3 ms·

OP here. I think the spoke movement is probably the most likely to be able to work out who reached the actual finish first. That is based on the spoke patterns

OP here. I think the spoke movement is probably the most likely to be able to work out who reached the actual finish first. That is based on the spoke patterns in this image: http://tglyn.ch/blog/images/amstel_Finishphoto_AGR21.png http://tglyn.ch/blog/images/amstel_Finishphoto_AGR21.png The curve of the spokes should mean we can determine the distance the rider has traveled after the photo-finish camera. I cover my other ideas in the 'Further research required section' about 75% of the way down the article. If you have any further suggestions please let me know. Tom

jhgb 5y ago
> having it in the wrong spot means we may never know if Tom Pidcock's extra speed would have allowed him to make up the small distance in the final 26.86cm. Isn't it possible to extrapolate the movement from the last few frames of the image sequence?
- tomglynch 5y ago
  Potentially - do you mean via the video or the photo-finish image? I've suggested in the article looking at when the wheel reaches 98% of the full height which I think is along the lines of what you're saying.
  - jhgb 5y ago
    I meant the photo-finish cameras, but nevermind, I forgot how these things worked. But I would expect high-speed 2D cameras being available today at the finish line as well.
masswerk 5y ago
I think, the spokes are a good approach, since these are actually objects recorded in time. However, I think @gorgoiler [1] has made a valid point regarding the intersection of the "finish plane" and the plane recorded by the camera. (On the photo shown on your blog, the camera appears to be mounted slightly behind the finish line, thus, intersecting the "finish plane" at the ideal height, should point to just before the finish line at ground level. But there isn’t sufficient information in the photo to measure such a minimal angle, or to confirm, if there's any at all.) [1] https://news.ycombinator.com/item?id=26977975 https://news.ycombinator.com/item?id=26977975
eCa 5y ago
Very nice write-up, it was a fun race to watch. On your future research, alternative 1: Instead of only looking at the width of the wheel, what about looking at the height/width ratio? The quicker wheel ought to be relatively more ”squished” horizontally. On the other hand, with the tight margins involved, it might be that the ratios are not comparable due to the fact that they are not the same distance from the camera.
mnw21cam 5y ago
The shape of the curves of the spokes doesn't depend on the speed. If you take the picture of the wheel, and fix the aspect ratio so that it is circular, then the spokes will have a curve independent of the speed of the wheel. Speed determination is purely based on the aspect ratio of the entire wheel. To reason on why this might be true - consider that the bottom of the wheel is stationary, and the top of the wheel is moving at twice the speed. This is the case regardless of the speed of the wheel. If you rolled the wheel past the camera really slowly, the entire wheel would be stretched out horizontally, but the spokes would all be in the same arrangement. The reason for this is that the camera is a fixed position line scan where the variable is time only. If we switch to thinking about standard video cameras with a rolling shutter, then these have a line scan where the variable is time and space - that is, the camera samples a scan that is moving at a known speed. If you have a video with a camera like this of helicopter blades, for instance, then you can determine the blade rotation speed from a single frame. But with this finish camera, that doesn't work. So, to determine speed, the best possible action is to pick two points on the rigid body that is moving, and time how long it takes to pass the recording line. The further apart these points are, the more accurate the average speed determination will be. The trade-off for this is that the speed measurement will be the average between the time the first point and the second point passes the recording line, and we are only interested in the average speed at the point the front of the bike passes the line. What we can show however, as pointed out elsewhere[0], is that one bike was in front of the other when the front of the wheel, the hub of the wheel, and the back of the wheel passed the recording point. When the back of the wheel passed the recording point, the front of the wheel definitely passed the actual finish line, so assuming the two wheels are the same size then the front of that wheel passed the finish line before the other one. [0] https://news.ycombinator.com/item?id=26978621 https://news.ycombinator.com/item?id=26978621
- tomglynch 5y ago
  Great comment! Super informative and something I had not properly thought about. But you're totally right, curvature of the spokes is based only on the fact it's rolling past the camera, and two wheels rolling at different speeds will result in the same spoke pattern.

jhgb 5y ago

> having it in the wrong spot means we may never know if Tom Pidcock's extra speed would have allowed him to make up the small distance in the final 26.86cm. Isn't it possible to extrapolate the movement from the last few frames of the image sequence?

tomglynch 5y ago
Potentially - do you mean via the video or the photo-finish image? I've suggested in the article looking at when the wheel reaches 98% of the full height which I think is along the lines of what you're saying.
- jhgb 5y ago
  I meant the photo-finish cameras, but nevermind, I forgot how these things worked. But I would expect high-speed 2D cameras being available today at the finish line as well.

masswerk 5y ago

I think, the spokes are a good approach, since these are actually objects recorded in time. However, I think @gorgoiler [1] has made a valid point regarding the intersection of the "finish plane" and the plane recorded by the camera. (On the photo shown on your blog, the camera appears to be mounted slightly behind the finish line, thus, intersecting the "finish plane" at the ideal height, should point to just before the finish line at ground level. But there isn’t sufficient information in the photo to measure such a minimal angle, or to confirm, if there's any at all.) [1] https://news.ycombinator.com/item?id=26977975 https://news.ycombinator.com/item?id=26977975

eCa 5y ago

Very nice write-up, it was a fun race to watch. On your future research, alternative 1: Instead of only looking at the width of the wheel, what about looking at the height/width ratio? The quicker wheel ought to be relatively more ”squished” horizontally. On the other hand, with the tight margins involved, it might be that the ratios are not comparable due to the fact that they are not the same distance from the camera.

mnw21cam 5y ago

The shape of the curves of the spokes doesn't depend on the speed. If you take the picture of the wheel, and fix the aspect ratio so that it is circular, then the spokes will have a curve independent of the speed of the wheel. Speed determination is purely based on the aspect ratio of the entire wheel. To reason on why this might be true - consider that the bottom of the wheel is stationary, and the top of the wheel is moving at twice the speed. This is the case regardless of the speed of the wheel. If you rolled the wheel past the camera really slowly, the entire wheel would be stretched out horizontally, but the spokes would all be in the same arrangement. The reason for this is that the camera is a fixed position line scan where the variable is time only. If we switch to thinking about standard video cameras with a rolling shutter, then these have a line scan where the variable is time and space - that is, the camera samples a scan that is moving at a known speed. If you have a video with a camera like this of helicopter blades, for instance, then you can determine the blade rotation speed from a single frame. But with this finish camera, that doesn't work. So, to determine speed, the best possible action is to pick two points on the rigid body that is moving, and time how long it takes to pass the recording line. The further apart these points are, the more accurate the average speed determination will be. The trade-off for this is that the speed measurement will be the average between the time the first point and the second point passes the recording line, and we are only interested in the average speed at the point the front of the bike passes the line. What we can show however, as pointed out elsewhere[0], is that one bike was in front of the other when the front of the wheel, the hub of the wheel, and the back of the wheel passed the recording point. When the back of the wheel passed the recording point, the front of the wheel definitely passed the actual finish line, so assuming the two wheels are the same size then the front of that wheel passed the finish line before the other one. [0] https://news.ycombinator.com/item?id=26978621 https://news.ycombinator.com/item?id=26978621

tomglynch 5y ago
Great comment! Super informative and something I had not properly thought about. But you're totally right, curvature of the spokes is based only on the fact it's rolling past the camera, and two wheels rolling at different speeds will result in the same spoke pattern.