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  1. brokenball is offline
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    #1

    Do you really want to learn something?

    I have simulations of TT ball trajectories. I started the simulation over 10 years ago. I haven't done much with they lately but since I am now retired, I have more time to do simulations. Years ago, I showed a simulation of a TT ball being hit from about net height or a little lower at about 40m/s and at a upwards angle of 10 degrees so the ball would go over the net and drop. I just plotted the path of the ball. It was interesting. I could change the speed, spins and angles to see the resulting trajectory. After doing this I found it amazing we are able to train our NN ( neural nets and muscles ) to do this at all. What I didn't do it plot the downwards force due to gravity which is constant, the downwards force due to the Magnus effect, the rotational kinetic energy and the translational kinetic energy. I think that might be interesting. OK, I am a nerd but if you never ask the question, you never will get the answer.

    What would be even more interesting is the right ratio of spin to speed you should have on the ball to land on the table from a given set of conditions.

    TT players have two "friends". One is gravity. This makes the ball drop on to the table instead of floating off the end. The other is the Magnus effect the is the result of putting spin on the ball. Top spin adds an additional downwards force to the ball that allows one to hit the ball faster and still land the ball on the table. The Magnus effect is the cross product of the spin and speed. To make this simple, assume the axis of rotation is perpendicular to the direction of travel so the Magnus force is simply proportional to the spin x speed. Increasing spin always helps increase the Magnus effect. So does increasing speed but if the speed is too great then the ball will not have enough time to accelerate downwards before going of the end of the table. There is an optimal spin to speed ratio. The reason why I ask this question is that too many of my loops have plenty of spin but it seems that the don't drop fast enough to land on the table.

    Slow spinny loops that are cause by brushing will have a lower speed and therefore a lower downwards force due to the Magnus effect. This is not a disaster because the lower speed gives gravity more time to accelerate the ball downwards. The problem is that the speed of the ball is low. However, the high spin will give lower skilled opponent troubles returning the ball even if they get to it and are able to hit the ball.

    I think I will do a few simulations to find the answers. I wonder if anyone cares. It is the forces, actually, impulses we apply to the ball that make it go. All this crap about this rubber or that rubber or boosting is secondary if you don't know what you are really trying to achieve.

    Ok, here is a question for you all. What do think think the engineers the program the Omron robot are thinking about?


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    #2
    Exactly the same things you are!! The Math and how to incorporate this into the robots programming.
    It will be figures and stats gathered by the sensors & camera’s etc that then help the robot to learn and adjust and to actually hit the ball back.

    A couple of questions
    1) the paddle / rubbers used by the robot, would these be scientifically tested to establish the paddles characteristics?
    2) the opponent and their paddle, does this really matter?
    Because perhaps the robot will be measuring the incoming balls stats, rather than how the opponent and equipment achieved those stats?

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    #3
    Looking at golf and the simulators used by coaches, the equipment measures what the player does, swing speed, attack angle etc etc and then projects the outcome, how high, how far, spin on the ball, distance hit, how far left or right of the target line etc etc

    This comes back to my 2nd question. Are the Omron engineers interested in how the opponent hits the ball? Or just the result of the stroke?
    Would this be a ‘higher function’? ‘Reading the game’ allowing anticipation to prepare rather than reaction after the ball has been struck?

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    #4
    Quote Originally Posted by IB66
    Looking at golf and the simulators used by coaches, the equipment measures what the player does, swing speed, attack angle etc etc and then projects the outcome, how high, how far, spin on the ball, distance hit, how far left or right of the target line etc etc

    This comes back to my 2nd question. Are the Omron engineers interested in how the opponent hits the ball? Or just the result of the stroke?
    Would this be a ‘higher function’? ‘Reading the game’ allowing anticipation to prepare rather than reaction after the ball has been struck?

