Hello Junk Sailors. I wanted to share my thoughts for a year or so, and now there is a good opportunity.

Regarding mast strength calculations I am certain, that relaying on the "Righting Moment" formula ONLY is not proper. This is a very smart  and easy in application formula, but proper for a beam reach (+/-) case. Just picture up sailing with the wind from the stern. Quite common case. What would be the righting moment then, when applying  the boat length instead of beam? Tremendous - no way to carry the mast that would sustain such a righting moment.For many reasons - stability for example.

Plying with calcs for my CARABELA 650, prior I got it from Jerome Delaunay,  I assumed different wind velocity generating pressure and load forces on the sail and mast, also when RUN, and checked the actual moment generated. I know, that my rig with a full sail on, should sustain a  sudden squall with apparent velocity of 40 knots from the stern. In this specific case the moment when broad reach/run was about 2,5 times of the righting moment when heel. Therefor application of safety factor/multiplier when relying on the "Righting Moment" method only is more then justified.

More on Wind Load calculation and some easy tools (one of hundreds available on net) here: https://www.engineeringtoolbox.com/wind-load-d_1775.html

Daniele, welcome aboard!
The weight (or needed strength) of the mast depends more of the displacement of the boat, than of the sail area (See chapter 6b of TCPJR). This is because the righting moment of the vessel mainly varies with its displacement.
My 2.15ton Marieholm IF, ‘Ingeborg’ has a hybrid aluminium mast, weighing about 53kg (total length 9.7m). I would say that the absolute max weight of a mast should be no more than 5% of the boat, but I strive to get the weight ratio below 3%, which makes the boat move easily in a head sea.

Good luck,
Arne

Google search results has defeated me once again, but I think this spot is OK. I had a visit from a local marine surveyor today, and the topic turned to polystyrene and masts.. I recall polystyrene cropping up here somewhere too, but i bit my tongue at the time. I suggested he avoid polystyrene, because:-

Expanded Polystyrene is hygroscopic.

It is toxic (deadly) in a fire. This was learned in aircraft fires.

It leaches plasticisers from other polymers when in contact, eg PVC (think electrical insulation, conduit etc, making it brittle, and potentially causing short-circuits and perhaps fire). This is known in the electrical industry.

Also, expanded polystyrene is transparent to sound. Ie it offers no sound insulation/attenuation.This is known in the building industry.

I am not a fan of hidden expanded polystyrene anywhere. 

Walter

David, thank you for the suggestion to compare my mast base with the standard H/McL specification for solid tapered mast – and thanks to Arne and Ueli for their follow-up comments.

I have now done this, but first, a little background:

My plan is to stretch the mast length out to the maximum I can achieve with the materials I have at hand. If this proves to be over the limit of what the boat can carry, I will reduce it accordingly. Any reduction will come first from the wooden extended heel plug.

The current untapered Bermudan mast stands at 9.05m above where the partners will be, its weight is estimated to be over 56kg (not counting spreaders and rigging) with CoG estimated to be 4.5m above partner. (To lift this mast from horizontal would require a “couple” with moment of greater than 56 x 4.5 = 252 kg-m. I might be mistaken, but this seems to me a good basis for comparison.) 

The proposed composite alloy/alloy tapered mast will be initially 9.7m above partner, weight of that part above partner calculated to be 52kg with CoG carefully calculated to be at 4.31 above partner. This gives a comparative “moment” of 224 kg-m. These numbers actually represent an improvement. However this does not take into account windage – and nor is it proven that the boat could carry the sail area which this new mast height could accommodate (an increase of about 30%). But part of the purpose is to explore these limits in preparation for a future sail-making project. I plan for the moment to use a sail which I currently have, which is 30.1 sq m (14% greater than current sail area), and can be fitted to this new mast with half a metre to spare.

Now for the “heel plug extension.”

(Thankyou David for that nice piece of nomenclature.)

It may prove to be temporary, but the issue now is, how would this "heel plug extension" compare in strength with a standard H/McL solid tapered mast base?

Using H/McL formula, the diameter of a solid mast should be

90% of (LAP+sqrtSA)/.85 = 90% of (9.7+sqrt35)/.85 = 165mm

(Here I can pay homage to Arne also by noting that my proposed maximum sail area of 35 sq m on an estimated 3.25 ton represents a SA/Displ ratio of about 16. The Arne “fake” sail area, using 14,  would be 30.1 sq m – exactly equal to the sail I will be using for the immediate future – and using that in the above formula the diameter would change to 161mm.)

My new alloy composite mast, at partner, will be actually 152mm diameter, 5mm wall thickness. At the point where the mast suddenly transitions to solid timber heel plug extension (0.8m below partner) the diameter will be 140mm. This is the diameter of the heel plug which is inserted into the alloy tube. Here is, I suppose, the weakest point in the base assembly. (diagram)

A Hasler/McLeod solid timber mast, if tapered to half its diameter at the heel, will, by simple geometry, be 128mm at this point 0.8m below partner. So, luckily for me, the geometry is favourable, and I think my 1.0 m heel plug extension, at 140mm diameter,  is well within the Hasler/McLeod recommendation.

That is, if my arithmetic and reasoning is correct.

Actually I don’t really trust either, which is why I have shown the “working” – maybe one of you good people would be kind enough to check.

However I must say it all looks “intuitively” OK, and I feel better now having done the calculation.

David’s comment about Weaverbird’s mast top also makes me feel better about using my flagpole for the top 4.5m of my mast. Thank you for that, David.

hi arne

the windloads won't bring any bending moment to the mast, if there is no hull with its inertia and righting moment to work against heeling. that's why the needed breaking strength of the mast is only slightly affected by the length of the mast (as i understand it, just by its inertia…)

ueli