Finally a carbon mast also on the Olympic Tornado!

No Typos in this post, quick google on defining moment of inertia :

Definitions of moment of inertia on the Web:

The property of an object associated with its resistance to rotation.It depends on the objects mass and the distribution of mass with respect to the axis of rotation.
fuse.pha.jhu.edu/outreach/kit2/glossary.html

A physical property of a member which helps define rigidity or stiffness and is expressed in inches raised to the fourth power. It is a measure of the resistance to rotation offered by a section's geometry and size.
www.hancockjoist.com/glossary.htm

The rotational analog of mass. The sum of the products of mass and the square of the perpendicular distance to the axis of rotation of each particle in a body rotating about an axis.
unistates.com/rmt/explained/glossary/rmtglossarylmn.html

The amount of force required to spin an object.
www.bowlingfans.com/faq/glossary.shtml

– the mass of a rotating object times the square of the distance to the axis of rotation
www.mhhe.com/physsci/physical/jones/graphics/jones2001phys_s/common/glos_m.htm

A physical property of a member, which helps define strength and deflection characteristics.
www.sentinelbuildings.com/glossary.htm

the rotational analogue of mass, in units of mass*length2 (see rotational kinematics)
people.ucsc.edu/~erowland/glossary.html

Amount of force required to spin an object.
www.jayhawkbowling.com/Pro_s_Corner/Glossary/glossary_new.html

The moment of inertia of the armature is measured about the torque motor's axis of rotation. The ratio of the motor moment of inertia to the damping factor with a zero-impedance power source gives the mechanical time constant of the motor. In direct drive systems, load inertia and damping factor have to be added to the motor inertia and damping factor to determine the mechanical time constant.
www.servomag.com/reference/glossary.htm

The resistance to twisting of any golf club head when that head is impacted off-center.
www.wickedsticks.com/glossary2.htm

the tendency of a body to resist angular acceleration
www.cogsci.princeton.edu/cgi-bin/webwn

Wouter,
What I mean is that redius of gyration is the conventional name for resistance of a mass from rotating. 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??). An aluminum T mast weighs 38 lbs and a carbon version can weigh 21 lbs. The overall radius if gytation of the entire boat is the summation of it's various parts. These can be combined by superposition just like the linear motion analogy (moments of inertia). So a carbon mast may help the boat overall by say 8% (a wild guess). 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). Does it make sense now?

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

I think you missed the fact that I asked Kevin to explain his use of the words "Radius of Gyration".

I, of course, suggested that what he was trying to describe is actually the Moment of Enertia.

I'm personally totally unfamiliar with the "radius of gyration" definition. This could be me but then again dynamics of bodies is something that I've been tested on many years when at the university and often in the English language as a well.

Even if the "adius of gyration" exists as a definition than Kevins use of it is awkward. The second point conveyed in my post. Mostly because "pitching moment" is a force on a lever while Moment of enertia (Radius of gyration ?) is not.

And a few other things.

Regards,

Wouter

I think I got the gist of the 'gyration' theori in the first post, so I will not comment on the quite heated discussion about the proper physical non-layman terms that has bloomed in the last couple of posts.

Mark: Regarding the "Society of Ordinary Tornado Sailors", where do I join It is a shame if public perception and politic scares people off the T..

Now, if I have understood the last part of the discussion right. Going for a strict one-design carbon mast, as is proposed in the ballot, will in fact take away the possibility of the olympic campaigneers to find a mast section suitable for their sailing weight and style ?
(Warning: I'm playing a bit of devils advocate here)

To all the non-Tornado sailors who has given their opinion, please continue to do so! In my opinion, all information is of the good, and different views on an issue only gives a richer base of information to make a decicion on..

Hi Rolf,
One of the smartest rules I have ever seen dealing with mast bend and how to make it vary with crew weight was in the International Contender Class. The mast extrusion can be fixed, one design. The location of the hounds can be varied within limits. This way the lighter weight sailors, for example, rigged their masts with a lower hounds position which resulted in a greater bending moment being applied to the mast for a given mainsheet tension. The larger sailors rigged their masts with a higher hounds position which reduces the lever arm to the mast tip. The shorter lever arm reduces the bending moment imposed on the mast for a given mainsheet tension. Since the heavier sailors must control their sails with more mainsheet tension, the higher hounds position keeps the mast from overbending and flattening their sail prematurely.
One might suggest that the heavier weight sailors just start out with a fuller sail and live with more mast bend. This is a compromise because it forces the heavier weight sailors to use a sail that is too full in light winds.
Bob Miller was a smart man.
Bill