    Actually, there are different types of golf simulators. I forgot the name but the top end one uses radar and multiple cameras to calculate the ball flight. Basically the cameras will be looking at the strike zone, which will be able to determine the speed and the angle in all directions of the club head, the ball hit position on the club head, the speed, direction and the spin of the ball. The radar will be used to track the ball flight trajectory, speed and spin for the first few feet, combined with the data gathered from the camera to calculate the final ball flight trajectory and display that on the screen. So ideally you can incorporate a lot more than just what the play does into the simulation, because we all know that no matter how good a stroke is, you gotta hit the ball first.


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    #5
    Quote Originally Posted by brokenball
    I have simulations of TT ball trajectories. I started the simulation over 10 years ago. I haven't done much with they lately but since I am now retired, I have more time to do simulations. Years ago, I showed a simulation of a TT ball being hit from about net height or a little lower at about 40m/s and at a upwards angle of 10 degrees so the ball would go over the net and drop. I just plotted the path of the ball. It was interesting. I could change the speed, spins and angles to see the resulting trajectory. After doing this I found it amazing we are able to train our NN ( neural nets and muscles ) to do this at all. What I didn't do it plot the downwards force due to gravity which is constant, the downwards force due to the Magnus effect, the rotational kinetic energy and the translational kinetic energy. I think that might be interesting. OK, I am a nerd but if you never ask the question, you never will get the answer.

    What would be even more interesting is the right ratio of spin to speed you should have on the ball to land on the table from a given set of conditions.

    TT players have two "friends". One is gravity. This makes the ball drop on to the table instead of floating off the end. The other is the Magnus effect the is the result of putting spin on the ball. Top spin adds an additional downwards force to the ball that allows one to hit the ball faster and still land the ball on the table. The Magnus effect is the cross product of the spin and speed. To make this simple, assume the axis of rotation is perpendicular to the direction of travel so the Magnus force is simply proportional to the spin x speed. Increasing spin always helps increase the Magnus effect. So does increasing speed but if the speed is too great then the ball will not have enough time to accelerate downwards before going of the end of the table. There is an optimal spin to speed ratio. The reason why I ask this question is that too many of my loops have plenty of spin but it seems that the don't drop fast enough to land on the table.

    Slow spinny loops that are cause by brushing will have a lower speed and therefore a lower downwards force due to the Magnus effect. This is not a disaster because the lower speed gives gravity more time to accelerate the ball downwards. The problem is that the speed of the ball is low. However, the high spin will give lower skilled opponent troubles returning the ball even if they get to it and are able to hit the ball.

    I think I will do a few simulations to find the answers. I wonder if anyone cares. It is the forces, actually, impulses we apply to the ball that make it go. All this crap about this rubber or that rubber or boosting is secondary if you don't know what you are really trying to achieve.

    Ok, here is a question for you all. What do think think the engineers the program the Omron robot are thinking about?

    Do you have any useful findings you can report?


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    #6
    I think it's a very interesting topic - certainly I have been given cause to consider it recently. By way of example I had been struggling with using my BH stroke to overcome backspin and turn it into a topspin opener - I also looked my FH stroke when I do this and noted two things 1) I have a tendency to use a long stroke from low down and really let the ball fall before brushing it 2) The resulting shot trajectory is usually much higher over the net than I would consider optimum

    I then watched my coach play some competitive matches (he is an ex Polish National player of a very high standard) and I noted he achieves an opening shot using a fairly compact stroke and sometimes over the table, even against heavy backspin. He does this seemingly by varying where on the ball he strikes (lower than me) and bat angle (more open) and then by using his wrist, he plays what looks like an easy BH stroke - an example at around 1:27 in the video (not heavy backspin but serve and third ball are backspin and both returned without resorting to a push)

    https://youtu.be/iF6R3ZHBVng

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    #7
    Quote Originally Posted by Wrighty67
    I think it's a very interesting topic - certainly I have been given cause to consider it recently. By way of example I had been struggling with using my BH stroke to overcome backspin and turn it into a topspin opener - I also looked my FH stroke when I do this and noted two things 1) I have a tendency to use a long stroke from low down and really let the ball fall before brushing it 2) The resulting shot trajectory is usually much higher over the net than I would consider optimum

