Each pixel column is a specific point in time. I added a few landmarks: when the front of the wheel passes the camera view, when the axis of the wheel passes the camera view, and when the end of the wheel passes the camera view. Blue for the top biker (Wout) and green for the bottom biker (Tom).
Every single event happened earlier for Wout. Both wheels are the same diameter. Therefore, the entire period where the wheel intersected the camera view, Wout's wheel was ahead. Including the exact period where Wout passed the actual finish line.
If Tom would have passed Wout, you would expect that the bottom wheel would be more "squeezed" such that the end of Tom's wheel would have passed the camera line earlier than Wout. Same for the other landmark (centre of wheel).
You can add more landmarks if you want (e.g. approximate when the wheel passes for 25% and for 75%), but it should be clear by pure margin that Wout had the lead for the whole duration where the front wheels passed the camera view. Pretty much all the computation in this article was unnecessary.
Amstel gold made the good call, though I agree that it was probably more luck.
This analysis assumes the camera was aligned perfectly parallel to the finish line, but offset from it.
Unfortunately, there's no reason to assume this was true. Almost the opposite! If the operator did set up the camera correctly initially, and we know the far end ended up pointing to the wrong panel (got a knock?), this makes it more likely it was skewed so as to advantage the most distant rider. And that was Van Aert.
Supporting evidence for your point comes, I think, from the fact that, for each bicycle, the left end of the handlebars appears ahead of the right one - meaning that it crossed the plane of the camera view first. I don't think the wheels could have been noticably misaligned from straight ahead here, could they? - in which case, this would imply that the camera plane is skewed as you suggest.
If this is correct, then it suggests a way to estimate, and correct for, the skew, as we have other photos and videos showing approxinately how far the riders were from each other and from the camera, as well as their trajectories as they crossed the line.
Having read the entire article, I believe the point was related to the photo-finish camera being positioned some distance before what is officially the "finish line", approx 20cm+ they say.
The argument is that if Tom was travelling faster, the distance could have been made up in that time, potentially for a win.
You're right, the camera was in front of the actual finish line.
My point is that Wout was ahead for the /entire/ duration where the front wheel intersected the camera line. The wheel's diameter is bigger than 20cm, so the moment when Wout passed the actual finish line is included in this interval. Therefore, Wout was ahead when the winner passed the actual finish line. QED.
If there was an overtake -during- the moment of the photo finish then one bicycle would eclipse the other. The overtaken cycle would be entirely longer than the overtaking bicycle.
Line judges go for wheel contact, so for an overtaking to count, the -front wheel- of the overtaking rider would have to be fully within the front wheel of the other.
As long as the rider and their bike is much wider than the misalignment, the only effect is to shift which point in the picture corresponds to the moment they pass the finishing line.
As the OP demonstrates Wout was ahead even at landmarks over 20 cm from the front of the wheel the only way Tom could win was if his front wheel physically elongated over 20 cm in those last milliseconds.
If it was 20 cm off it might just as well have been a few degrees off from being perpendicular to the road/parallel to the line that marks the finish.
The rules are the outcome of reluctant evolution since back in the 19th century, it's hardly surprising that the camera isn't necessarily considered the ultimate source of truth.
(history of techno and a road cycling race on the first lines of hn, today it's really looking as if tailored to mock my interests)
I suspsect the camera was most likely positioned exactly on the finish line, but aimed ≈20cm behind it. This implies the rider furthest from the camera would be given an unfair advantage.
If it was nudged by a gust of wind or something, it seems very unlikely that the camera would have moved a full 20cm but remained parallel to the finish line.
I agree that you're probably correct that Wout did win. However, I don't think you've correctly lined up the center of the wheels, nor the rear of Wouts wheel.
For the center of the wheel, Wouts looks slighty too early and I think due to the larger size of Pidcock's hubs it's hard to determine the center here too. As for the rear of the wheel, Wouts gum wall tyre is hard to see.