Wouter,
The radius of gyration is also called the radius of inertia. It is a fictitous radius that when squared and multiplied by the mass of a body produces the same moment of inertia as acquired by integrating the elements of a body times the radius squared to each element over the entire length of the body from some reference axis.
(Radius of Gyration = Moment of Inertia/mass) The comment about the carbon mast having 1/4th the radius of gyration of an aluminum mast can only be correct if the carbon mast has very heavy elements near its base and very lightweight elements near its tip. I doubt that this the case.
Bill

Bill,

Thanks for confirming that to me.

So in basis the Radius of gyration will not change at all when making a mast lighter UNLESS the relative distribution of the mass is changed as well.

Yep, got that

Wouter

Wouter,

Exactly. Note that the radius of gyration can be reduced simply adding weight to the mast foot, but this doesn't improve performance. Add more weight and the radius gets smaller and the boat slower.

Something like this could happen if the new rules maintained the minimum mast weight unchanged but eliminated the mast tip minimum weight.

I wouldn't expect them to do that (I hope so) because it would be weird to use new carbon masts with lead weights in the mast foot... The gyration radius would be small, but reducing the minimum mast weight and tip weight obviously make a lot more sense.

Regards,

Mike Grandfield's letter to the US Fleet
followed by Roland Gabler's point of view.

Dear All,

Although I have great respect for Roland, I believe that he has NOT given you good advice regarding the carbon mast ballot proposal.

Here are the reasons why:

1). THE PROBLEMS OF THE FINN SAILORS HAVE NOTHING TO DO WITH THE CARBON MAST PROPOSAL IN FRONT OF TORNADO SAILORS.

- The Tornado ballot proposal includes both pricing and price guarantees. The guaranteed price is 40-50% more than the current Marstrom aluminium mast.

- The Finn mast is not a strict one-design mast. It is customized for each sailor.

- The Tornado carbon mast is a strict one-design, with very precise tolerances; and the design will be transferred to ISAF to protect the class and ensure that other builders can be licensed.

- The problems of Finn mast breakage are not relevant; the proposed Tornado carbon mast was designed for strength and durability, and Marstrom has built over 3000 carbon masts.

2). The aluminium masts have never been equal for all TORNADO sailors; and by next year no one WILL believe that they are TRULY one-design.

- There are 5 flexibility groupings of the current Marstrom masts. Only a few top sailors find really good masts, most of the fleet gets average masts.

- Most current Marstrom masts bend differently to port than to starboard. How many sailors have noticed that they point better on one tack than the other?

- Today, there are commercially available aluminium masts from Marstrom. Hobie, Nacra, and soon from Swiss Carbon; and there is a privately developed mast that was designed the UK with funds from the RYA - this mast has been used at Hyeres and SPA, but it is not commercially available.

- There are at least 2 additional mast designs that could be built if we stay with aluminium.

- So, we will have between 5-7 different aluminium masts. Each one has a different die and different cross-section; BUT each of these measures in as a LEGAL Tornado mast.

- Is that ONE DESIGN? NO!

- If any of the new designs are better than the current Marstrom aluminium mast, then EVERYONE will have to buy a new mast.

- If the RYA mast is the best, but not commercially available, then EVERYONE will complain that it isn’t fair and could easily spend a year or more trying to develop a mast that is competitive.

- If we keep the aluminium mast, we could easily become LESS one-design than ever before.

- There is no price protection with aluminium. A higher performance mast could easily be as expensive as a carbon mast.

- ONLY FULLY FUNDED TEAMS WILL BE ABLE TO AFFORD THE COST OF TESTING NEW ALUMINIUM MASTS AND THE SAILS THAT MATCH THEM.

3). THE REASONS TO CONSIDER THE CARBON MAST ARE NOT “LIGHTER WEIGHT” or “HIGHER PERFORMANCE”

- The Marstrom aluminium mast is not strong enough; Marstrom is selling over 3 times as many masts as new boats! The fleet has spent over ½ MILLION EUROS (Before VAT!) on spare and replacement aluminium masts since the new rig was introduced.

- The Marstrom aluminium Masts are not equal in performance; by next year there will be at least 5 different aluminium masts to choose from.

