Ski Stiffness - Hero, Whiteout and #1SC Compared

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Dakine

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I remember reading that Kästle also uses the rubber layer for damping. No one in this thread is talking about Kästle. Any thoughts or comparisons with Stöckli?
My first gen Kästle RX's appeared to have a full rubber layer.
I skied them to death because they were close to a good cheater GS but I could ski them all day.
Smooth they were but they were 3-5 handicap points slower in NASTAR than my orange Völkl Racetiger beasts that worked so well.
 

cantunamunch

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What you seem interested in is how an impact on the underside of the ski, kind of directly under your foot (otherwise it would create oscillations/vibrations in that part of the ski) is transmitted to your foot. That is not a vibration. This happens when the underside of your ski drifts and catch-and-release with the snow. The frequency of that is driven by the weight of your foot/boot/ski, the stiffness of your leg, the mass of your upper body, the edge angle, the snow, etc. I would generally think that the ski construction changes nothing to that frequency ( around 5ish Hz).
You have it the wrong way around.

The term of art for impacts to the underside of the ski, or any vibration that puts energy into the system, is 'forcing vibration'. Let's call the frequency of the forcing vibration the forcing frequency.

There is also something called the natural frequency of the system, i.e. the frequency at which given a single impact, the system would continue to ring.

Here is the thing you need to know: the natural frequency of the system has to be at least three times lower than the vibration frequency in order to not transmit the forcing vibration.

(For the geeks, the forcing frequency has to be higher than the third harmonic of natural).

So a 5Hz forcing frequency needs the ski and skier system to have a natural frequency of 1.6 Hz or lower. So, yes, ski construction has *everything* to do with not transmitting your scenario.

The simplest way to figure out approximate natural frequency is by static deflection. Using a static deflection vs natural frequency graph, we can see that we will probably need a ski that bends at least 5inches under the skier in order to not pass that vibration back. How is that not related to ski construction?


1613584911768.png


Fortunately, most of the harsh objectionable vibrations from snow have forcing frequencies that are a lot higher than 5Hz - or we'd all be skiing noodles.
 

AlexisLD

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Here is the thing you need to know: the natural frequency of the system has to be at least three times lower than the vibration frequency in order to not transmit the forcing vibration.

(For the geeks, the forcing frequency has to be higher than the third harmonic of natural).

So a 5Hz forcing frequency needs the ski and skier system to have a natural frequency of 1.6 Hz or lower. So, yes, ski construction has *everything* to do with not transmitting your scenario.
I am talking about the ski catching-and-releasing with the snow. More than 80% of the edge pressure is directly underfoot. Tip and tail, and the ski's stiffness, have very little to do with this behavior. You would get the same behavior with snowblades.

The 5ish Hz frequency that I am talking about is driven by the mass of the boot/lower leg, the stiffness of the ski and the mass of the upper body. Your rule of thumb applies for the force felt past the spring, i.e., on the upper body mass. I don't think that is what we care about here. There are very little vibration that are transmitted to the upper body:

My guess would be that what you feel when skiing is through your feet. The mass/spring system related to this system would be some combination of the mass of the center section of the ski, the binding and the lower part of your boot. The spring would be the boot liner, binding vertical stiffness and your skin (and in the case of Stöckli's skis the rubber layers in the ski). Then, the next mass would be the lower leg, which would be connected to your leg (a spring), etc. The stiffness of the spring between your boot and the snow would be extremely high, but lower with Stöckli's skis. My guess would be that in both cases, you would feel pretty much everything. I doubt that ski construction can change that.

The simplest way to figure out approximate natural frequency is by static deflection. Using a static deflection vs natural frequency graph, we can see that we will probably need a ski that bends at least 5inches under the skier in order to not pass that vibration back. How is that not related to ski construction?
You are making a number of assumptions with this statement. Natural frequency is determined by mass and spring stiffness. Static deflection is determined by spring stiffness and force, which is not necessarily related to mass. In the case of the 5Hz frequency, the mass/spring system is upside-down, with the important mass at the bottom on the snow. So I don't see how you think about static deflection in that case.