So all in all, it does seem likely Wout held the lead. However, a well times bike throw can change a riders speed momentarily for a short period of time and based on the video Pidcock's bike throw was significantly more effective than Wouts. So while I'm not going as far to say Pidcock would have won, I'd say there is a chance Pidcock had the lead momentarily, and that moment may have occurred as Pidcock crossed the actual finish.
Assuming Pidcock was in front on the actual finish line, his hub would have been about 5cm in front of the photo-finish line. That leaves about 3ms for him to finish the bike throw and return his hub behind Wouts hub. Seems like a stretch, but still a possibility :-)
Maybe you could also look at how deformed the wheel perimeter compared to a perfect ellipse to estimate the speed at different points?
EDIT: Or you could calculate whether it's humanly possible to move a bike a few centimeters forwards and back again in about 15ms, which I think the hypothetical bike throw must have been for Pidcock to be the actual winner?
The wheel perimeter idea I did suggest (cmd + f for the '40%' bit down the bottom of the article) but I think the tolerances are likely too small to do it properly. Would love someone to give it a go though.
I think you're right. Stated in simpler terms, both the front and the back of Wout's wheel passed the line of the camera before the front or back of Tom's bike.
Even if the camera were 10 cms off, the fact that the back of Wout's front wheel passed that mark before the back of Tom's front wheel must means that the front of his wheel was still ahead at that moment. (Assuming same sized wheels.)
Thanks, I was thinking about doing the same plot as you. Watching the race, I believe Wout even appeared to be faster after the finish line, if I recall correctly.
side issue- the distortion of the spokes is screaming "rolling shutter effect", which tells me that the sensor was only read from one edge to another. If it was top-to-bottom, then the top pixels really could be older than the bottom ones, and vice versa for bottom-to-top scans. If it was left-to-right it's not clear to me whether that could cause false impressions, but it's certainly not a perfect representation of a discreet instant of reality.
It is a kind of rolling shutter effect, but you're misunderstanding the finish camera's design - they capture a single column of pixels and the horizontal axis is actually time. This is why the background of photofinishes is a bunch of streaks.
> Your comment clearly shows that you haven't read the article.
This was my first thought. Then I thought about it some more, and became persuaded I was wrong. I definitely did read the article.
According to the explanation in the article, it’s a narrow slice, so the back of the wheel would be photographed when that passed the finish line, even if ~30cm out – at which point the front would be clearly over the finish line.
The point being that the wheel is bigger than 30cm. It’s subtle, but I’m persuaded – unless I’m missing something, like them not having or not actually enforcing wheel-size regulations.
I personally find it very difficult to reason about something that looks so much like a photograph where only vertically-aligned points were taken at the same time.
I think you misunderstood how a photo finish camera works. Please try re-watching the explanation video. The photo isn't a snapshot of the race at a specific time, the photo shows an entire interval where the top cyclers passed the finish line. It's like having long shutter time and a narrow slit and slowly moving the camera such that you get the view of the slit projected along the entire camera sensor.
You don't understand his point. He states "Each pixel column is a specific point in time." He's saying you can observe when the BACK of the wheel crosses the too-early "camera line" and determine the winner.
Unfortunately this isn't true if the camera line is not parallel to the finish line, which it probably was not.
The right wheel appears to be elevated, per another article they both threw their bikes forward at the finish. That would impact the view from this angle to the point where I don’t see that as definitive.
> The black line is a visual approximation of the placement of the finish, but the image from the photo finish camera is the true arbiter of the result – not the other way around. It’s technical and it’s a bit confusing, but it’s clear-cut and the riders and officials are playing the same game with the same known set of rules.
> According to UCI regulations, the photo finish verdict is final, because the finish line is what the photo finish says it is.
Which makes most of the detective work here sadly pointless.
If there are supposed to be two photo finish cameras, how can the photo finish be the true arbiter? The two cameras cannot possibly be perfectly aligned.
I'm not an expert but the UCI document labels it as "1 main camera, 1 opposite". So I would guess the "main" camera is the source of truth and the other is a backup?
Either way, presumably both cameras ideally need to be aligned to the line as stated. That should be possible and perfect alignment between the two cameras isn't required. I can't see anywhere that it states the two cameras actually need to agree, isn't it fine providing one of them is used consistently.