- The reasons to choose between aluminium and carbon are:

o Strength

o Safety

o Equal Performance

o No advantage to teams with bigger budgets

4). I DON’T WANT TO SPEND MONEY ON A NEW MAST; I STILL HAVEN’T BROKEN THE ONE I BOUGHT IN 1998.

- But, by next year there will be a better carbon mast or a better aluminium mast.

- In 2005, we will all have to consider buying a new mast to remain competitive.

- I believe that the carbon mast ballot item is a very good proposal and the best way to provide a level playing field.

- I’d be excited to sail with a new carbon mast; but I’d be frustrated and angry to have to buy a new aluminium mast instead.

For many years the Tornado fleet has been protected because all of the boats and masts came from Marstrom. THAT TIME IS OVER. The real choice is a one-design carbon mast or a new “arms race” to build a better aluminium mast. It is unrealistic to think that nothing will change.

Clearly, the RYA has already committed to the new aluminium mast effort. SOME OF YOU WILL PROBABLY RACE WITH IT OR AGAINST IT IN ATHENS.

The carbon mast ballot item is your opportunity to choose the future you want for the class. I hope you choose wisely.

Regards,

Michael

-----Original Message-----
From: Roland Gäbler [mailto]
Sent: Wednesday, July 14, 2004 7:50 AM
To: yann.guichard@wanadoo.fr; Hugh Styles; Hugo Rocha; iorpas@yahoo.gr; Jim Young; John Forbes; John Lovell USA 808; Jpolgar@aol.com; Jürgen Jentsch; Kristof Koch; mail@sailcenter.se; Marström AB; mgrandfield@sailingwind.com; Mitch Booth; Niko Mittelmeier; obackes@aol.com; Nuno Barreto; p.wetzig@gmx.de; P. Egger; Patricia Kirschner Ross; Patricia Tornado; Patrick Egger; Philip Wetzig; pres@tornado.org; Ralph Mittelmeier; ramirami@t-online.de; Sail Center Per Wearn; Sebastian Moser; sec@tornado.org; slange; tornado@topica.com; Wolfgang Heinemann; Will, Fabian; will.howden@virgin.net; xavier-revil@wanadoo.fr; Aaron McIntosh; Aaron McIntosh; Guenter Moertl; GunnarStruckmann@aol.com; funinthesun@juno.com; Ullman Sails - GZ S.r.l.
Cc: Jürgen Tiemann; Darren Bundock; BSG Sports
Subject: Carbon Mast
Importance: High

Dear Tornado Friends,

just some days ago I had some nice talking with some Finn Sailors in Athen about their change to the carbon mast some years ago.

- 4-6 times more expensive (and the mastbuilders said before it will cost just the half more) ha, ha, ha, ha.....

- A carbon Finn Mast cost 2.800-3.500.- euros now !!!! ask your national finnsailor

- A Aluminuim Mast was 700-800.- euros !!!!

How much we must pay to make our boat 8 KG ligther? My Finn Friend sayed, he can finance a new house with all the money he spend in carbon masts last years. Hy guys, wake up................

Security. Safe Sailing? We are the Formula one of sailing. Who wants to go save with this boat. Just not go out when it blows 30knots plus offshore.

Do you think if you open to much the sheet under spinnacker what the carbon mast will not brake? The Finnclass broke more mast than ever in the last years!

Each Finnsailor has 3-6 Mast plus 3-6 light cloth sails. Also forget the cubenfibre sails, they are shrinking.

Instead of getting more milliseconds of speed, we should not forget the think about the youth. How they should finance the new masts? Plus Spinnackers, Plus Cuben Fibre Sails?????????

Do you think only Sail Center of Sweden will make the mast? Many others will come.

I can easy make each mast different. What a nice and expensive mixture???

One Question: How much money you spend in Spinnacker last 3 years? Worth one Car? Ok, we have max fun with our spinnacker. Yes, yes, yes we enjoy........But do we get some much fun-factor with the carbon mast?

Lets concentrate to get back on our One-Design and Olympic Idea.

If you want go faster, buy the M20

I donnot want to talk about the carbon mast. I just wrote my way. Please do not answer this mail. Just answer the ballot and SAIL FOR FUN

See you in Athen. Cheers,

Rolando

There's that "one-design" phrase being misused again.

Well you comment immediately proofs that Radius of Gyration is bad measure then.