It seems that you are thinking that the ski as a spring that acts to modulate that catch-and-release behavior with the snow. I don't think that is what happens, although I agree that the tip and tails are vibrating and that depends on the mass/stiffness of the ski.

Fortunately, most of the harsh objectionable vibrations from snow have forcing frequencies that are a lot higher than 5Hz - or we'd all be skiing noodles.
This article measure the vibration that are transmitted to the foot:

1613602220949.png


Most of it is at 5Hz, specially if you are carving. If you slide your skis on the snow, you will also excite the tip and tail vibration modes at around 20 Hz. There is not much pass that.

Humans are most sensitive to vibration at around 10 Hz. Exposure limits are not defined above 100 Hz. It is probably not that important. Look at figure 50.1 here: http://www.ilocis.org/documents/chpt50e.htm
 

cantunamunch

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It seems that you are thinking that the ski as a spring that acts to modulate that catch-and-release behavior with the snow. I don't think that is what happens, although I agree that the tip and tails are vibrating and that depends on the mass/stiffness of the ski.
Yes, that is the model I am using, except I am asserting the opposite: most skis are not soft enough to isolate that catch and release behavior with the snow at 5Hz.

I am also saying that a 5Hz forcing frequency will excite vibration and harmonics in the ski above 5Hz - very much including the 10 Hz -20 Hz range your references are most concerned with.
 
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AlexisLD

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Yes, that is the model I am using, except I am asserting the opposite: most skis are not soft enough to isolate that catch and release behavior with the snow at 5Hz.

I am also saying that a 5Hz forcing frequency will excite vibration and harmonics in the ski above 5Hz - very much including the 10 Hz -20 Hz range your references are most concerned with.
It is interesting to think about it this way. Many papers cite the spring stiffness of a skis as around 7000 N/m. You could either assume that a 50 ish kg mass is suspended to that (a little more than half the body mass if you consider the legs as stiff), or maybe just the lower leg and boot (10 ish kg) if you consider that the leg/body will be another spring mass system on top of that. The frequency in both cases would be 1.9 and 4.2 Hz (frequency in Hz = sqrt(k/m)/(2*pi). The second model is maybe more in line with what is measured on the snow. However, the ski is in contact with the snow. It is not free to oscillate. It just deforms the snow and it is not strong enough to push you back up. I doubt it really acts like a spring/mass system... but I could be wrong. Both of these models are also failing to explain why you would measure a 5 Hz resonant frequency while going in straight line (see graph above). The ski is not really flexing when your bases are flat on the snow (or definitely doesn't have enough force to push you back up).

Human leg stiffness is on the order of 70 kN/m for both legs (that is, for a 4Hz hopping motion... about the fastest you can go: https://pubmed.ncbi.nlm.nih.gov/15088239/). If you consider a body mass of 70 ish kg on top of that (and the ski/boot as relatively light compared to that), then you get a frequency of 5 Hz. So this would be the resonant frequency of your legs/body...

I don't think you should think about a "5Hz forcing frequency" anywhere in this system. Your skis are impacting the snow repeatedly, specially when you drift them sideways (it always happens to some extend). Impacts excite all the modes of your system at all frequencies. When you ski, I think you have your legs/body mode at 5 ish Hz and the tip/tail modes at 10-20 ish Hz. The legs/body mode depends on your legs/body. The tip/tail mode depends on the ski construction...
 

cantunamunch

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It is interesting to think about it this way. Many papers cite the spring stiffness of a skis as around 7000 N/m.
Ok, that is about double the stiffness of a beginner/intermediate ski, but let's assume that's correct. I think that's actually closer to expert/race ski flexes.

The ski is not really flexing when your bases are flat on the snow
When the bases are flat on the snow the center is constrained, yes, but are we talking about also carving? Of course the ski flexes in a carve - and the racers on this forum will tell you about "poppy" skis that very definitely return energy from a carve.