The “finish line” could be thought of as a two dimensional plane. The winner is the first person to touch or pass through the plane.
If you’re painting a line then the “finish line” is where that plane touches the ground. For other races it might be a piece of tape held at chest height — the part of the body that usually goes through the plane first.
When the competitors are bicycles then they all the same height — the middles of the front wheels are all the same height off the ground, something on the order of 400mm. The finish line is floating about a foot off the ground.
The specialist streak camera photographs objects passing through a 2D plane. Ideally you would have that plane aligned vertically so that the finish plane and the camera plane were the same.
If for some reason you couldn’t do that — let’s say the camera could only be placed a few feet in front of the finish line so as to see around an object — then you would have to arbitrarily angle the camera plane to intersect the finish plane.
The intersection of these two planes will give you the “finish line”. For a bicycle race, do you set it up so that the finish line is on the ground, or floating 400mm above the ground? If you do the latter then the projection of the camera plane into the road will indeed give a line that stops short of the finish plane, but that’s irrelevant — the actual finish line at the
middle of the front wheel is in the correct place.
I think the article assumes the former when the organisers did the latter?
Ah this is an interesting thought though I don't think this is what the organisers were trying to do. Or if they are, it does not match up with what they are meant to do as per the UCI specs (the UCI is the international cycling governing body).
In another comment I was discussing the tech being somewhat outdated - perhaps your suggestion is part of the solution. Would two cameras on different planes result in more accurate results?
It’s probably quite hard to make an orthographic streak camera that is pointing vertically down in the same plane as the finish, but that seems like the optimal solution.
Moreover, if the camera is used to identify the times and finish positions of all the riders, it’s probably quite hard to identify them from above. Perhaps a streak video synchronised with TV footage would be convincing?
How about a prismatic laser and fog machine at the finish? It’ll look like an 80s rave but the streak camera will clearly show where the finish is.
It's my understanding (and confirmed by other comments on HN to this article) that the rules define the camera's sensing plane as the finish plane. So, regardless of the paint on the ground (which can not and will not ever form a perfect line), it's the camera that matters.
I used to work with these line-scan photo finish camera systems (we used FinishLynx) timing track meets.
This error is pretty comical to me because aligning the camera is the first thing we do after putting the camera up and looking at their images, it's pretty clear it wasn't aligned properly. The cameras can auto-align, but we didn't trust it and manually aligned it, but I'm wondering if maybe the event organizers auto-aligned and didn't bother to check? The cameras are mounted on a motorized base that can move in 3 dimensions with very fine precision [0]. In the OP, you can see the event organizers have a black line across the finish on a white base. In order to manually align it you just have someone run back and forth across the line and move the camera with the computer until you pick up the very left edge of the black line, which is very clear because you can see the ground change from black to white in the image (or vice versa depending on where you start).
We also used to always put a white piece of wood behind the line so that the images would always have a white background. This makes it so much easier to detect the edge of a torso when clicking on a person to indicate their time. In the OP, if their camera was aligned correctly, red would've been a tough background color. Also a black line is questionable. I would've had a white line on black base for the same reasons.
Some thoughts from looking at amstel_Finishphoto_AGR21.png.
a) in the horizontal axis, everything changes at 6 pixel intervals, I'm going to call those samples
b) I count ten samples as the narrowest of the front tire at both the early samples and the later samples of both riders. (including the fringing).
c) there's a two sample gap between the front of the front tire of the top rider and the bottom rider (pixels 835 - 840 for the top rider, and 823 - 828)
d) there's also a two sample gap at the back of the front tire (pixels 355 - 361 for the top rider and pixels 343 - 348 for the bottom rider)
I'm not invested enough to try to figure out other points of reference to compare, but it seems likely that if the riders were separated by two samples when their front tires entered the line of sampling, and also separated by two samples when their front tires left the line of sampling, that they were separated by two samples throughout that time. Since they would have crossed the (marked) finish line while their tires were being sampled, I'm comfyish saying the bottom rider was 2 samples behind the top at the finish line.
