I'd always wondered about this claim, comes up all the time, just 5 minutes ago in another topic. So while waiting for the noreaster to pick up I've done some back of the envelope calculations.

Got the old 30% NP 400 out, clamped it to the back veranda with the length above the boom ~ 2.7 metres hanging out. Loaded it up at the 2/3 out point, (900mm back from the tip) with 5 kg and measured the deflection. It was 60mm.

Now going to apply the equations for simple harmonic motion and figure out its oscillation frequency. Simple harmonic is normally applied to a spring working in a linear fashion with a non-rotating point mass rather than a bending beam with a distributed mass. The fundamentals are the same. I'm confident that using a centre of mass and "centre of spring constant" analogy will get us in the ball park. The calculations for a distributed mass are a bit frightening.

The mast from memory weighs about 3kg, the top 1/2 which is doing all the flexing probably weighs about 1kg. The sail centred on the flexing area weighs say 2 kg. Thats a 3kg mass oscillating on a spring with a spring constant of k = 833 newtons/metre.

For simple harmonic motion the oscillating frequency w = sqrt(k/m) = 16.66 radians per second. or 2.6 cycles per second.

A full carbon mast weighs about 2/3 as much so instead of (2 + 1)kg we put in (2 + 0.67 ) kg

the new oscillation period is 2.8 cycles per second

Not much difference. I haven't measured the "spring constant" of the full carbon mast because it should be exactly the same if the IMCS is the same.

What's that mean? Well you want the sail to keep up with the eddies passing the sail, flexing away and returning as one goes past. What's the smallest eddy that you might want a sail to respond to? I've gone for an eddy of dimension 1 metre. Any smaller than that and there will likely be a matching lull just below, the mast might as well do nothing.

Using Taylor's simple embedded eddy theory of turbulence a 1 metre eddy embedded in a wind speed of 10m/sec(~20 knots) will pass by in 1/10th of a second. The mast has to do a 1/4 oscillation cycle to return to its previous position as it passes. The 30% mast takes about 1/10 th of a second to do this naturally, so it should return without too much effort. The 100% mast can do a little better. But then again the back end of this embedded gust is only half a metre so should that be a 20th of a second?

All rough calculations, don't worry about the exact numbers. Larger gusts are probably of more interest and both masts have ample response to return after one passes.

Better mention that the simple embedded eddy model of turbulence is a little primitive these days, but it still serves the purpose for rough calculations.

These calculations have all ignored the damping component which will slow down the response. Maybe just a little bit, maybe a lot if the system is overdamped. Hard to estimate the damping component so haven't attempted any calculations. The air itself will contribute some damping. A lot could be contributed by the luff rubbing on the mast. Why do high carbon masts have a polished surface and low carbon ones a rough finish? Product differentiation?

Anyway I've concluded - It's surprising that sailors claim to notice an improvement in response with high carbon masts.

My 30% has a rough finish, my higher carbon smooth. Is this common? If so the damping component may be what sailors can feel. I can't tell the difference when sailing in a straight line for what that's worth.

"From memory", "weighs about" is scientific provided I provide the figures I have used in my calculations. I've also listed all the approximations I've made and all the assumptions.

One correction Taylor's "embedded" eddy concept may have been better known as the "frozen" eddy approximation. It was initially used years ago to make a simple link between the spatial and temporal statistics of turbulent flow.

Science is about repeating other peoples calculations and experiments. The main thing for me to be scientific is that I give you all the information and description of my method for you to to be able to repeat what I've done and correct me if I'm wrong. I think I have, if not ask me.

The basic point is that the speed of restoration of any deflection is dependent only on the spring constant and the mass of the system. It's just F=ma for springs. The ICMS rating of a mast is a just an alternative way of expressing the spring constant. Carbon masts are lighter, but with the same sail attached the relative gain drops. With a square root rather than linear dependance of mass in the response time it drops again.