Human leg stiffness is on the order of 70 kN/m for both legs (that is, for a 4Hz hopping motion... about the fastest you can go: https://pubmed.ncbi.nlm.nih.gov/15088239/). If you consider a body mass of 70 ish kg on top of that (and the ski/boot as relatively light compared to that), then you get a frequency of 5 Hz. So this would be the resonant frequency of your legs/body...
That's fine, I have no problems with that.


Both of these models are also failing to explain why you would measure a 5 Hz resonant frequency while going in straight line (see graph above).
. Impacts excite all the modes of your system at all frequencies. ..
There is a really easy way to explain 5Hz in a straight line. Using that picture of a ski that is constrained in a center section with the tips relatively free to vibrate, we can ask, how long does it take a flaw in the snow to traverse that section? Let's say boots are between 245 and 355 mm long, let's say the center section of the ski is, therefore, 40 or 50cm. 5Hz is 0.2 seconds. If a skier with a 50cm locked center section sees an incompressible bump in the snow, 0.2 seconds is 6mph.

Neither the mass of the skier nor the size of the incompressible flaw in the snow matters to this calculation - we should start seeing 5Hz vibration at anything over 9km/h aka 6mph. What we're really seeing is traversal of relatively small imperfections - repeated impacts. This is why I say there is, effectively, a 5Hz forcing frequency.

Notice that by the model I presented we should see a shift in peak power density to higher frequencies as skier speed goes over 20mph - at which the tip and tail very much become engaged.
 

AlexisLD

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Ok, that is about double the stiffness of a beginner/intermediate ski, but let's assume that's correct. I think that's actually closer to expert/race ski flexes.
Agreed. I was just trying to help your argument. :)

A lower stiffness would make for lower frequencies, making these models even less likely...

There is a really easy way to explain 5Hz in a straight line. Using that picture of a ski that is constrained in a center section with the tips relatively free to vibrate, we can ask, how long does it take a flaw in the snow to traverse that section? Let's say boots are between 245 and 355 mm long, let's say the center section of the ski is, therefore, 40 or 50cm. 5Hz is 0.2 seconds. If a skier with a 50cm locked center section sees an incompressible bump in the snow, 0.2 seconds is 6mph.

Neither the mass of the skier nor the size of the incompressible flaw in the snow matters to this calculation - we should start seeing 5Hz vibration at anything over 9km/h aka 6mph. What we're really seeing is traversal of relatively small imperfections - repeated impacts. This is why I say there is, effectively, a 5Hz forcing frequency.

Notice that by the model I presented we should see a shift in peak power density to higher frequencies as skier speed goes over 20mph - at which the tip and tail very much become engaged.
If I understand correctly, you are saying that the resonant peaks in the graphs above are a function of speed? And that you would get 5Hz forcing frequency at around 6 mph and 20 Hz at around 20 mph (and anything in between)? I think that you would get the graphs above for any speed. The only thing that would changes with speed in my opinion is that the full curve is shifted up/down.

** The paper actually lists the speed at which these test were performed. It is 31 mph for the carved turn where they only observed 5 Hz. It is around 15 mph for all the other conditions.

Your model also seems to assume that the bumps in the snow are spaced by 50 cm. I agree that 50 cm is a reasonable length for the center ski section, but bumps could come with any spacing between them and in any size.

Again, it all works really well if you assume that the bumps are white noise (i.e., coming in all frequency and size) that excite two systems. One with a resonant frequency of 5 Hz (leg stiffness + body) and another one with a resonant frequency of 10-20 Hz (ski stiffness + ski mass). You can train to get stiffer legs and loose weight (or gain muscle mass) to modify the 5Hz resonant frequency, but only the second system can be modified by ski construction...
 

cantunamunch

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Your model also seems to assume that the bumps in the snow are spaced by 50 cm. I agree that 50 cm is a reasonable length for the center ski section, but bumps could come with any spacing between them and in any size.
The model makes no assumption about the snow - it just notices that spacing the impacts 50cm apart creates the greatest possible disruption per impact. Space them closer and the net energy per impact is a lot smaller because the center sections bridges between them.

