October 4, 2003
updated October 18, 2003
Calculator links modified March 25, 2004
Conclusion modified June 06, 2004
This last weekend a short little notice was posted on the International News section of the tabletennis.about.com forums. Apparently a New Zealander, Lark Brandt, won the inaugural "Worlds Fastest Smash Competition" with a smash of 112.5 kilometers per hour (69.9 MPH). A fair bit of discussion ensued and many people were surprised that the table tennis ball was travelling at a relatively slow pace compared to other sports.
So I did a bit of research and discovered that there was very little information about table tennis ball speed available on the internet. And the few claims that I could find gave very little information about how the claimed numbers were determined. So I decided to do a little bit of research on my own and that is what this article is about. Hopefully it will serve as a starting point so that we can eventually get more detailed and accurate information.
There are many ways to measure the speed of a table tennis ball. Each seems to have its shortcomings. The smash competition used a radar gun. But a radar gun raises two questions. At what point in the flight was the ball speed measured and are you sure you measured the ball and not the paddle? I don't have a radar gun, so I don't know how those issues are resolved or if they are resolved (though I assume that they are).
|On 10/16/03 I received the following from Peter Hau about the methods used in the smash competition: "They used a radar gun that measured both the average and peak speeds in the measurement (I think it's in the measurement area, not time, but I'm not sure. The radar was on continuously anyways). If the average and peak speeds were the same, it was considered to be taken off the bat rather than the ball."|
I used three different methods to measure average and near instantaneous ball speeds. This was all done with pre-existing data in the form of photographs and video clips. I did not set up any specific trials. The three methods I employed are:
1) Given a known camera shutter speed, estimate the distance that a ball travels over that duration by measuring the length of the blur and calculate the average speed from that information.
2) Analyze video footage of a table tennis smash and use the frame rate of the video and the ball's location as shown by the video to calculate distances travelled during intervals.
3) Use the sound recorded by video to measure the interval between the paddle striking a ball and the ball subsequently striking the table to calculate the average speed between the two events.
Each of these methods has their strengths and their weaknesses. The reason these methods were used is simply because the recordings were readily available and there was no need to perform any special experiment.
Method 1: Still Photo "Streak" Analysis
I usually take my digital camera to club ( Phoenix Table Tennis Club ) tournaments and take pictures once I'm out of the competition. So I have quite a few digital images hanging around on my computer hard drive. I dug through my images and came up with a couple where the ball appeared to be hit with a good deal of force by one of our better club players. I then analyzed the ball streaks.
The first image is of Gia Leu playing against a top player (or perhaps the top player) from India, Chetan Baboor. Considering the height of the ball before Gia struck it, I assume that Gia can hit faster than what this shot shows. But Chetan is clearly a very long distance back from the table, so seems that Gia is hitting very hard. As I have noted on the photo, the streak is approximately three and a half ball diameters in length which means the ball has travelled two and a half ball diameters or 100mm. The shutter speed was 1/250 of a second which means that the ball is travelling about 56 mph. This is only about 14 mph slower than the "Worlds Fastest Smash" recorded in New Zealand.
The second image is also of Gia but this time he is hitting against Mario Lorenc also one of the club's top players. Mario is barely visible, so you'll just have to take my word that its him. In this image, the ball streak is an estimated four and three quarter ball diameters meaning that the ball travelled three and three quarters ball diameters distance or 150mm. But since the camera shutter speed in this shot was 1/125 of a second, the estimated ball speed is only 42 mph. This seems consistent with Gia's less forward body position which suggests this ball was struck with less force.
The original images have four times the linear resolution of the images posted here and I used the vertical thickness of the streak to determine the length in pixels of one 40mm ball diameter. I also fudged the streak lengths a bit to try to account for the fact that the ball is not travelling directly parallel to the camera's sensor plane. This difference in angle will cause the streak to be a bit shorter and the estimate of speed to be a bit less accurate.
Because these shots capture the ball very shortly after it has left the paddle, this gives a ballpark estimate of the maximum ball speed that could be expected from a top club player during tournament play. Some shots would probably be a bit faster and some a bit slower. But this doesn't tell us much about the speed of the ball once it reaches the opponent. We all know that table tennis balls slow down rapidly once hit. It does, however, give us a notion of what the top speed of a well hit ball might be.
If you have some table tennis photos and happen to know the shutter speeds that the images were taken at, you can easily duplicate this analysis. I've put together an Excel(tm) spreadsheet that will do these (and a few other) calculations for you. Also, this image illustrates why it is necessary to subtract one ball diameter from the streak length in order to determine the length that the ball travelled.
You can also perform table tennis ball calculations using my Table Tennis Ball Speed Calculator or my Ball Speed Calculator.
Method 2: Analyze Video Footage
Video and film cameras take a series of images at fairly accurate intervals usually ranging from 24 frames per second (professional film) and 25 fps for PAL video (used in Europe and other countries) to 30 frames per second for NTSC video (used in the U.S.). These frame intervals can be used to determine the elapsed time between events with a fair degree of accuracy. Since I had recently been looking at some of the clips on Timo Boll's website, I decided to see if there was a shot that showed a particularly hard smash. I found such a shot in the clip where Timo is playing Korbel.
About six seconds into this point, Korbel moves in quickly, taking a three step approach, and smashes the ball to Boll's backhand side. Korbel's smash is taken at around shoulder height and appears to be a very hard hit using good hip rotation. I have saved off five key frames of this hit as individual images.