One can reduce the radius of gyration by the way you decrease and end up with worse performance. One can increase radius of gyration adn also end up with worse performance. This makes this measure a bad to optimize upon. Better to use the real thing : the total moment of enertia.

>>Something like this could happen if the new rules maintained the minimum mast weight unchanged but eliminated the mast tip minimum weight.

It sure could but why would you want to rule against that ? You end up with a worse performaning bad so this will selfregulated itself into oblivion. No class rule needed for that.

Wouter

I still see some misunderstanding in the posts and since engineering jargon confuses people and is not appropriate for the forum I feel obligated to do a better job explaining in terms of concept (no fancy words). This can be done by comparing two imaginary boats that are identical in their shape, volumes and rig geometry. Boat A is the stock Marstrom Tornado built of S-glass and aluminum spars. Boat B is a tornado made out of imaginary stuff that is infinately strong and stiff so it dosen't weigh anything. Say we want to correct boat B so it can race fairly with boat A. One approach might be to fit a single large weight correction on the centerline just aft the beam of boat B and a few inches above the designed waterline. So now boat A and B float on the same waterline and if we pull them through still water they have the same resistance. But are they fairly handicapped? Next boat A is sailed against boat B in a seaway and boat B beats the crap out of boat A. Why? What's the difference? Boat B has smaller radius of gyration with respect to it's three rotational axes: pitch, roll, and yaw (this is the technically correct term in continuum mechanics in this country). The concept here is fundamental to boat design. It is expressed by the sailors intuition to keep weight out of the ends and as low as possible.

Kevin

Mark,
I agree with the points you make. Another thing to consider is that the variability between carbon tubes in terms of weight and stiffness can be quite a bit less than the current alumunum hardware. This is assuming you standardize on one builder using identical prepreg material and layup schedule. Variation in the weights of the Marstrom prepreg platsorms run in the neighboorhood of several ounces for a 284 pound weight. So, we are talking in the nieghborhood of .1% weight variation. This is also the type of results obtained with aerospace composite parts. I suspect this is less than the current tolerance on the aluminum sticks. The goal is to to make sticks with enough similarity that no one has an incentive to shop for multiple masts optimized for crew or wearhet conditions. To do this with composite tubes you almost have to commit to a single builder because even if material an tooling are specified the layup (individual ply orientations) can be manipulated to produce tubes with a wide range pf properties even though they weigh and look the same. Thus, you would also have to specify and control layup schedule. Not a hard thing with one builder but becomes more difficult with multiple builders.

Kevin

Kevin: In the ballot proposal, they do mention some stringent stiffness measurement procedures to make sure the mast has the proper one-design virtues. I guess masts not buildt to the spec. will not be accepted at measurement before competitions.

Kevin,

The best parameter to compare a normal boat and one with less weigth in the extremities is the moment of inertia (around each axis).

Equal boats or masts have the same weight, the same moments of inertia and the same "stiffness". It is simpler then using radius of gyration as a parameter, which only confuses things.

If I understood correctly, the idea is to have a one design mast in order to reduce its price and the work done to tune the rigging. The downside is that it will create an optimum crew weight in the Tornado (for each wind force) and the sails will be more complicated to customize for each crew.

Cheers,

Problem with radius of gyration is as follows :

Lets take your Boat A = the stock Marstrom Tornado built of S-glass and aluminum spars.

Keep your boat B is a tornado made out of imaginary stuff that is infinately strong and stiff so it dosen't weigh anything. This one has a reduced radius of gyration and performs better.

Then we introduce boat C this one is the same as boat B but has a given weight strapped to it dolphin striker pin. As the radius of gyration is defined as "Moment enertia / totall mass" we can say that this boat has a reduced radius of gyration as well ! But we all know this boat to be a worse performer. So the net result is one where the radius of gyration is reduced and the boat performs worse.

In the imginairy case we could strap an very large weight (infinite even) to the pin and arrive at the same radius of gyration as boat B. Naturrally this boat C will have far war performance than boat B because it will be on the bottom of the lake ar form a black hole (different topic)

Point of this example is that a similar reduction in radius of gyration can be had by both increasing and decreasing weight; both leading to better performing and worse performing boats. Radius of Gyration, although technical useable, is therefor a traiterius principle to use.

Moment of enertia calculations don't have this problem and will assign a higher value to boat C no matter what the added weight.