I am saying that because we are not seeing the 5Hz drop off with increased skier speed (and because we are using relatively stiff skis which do not have the amount of deflection that would isolate 5Hz at any normal skier mass), it is not reasonable to use the center-section-only model.

You can train to get stiffer legs and loose weight (or gain muscle mass) to modify the 5Hz resonant frequency
Remind me again of why we would even try to change that body resonance point? Changing the frequency of body resonance doesn't seem useful.

Is the goal not to reduce objectionable vibration at the feet?
 

AlexisLD

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I am saying that because we are not seeing the 5Hz drop off with increased skier speed (and because we are using relatively stiff skis which do not have the amount of deflection that would isolate 5Hz at any normal skier mass), it is not reasonable to use the center-section-only model.
You can read this: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.200810713

In this case, for both asphalt and sett, and at different vehicle speed, we can notice the car suspension mode at 10 Hz in the PSD. It is pretty much fixed at 10 Hz regardless of speed or surface. They don't give much detail in this paper about how they performed the measurement, but typically you would measure at each suspension corner of a car, with each corner acting like a single point of contact.

Remind me again of why we would even try to change that body resonance point? Changing the frequency of body resonance doesn't seem useful.
Is the goal not to reduce objectionable vibration at the feet?
I was joking. Yes, the goal is to reduce the vibration of the feet. My argument is that you can't do much in a ski to change the vibration mode at 5 Hz of the ski-human system. I believe that vibration mode is mostly driven by the human leg stiffness and mass...
 

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You can read this: https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.200810713

In this case, for both asphalt and sett, and at different vehicle speed, we can notice the car suspension mode at 10 Hz in the PSD. It is pretty much fixed at 10 Hz regardless of speed or surface. They don't give much detail in this paper about how they performed the measurement, but typically you would measure at each suspension corner of a car, with each corner acting like a single point of contact.



I was joking. Yes, the goal is to reduce the vibration of the feet. My argument is that you can't do much in a ski to change the vibration mode at 5 Hz of the ski-human system. I believe that vibration mode is mostly driven by the human leg stiffness and mass...
Since you mentioned cars again, the characteristic of ski vibration that I've been discussing here is similar to automobile NVH (Noise, Vibration, Harshness). Certainly the car suspension plays into this, but there's a lot more to it. Auto manufacturers use multiple methods and materials to suppress NVH to give a car a "quiet ride". Similarly, there are ski manufacturers who incorporate materials, design, and build methods to suppress NVH in skis. One example is the Stöckli epoxy resins and their process for gluing up a ski that is a trade secret because it results in a more smooth feeling ski on slope.
 

AlexisLD

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Since you mentioned cars again, the characteristic of ski vibration that I've been discussing here is similar to automobile NVH (Noise, Vibration, Harshness). Certainly the car suspension plays into this, but there's a lot more to it. Auto manufacturers use multiple methods and materials to suppress NVH to give a car a "quiet ride". Similarly, there are ski manufacturers who incorporate materials, design, and build methods to suppress NVH in skis. One example is the Stöckli epoxy resins and their process for gluing up a ski that is a trade secret because it results in a more smooth feeling ski on slope.
Read this:
https://en.wikipedia.org/wiki/Noise,_vibration,_and_harshness

NVH is about sound. It makes sense in a car because you want to talk and listen to music. NVH technologies are tuned specifically to reduce sounds (in the kHz range) and they might not work well for other vibrations. NVH technologies purpose is not to reduce what you feel through your hands and butt when you are sitting/driving a car. It is to reduce/absorb sound.

My question is: would you be able to differentiate Stöckli's skis if I ask you to wear earmuffs? If your answer is yes, then it is about something that you feel through your feet. It is about vibrations and not sound. It is highly unlikely that you can feel something with your feet above 50-100 Hz. It is highly unlikely that NVH as applied to car will be effective to improve a ski...