    I then watched my coach play some competitive matches (he is an ex Polish National player of a very high standard) and I noted he achieves an opening shot using a fairly compact stroke and sometimes over the table, even against heavy backspin. He does this seemingly by varying where on the ball he strikes (lower than me) and bat angle (more open) and then by using his wrist, he plays what looks like an easy BH stroke - an example at around 1:27 in the video (not heavy backspin but serve and third ball are backspin and both returned without resorting to a push)

    https://youtu.be/iF6R3ZHBVng

    I'm sure your coach will say the same thing here (and I don't want to be "one of those guys on the internet spouting random advice"), but I would 100% avoid that sort of shot if you are looking to play attacking table tennis.

    He can do it because he has a very slow backhand rubber that isn't sensitive to spin at all.

    If he tried a similar shot with your typical European ESN rubber, that ball is hitting the net 100 times out of 100.

    A better technique for you to look at would be his opponent at the 30 second mark.

    Backspin serve, push return (that isn't too loaded) and a nice spinny backhand loop to force the opponent back.

    From there, he's completely in control and can play safe, high loops all day long.

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    #8

    Thanks - that makes sense as he plays with pips on backhand and so this shot comes into play. I have watched the 30s shot and can see what he achieves with. it - I guess my point remains though that it is short and compact and overcomes the backspin (not too heavy) without being long and slow, and it is this that interests me here - how to overcome backspin (light or heavy) by altering point and angle of attack?


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    #9
    Quote Originally Posted by Wrighty67

    Thanks - that makes sense as he plays with pips on backhand and so this shot comes into play. I have watched the 30s shot and can see what he achieves with. it - I guess my point remains though that it is short and compact and overcomes the backspin (not too heavy) without being long and slow, and it is this that interests me here - how to overcome backspin (light or heavy) by altering point and angle of attack?

    There are certainly levels to this, and as I'm not your coach, I would be hesitant to advise one way or the other.

    Personally, I think you need to be playing a shot with fast bat speed (whether it's compact or not).

    You can change the angle of the bat to compensate for the various incoming spins, but if you are playing a fast shot, you'll never have an open blade like that.

    It will be a mix between a pretty closed blade (if the incoming spin is side/top) and a slightly more open blade if the incoming spin is backspin.

    You then need to adjust the angle you hit through the ball - For top/side, you'll want to go through it more, and for backspin, you'll want to go slightly more up.

    Once you nail your backhand attack (especially in UK Local League), it's an absolute game changer!

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  10. WingTT is offline
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    #10
    I'm assuming as an offensive player, we are trying to place the ball on the table somewhere with as much speed and spin (quality) as possible (or as little as possible depending on tactical situation) to increase the chances of the ball not coming back. All the crap about rubber and boosting is to make the transfer of power into speed and spin as efficient as possible. If the ball is above the net, smacking it at a 45 degree loop is a general good baseline for me.

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    #11

    Makes sense - thanks.

    I have definitely seen the scope for winning that a decent confident BH attack gives you - hence my focus on how to get to it as soon as possible!


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    #12
    Quote Originally Posted by TaiHaoPingPong

    Do you have any useful findings you can report?

    Yes! Engineers/physicist can't agree on the correct formula for the Magnus effect. I have found two sources that are almost the same except for a constant that is just a little different. Both formulas have the correct units. Testing for the correct units is the first step in testing whether the formula is correct. The formula for the Magnus effect should have units of force. Some of the formulas I have seen don't. In my simulation, the Magnus force is divided by the mass to get an acceleration and the sum of the two accelerations are then integrated to yield a vertical velocity and the vertical velocity is integrated to get the vertical position. This is necessary to see of the ball clears the net and lands on the table. I must do something similar with the horizontal acceleration but there is no gravity term for that. The big thing is that the units must be consistent. In my simulation they are. The trajectory of the ball looks reasonable. Where I have problems with my simulation is that the Magnus force seems to be way too high. It shouldn't be many times the force due to gravity.