Wouter

Hi Jake,
You bring up an interesting question, "what is one design"?
Is it exactly identical equipment for all sailors within a given class? If so, how do we handle the fact that "people are not one design"? Heavier people make the boat have more drag going through the water; lighter weight people have an advantage with less hull drag. When the wind blows hard, say 15 knots and up, the heavier people have an advantage because they can generate more righting moment and therefore have more sail thrust. Even enough more sail thrust to more than offset their greater hull drag. We all know from experience that lighter weight teams have a speed advantage in light winds and heavy weight teams have a speed advantage in strong winds. Putting non one design people on our class boats has shot a big hole in our one design class objective of having all competitors having the same max boat speed potential on all points of sail in all wind conditions. How do we fix this? What is the best way, the most fair way, to compensate for this inequality?
Let the ideas flow....
Bill

Bill,

In response to the argument that the Tornado class should allow other manufacturers to produce Tornado parts, I was actually trying to point out the difference in the phrases "one design" as defined in the spirit of the Tornado rules and "one manufacturer" that everyone now seems to consider the Tornado. The very context of the phrases indicates that while a "one manufacturer" class can also be a "one design" class, a "one design" class doesn't neccessarily have to be "one manufacturer". I don't interpret any intention for the Tornado to be a "one manufacturer" in the class rules.

However, I agree with you (did I say that?)

Louis, Wouter,
I follow what you are saying. We are trying to describe the same effect but are tangled up in terminology. You have raised enough question for me to go back and check. I have always been under the impression thet RG is defined as mass X moment arm. But from the point of view of the forum, probably nobody else is interested in this and next time I will avoid using any technical words - we all should.

Jake,
What about this "one design problem". How do we compensate for the fact that sailors, people, are not one design and this by itself has a large affect on the outcome of sailboat races???
There seems to be two schemes in place today.
1. One is the factory class where only factory parts are legal. All other parts are illegal. This is a money driven idea and does not inhance one design sailboat racing but is used as an excuse/example of "one design sailboat racing".
2. Another plan is to have all identical boats, masts, etc except for the sails. In this plan all sails are the same size/area but the camber distribution, the shape in the sail, differs. There are full cut sails and medium draft sails and flatter cut sails. The heavier weight teams use the full cut sails because with their greater weight, they are going to bend the one design mast more and therefore their sail must have more luff round. The medium/average weight teams use the medium cut sails and the light weight teams use the flatter cut sails. This plan has shown in many different one design classes over several years that it leads to tighter competition than giving all sailors the same cut of sail.
Let's look at Olympic class sailing and see how "the best", the ultimate sailing classes/contests, do it. If there is a more correct way to handle this problem, surely it is done most correctly in the Olympic sailing contest. When I check on the Star and Soling and Yingling and Tornado and Finn and other Olympic classes, I find that the Laser is the only class requires all sailors to use the same cut of sail. All other classes allow variations in sail cut within some max limits for that class. Who is right? Other large one design classes in the US such as Snipe, Thistle, Lightning, J24, etc all allow variations in sail cut within max sail measurements for that class.
Both of these schemes cannot be more correct. One of them has to be more fair and the other less fair, less correct, in compensating for variations in sailors weight.
We can require the light weight teams to add weight up to the average teams weight and this fixes the light weight teams advantage in light winds. How do we help the light weight team out in heavy weather sailing? To take away their light wind advantage and not fix their heavy weather disadvantage is not fair.
What do we do to get it right???
Bill

Kevin,
The radius of gyration squared equals the moment of inertia divided by the mass. RG**2 = I/m. Therefore I = RG**2 x m. RG is a radius at which if all the mass was concentrated there, it would have the same inertia as arrived at by integrating (r**2dm)of the body over its entier length.
Bill

Kevin,
Now you are really confusing me. You are saying that the variation in Tornado platform weight is several ounces out of 284 pounds or about 0.1%, one tenth of one percent. That platform is made up of two composite hulls, some fixed rigging and two aluminum beams 10ft long each. These aluminum beams are extrusions. They seem to be very consistent in weight and therefore other properties. Why is it that the extruded beams can be so consistent and yet the extruded masts are out of control??? The company that manufacturers the carbon mast also manufacturers the aluminum mast. The only company that manufacturers the carbon Tornado mast is the company that is partitioning the class officials to change to the carbon mast. Is the fox in the chicken coop??? Other classes have no problem extruding aluminum masts by the hundreds that are identical. If the Tornado class has a problem doing this, maybe they need a new aluminum extruder with better quality control.
There is one other important point relative to the carbon mast. Carbon sands very very easy, cuts fast. Sandpaper cuts carbon like crazy. What is to keep a carbon mast owner from sanding his mast to make it bend to fit his weight? If he does is this legal or illegal???
Bill

mastrom quality control allows him to make

285 lbs = 129.105 kg platform within a margin of no more than 0.1% = 0.129 kg = 129 gram or the equivalent of 1 and a halve ronston smart ratchet blocks (the small kind) ? The pre carbo ratchmatic Harken ratchets were 142 grams per single block.