You'll get different figures using more carefully calculated weights, different figures using more complex calculations using distributed mass, but for a given ICMS the relative differences in response will always be proportional to the inverse of the square root of the mass of mast and sail combination. According to my calculations less than 10% gain in response time using a 50% lighter full carbon mast.

Ok, so....

Amex 100% carbon skinny - Centre of mass 180cm from base - weight 1.6kg
Severne 75% carbon skinny - Centre of mass 178cm from base - weight 1.7kg

What's the centre of mass of your mast Ian?

Damn it, next thing you will be proving that the penny farthing was really the apex of bicycle design. It seems like windsurfers are not alone in being duped by the ad men. According to the video old hickory golf clubs are just as effective as the more modern golf clubs (the video may have been produced by a manufacturer of hickory clubs).

You could probably create a bit of a stir at Sandy Point by setting some fast times with a custom hickory mast and boom though concessions might have to be made for modern sail material.

sailquik said...
Fireproof suit on!

My attention span is shot so I only sped read this post but I'm fairly sure I agree with the master Daff 100%

I use 90 / 100% RDM's never ever a problem, I see mobs of tears with 100% SDM's me included until I saw the light. I digress, the average Joe Blow if he is using a SDM will be happy with 30% carbon, if you're the local hot shot with plenty of money and must win at all costs get a 100% SDM. Yes I've had a couple of reds

just found a calculator on the web for the bending of hollow tubes.

www.meracalculator.com/engineering/deflection-round-tube-beams.php

The formula for deflection is still linear with force, so it doesn't look like the tube going out of round adds non-linearities. But I can sort of envisage Sailquick's notion of skinnies bending beyond ICMS a bit easier than SDMs - keep looking.

An easier one to use.

easycalculation.com/mechanical/deflection-round-tube-beams.php

still linear with force.

petermac33 said...
The 'heavy' feel of race sails 7m plus a sail rigged on mismatched spare parts, however light or responsive the components will still be there.

damping

Ian, I'd put money on it that the spring constant... isn't... for masts. Because:

- the material construction isn't consistent (say like a metal lattice). ie: just like the leaf spring example, the fibre layout would have some affect.

- the tensile (Young's) modulus of carbon, fibreglass, epoxy, etc are all different -> you would need to consider the "composite-properties".

- as Slowey said, Damping... Here is an example (specific to this company's fibre's) http://www.vectranfiber.com/BrochureProductInformation/VibrationDamping.aspx


I also dont think we want "...springiness to be constant regardless of construction...". We have some somewhat tenable theory that suggests that modern sails (ie: twist, draft stability, skin tension) do indeed need different mast-characteristics throughout the length of the mast.**

** I always wonder how much effect the two-piece-mast-joint, has on these characteristics.

Thus our masts and sails have evolved to match our current need (and some of us will care enough to choose specific mast/sail combinations). What is most surprising of recent years, is to RDM masts in high-performance scenarios, given that RDM's are relatively constant radius**.

** Indeed previous generation RDM's performed poorly in said scenarios; but with the latest gen (thanks Daffy), RDM's have come into preferred use.


My $0.02... I am pretty sure that, say in a single-blind test, I can feel the difference between a 30% and say 70/100% -> the 30% feels somewhat lifeless, but I cannot feel the difference between 70 and 100. Of course to complicate matters, I have found what I feel to be a good combination using a KA Koncept 5.8 and a relatively soft 30% Gaastra mast.

Ian K said...

slowboat said...
damping

Is that damping of the mast in the air, by the rubbing of the mast on the luff sleeve or something intrinsic to the mast? If it was intrinsic to the mast you'd say it didn't have reversible elasticity. There would be hysteresis in the bend curve.

Intrinsic to the material. Wont restore? why not? Are you changing the laws of physics? Basic lump model theory shows it will restore. In laymans terms the spring component will always provide a force with displacement (it stores the energy). The damping component only provides resistance when its moving. So the combination of these two "components" means that the mast returns slower from a point of deflection when there is more damping. Think of a shock absorber and spring on the car...

slowboat said...

