And I'm in a reall antagonistic mood so please pardon my excessive use of sarcasm.

Let me see if I understand it now :

>>What I mean is that redius of gyration is the conventional name for resistance of a mass from rotating.

Actually the radius of gyration is nothing more that the "radius of gyration" it takes a little bit more to express the resistance of a spinning mass to CHANGES IN ANGULAR SPEED. Or in other words, There is no "resistance to rotating": unless you are trying to discuss the principle behind gyroscopes but that is a whole different matter.

More comments later.


>>If you take a long slender object such as a mast and reduce the weight by half it should cut this property by about 4 (or is it 8??).

It is neither. Right answer is "cut in halve". You are talking about the Moment of Enertia here which is defined as the sum or integral of the product :

lever^2 * mass (techies call this a second order moment because of the squared lever)

With a mast you must use the integral expression but this one behaves the same as the some of a given number of finite elements with a finite mass. In short the lever (or radius of gyration for that particular element or part) is squared while the mass is not. Therefor if you reduce the mass by a factor of 2 then the moment of enertia (the true expression for resisting changes in angular speed) is also reduced by 2. Reducing the lever is more efficient of course as that is a squared relationship, but that would leave you with a short mast. (And they say that reducing the mast height in the F16 class was a bad idea)

Anyways:

Somebody else claimed that a carbon mast would not be much better as their was the tip weight rule. Meaning, any mass lost must be put back on the top (in part) to arrive back at the correct tip weight.

This is a HUGE consideration as the tip weight is determined using the gravity force (1st order moment) while the performance improvements are linked to the moment of enertia (2nd order moment).

For techies under us. The mast tip weight test is a process that is dependent on the first order moment (lever * mass) while the performance is dependent on the second order moment (lever^2 * mass)

This results in the situation where the extra piece of lead used to correct tipweight results in a inferiour mast when compared to a mast that has perfectly spread out all the mass over its full length while still just satisfying the tip weight rule.

This is one of the reasons why I never understood the fact that people tried to make masts as light as possible only to have a piece of lead in the top to compensate for being underweight.

The problem is in the Lever being squared in moment of enertia.

Simple example and I will not bore you with the integral calculus:

mast - 10 mtr long
weight 10 kg (no fittings etc)
Assume all mass evenly distributed (no taper etc)
mast tip weight when layed horizontal = 5 kg

Moment of enertia = 300 kgM^2

New mast !
mast - 10 mtr long
weight 5 kg (no fittings etc)
Assume all mass evenly distributed (no taper etc)
mast tip weight when layed horizontal = 2.5 kg
To compensate for tip weight rule (as present in Tornado rules) additional 2.5 kg needed at top (= 1/2 of weigth savings)

Moment of enertia = 150 kgM^2 + that of corrector weight = 150 + 2.5*10^2 = 150 + 250 = 400 kgM^2

Making the second mast absolutely worse in performance. This new mast with corrector weight in the top compares with regard to Moment of Enertia to a mast that is overall 13,33 kg (= 77% heavier) but evenly distributed.

Tipweigths are dumb. One reason why F16 class is advicing against using them although it uses a minimum tipweight rule. It is adviced to use the excess weight in making extra loops around the mast when using carbon, making the mast more robust as well. The F16 tipweight is below what is feasable in alu so this rule will never have a problem there. Pardon me for the shameless promo for the F16 class, I just couldn't resist. However it is also an example of how the tornado class could modify their tipweight rule to keep carbon masts under control and secure the continued use of alu masts for some time.



>>An aluminum T mast weighs 38 lbs and a carbon version can weigh 21 lbs.

Well, we did some investigating on 8.5 mtr carbon F16 masts and the quotes gave about 9.35 kg for the blank = 20.6 lbs. I think your 21 lbs for the much taller and the more heavily loaded Tornado mast is a bit optimistic.

Lets continue with an estimate of 25 lbs. Ratio between new vs old = 25 / 38 = 66 % => mom enertia ratio new / old = 66 % as well when only taken on the mast and no corrector weights. Than we need to add sails 7kg's and fittings 1.5 kg halyards etc. A quick calculation ends up with a ratio of new/old = 0.85 = 85 % A long shot from the initial statement concerning the magnitude of improvements as made by you. The reduction is more like 1/6 th


>>>The overall radius if gytation of the entire boat is the summation of it's various parts.

No, that would be the summed moment of enertia.


>>These can be combined by superposition just like the linear motion analogy (moments of inertia).

Actually the lineair analogy is "Enertia" (often just called "mass") while the rotational variant is "moment of enertia" or even angular enertia in less correct fashion. You can also replace "superposition" by "adding" or "summing". Superposition is not entirely wrong in the strickt sense but suggest something more complex than is really adressed. Besides superposition is far more used in relation to waves and more complex vector calculus although even in these cases it amount to not much more then "adding"


>>So a carbon mast may help the boat overall by say 8% (a wild guess).

In what sense ? A ratio without reference framework is useless. 8 % more speed ? No way ! 8 % less moment or enertia overall ? Not likely especially not with 150 kg of crew hanging of the wires some 1.5 mtr behind the fulcrum of the rotation. In addition to that a rearbeam of 6 kg at 2 mtr and some rudder setup of 3 kg at 2.5 mtr. It is probabaly more like 4 %. 8 % less amplitude in oscillation ? That could be the case but that doesn't say much to most sailors not educated in these matters.


>>The boat radius of gyration is directly related to the amount of energy it takes to move a boat through waves (reduces pitching moment and rolling moment).


Some claim that reducing pitching inproofs performance by improving the flow over the sails that are otherwise more disrubted by constant (sometiem violent) changes in 3D. I'm not even sure that the reduction in mast related moment of enertia are even significant in the amount of energy needed to propel the boat through the water. But I guess I'm more an acceptive of the improved flow over the sails explanantion. Jury is still out on this one.


>>Does it make sense now?

Yes, thank you for explaining all this to me.

Of course I wasn't really asking for that in my last e-mail as I was asking about the proces that lead to some weird statements concerning the dynamics of finite bodies under the assumption of classical physics. But I think I understand that as well now.

Thank you,

Wouter