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.
Good morning, Ian,
Trolling? but for what it's worth……
In my windsurfing career, I've moved my masts from fibreglass to aluminium, to carbon. There was a significant improvement in “feel” after each move.
When changing from aluminium to carbon (caused by the allie mast breaking, same day, same sail, same conditions), the “feel” was incredible and I was so impressed, I immediately (same day) changed to carbon masts (proof of the old saying that once you've had black, you'll never go back).
Have to disagree that the surface finish is a contributor to the improvement, because, until recently, all my carbon masts have been smooth finish and the improvement was apparent.
Your essay uses the expressions “from memory” and “probably weighs” and "weighs about"….this is unscientific and not in line with your calculations, hence your calculations are suspect. Garbage in, garbage out.
A pox on your calculations anyway ….... in well-powered conditions, on the same day, using the same sail, rig and sail on a C30 then rig and sail on a C100. That's the proof.
Hope this helps.
"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.
Good work! This got me thinking. I'm a fan of light masts (and being tight with money) so it didn't feel right.
Method?
Is it possible to measure the oscillation frequency?
High speed go pro setting and setting it bouncing.
60fps should be fast enough to capture 2.6 cycles per second.
The calculations look sound (physics degree but a long time ago) but if you can measure the frequency directly then it would be more precise.
This method wouldn't allow for the mass of the sail which effectively acts as a leveller for any differences in mast mass.
Action of centre of mass in the oscillator?
I'm not sure about where the mast centre of mass sits either. If the centre of mass is lower then the spring constant would be higher (I think) and therefore the cycle time would be faster.
Do 100% carbon masts have a lower centre of mass? No masts are really 100% so is there more difference in the top section (less load) than the bottom section.... this would lower the centre of mass, increase the spring constant and then explain the response difference.
All of this is independent of swing weight anyway, which affects how a mast feels in transitions.
ps it's not windy in Victoria either - in case you hadn't guessed.
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.
A big thanks to Ian for providing credible evidence of what I 'knew' all along.
'Reflex Response' was a marketing term invented by Fiberspar. Just plain bull**** marketing spin. [}:)] OK, there may be a small difference but it is insignificant in the way the spinners describe it.
The much better 'feel' of a carbon mast is, mostly, directly related to its lower swing weight.
But I believe there is another factor. This is evident when you switch a SDM mast out for an RDM mast of the same Carbon content. Suddenly the sail/mast combo feels more 'springy'. The static shape can be very similar but under load it is different.
This seems, from my experiments, to be because the mast deflects differently under load. The MCS tests the same with 30KG, but put 40 KG on it and the RDM keeps deflecting more. From my extensive historical experience with first 3.5 to 4kg Fiberglass masts, then aluminium masts and finally various types of Carbon masts, I recon the very real difference in 'feel' between the alloy masts and the Carbon masts Windman experienced was all to do with the difference in dynamic deflection stiffness and weight, and almost nothing to do with some bull**** 'Reflex Response'. [}:)]
Fireproof suit on!
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.
Know nothing about this reflex response but i tried a mega light mast,around 1.4 to 1.5kg in my KA race 7.1m.
Made up from the top half of a 100% Tushingham 430cm and the bottom half of a 100% Arrows 490cm.
The sail still felt a million times heavier than my 6.3m with a 80 percent carbon 430cm.
The 'heavy' feel of race sails 7m plus, however light or responsive the components will still be there.
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.
Completely agree with mathew. A composite mast may not be best described by Hooke's law / spring constant.
Since this may be difficult to model or film accurately, perhaps an option would be to attach a lightweight 3-axis logging accelerometer to the mast tip, collect lots of data, and analyze for different type masts used in comparable conditions.
Glass laminates are good for damping. Carbon laminates have a lot less damping.
A 30% carbon mast will feel relatively heavy and dull on the water because the damping component resists rapid changes in deflection. ie it pulls more on your arms before the mast is bent to twist/depower the sail in a gust, thus feeling heavy.
It will also feel sluggish and soft/underpowered because it takes a while for it to spring back into shape.
100% masts are faster on a race course because they respond faster, so we can track changes in apparent wind much faster and so achieve more optimal power coupling.
I've done the quick experiment. Didn't take long. I firmly clamped a NP 30% 400 by the bottom 1 metre to a solid back veranda. I deflected the tip down 300mm and counted the number of oscillations before the amplitude had damped down to the dimension of my big toe. For the 400 30% it was 30 oscillations for the 95% ck95 460 it was 33 oscillations. Not an exact measure, but both bare masts are very much underdamped. It would be interesting to perform the experiment in a vacuum. And maybe with an even firmer mounting. But compared to the mounting on a boom and in a mast sleeve any damping due to the mounting is insignificant. I'll put up some photos, that might take longer than doing the experiment.
Preliminary findings: Any intrinsic damping or differences in the damping within either mast is insignificant and not apparent to the naked eye.
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.
Have to agree the 100% masts are and do feel lighter or is it my wallet that's lighter? such a simple sport can be made so complicated
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.
Ian, your going to great lengths to justify buying a lower carbon mast..
We definitely need some wind, I' d be happy with a bamboo pole as long as I could get out for a sail! When I'm not working that is!