# Is it fair to judge this speedskating race by only 3 thousands of a second?

Zbigniew Brodka of Poland won the Olympic men's 1,500 meters speed skating title by just 0.003 seconds at the Adler Arena on Saturday.

Brodka clocked one minute, 45.006 seconds with Koen Verweij of Netherlands crossing the finish line in the final heat just outside the Pole's time. Denny Morrison of Canada took bronze.

I'm a noob with physics, please forgive me.

The first thing I think is: Can you ever measure this so precisely. I'm not sure how exactly this is measured, but normally in physics, I think that you must say that a measurement is 1.45.006 $\pm$ 0.002 or something. I think that someone would have to know how this is measured to judge this, and this is maybe not so relevant on this website. But if someone knows more about this, I would like to hear it.

Now comes the physic question. Here is the start photo of Koen Verweij (in the orange suit, on the right):

The start shot is given by a man on the left, which you can't see on this photo.

Here is the start photo of the winner (Zbigniew Brodka, in the red suit on the left):

As you can see, Zbigniew Brodka is much closer to the source of the start sound, than Koen Verweij is.

I'm wondering how much the time differences would be between when Koen Verweij hears the start shot and when Zbigniew Brodka hears the startshot. Could you say that Koen Verweij was faster, if you would start the time at the moment the sounds has reached the skater ?

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Your reasoning doesn't make sense to me Kyle. –  Kasper Feb 15 '14 at 19:09
@KyleKanos it still makes no sense to me. The reaction time has nothing to do with the fact that one competitor is in advantage. –  Martin Drozdik Feb 15 '14 at 20:39
@KyleKanos: Lets make the silly assumption that both have the exact same reaction time (0.1s), and need the exact same time for the course (60s). Due to distance from the sound source, A will start 0.03s after measurement started, leading to a total of 0.03+0.1+60, while B will start 0.06s after measurement started, leading to a total of 0.06+0.1+60s. –  PlasmaHH Feb 15 '14 at 21:03
@KyleKanos: The question is whether it is fair to judge this race by 0.003 seconds. The winner was decided based on a difference of 0.003 seconds, so clearly 0.03 second difference in hearing the sound wave would be very significant. –  JiK Feb 15 '14 at 22:24
Kyle, I think that you either missing some context here or you are having some brain malfunction. The reaction time, doesn't matter at all. You must add the reaction time to the time the sound travels as plasmahh points out. –  Kasper Feb 15 '14 at 22:34

At the ambient temperature and pressure (assuming atmospheric pressure), the sound speed is pretty close to $340\ \frac{\text{m}}{\text{s}}$, and it seems (from internet research) that the first contender is about $16\ \text{m}$ further away from the guy firing the gun, which comes down to a delay of about $.05\ \text{s}$ in hearing the sound if the sound is coming from the guy firing the starting shot.

However, this is something that is taken into account: different speakers are placed near each skater so that this apparent disadvantage is minimized/eliminated. That being said, a $\frac{3}{1000}\ \text{s}$ difference in a race like this is so miniscule that any tiny random event can influence who ends up winning, rendering the outcome essentially random.

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Not to mention that, at least from my running days, we were trained to look for the flash of the gun rather than wait for the sound when we didn't have speakers behind us. –  tpg2114 Feb 15 '14 at 16:53
I think that, at the Sochi olympics, there is actually no flash (it's not a gun or even something remotely similar anymore at this point) –  Danu Feb 15 '14 at 17:04
Do you know where the speakers are in the adler arena ? If it something like this: geluidnieuws.nl/2010/mar2010/schaatsen2.jpg than it is still not fair. But thanks for your clear answer :) –  Kasper Feb 15 '14 at 17:06
Also, at this level of precision, the position of the sensor will sensitively determine the winner -- one contestant's head might cross before the others' head, but the feet may cross in the opposite order. –  Jerry Schirmer Feb 15 '14 at 17:15
@JerrySchirmer A finish camera is in essence a continuous roll of film exposed through a slit aiming at the finish line while the film moves. This translates temporal order to spacial arrangement on the photo (and is responsible for the somewhat distorted shapes the runners get when moving their limbs while crossing the finish line). Not sure if this has changed in the digital ages, but maybe not (cause CCDs are read out sequentially). –  Hagen von Eitzen Feb 16 '14 at 18:08

Is it fair to judge this speedskating race by only 3 thousands of a second?

Yes, it's "fair". Not only is it according to the current rules of the event**, but also:

There are at least three asymmetries that have far larger impact and are all considered "fair".

1. They happen to start in different lanes (and must cross-over thereafter). That means they follow completely different trajectories, the distance of which might be calibrated* to some extent, but not to the precision of $0.003\text{ s}$ (and certainly not specifically for these two contenders). (Note that, if there were such calibration, it would take the sound effect implicitly into account.) It is not trivial to compute the distance for both tracks. There is a 'shortest' path and a 'measured' path, but neither has much to do with the skaters' actual paths.
2. They have different direct opponents. (Think of the drafts during cross-over. It might be that Brodka benefited more (from Davis, I believe).)
3. One of them skates knowing the other's time. (In this case, Verweij was last to race.)
4. (The conditions of the ice change during the competition.)

It's all in the game.

*This is not done explicitly, but the calculation of the distance has some subjectivity in it: "The measurement of the track is made half a meter into the lane." One might consider this implicit calibration. (I assume that if there was significant statistical evidence for one lane being faster, that half a meter would be adjusted to negate the difference. And the half a meter itself was probably determined with this issue in mind.)