I think this to be a really strong claim. Halve of a plastic coffee cup with resin weights the same 120 grams if not more.

If you spread that out of two hulls of about 15 - 17 sq.mtr. overall surface you would add a film of only 42 micrometers = 1/600 of an inch.

And the funny part is that people can easily differ by some 5-10 kg's per person or 50 - 100 times the margin that Mastrom gives his boats. What is the use ? That is a whole lot of accuracy for nothing.

Better still is one of the sailors decided to take a cup of coffee for the race, as Mitch did at the 2004 F18 worlds, than that crew would allready by 2 times the marstrom margin overweight. No wonder Mitch finished 15th in that race. (joke). A pair of sunglasses weight 100 grams or more

Wouter

Bill: I dont know about the quality control on the Marstrøm masts, but generally Marstrøm has _very_ good quality control. As I know Gøran, he has done his best to get mast extrusions with identical physical properties. Gøran seems to be doing quite good business supplying alu. masts. 500K EUR is real money spent on masts since the new rig.

Regarding sanding the proposed carbon mast: There are a whole new regime of measurements to be taken with regards to stiffness. These rules are designed to weed out masts with differen properties than the one design mast.

As Mr. Granfield wrote, the RYA has developed a propetiary alu mast that measures in under the current rule. This mast is used by the very succesful british team. He wrote quite a lot about why he was not happy to spend money buying a new alu. mast.

Interresting times...

Hi Rolf,
I know Marstrom tries to do his very best and his very best is very good. That is why there is only one Tornado manufacturer now. He is not in the extrusion business. Some company extrudes masts for him. Marstrom is not in control of the mast extrusion quality although he can reject masts upon inspection.
Aluminum shapes, tubes,angles,flat bar,T bar, all kinds of special shapes are extruded all around the world and done so very consistently. The aluminum Tornado mast should be no exception.
I remember from my SC days, initially we had a problem breaking the mast extrusion die at the part that formed the sailtrack. A diemaker advised a slight change in the internal shape of the track and no more breakage of dies. There is a little art in the die making and extrusion business/process.
I remember reading not too long ago about a new aluminum alloy that is superior to the 6061T-6 aluminum alloy commonly used for sailboat masts. It is both stronger and lighter in weight. It is used in the commercial aircraft business, airliners, and is making a significant increase in aircraft range. If the Tornado class is going to make a change, this new alloy should be investigated for all their extrusions.
The situation of the Finn class carbon masts is scary. I'm sure before they started building carbon masts, the situation was thoroughly investigated and the conclusion was that the carbon mast was the best answer. Now the class has a big mess on its hands. I'm sorry to learn this. It hurts the Finn class and Olympic sailing.
Bill

Well, I dusted off the textbooks and the right term for what I have been trying to express is "polar moment of inertia". In my case I confused the term with RG. The polar moment is a different mathematical expression from what is commonly called "moment of inertia". So, we are all guilty of using less than accurate terminology.
The assertion that Tornado hulls have very little weight variation came from a 1996 article in Cat Sailor magazine that was describing preparation for the Olympics in Savannah. The measurer stated he was surprised that weights of the Marstrom boats only varied a few ounces. But, if the measurer's claim is still suspect, there is data from many other composites applications. For instance, carbon helicopter blades completely out perform aluminum and have better tolerances on both weight and stiffness.
It would not be practical to alter a carbon stick by sanding it. You could not remove material with enough uniformity to achieve any desired end result. Whatever you ended up with would be sheer luck. If someone really wanted to cheat, it would be much more feasible to chemically mill an aluminum tube than sand a carbon one.
There is a potential problem with measuring stiffness as a way to ensure consistency. This is because even if stiffness of both the major and minor dimensions were measured, games can be played by altering ply lay up alter stiffnesses in other orientations. What makes the unidirectional fiber such a flexible material to design with becomes a liability when trying to assure exact properties from one builder to another. To remove variation in composite sticks it drives you towards a single builder. I reserve judgement whether this is good or bad. It's certainly not in the spirit of the original Tornado rules but then the current aims of the class are different.