    Golf is mentioned above, and it provides a reality check. If you have ever watched a good player drive a ball, you know it has back spin on it. It almost seems like the ball will accelerate upwards. This happens due to the Magnus effect. The fact that the ball seems to increase the rate at which it is rising shows that the Magnus effect can offset or be greater than the gravitational pull, but not MUCH greater. The same can be seen in TT where a chopped ball seems to float across the table due to its back spin. So basically, the Magnus force is roughly equal to the force due to gravity.

    The reason I have been quiet the last few days is that my simulation shows the Magnus force being over 10 times greater than the force due to gravity. This bothers me. I have a video of a young Japanese player named Sakai who makes the fastest server ever. From that video I deduced that the Magnus effect is about 2 times that of gravity and Sakai is putting a lot of spin on the ball. This is not close to the over 10 times I am seeing in my simulation. However, the trajectories look realistic. I am just having a hard time believing the Magnus effect can be that strong.
    I am using params such as
    The ball is hit 1.5 m from the net and 50 mm above the table. This means the ball must be hit up at about 10 or 11 degrees to get the ball to go over the net.
    The ball is hit at about 40 to 50 m/s with a spin of about 75 rev/sec. The resulting trajectory results in the ball landing on the other side of the table in between 0.06 and 0.07 seconds. This is basically a loop kill type of shot. The fastest spins are in the area of 150 rev/sec. I have a Butterfly video where the chopper returns the ball at 137 rev/sec so my 75 rev/sec isn't unreasonable. Everything looks reasonable except for the strength of the Magnus effect bothers me. I do not see TT balls accelerate upwards a great speed like would happen if the Magnus effect is as strong as I calculate. I just don't understand where the problem could be because the units are right. This means a constant is very wrong.
    I will post pdf shortly.

    This is the first step. What I plan to do next optimize the trajectory by minimizing the flight time of the ball and the height of the ball over the net.
    I have documents for simulating the bounce too.











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    #13

    > I just don't understand where the problem could be because the units are right.
    2π here or there?


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    #14
    This is interesting, I don't know much about this but I have built a Table tennis robot and I have built a deep learning model to detect a table tennis ball . From my perscpective apart from the trajectory, from a robot end I would be looking at

    - Figuring out the spin generated on the ball (right now we can only use the print on the ball to calculate the rotations)
    - another factor is that depending on the spin on the ball, it either bounces off or skids off the table, this has to be considered to figure out how to hit the ball, this condition amplifies as the rotations get higher


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    #15
    Does the ball also start to lose spin as it goes along it's trajectory due to this Magnus force somehow?

