Malcolm,

that safety factor makes sense to  me, in this case. For a real sailboat, meant for offshore work I would have wanted a mast with the breaking strength 3 times stronger than that of the boat's righting moment, but your safety factor will be ok for your use. A fine thing with unstayed masts is that they bend a lot before they break, so you get a warning that you should reef, and possibly build a stronger mast, next year. If you read my 2 stories  (here and here) about my dinghy Broremann, you will see photos of her (him, actually), with two different masts.

Arne

I have tested some of the elements in Oscar’s Junk Rig calculator against some of my masts and boats. Here is what I found:

Hull Properties.
This appeared to work well, with a plausible righting moment. However, this will vary with the ballast position and percentage, so remember to add a bit if heavily ballasted and subtract a bit if your boat is lightly ballasted (or with only inside ballast). I found the Displacement to LWL calculator handy  -  I have never used that parameter, but it makes sense.

Spar-mass-strength.
Appears to make sense. The only snag is that the sort of available aluminium alloy varies, and so does the strength. Is this calculation done with yield strength of 250MPa (250Newton/mm²)?

Sail Properties
I have only checked the Johanna type. It appears to be based on Johanna’s own sail, which has a quite low aspect ratio (AR) of only 1.87. Problem is that we often need to vary the aspect ratio quite a bit to get the sail area  and centre of effort (CE) right. That is why I have expanded the Johanna-sail into a whole family of “Johanna-style” master sails, with AR ranging from 1.80 to 2.25 (look up chapter 4 in The Cambered Panel Junk Rig  -  TCPJR).

To make a quick estimation of a sail area (SA) on a Johanna-style sail, if you know the length of boom and battens, B, and the AR, I suggest you make use of this simple formula:

Sail Area = 0.78 x AR x B²

The result is generally well within 2.5% error. This is actually a combination of the formulas for SA and AR on page 6 of Chapter 3 of TCPJR.  In real life we often have to start the rig designing process with the boom to get the CE in the wanted place (CE is close to the middle of the boom on the Johanna-style sails). Then it is a question of trying different AR to see if we can get the wanted SA without ending with a super tall or supper low sail.

Cheers,
Arne

Malcolm Duckett wrote:

Does anyone have a view as to how this translates into alloy masts?

Hey Malcolm. A shortcut would be to play around with the Junk Rig Calculator. Create your mast first with the wooden parameters and check out the breaking strength (in kpm) it outputs. Then you can play around with different values for an aluminium mast, aiming for the same breaking strength.

Disclaimer: If your mast breaks and you perish at sea I am not to be held responsible. I'm not an engineer, I just hacked that thing together during a a few evenings with formulas I found on the intarwebs.

Regarding to your other question about whether aluminium is expensive; it depends. Tapered extrusions are hard to find. Straight tubes aren't and are generally good value compared to their wooden counterparts.

Hi Malcolm

That figure seems to be too large for your requirements. PJR is known to be pretty conservative in specifying mast scantlings - see Arne's chapter on the subject in his public domain files under 'Junk Information' in the menu. You could also look at our Mast database for examples of what others have used for solid & hollow timber and aluminium masts.

Chris