If your answer is no, then it means that you care about the sound of a ski that you ear through your ears. How does a kHz vibration of the ski can affects its performance? Can the snow feel the minuscules vibrations at these kHz frequencies? Does it change how the ski interact with the snow? I believe that the effect is more likely that it effect how you ski through psychoacoustic, but it doesn't have too. If you don't care about the sound or don't notice it, it is unlikely to have an effect. But I don't doubt it can have an effect. Many other things affect my skiing, and it is not always about the ski.

Did you ever heard about the stories of car designers spending endless amount of time tuning the sound of a door closing? Or the stiffness of a seat cushion? It doesn't make for a better performing car, but one of the thing that you do at the dealer is to close the door and push on the gas to accelerate during the drive test. If the sound of the door closing is nice then it leaves you a nice impression. If the seat is stiff, you will feel the acceleration more. None of that is about making a better car. It is about making you feel good about a car and closing a sale.

We can talk about it endlessly, but I think we need to blind test skis with earmuffs to be sure! :)

** There is another thread on this forum detailing Stöckli resin trade secret (https://www.SkiTalk.com/threads/the-never-ending-stöckli-discussion.8747/page-17)... their resin has been used to make skis (and other things) since 1940...
 

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Read this:
https://en.wikipedia.org/wiki/Noise,_vibration,_and_harshness

NVH is about sound. It makes sense in a car because you want to talk and listen to music. NVH technologies are tuned specifically to reduce sounds (in the kHz range) and they might not work well for other vibrations. NVH technologies purpose is not to reduce what you feel through your hands and butt when you are sitting/driving a car. It is to reduce/absorb sound.

My question is: would you be able to differentiate Stöckli's skis if I ask you to wear earmuffs? If your answer is yes, then it is about something that you feel through your feet. It is about vibrations and not sound. It is highly unlikely that you can feel something with your feet above 50-100 Hz. It is highly unlikely that NVH as applied to car will be effective to improve a ski...

If your answer is no, then it means that you care about the sound of a ski that you ear through your ears. How does a kHz vibration of the ski can affects its performance? Can the snow feel the minuscules vibrations at these kHz frequencies? Does it change how the ski interact with the snow? I believe that the effect is more likely that it effect how you ski through psychoacoustic, but it doesn't have too. If you don't care about the sound or don't notice it, it is unlikely to have an effect. But I don't doubt it can have an effect. Many other things affect my skiing, and it is not always about the ski.

Did you ever heard about the stories of car designers spending endless amount of time tuning the sound of a door closing? Or the stiffness of a seat cushion? It doesn't make for a better performing car, but one of the thing that you do at the dealer is to close the door and push on the gas to accelerate during the drive test. If the sound of the door closing is nice then it leaves you a nice impression. If the seat is stiff, you will feel the acceleration more. None of that is about making a better car. It is about making you feel good about a car and closing a sale.

We can talk about it endlessly, but I think we need to blind test skis with earmuffs to be sure! :)

** There is another thread on this forum detailing Stöckli resin trade secret (https://www.SkiTalk.com/threads/the-never-ending-stöckli-discussion.8747/page-17)... their resin has been used to make skis (and other things) since 1940...
Your own link you posted states that NVH is about sounds and VIBRATION. Why won't you just accept that this is about vibration that is felt through the feet of the skier. Honestly, I'm done going in circles on this. Sometimes I wonder if you've ever actually skied. I'm out on this thread...
 