If my calculation is right, each front tire took 80 samples to clear the line of sampling; and if it was 2000 samples per second, that's 0.04 seconds for the bikes to clear the camera; might that be enough time for the second bike to have been pushed forward and pulled back such that it may have won; I dunno.
also e) now I've used up my evening time I had meant to do something else with :P
Very good analysis. I'm just wondering if a 'bike throw' could cause a sudden acceleration and then deceleration both within the time the front wheel travelled over the line. Which could mean the rider in 2nd may have crossed the real finish line first. Though it's true that this does seem unlikely and therefore i'd also be comfy-ish with what you are suggestion.
If I hadn't forgotten where I put my physics hat, maybe we could figure out what sort of acceleration would be needed to get the bottom bike ahead of the top bike, assuming the top bike was traveling at constant velocity.
If the front hubs were easier to distinguish, I'd have liked to compare those, but it didn't seem clear like the tires.
Fascinating article, and great to see a problem solver at work.
However, I question humanity’s sanity when we declare a winner in a 216.75km long race by someone who (possibly) won by 0.016 seconds (and poorly declared either way from the article).
At what point do races become a tie instead of 1st/2nd ? Just because we can doesn’t mean we should. I mean, if we had a camera that could take 350,000 photos per second does that mean we should use it to declare the winner?
I remember this issue came up in swimming a few years ago, and people were arguing that the timing measurement was finer than the tolerance for error of the measurement of pressure on the pad. We still talk about that race venue today: https://www.theringer.com/2020/7/29/21345181/milorad-cavic-m...
With regards to swimming, I once read they measure times only up to hundredths of seconds, because the individual lanes of the pool cannot be built to be the same length within a margin of error that would warrant measuring times more accurately.
Same reason why in athletics the starter pistol sound is transmitted via a speaker behind each individual lane. Otherwise the speed of sound would disadvantage the lane furthest from the starter pistol by more than a hundredth of a second.
Interesting factoid: the human brain processes sound faster that sight [1]. The difference cited in the paper below is roughly 40 ms, which is small in an absolute sense, but compared to the relative time tolerances we are discussing here in this parent article, it's huge!
Naturally this effect cancels out if all competitors get the same visual cue, however it's still to the benefit of athletes and fans to want quicker reaction times:
- Shorter overall reaction times means faster races means better records
- The standard deviation of reaction times is smaller for sound than for sight, which means the reaction time is more fair to all
Vision is amazingly sluggish. Turning an incoming photon into a nerve impulse involves a whole mess of slow (and fascinating) chemistry, just to leave the rod or code. Once it does that, the resulting signal bounces around the retina and then a huge portion of the brain before it's available for "action."
The auditory system, on the other hand, is optimized for speed. It has a giant synapse (=connections between cells), called the Calyx of Held, that is specialized for extremely fast (sub-millisecond), reliable transmission between cells. They're really cool looking: https://www.eurekalert.org/multimedia/pub/213595.php?from=44...
At least some swim meets use a light and a buzzer. I first encountered that many years ago at Gallaudet, a school for the deaf. I think that has become common at all swim races. It certainly makes sense to not exclude racers who can't hear.
I did note at the time that the gunshot sound put an extra oomph into the start over a buzzer. No idea whether that actually made a difference to my time, but it sure got my heart rate up.
When I ran cross country in high school our coach always said to go on the sight of the smoke not the sound of the shot. This was when the starter was in front of the whole mass of runners. Not sure if it ever helped me given we were mass starting a race that lasted for 3ish miles.
If you were by yourself, that would only shave a fraction of a second off your 5k time. However, getting out in front of a big mass start also helps you avoid getting caught in "traffic", which can really bog you down.
My father was a world-class competitive swimmer and is a Deaf man. His stories about needing to rely on a visual cue when his hearing competitors benefited from the pistol sound were always fun -- as is the joy on his face when he narrates that he always beat them anyways.
Sprinters, for whom small margins make the biggest difference, are most often not looking at the starter. Granted, could be because they don't have to because someone is firing a .32 caliber blank nearby, but that horse has left the barn for now.
