Thank you Roger.
With those data in place, it should be possible to guess the righting moment of the Underwood 33 within about 20% accuracy.
With a decent ballast ratio of 2000kg/4500kg = 44%, but with a quite shallow draught of 1.0m, I would guess that the righting lever is hardly longer than 1/5 of the beam of the boat (probably a bit shorter).
That is, Lr = Beam/5 = 3.4m/5 = 0.67m
Then the righting moment,
Mr = Displacement x Lr = 4500kg x 0.67m = 3015kpm, or rather, the righting moment,
Mr will sit somewhere between 2400kpm and 3600kpm (+/-20%).
Then it is the question of strength factor, depending on the kind of sailing one has in mind. As I did in an earlier posting, I suggest that the actual breaking moment of the mast should be between 3.0 x Mr for ocean voyaging, down to 2.0 x Mr for lighter coastal work.
Those numbers were with a spruce mast in mind. I think that one can cut these factors a bit lower when using aluminium poles or carbon masts (provided that the mast builder knows his/her stuff). The reason for me reasoning like this is that the lighter CF and AL masts put much less peak stress on themselves (whipping) as the boat is rocking and rolling in a seaway. Maybe the strength factors 3.0 and 2.0 could be reduced to 2.5 and 1.5 on CF masts.
The strongest CF mast should then - at strongest version - have a breaking moment
Mb = 3600kpm x 2.5 = 9000kpm
I realise that I am on thin ice on this matter of strength factor. Anyone would be. The only way to collect some real data on this, would be to fit pressure sensors with logging capacity on either the mast partner(s) or the mast step(s).
Cheers, Arne
PS: Roger, could it be that Gary Underwood already has worked out the curve of the righting lever (righting arm)?