Questionable accuracy of sub 1/1000″ differences

Differences in Short Track Speed Skating at the finish line can be small, very small. As photo finish line technology advances, differences are decided even when that difference is below one thousand of a second. That is 0.001 second or a millisecond, which is the accuracy in which times are reported on international competitions with finish camera equipment. Simple mathematics provide us a tool to convert the time difference to an actual distance, given the speed at which skaters are moving. Let us assume (for simplicity) two skaters moving at the same speed of exactly 45.00 km/h. That is 12.5 m/s. Which means that these skaters cover 0.0125 m in 0.001 seconds. That is 1.25 cm. That is measurable with a tape measure and also with a photo finish camera in ideal circumstances. Some finish photo cameras claim an accuracy of just 0.1 thousand of a second or in the example above, a difference of only 1.25 mm. It is nice that the technology is able to detect those differences, but a lot can be said about the actual accuracy of the whole process.

First of all, you need to understand how a photo finish camera works. It is a very ingenious piece of technology which takes very small vertical pictures at a very fast rate. Most photo finish cameras obtain 1,000-10,000 of such images per second. In the ideal case, a photo finish would capture a single line, vertical to the actual finish line. All these images next to each other show the so called finish photo which is actually an image in function of the vertical axis of the photo finish and time. This is very different from a regular image. The implication is that the photo finish camera itself dictates the finish line. On every track there is a visible finish line marked in the ice, but for the competition, it is the photo camera itself that decides what is the line. If the photo camera is no longer aligned with the actual line, the finishes are actually incorrect. So, if the camera moves even the slightest bit between races, the finish line, is not in the same position anymore. Therefore comparing times is also very doubtful when it comes to small differences. Rotating the camera for only a slight bit, will create an advantage or disadvantage for the skater ot the inside comared to one at the outside depeding on the direction of the rotation.

To illustrate the ambiguity, I invite you to expect the image below. We see the the exact same finish by a skater in green and a skater in red (these blocks are their first crossing blade over the finish line). However, depening on the alignment of the camera (black line) with the finish line (blue line), the photo finish photo is different as shown underneath each situation. In situation B, the red skater is even assumed to have finished before the green skater. Clearly, in the example the angles is exaggerated, but the bigger the distance between the two finishing skaters, the smaller the rotation of the camera needs to be to introduce errors. Even the slightest angle shift introduces errors. Case A and B produce the same end result in this case, but the time difference between the two skaters is registered differently.

On the big competitions like World Cups and European and World Championships, two photo finish cameras will be installed on both sides of the track. The advantage is redundancy when one camera fails or to solve occlusion when the skate of one skater is behind the body of another skater, seen from one camera. However, the accuracy of both cameras can also be doubtful. Since there is one camera 20 meters away from the finish line, usually solved with a zoom lense, inaccuracies in lenses pose problems as the light needs to travel further. Fortunately the speed of light is a wobbling 300,000 km/s which is much faster than the objects of interest are moving. However, the differences between two skaters should be the same. After some days of competitions, letting the cameras drift slightly, it is hard to believe that is indeed the case. Some doubt arises when claming that both cameras are still covering exactly the same line. In the image below, image A shows a perfectely aligned setup while the bottom camera in image B is slightly rotated. Due to the distance of 30 meters, a small rotational error produces a significant offset at the opposite side of the ice rink.

Of course, we believe that calibration is done as good as possible by the people who make photo finish possible. This article is just meant to raise awareness about accuracy, because the smaller the allowed time differences between two skaters, the higher the impact of a small rotational error in the camera setup.

After reading this, you have acquired some more background information to how a photo finish camera works. What do you think? Should there be a limit to the difference between two skaters to place them at the same finish position or do you think it is fair to place the one skater before the other when the difference is smaller than 0.001 seconds? Where does this end? Do you really want to lose with 0.00001 seconds in the future (given the arguments about accuracy above)? Or should there be a limit to it? Currently, the photo finish referee decides the order and therefore he can either decide to place two skaters within the same millisecond on the same position or the one before the other.