AlexisLD

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Your own link you posted states that NVH is about sounds and VIBRATION. Why won't you just accept that this is about vibration that is felt through the feet of the skier. Honestly, I'm done going in circles on this. Sometimes I wonder if you've ever actually skied. I'm out on this thread...
I am a little confused because you were the one talking about quiet/loud. I do believe that vibrations are felt through the feet. I am not debating that. I am interested in understanding, measuring and improving ski's behaviour. To that end, I tend to break it down in three parts according to the vibration frequencies and how I think they are generated. I could be wrong and I am happy to change my thinking, but I have measured the on-snow vibrations of dozen of skis and devices over the last two years... I am not debating your feelings, just how they are generated and how it can (or can't with standard construction) be improved. Here is how I break it down:
--> 5-10 Hz : This is what some people call chattering. You can clearly feel that. I think it is related to the catch and release behaviour of the edge and that it is driven mostly by your technique and leg stiffness. I think it has little to do with ski construction but I could see Renoun's construction being useful here (but maybe not).
--> 20-30 Hz : This is the tip/tail main vibration mode. Ski construction strongly affects that. I think you can feel it, but it is subtle.
--> above 100 Hz : I doubt you can feel anything through your feet above these frequencies. At 300-400 Hz, it starts being sound. You can hear something when you tap/bang the ski, but I can't think of a good reason it would affect lower frequencies behaviours. There could be a correlation between sound and low frequency behaviours in many skis, but that doesn't mean it is the cause of what you feel. We see strong correlation between bending and torsional stiffness all the time because many in the industry use the same triaxial fiberglass fabric, but it doesn't mean that torsional stiffness is related to bending stiffness. Same can happen with sound and low frequency behaviours that both depends on mass, stiffness, etc.

If anyone has a deals on Stöckli, Renoun or any other skis of that kind, or would like to donate them for ski science, please let me know. I will measure the shit out of them and share the results.
 
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Dakine

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--> above 100 Hz : I doubt you can feel anything through your feet above these frequencies. At 300-400 Hz, it starts being sound.

Sound is not defined by a frequency range, it is pressure waves transmitted through a medium as sensed by a being.
Generally humans can hear from 50-20,000 Hz if they are young but bats can hear well into the ultrasonic (>20kHz) and dolphins can hear way down low.
It is being sensed by an organism that makes it sound otherwise it is vibration.
Virtually everybody can hear 60 Hz hum.

A ski scraping across a surface makes a very broad spectrum "white" noise.
The ski may vibrate at numerous resonances to amplify some frequencies.
If these resonant vibrations are transmitted through the ski, the binding system and boot to the body they can cause fatigue quite quickly.
As a Geezer (and proud of it) I get fatigued quickly by high frequency vibration that is most intense with flat mounted bindings.
That's why I'm such a fan of the marker Piston Plate system which I believe (no data) does the best job of damping high frequency vibration of any binding system.

Snowboards on hard surfaces become a huge "sounding board" which is one more reason they suck except in deep snow.
 

James

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Snowboards on hard surfaces become a huge "sounding board" which is one more reason they suck except in deep snow.
The damping occurs in the soft boots?
Anyone ever ski on the Rossi Softboot? It only lasted like a tear or two.
 

AlexisLD

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@Dakine I agree with your definition of sound. I guess what I meant is I doubt you can feel anything pass 300Hz and the only thing you can "feel" is the sound. I also doubt that the 1-100 Hz noise generated by a ski will be very loud when compared to the higher frequency noises (and other noise around).

I also agree that a ski scraping across a surface makes a very broad spectrum "white" noise and that the ski will amplify some frequency.

Do you know which frequencies you care about? Which part of your body gets fatigued?

I find this article interesting:
https://www.frontiersin.org/articles/10.3389/fphys.2017.00522/full
1614947383858.png

Figure 3. Group average power spectral density (PSD) curves of all segments in GS skiing visualized as the area of uncertainty around the estimate of the mean (±SE). Red, right shank sensor; blue, right thigh sensor; gray, sacrum sensor; green, sternum sensor.

It seems to suggest that not much above 30 Hz get transmitted to your upper body. I am trying to understand which frequency is coming from what component, so that we can try to minimize that at the source. I doubt that the 5Hz peak can be modify much by ski design (stiffnesses, damping and laminate... but geometry will have an impact). I am however confident it could be modified by binding, boot, technique, snow type, etc. I can be wrong though...
 
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