I don't think the competition really is: who's the fastest in a 216km race? Rather: who's strong enough to endure a 200km tour, and then still have the energy for a 16km race? I say this half jokingly only.
I was in a conversation with some professional runners. A hobbyist in the same club asked, "when does it stop hurting?" They laughed and said, "It never stops. It's about how much you can make the other guy hurt."
Cycling races are much the same with a team dynamic included. It's a matter of choosing between setting a pace that a sprint finisher can't follow over a long period, or sheltering a sprinter from the wind so he can put in maximal effort at the end of the race. There are all sorts of variations based on strength of team, weather, terrain, luck, politics between teams, race goals, etc...
At the elite level of endurance sports everyone is in excellent condition and has optimal genetics. What really makes a winner is the ability to suffer.
That's the beauty of cycling isn't it? Sometimes the race-winning move is decided in a team car 150km from the line, and the next day it comes down to millimeters. This unpredictability is what keeps most viewers hooked to their TV sets for 6 hours on big race days.
Sometimes, as in when it happens, people might still be talking about it decades later (I'm only slightly exaggerating)
But all spectator sports seem to gain much their appeal from the imperfections that make them special. In road cycling, it's the imbalance of many hours of what computer gamers would call mostly cooperative PvE serving as a buildup for the few seconds of the finish (unless it's a solo, which is super attractive for the audience because it's rare, but would be rather boring if it wasn't).
This is really a team sport. There is a lot of strategy that goes into aligning the proper resources to win the race - From controlling the field, pulling in breakaways, supporting your teammates through mechanicals and still having the energy to finish out the final sprint. I would suggest catching the 30min breakdowns of the race on NBC Sports and the Latern Rouge on Youtube to better understand the race in a compressed format.
I occasionally see him around town here in Bend, which is kind of cool. His was... a difficult era in pro cycling. But putting that aside, his analysis of tactics is good, I think, and of interest for those looking to learn more about how a team runs things.
He's saying "it's not a 200km race, it's a 199km 'warmup' followed by a 1km sprint", so yes, it does change the perspective on how to judge how tight a race is
Many or most of the competitors would disagree it's not a race until KM 199. Only in boring flat races where the pack stays all together and there are no serious breakaways is that true.
I know, but for someone who wonders how a 200+km race can be decided at photo-finish it would maybe be more intuitive to split the race into "regions", with a sprint at the end between those in the lead. And that sprint is usually very similar to what a normal sprint stage would look like. I can see the point of asking "is it really necessary to separate them if they've been pretty much equal for the whole time?", but to me at least it does improve the experience of watching the race unfold on a few levels. It's supposed to be a competition, after all.
I know next to nothing about competitive cycling (I'm a commuter and occasional touring cyclist) but would it be accurate to say it's a strategy game for something like 180 km interspersed with 20 km total of racing?
Regarding the swimming issue, there is no underwater photo at the website which you linked, but one can google it, and it clearly shows that Phelps came in second. Arguments were made by Omega that the finish pad did not register Cavic's press on time since the force used was not enough.
Moral of the story is that human error (be that of a mechanical nature) will always exist, but more care should be given in competitive sports.
If you do not have the means to decide the winner, call it a tie, but if you do, even at the cost of a 350,000 photo/sec camera, then do it, but by all means do it correctly, because it might cost someone a gold medal at the Olympic games, and for the sake of people who put their life into competitive sports, this should not happen.
Apart from Omega's and FINA's statements that Cavic touched first, but Phelps was the first to trigger the mechanism with enough force, you can find the photos here
> 216.75km long race by someone who (possibly) won by 0.016 seconds
In cycling races that are not time trials it is disadvantaged to be in the lead until the last 0.016 seconds. The peleton in the video was quickly catching up to the three lead riders not because they were tired but rather because they were fighting to be in third position. It is just as much like a strategic game of chess as an endurance sport. Because of this, the game only works if a contender can win by a hair's length.
To me at least the length of the race just makes the situation less likely to occur. The problem is still in play for a 4 km pursuit or in theory the transcontinental race (though the likelihood of a sprint finish is near 0).