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    #16
    You guys should know by now I am a geek, nerd and skeptic. Just because I post this doesn't mean it is right. Math looks right but it doesn't seem right to me.
    It is 8 pages long so a I posted a link to my website.
    Mathcad - TT Trajectory 10 deg.xmcdz (deltamotion.com)
    I am using CAS (computer algebra system) called Mathcad. Mathcad is very good at converting and checking units.
    Page 1 is just assigning values to variables. What I question is that I have two equations for the variable M. Two sources have slightly different versions. However, this difference is slight compared to the BIG differences I get in the acceleration due to gravity.
    Page 2 is solving 3 linear and 2 non-linear differential equations simulataneously. I cam calculating the accelerations in the X ( horizontal ) and Y ( vertical ) directions. The accelerations get integrated into velocities and the velocities get integrated into positions as a function of time. I also calculate changes in spin.
    Does the ball also start to lose spin as it goes along it's trajectory due to this Magnus force somehow?
    Yes, my simulation slows down the spin by 3% a second. I would think it would slow down faster. I know balls can seem to spin for a long time. I copied that -3% value from another document.
    Page 3 shows the results. My update period is 250 microseconds and the simulation lasts 2 seconds which is long enough for the ball to go over the table and then some.
    x is the horizontal position from the net. x` is the horizontal velocity, y is the vertical position above the table. y1 is the vertical velocity. ω is the spin in radians per second. There are two PI radians per revolution. This may be where there is a problem. Engineers assume ω has units of radians/second. However, if the people that wrote these formulas uses revolution/seconds, the magnitude of the Magnus effect will be 2*PI less which make it seem reasonable. The problem is that NO ONE documents or shows their calculations like I have done here.
    Page 4 shows the trajectory of the ball. I can change the initial angle, velocity, spin, distance from the net and elevation relative to the table where the ball is hit. 5 things. I can see the results in a second. The green line is the net. The red line is the trajectory of the center of the ball. It must clear the net by radius of the ball or the ball will hit the net. The horizontal blue line is the table top. Notice it only extends +/- 1.37 meters from the net because that is how long the table is. I haven't bothered with hitting at an angle yet. That would make the table seem to be a little longer. You can see the ball lands on the table. I can change the angle just a degree or the initial velocity and see if the ball still lands on the table. I was trying to simulate a loop kill.
    Page 5 shows the kinetic energy. Most of the kinetic energy is due to speed, not rotation. If I increase the speed just a little bit, the ball will go off the end of the table. If I reduce the spin just a little bit, the ball will go off the end of the table. If I increase the angle by a degree, the ball will go off the end of the table. When hitting the ball that are below the net, speed isn't your friend, spin is. This is what I am really interested in.
    Page 6 shows the accelerations due to gravity, and the Magnus effect. Notice that there is a horizontal acceleration due to the Magnus effect when the ball is traveling at an angle up or down relative to the table. The Magnus effect is perpendicular to the direction of travel. Notice how big the number are. This is what I can't believe.
    Page 7 is where I assign units to the variables. The routine that integrates the non-linear differential equations doesn't like to deal with units so I couldn't assign units in page one.
    Page 8 is where I make sure that all the terms end up being acceleration units in meter/secound^2. Notice that the acceleration due to drag is also quite high and at a similar size as the acceleration due to the Magnus effect so maybe everything is good. The trajectories look right. Maybe I am to skeptical.

    When I verify this is right, I can find the optimal trajectory by varying the initial angle, speed and spin.
    I started this simulation years ago before I learned how to program in python. When I get really serious I will use python.









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    #17
    Quote Originally Posted by longrange

    > I just don't understand where the problem could be because the units are right.
    2π here or there?

    You better not be right! However, I don't have a better explanation for now.
    Physics documentation uses ω as the symbol for rotation in radians per second.
    A thousand curses on any nit wit that uses ω for revolutions per second.
    So if I use a reasonable topspin of 75 Hz, I must multiply the Hz*2π to get ω (radians per second)
    However, if the nit wits that wrote the equation really meant revolutions per second instead of radians per second then my simulations have a reasonable Magnus force. Revolutions per second is 2π less than radians per second and that is a big difference when it comes to the Magnus force.
    Wikipedia list the Magnus force as
    Fm=(4/3)*π*ρ*(r^3)*(v*ω)
    ρ is the density of air 1.225 kg/m^3
    r is the radius of a TT ball. 0.020 m
    v is the velocity of the ball. 40 m/s
    ω is the angular velocity of the ball . 75 rev/sec*2π=471.239 rad/sec.
    Wikipedia has little tick marks over the v X ω showing they are vector quantities and the result is a cross product of the two vectors. However, if the axis is spin is perpendicular to the trajectory of the ball, the result is simply v*ω
    The mass of the TT ball is 0.0027 kg
    A reasonable top spin is 75Hz or 471.239 radians per second and that is multiplied by a reasonable ball speed of 40m/s the result is still too high.
    From Wikipedia, the acceleration due tot the Magnus effect is (4/3)*π*ρ*(r^3)*(v*ω)/mass=286.584 m/s^2 which is 28 times gravity which is way too high.
    Other variations of the same formula also yield Magnus forces that are way too high.
    Notice that Wikipedia doesn't document what the symbols mean.
    It seems that NO ONE DOES and that is why the topic of Magnus effect is so backwards.
    I am bitter/pissed. The nit wits are wasting our time.
    Still working on it






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    #18
    When I was a student, I really liked mathematics. Now I regret that I did not connect my life with this science.

