The easiest way to get at the size of the mast (to give a safety factor of between 2.5 and 3) is to make a spreadsheet with all the formulae in, and then keep entering different diameters at the partners and letting the figures flow through until it produces suitable results.

For other materials the calculations are exactly the same, except that we need different values for R, E and W:

For aluminium alloy:

 R 255 N/mm^2 0.2% Yield Point E 69,000 N/mm^2 Modulus of Elasticity W 2,700 kg/m^3 Weight

And for carbon fibre:

 R 570 N/mm^2 Ultimate Compressive Strength (UCS) E 70,000 N/mm^2 Modulus of Elasticity W 1,580 kg/m^3 Weight

Note: The figures for carbon fibre will vary considerably depending on the lay-up. These are average and should be used with caution.

© George Whisstock. This article is for information only and may not be commercially reproduced in any form or used in any way without permission. Do not use this material as the basis for designing a mast without professional advice.