In general I think in sport we should use replay tech to eliminate errors that human judges can make, not improve accuracy beyond what was possible for them to see (because fundamentally these are philosophically vague). And then just have rules for ties that are good for the sport: ties go to the runner in baseball, offsides go to the attacking player in soccer (I believe the dutch do something like this by using thicker lines for their VAR?), etc.
But with cycling the whole game is decided by the finish, so I think that makes a bit harder to come up with a satisfying approach.
I was curious what the actual rules are about calling ties. Apparently if there's no photo finish tech and the sprint between 2 riders can't be decided its called a "dead heat":
> if the finish takes place on a road, the two riders will race against one another over a distance of 1000 m, from a standing start
Which sounds awesome to me. If it's a group of 3 or more they are just declared 'equals'.
The rules for ties with photo finish tech (basically all pro races afaik) is kind of weird? All I could find was:
> If, after all technical means available have been exhausted, it is still not possible to separate riders for one of the first three places at the world championships or Olympic Games, these riders shall each be awarded the placing in question. No award shall be made for the following placing, or, where there is a three-way tie, for the following two placings
- Rule 2.3.043 in the UCI Road Race rulebook
Not clear what that means for races like Amstel...
I agree with questioning the sanity ... There are likely all sorts of advantages and disadvantages that might exist at this level of granularity. For example who is on the inside at the start of the first curve of the race? Are the start and finish lines in exactly the same orientation (direction) and (as somebody else mentions) is everybody at the same distance from the starting gun? Speed of sound is finite. Call it a tie!
I think this is the key. The strategy that makes you most likely to beat your personal best, isn't the same as the strategy that makes you most likely to win the race. Races this close don't mean that the athletes were incredibly exactly matched, but that their racing strategies kept them close to each other.
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
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
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.)
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.
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.
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.
> 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?
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.
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.
As a child I was taught that sport should be "sportsmanlike". Perhaps in a situation like this, the real solution should be "I say, it's a draw, well done chaps, you have both proved to be at the top of your field! How remarkable that the result is so close that our best technology cannot even distinguish between the two of you. Well done everyone, what a great race, now let's all go to the pub and celebrate."
This happens in swimming because of the tolerance of making an olympic spec pool. A good swimmer goes a bit over 2mm every 0.001s. The pools have 3cm tolerance meaning the lanes are not the exact same length (it would be crazy expensive to make pools to smaller tolerances)
So to solve this they just don't measure beyond hundreds (no human can swim fast enough that the distance they travel within 0.01s could make a difference). And thus can not use photo finish either as again the lanes are not guaranteed to be the same length.
edit: In other sports like running it is easy to have accurate track length as you just paint the lines after building the track so you can have it as accurate as you want (+photo finish). In swimming it just does not work like that.
> This happens in swimming because of the tolerance of making an olympic spec pool. A good swimmer goes a bit over 2mm every 0.001s. The pools have 3cm tolerance meaning the lanes are not the exact same length (it would be crazy expensive to make pools to smaller tolerances).
It would be crazy expensive to make the pools to such a small tolerance, perhaps, but it is not the length of the pool that actually counts, is it? It is the distance to the touch pad that counts.
Would it be crazy expensive to make the touch pad mounting system adjustable so that the position of each lane's pad could be adjusted to millimeter or even sub-millimeter tolerances?
Main problem is old pools that don't have space for this (would make the pool under length). In general the same rules are used in all levels of competition. The only difference at the moment is minimum pool depth for world championships and olympics which is a bit deeper.
But yes in general new competition pools are built to be slightly larger than 50m and you just adjust the pads at the ends.
You could equalize the length of the lanes, but there are water currents that give different lanes "headwinds" or "tailwinds". These are caused by the pumps, wave action, and thermal convection.
Swimming is worse than that as the inner lanes have inherent advantage of less water drag as the waves bounce off the walls. Of course inner lanes are seeded with the fastest timings from the previous heat.