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    #19
    I found a problem. I have an initial ball speed of 40m/s which is too high. The higher ball speeds are about 30m/s.
    I posted this problem on
    https://www.physicsforums.com/thread...avity.1015219/
    One person has responded. He too calculate the Magnus force to be about 1N. We agreed within tolerances.. However, 1N can accelerate a 2.7 gm TT ball way to fast. Even if I reduce the initial speed to 20m/s the acceleration due to the Magnus effect is still too high.
    The other person posted a video to a YouTube video. It is bogus. The units are not correct and there is no calculation done.
    Basically everyone is clueless and don't really know anything except the units are right but the magnitude is wrong.

    I updated my original simulation to use a more realistic ball speed of 15 m/s which is about half the maximum.
    I added a chopped ball version.
    https://deltamotion.com/peter/TableT...ped%20ball.pdf
    I am trying to simulate this Butterfly video where the chopped ball has back spin of 137 rev/sec.
    https://deltamotion.com/peter/TableT...is%20Video.flv
    I was using this
    https://deltamotion.com/peter/TableT...s%20Effect.PDF
    Document for the formula for calculating the Magnus effect. Notice that the document say the Magnus coefficient, Cm, is 0.25. That value doesn't work. It is too big and makes the Magnus effect too big. If I reduce Cm to 0.05 then I get reasonable results. What is interesting is that 0.05 is about 2PI less than 0.29.

    Basically everyone is clueless. I just know that if I make Cm 0.05, the simulated chopped ball rises a little bit like a golf ball does when it is driven but it doesn't rise much.

    Last edited by brokenball; 5 Days Ago at 06:51 AM.

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    #20
    I haven't resolved the problem with the simulations yet but it is clear to me the problem is with the coefficient of drag, Cd, and the Magnus coefficient, Cm. These are unitless numbers and are used to scale the results. It is clear to me the Magnus coefficient of 0.29 is way to big for a TT ball.

    TT knowledge or science is relatively backwards relative to other sport. So I chose to simulate a pro golfer driving a ball. This simulation looks good using the "standard" values of the coefficient of drag and the Magnus coefficient. I went to golf websites. A pro golfer can hit the ball at 180 mph with a back spin of 3000 rpm at an optimal angle of 15 degrees. The result of the simulation is
    https://deltamotion.com/peter/Mathca...Trajectory.pdf
    I am pretty sure the formulas I am using for calculating the acceleration of the TT ball or the golf ball are correct. The problem is that the coefficient of the Magnus effect for the TT ball and the golf ball seem to be much different. The flight of the golf ball looks good.
    So my question is what is the real Magnus effect coefficient.

    Also, I have learned that I need to calculate Reynold's numbers. The coefficient of drag changes depending on the Reynold's number. For a sphere the coefficient of drag is about 0.5 for must Reynold number but NOT ALL. The coefficient of drag increases A LOT at slower speed which explains why slow ball just seem to drop.

    I can't find any data about how the Magnus coefficient changes as a function of the Reynold's number.

    So why am I doing this. Obviously I have run into some road blocks because the "science" behind the trajectory of TT balls is not that well known.
    I was trying to show that usually the maximum spin( about 150 rev/sec ) and maximum speed ( about 30 m/sec) is not required most of the time.
    The optimal trajectories can be achieved with mediocre spins and speeds. The problem is that deviatiing from the optimimum spins and speeds will result in a loss of point. It is amazing that people do as well as they do.






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