How do I calculate mast thickness?

[daveyjones]

I am restoring an old wreck of a ketch which came without spars, photos or drawings. I want to build new masts, but I don't know how to work out the correct thickness. I know there is stuff on the web about this, but it seems you need to be a mathematical genius to understand it- righting moments, forsooth!

Here are the relevant figures: both mizzen and main will be hollow sitka spruce spars,(solid at stress points) epoxy glued in an 8 part birdsmouth arrangement, and tapered. Wall thickness will be 22.5% throughout the length (ie the thickness of the staves composing the mast will be just under a quarter of the mast diameter, and the staves will taper upwards to reduce the mast diameter but retain the wall/diameter ratio). Both stepped on the keel and chocked at deck level. Main is 34ft from deck to mast head, mizzen 25ft. Gaff rig on both, mainsail is 250 sq. ft , jib about 160 sq ft, staysail about 100 sq ft. Mizzen sail about 125 sq ft. I am not planning to have a topsail at the moment.

Boat is a fairly typical long keel heavy displacement type, 34 ft loa, 10 ft beam, 6ft draft, weight probably about 7/8 tons (just a guess), ballast keel about 3 tons (another guess).

What I would really like to know is how thick the masts should be at deck level. I am guessing that 7ins would be about right for the main, and 5ins for the mizzen. Any comments? Better yet, does anyone have or know of a similar yacht and what size its masts are? Thanks in advance for any contributions.

 

[Rob Gates]

CJ Watts, formerly chief draughtsman at C&N and lecturer in naval architecture at Southampton, writing in Practical Yacht Construction around 1947, says this:

'Notice that the duty of the mast and the way in which it is stayed and supported naturally require that its largest diameter should be about midway between the deck and the hounds, above and below which it may be tapered down. Its diameter at this point should be about 7/32 in. for every foot of length from deck to head of lower mast (cap band.)'

He also mentions aft rake; 'usual figures being..3/8 in. per foot for a ketch..'

For a gaff ketch the 7/32 in. per foot figure is also quoted for the topmast diameter at the middle, the main boom diameter at the middle, and the gaff diameter at the middle.

For the mizzen boom he quotes 1/4 in. per foot.

For the bowsprit diameter at the stem he quotes 9/16 in. per foot, with 0.89 taper to the end.

Other figures for gaff ketch spar tapers:

Mast taper to deck: 0.98
Mast taper to masthead: 0.77

Topmast taper to heel: 1.00
Topmast taper to shoulder: 0.89

Mizzen boom taper to mast: 0.81
Mizzen taper to outer end: 0.81

Main boom taper to mast: 0.78
Main boom taper to outer end: 0.78

Some numbers to juggle with anyway!

 

[dur]

CJ Watts, formerly chief draughtsman at C&N and lecturer in naval architecture at Southampton...

...Some numbers to juggle with anyway!

Presumably for solid spars?

 

[Rob Gates]

Presumably for solid spars?

I think CJ Watts is talking about hollow spars, both round and with a streamlined section depending on what you fancy. Immediately before recommending 7/32 in. per foot for the diameter he says:

The thickness of the walls for a hollow mast should be about 1/5 of the diameter, or if not round, 1/5 of the breadth each way.'

 

[daveyjones]

So with a mast length of 34ft, the 7/32 rule gives 7.43 ins. For the mizzen at 25 ft, it gives 5.46 ins. This is close to my estimated 7 and 5 ins. I thnk I'll build them at 7 1/4 ins and 51/4 ins, to allow for shaving a bit off if necessary. I intend to make the walls a bit thicker at 22.5% of the outside diameter, not 20%, so I will have a bit of leeway there.

If they fall down or are too heavy, I can always build new ones!

It seems that with traditional heavy displacement boats, if it looks right, it is right. I also designed the sail plan by eye before doing the sums, and they all came out spot on. Anyway, thanks for the contributions.

 

[oldsaltoz]

Why not just get a rigger involved, this may also save loads when you have a claim on insurance......