Exactly- in a few days earlier, Mahe Drysdale of New Zealand won gold in the men's single sculls after being maybe a centimetre ahead of Damir Martin of Croatia at the line:
That still doesn’t guarantee that the winner was the fastest.
Let’s say real times were 58.994999 and 58.995000 seconds. The first gets registered as 58.99, the second as 59.00. Actual difference is a millionth of a second, or, at 2 meters a second, 2μm.
I think they do this in swimming more because swimmers, certainly at shorter distances, more race themselves than their competitors. That’s a huge difference with road cycling, where typically the front riders in a sprint could get over the finish earlier, if they wanted to, but don’t want to do that, as, if they did that, their competition would tail them up to the last few meters and then jump over them.
Rowing is somewhat of a middle ground. They do use finish photos, even though there’s the same. “Tracks aren’t guaranteed to be the same length” problem as in swimming.
I don’t understand why you think it’s easy to have accurate track length in running. Temperature may affect track length. A lot more importantly, I don’t think it’s even doable in events where runners all start in their own track but are allowed to move to the inner track after x meters. But again, it’s less important there because runners race against each other there more than in short swim races.
Rowing alignment is slightly different from swimming alignment.
In swimming, the start and finish are both fixed physical objects that the swimmer must touch (though in all events except backstroke, the start is a bit weird because it's outside the pool).
In rowing, the finish line is an imaginary line much like cycling or running. While at the Olympics there are 'clogs' to hold the bows of the boats which drop down at the start:
a race official is always required to certify that the bows are aligned, which is why the gates are transparent (and the system includes video cameras to help this official).
> “Tracks aren’t guaranteed to be the same length” problem as in swimming.
In rowing you row between 2 imaginary lines. You don't even have to get the distance of these lines perfectly just make sure they are both in the same direction and neither boat gets the advantage.
With swimming you have to build a 50m long and quite wide concrete structure that has straight angles at all 4 corners and has perfectly straight walls. This is actually much harder to do then it sounds.
We could do it in swimming by building the pools a few cm longer, and then having adjustable touchplates to give the precise distance for each lane. :)
This is actually how it is done for new pools. They overbuild them by a couple cm and then adjust the touchplates. But the rules should work for the 50y old pools too.
> You don't even have to get the distance of these lines perfectly just make sure they are both in the same direction and neither boat gets the advantage.
Nitpick: that is not correct. If the shape of the course is a parallellogram, the shortest course between the short sides is perpendicular to those sides. Teams in some of the lanes my be able to pick such a course. For example:
A crew starting in the AB lane can row to D instead. That’s legal, if they don’t hinder other crews. A crew starting at C doesn’t have the option to row a shorter course.
It is very unlikely they won’t hinder other crews if they cross all lanes, but they might just cross lanes of a few much slower boats.
That’s all theoretical, though. The net gain on a normal course would be very, very small, and buoys will typically hinder crews that would try this so much that it wouldn’t be worth it, to start with.
Also, for the true nitpicker, “the right direction” can be difficult. Drawing equidistant lines on a globe isn’t trivial (I don’t think the effect will be large for a 2km course on earth, though)
>Let’s say real times were 58.994999 and 58.995000 seconds.
How do you achieve a million frames per second? Even analog input (like touching - which would be capacitive [hence more tolerances]) will have a very hard time registering that, just based on cable and PCB traces length, temperature differences (which affect silicon and resistance in general). 7 digit precision is a non-trivial task for non-controlled environment. For example 8.5 digit voltmeters take one 1 minute for a single measurement and they have to have extremely good temperature controls.
Then for the microsecond precision you have to consider the speed of sound just to propagate to participants to hear the gun.
They’re not hypothesizing a measurement device recording those times and then rounding. They’re just setting up a “let’s take as a given that this is what really happened in the world” and asking what errors our processes could do if we do a series of imprecise measurements and then compare those measurements.
Side note: my HP 3458A can do a small handful of 8.5 digit DCV measurements per second.
>my HP 3458A can do a small handful of 8.5 digit DCV measurements per second.
I thought they had like 100k samples a second. Is it really sufficient for 8.5 precision?