The first image shows the ball just before contact. Contact is made at the beginning of the exposure of the second image. You can see a very long streak in this image. The beginning of the streak is the ball's position at the beginning of the exposure and the end of the streak is the position at the end of the exposure. Unfortunately, we don't know the shutter speed and can't easily use the streak length like we did in the still photo analysis. But we do know the frame rate (25 fps - PAL video) and that 1/25th of a second passes between the beginning of each exposure. So we can see that it takes three frames for the ball to travel from the point of contact with the paddle to a point just after the ball bounces off of the table. This is 1/8.333 of a second. It appears that the ball was hit while it was a short distance beyond Korbel's end of the table and that the ball isn't quite past the end of the table at the beginning of the fifth frame. So it seems that the ball has travelled horizonatlly about the length of the table (2.74 meters) in this time interval. But the ball was hit with a downward trajectory and slightly crosscourt. So I adjusted the 2.74 meters distance to 3.16 meters of absolute distance travelled. I estimated a 30 degree ball angle and increased the ball path distance by 15.47% (1/cos(angle) * distance). I used the Excel(tm) spreadsheet to calculate an average speed of 58.9 mph. Since this is the ball's average speed, we can be sure the ball was travelling faster at contact and slower as it passed the edge of the table. We don't, however, know how much faster or slower. But since the average speed is only 10 mph slower than the new world record recorded in New Zealand, it seems reasonable to guess that the ball came off Korbel's paddle at very close to that "world record" speed. Very possibly, it was even faster.
Method 3: Analyze Sound From Video Footage and "reconstruct" the event.
By measuring the interval between the sound of the paddle hitting the ball and the ball hitting the table, it is possible to get very precise event timing. This is possible because sound recordings take many thousands of samples every second yielding very high precision. This image shows a portion of the audio waveform from the Timo/Korbel clip that corresponds to Korbel's smash. You can see that the interval between events (lower right) is .105601 seconds (1/9.47 seconds).
But we still have the problem of measuring the distance that the ball travelled. We know that it is somewhere near the length of a table tennis table (9 feet or 2.74 meters), but I wanted more precision.
I decided to "reconstruct" the event in a 3D program (Lightwave) so that I could more accurately estimate the point of contact with the paddle and the table. I constructed a virtual table tennis table with the dimensions of an official table. I made a composite image (showing key ball position) made from multiple image frames from the Boll/Korbel video clip as a reference plate. Then through trial and error, I positioned the virtual camera until I had established a camera position that closely approximated the actual camera's position (which happens to be about 5 meters above the floor and about 11.5 meters back from the center of the table). This allows me to use the visual cues from the background plate to position a virtual ball path with a fair degree of accuracy.
This image shows the reconstructed scene with the simulated ball path in place. The camera was moved and its focal length adjusted until the table was aligned to match the original setting. The thin blue lines are the outlines of the 3D elements that have been superimposed over the 2D image in 3D space.
This is an imageimage showing the rendered synthetic ball streak and table composited over the background plate. This shows how the virtual path and visual cues of the original footage match up. The light blue corner in the lower right it the background plate from the video clip and shows the streak of the ball right after it bounces off of the table.
And finally, just for fun, this MPEG flies the camera down around the table and ends up at approximately Korbel's point of view. This doesn't help us calculate anything to do with the ball's speed, but it gives you a 3D view of what I estimated the ball's path to be.
I estimated a ball distance travelled of 2.576 meters based on this reconstruction. This works out to an average speed of 54.5 mph. This is a little slower than the estimate provided by Method 2. This estimate should be more accurate due to higher precision in the timing and because the ball path estimate should be more precise as well.
After entering a variety of values, I find that an initial ball speed of 65.973 mph (29.4929 meters/sec) yields a distance travelled of 2.576 meters, an average speed of 54.5658 mph and a speed on contact with the table of 45.65 mph (I used 10,000 iterations for the calculations).
A speed of 66 mph is very consistent with Lark Brandt's new speed record of 69.9 mph. This further corroberates the notion that well hit table tennis balls don't get near 100 mph in speed. Of course, a smash competition does differ from a competitive match in a number of significant ways. For instance, the ball is hit from a dead drop, so there is no inherent rebound from the ball's inertia. It also seems likely that the radar gun will be most accurate when the struck ball is directed almost directly at the gun. The further the deviation, the lower the measured speed. So the actual struck balls are going at least as fast as the indicated speed and probably a bit faster. On the other hand, the smash contestants have the opportunity to work on specific technique and to experiment a little bit with equipment with the specific purpose of generating speed. The predictable ball drop probably helps them dial in their technique a bit. So, Korbel shouldn't feel bad if his smash - struck in the heat of competition - is a bit off the mark of the world smash record.
Since the speed estimate for this very hard hit ball from a world class table tennis player is less than 70 mph, we can be pretty sure that any table tennis ball likely to be seen by a club player is travelling much slower. But keep in mind that at an average speed of only 25 mph, a table tennis ball will travel the length of table in about 1/4 of a second - the approximate limit of human reaction time. 70, 60 and even 50 mph is extremely fast when short table tennis distances are factored in. This, of course, explains why Boll is so far back and why players who play close to the table need very quick reflexes.
|My original conclusion included a mention that Lark Brandt had used a paddle that was "loaded" with non-ITTF approved glue. That comment had the unfortunate effect of possibly suggesting that the use of non-ITTF glue might have diminished Lark Brandt's accomplishment in some way. That was not the intent. While the use of such a glue might provide some slight speed benefit, rest assured that it would be very slight. This is supported by the fact that other competitors used that very same paddle and were very far off of the winning mark. It is further supported by early qualification rounds where Lark found the difference between the "glued" paddle and his normal non-speed glued competion paddle to be about 3km/h. This difference could be easily attributed to the fact that his normal paddle is heavier than the paddle that was glued. It is quite possible that the non-ITTF approved glue gave no advantage or even gave a disadvantage that was overshadowed by the paddle's light weight. Either way, all competitiors had the opportunity to use similar equipment Some even had the opportunity to use that very same paddle.|
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