Flagpole specs for junk mast

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steve

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Has anyone got the specs (diameter, wall thickness) for an aluminium or steel flagpole that will have the necessary structural characteristics to serve as an unstayed mast for a junk rig? Thanks in advance.

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I've never seen a sensible analytical approach to the sizing of Junk rig masts, so here goes. Someone shoot me down if I'm wrong.

I presume you know the righting moment of your hull. The bending moment on the mast cannot exceed this, as the vessel will spin at lower loads and not provide more resistance. So the maximum moment, M = vessel righting moment in lbf - inches or Newton-Millimetres.

In the following calculations BE CONSISTENT in the units you use.

Stress in a circular mast tube at the partners due to bending is calculated from the following formula:-

Bending stress = M * y / I

where
M = vessel righting moment
y = half mast tube diameter = D/2
I = 3.1415 * (D^4 - d^4)/64 (Ref Roark 6th edition)
D = mast tube diameter
t = mast wall thickness
d = inner mast tube diameter = D - 2 * t

The bending stress must not exceed the yield stress of the material or the mast will be bent after a knockdown. A reasonable safety factor is 2, so the allowable stresses will be:-

Steel (grade 43/ S275) yield = 275 N/mm^2, allowable = 140 N/mm^2 (approx 20000 psi)
Aluminium (6082-T6) yield = 255 N/mm^2, allowable = 130 N/mm^2. (approx 19000 psi)
Timber (douglas fir) allowable = 5000 psi (approx 34.5 N/mm^2)

The calculation procedure would be to use a spreadsheet or calculator, decide on the outer diameter and then find a thickness that gives a bending stress lower than the allowable. If the sailplan has 2 or more masts, proportion down the moment applied to each mast by the same proportion as the sail area on that mast relative to the total sail area. For a solid mast, set t = D/2 (ie d = 0).

The diameter at the top may be 0.5x the diameter at the partners.

I hope that gives an adequate design guide..

Regards,

Richard.


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Wow. Thanks very much. I don't know the righting moment for my boat, but I assume I can get it from the designer.

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Richard,

I reckon transient load on the mast could easily be higher than the righting moment, due to the inertia of the system. This dynamic load would be pretty complex to calculate.

I wonder how yacht designers normally decide on required rigging strength.

Tony S

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Shouldn't the sail area enter into the calculations? Surely a mast supporting a sail of say 45m2 would have to be stronger than one with a 20 m2 sail.

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You could well be right, but I have a Junk Rig with an 11" wooden main mast as per Bruce Robert's design for my vessel, BUT the calculations I've given seem to indicate a fraction bigger than that - so it can't be too far off.

Regards

Richard.


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Definitely so.

But if the vessel lays flat when you have 30m^2 on it there really is no point in designing the mast to be OK for 45m^2. It's the vessel's stability that puts an upper limit on the maximum load that can be applied to the mast. It strikes me that designing to the stability is a safe option, as the load can't be exceeded even if the yacht is over canvassed. Admittedly, if it's undercanvassed you'll have a heavier rig than is warranted and will pay weight/speed penalties.

The reserve factor of 2 I suggested does give a fair margin for unexpected effects.

Regards,

Richard.

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