Ian K said...

slowboat said...
damping

Is that damping of the mast in the air, by the rubbing of the mast on the luff sleeve or something intrinsic to the mast? If it was intrinsic to the mast you'd say it didn't have reversible elasticity. There would be hysteresis in the bend curve.

Intrinsic to the material. Wont restore? why not? Are you changing the laws of physics? Basic lump model theory shows it will restore. In laymans terms the spring component will always provide a force with displacement (it stores the energy). The damping component only provides resistance when its moving. So the combination of these two "components" means that the mast returns slower from a point of deflection when there is more damping. Think of a shock absorber and spring on the car...

I didn't mean that it could not be intrinsic to the material, I just doubted that the dynamic friction could be all that much. The car spring and shock absorber absorbs energy by pushing a fluid through a small hole. It's not hard to envisage the resins in the fibre matrix doing a similar thing. But at what scale?

If this intrinsic damping is significant it should be very easy to estimate by clamping one end of a mast firmly to a bench, giving it a deflection and seeing how many oscillations we get. Most of the damping will be pushing air about but maybe the difference due to the intrinsic mast damping will show up. The differences might show up better if we slow down the oscillation by adding a couple of kgs to the tip.

I'm about to go clamp an old CK95 460 and a 30% 400 to the back deck and give them a flick - I'm guessing there'll maybe be a bit of observable difference. Maybe not. Will the extra damping in the 30% be significant compared to that of the surrounding air and the friction of the luff sleeve and camber inducers graunching away every time the sail flexes?

Then again the noreaster is building up.

ps. No not trying to change the laws of physics, was a bit slack with terminology, but then again I've seen masts retain a bend after being up a luff sleeve, and in the old days of electronics we used to tap the dial to get the (static friction induced) hysteresis out of the milliammeter.



Can we call it even on that one?

Each mast was firmly mounted to the back deck by the bottom 1 metre.



The NP CK95 460



The NP 30% 400



Here I have deflected the mast down by 300 mm, released it and counted the oscillations until the amplitude has damped to approximately the dimension of a big toe. The oscillation frequency was about as fast as you can count, There was a bit of a rattle at the deck end so you counted by ear. The frequency for both masts was about 3 hz,

Hi Ian,
What was going on at the ferrule or mast join during the oscilations. If there was the standard movement at the join you get when the mast is straight ie./ not prebent or rigged I'd guess the that could deaden dramatically the reaction of both masts and level the results between the 2.
When a sail is rigged the mast is always under some load so this slop is gone and the sharpness of a higher carbon mast may be shown better.
You may have explained earlier but as I couldn't tell by the photos and often vague out when reading this sort of thing so I thought I'd ask.

Sam.

Hi Sam,

Best I can measure with the calipers is that there is 0.6 mm of play at the ferrule on the CK95 and 1.0 mm of play on the 30% carbon mast. And you're right, that ferrule rubbing backward and forward, because it's not under preload, would add to the damping. If you had that cricket hot spot camera you might just detect the area around the ferrule get hot, maybe not.

But even with that extra damping, they still are doing 30 or so oscillations, they are both under damped. It's pretty certain that if you somehow reduced the internal mast damping to zero the return time after being bent would be only be an undetectable amount of time quicker.

I'd guess the oscillations are mainly dying out because of friction with the air, ie. the energy I've put in by bending the mast has mostly ended up heating the surrounding air by a small amount rather than warming up the inside of the mast by a small amount.

slowboat said...
only 300mm with no preloading?

OK I'll give it another go after work with a bit more. Really just trying to see if we can detect any signs of damping intrinsic to the mast material. If pre loading does for some reason get it into a range where more intrinsic damping occurs, would weighing it up with 10 or 20 kgs and letting it do short oscillations around a large pre load be a better test?

I've realised that I don't have to "guess" that most of the damping in that last test is due to the air. We can get a better idea by observing the amplitude and period of the first few cycles, solve the SHM for the velocity, look up the aerodynamic drag coefficient of a cylinder, and compare the energy lost each cycle with the work we did doing the first deflection.