The measurement of the track shall be made half a meter outside the inner edge.

**From the ISU:

Over all distances the times shall be measured and recorded in the protocol to the accuracy of one hundredth of a second. If the watches used display accuracy beyond one hundredth of a second, these decimals shall be ignored. However, if a photo-finish system with resolution of one thousandth of a second is in use, the third decimal digit shall be recorded for the purpose of breaking ties in accordance with Rule 265, paragraph 1.

and

However, if a photo-finish system (as specified in Rule 251, paragraph 2) with a time scale showing time resolution in thousandths of seconds is in use, the recorded times from the photo-finish system in thousandths of seconds will be used to determine the order of Competitors (or teams) in the final results. In this case the official protocol shall indicate tie-breaks by displaying the recorded time for the Competitors (teams) concerned in thousandths of a second.

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All races at this level, be they skating or running, have a speaker placed directly next to or behind each competitor. There's no sound-lag problem. As to whether we should consider sub-millisecond, or even sub-second, differences in run time is more philosophical. There's a ton of prejudice against ties. Fans want a "winner" (or at least for the other guy to lose :-( ) .

There are a few exceptions, such as the pack in a bike race all getting the same finish time, primarily to avoid the risk of massive crashes.

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Well, seems to hold only for guys then ;) dailynews.com/sports/20140212/… –  PlasmaHH Feb 15 '14 at 21:26
Massive crashes are ok in skating. –  Andrew Grimm Feb 16 '14 at 5:39
@AndrewGrimm Nope, that's shorttrack, which is a completely different sport. –  Danu Feb 16 '14 at 10:32
@PlasmaHH Nope, the difference is between the sports: ice skating vs. alpine skiing. It is much harder to get millisecond resolution for skiing, to some extent because their velocity is about twice as high when crossing the finish, but mainly because the photofinish is harder to align/visualize due to snow spraying around. Because of that the rules in the two sports are different, leading to millisecond resolution in ice skating and 'only' 1/100 s resolution in alpine skiing –  Michiel Feb 16 '14 at 12:04
For sprint running races, there is a loudspeaker in each set of start blocks but I'm not aware of any other sport that goes to such lengths. For example, in speed skating, there can be eight competitors in a single race but no equipment is placed on the ice; even with speakers at each side of the track, skaters at the middle will hear the sound slightly before those at the edge. Also, the intense dislike of ties seems to be mostly an American phenomenon. For example, soccer matches throughout the world routinely end in ties and that result stands, except in the knockout phases of tournaments. –  David Richerby Feb 16 '14 at 13:06

1500 meters in 105 seconds is an average speed of 14.3 meters per second. At that speed, a difference of 0.003 seconds means the winner crossed the finish line 43 mm ahead of the second-place finisher. Race timing is done by measuring when the leading edge of the leading skate blade crosses the finish line, and a 43 mm difference is well within the ability of the timing equipment to measure.

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On both the sides of the track is a speaker wich processes the sound of the gun. The gun doesnt process the sound.

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Do you have a source for this claim? I heard that the speakers are placed, more like this: geluidnieuws.nl/2010/mar2010/schaatsen2.jpg –  Kasper Feb 17 '14 at 11:15
This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. –  Ali Feb 17 '14 at 12:33

In physics, you are taught that any measurement needs to be accompanied by a tolerance range so that the degree of accuracy can be ascertained. How ever, in this particular situation, the equipment used to make the measurements is the same, therefore the "built in" inaccuracies (if any) are the same, so they cancel! To compensate for the difference in track lengths, the competitors alternate the tracks.

If the situation was as you describe (sound source on left), with a separation between competitors of 10 feet, that would incur a delay of about 25 ms, which would place the competitor farther away from the sound at a disadvantage by 25 ms! If the sound source are speakers placed equidistant from the center of the track, then the competitors would hear the sound at the same time, and there would be no disadvantage. As you can see, different steps are taken to insure the accuracy and fairness of the competition. So, yes, I believe it was fair to judge the competition by a difference of 3 ms. If they could not ensure this accuracy, then a tie would have been declared.

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Sound to start is laid out above.

A cheap quartz watch has a 32.768 kHz (2^15 Hz) crystal oscillator lock. Over one hour it has a typical stability no lower than ${2\times10^-8}$ relative. Even a cheap watch is more than up to the task, certainly after calibration to a master oscillator. Temperature variation is small. Thermostat the clock, or use a double-rotated cut crystal for frequency independent of temp.

http://tf.nist.gov/general/pdf/2276.pdf

Lightspeed is a bit more than a foot/nanosecond. Signal speed through fiberoptic or copper wire is about a third that, 4 inches/nsec. Given 10,000 feet of wire between start and stop signals, that adds (if uncalibrated and uncompensated !) 30 microseconds.

But wait! Absolute time is not being measured. Relative time, end versus beginning, is measured. Systematic errors cancel. That leaves statistical errors. Elapsed time interval is locked.

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Don't forget the position of the sun which by its gravity influences time ... –  Hagen von Eitzen Feb 16 '14 at 18:12
Did you take the Coriolis force into account here? –  Bernhard Feb 17 '14 at 7:46
Is this spam? I cannot make any sense/answer of this. –  phresnel Dec 5 '14 at 11:44

## protected by Qmechanic♦Feb 17 '14 at 11:26

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