Well,

It is also known.

I(polar) = I(axis 1) + I(axis 2)

So I(polar) is nothing more than the sum of I(axis 1) + I(axis 2) where the two axis are perpendicular.

Of course with a mast the I(y-axis) is very small compared to I(x-axis) ; a ratio of 1 to 30,000. So it is very convenient approximate masts (the thing we wre initially talking about) by calculating only I-(x-axis). In short Ipolar of the mast is very closely approximated by I(x-axis) alone.

In basis you are right however. I(polar) is the thing you need to do math on rotations dealing with the whole platform. However for dive decelleration calculations you'll need I(x-axis) again and not I(polar).

Things are getting easier by the post aren't they.

As Radius of Gyration was not incorrect in the strickt sense but a it is a confusing expression to use.

may point was however than reducing mast weight by a factor of 2 reduces the polar moment of the mast by 2.0000333 when looking at rotational oscillations. For decelleration dives only one of the normal moment of enertias is involved and this is reduced by 2. This is only for the mast and the total of I(polar) is determined by many components INCLUDING for example the crew itself especially when far away from the main beam. The overall net effect of reducing the weight of the mast by a factor of 2 can have a net result of about 5-15 % overall depending on several factors

I think ths wraps it up nicely for all of us.

Wouter

It seems the construction/manufacturing tolerance is why the sailors have found masts with different stiffnesses. Skiffness of the mast is a function of dimensional properties and physical properties.

Aluminum dimensional properties will vary http://www.almag.com/tolerances.htm
Yes, you can reject masts, but at what cost?
In the manufacturing world no one likes their product to be rejected.
What dimensional tolerance are the sailors willing to pay for?

For aluminum physical properties, to my expensive/suprise I have found the Modulus of Elasticity (Young's Modulus) for one sample of aluminum alloy 6063-T6 to be 9 msi, when it is supposed to be 10 msi (10 percent difference) How is this possible?

For carbon dimension properties what if someone misses a layup?
How are dimensional properties of carbon mast going to be checked?

For carbon YM I have found it can vary from 30 msi to 100 msi.
Someone could accidentally ship 40 msi carbon fibre.
How is carbon YM going to be monitored?

Rather than the TRADITIONAL quality control of the dimensional and physical properties of each mast to decide weather to accept or reject it; use the RESULTS OF the above properties AND field measure the deflection/stiffness by placing a weight. (I don't think to many extuders would be happy doing this, but you get what you pay for)
Some type of mast rating system could be used; ie, this could be based upon tip or midspan deflection in both major and minor axis.
Again, measuring the RESULTS OF the manufacturing process, after all the sailors are interested in the results/stiffness not the thickness or YM. (provided of course is it properly designed for bending and shear)
The resulting measure of mast stiffness could then be catalogued to crew weight (but how many catagories is another thread)

The most important thing is to have a sail and mast that make a good combo.

Most differences between masts, I'm told, can be taken out of the equation by measuring your mast bend characteristics and order a mainsail to fit your mast.

Ordering custom sails for a given mast flexing is standard stuff with many sailmakers. The testing itself takes two saw horse a bucket able to hold 20 litres of water and about 2-3 hours of your time.

Also I would like to add that an oddset need not be the same over the full length of the mast. Meaning inconsistancies can wave over the full length of the mast and average themselfs out a bit as a result.

I personnally think it to be cheaper if the class collects the batch of produced mast and puts in a day of measuring each mast and marking each mast with the basic characteristic. The sailors can then request their perferred mast section and only pay for one mast. This is always inmensely cheaper than everybody getting carbon and due to the normal distribuation of crew weigths and sailing style all masts will be sold. Remember that the off sets of the mast themselfs , as a result of a natural proces, has a normal distribution as well. I think people familiar with Random variables ar familiar with the term "normal distribution"

At least it is this approach that I think I will propose in my class when the differences between mast proof to be to great to be acceptable. We are already sharing mast stocks between builders.

I think it would be a small feature for either the Tornado class or the marstrom yard to perform this trick as well.

Would leave everybody happy and keep cost down. That is unless other reason lead to the decision to go for carbon.

Wouter