Edit: perhaps measurement should be confined only to relative finish between the participants, e.g. finish within 1ms should be considered the same (regardless if they fall in the same hundreds of a second bucket)
I don’t keep mine in cal (or even powered up all the time), so I can’t claim full volt-nut status here, but my understanding is the 100K/sec 4.5 digit measurement rate is limited by communications not by sampling rate. (The 5.5 digit rate is 50K/sec, implying the 4.5 digit rate limit is not in the measurement but more likely in the GPIB.)
On thing I know with perfect precision: HP/Keysight knows more than me about this. :)
Well, they could have everyone swim one after another in the same lane. It's not like there's much interaction between racers, as there is eg in a boxing match.
(Of course, this would totally ruin the sport for spectators.
Following this logic, for any sport with no interaction, everyone could just stay home and run around their own track whenever they feel like and just send in their times to a central record keeper.)
Having a competitor next to you provides a stronger absolute result. It's believed to be a standard natural selection/evolution effect. Even pain tolerances increase.
Also conditions change over time. Indoor pools are much less affected than e.g. a ski run in inclement weather or ski flying where competitions are basically lotteries in who gets a favorable gust, but subtle changes in e.g. air oxygen content could easily cause performance differences in the range we are talking about here.
>ski flying where competitions are basically lotteries in who gets a favorable gust
That has always bothered me that there are some calculations/arbitrary numbers based on the wind... to a point the length of the ramp gets adjusted. I recall when the V shape was introduced, initially it was shunned by the judges for bad style (negative points), regardless it was obviously aerodynamically better. However, swimming would also be affected as the water temperature won't be constant either.
I agree that sport should be sportsmanlike, but there is also an entertainment factor. These pro cyclists are public figures, paid by teams funded by corporate sponsors, cyclists have public rivalries and journalists pour fuel on the fire. Events from one race carry over to the next. There is lots of drama, there are rules which change over time (and usually lag a few years behind technology advances), race officials have to make decisions in the heat of the moment, usually very controversial decisions after rule changes. (look at the recent disqualifications due to the new anti-littering and dangerous-bike-position rules this year, and the bike-lane rules a few years ago)
On one side it's unfortunate that technological details and possibly human error make it hard or controversial to decide the winner for this race, on the other side this event has kept the cycling community talking for 3 weeks (even HN is talking about it right now). And most likely in the next few months or years we'll see some rule/regulation changes to handle these cases better. Just like in politics, something needs to happen first before action is taken. All the recent rule changes were triggered by dangerous crashes or other events.
And imho all of this combined makes pro-cycling one of the most exciting forms of entertainment to watch or follow.
A little side note: Many amateur races don't have photo finish equipment. In my race days sometimes not even a camera, and 3 race officials would stand on a little platform above the finish line with voice recorders just calling out jersey numbers and then get together in a room for 20 minutes to compare recordings and compile the final result. Draws were much more common back then.
edit: all of the previous races and media coverage and drama and the first 250k in this race have led to this super exciting final 1k that is ultimately decided by millimeters. To me that is beautiful.
I don't see how declaring this race a draw would deter from the excitement or from the entertainment value. If anything, it would add to it, since this is such a rare occurrence.
Agreed, my response was not meant as a judgement on whether a draw would be a better or worse conclusion. I was trying to highlight the broader context around the events and their outcome.
In this case it wasn't immediately clear who won and the officials had to make a call under pressure with millions of people waiting. They called Van Aert as the winner based on the imperfect data they had. Was it the right call? Maybe, maybe not. In an alternate timeline they might have called Pidcock, or a draw, or a redo of the last 1km.
The takeaway is that this rare occurrence happened and sparked lots of discussion, which hopefully leads to technological and/or regulation changes to could handle these occurrences better in the future. I would call that progress.
> A little side note: Many amateur races don't have photo finish equipment. In my race days sometimes not even a camera, and 3 race officials would stand on a little platform above the finish line with voice recorders just calling out jersey numbers and then get together in a room for 20 minutes to compare recordings and compile the final result. Draws were much more common back then.
Interestingly, technology makes this trivial these days:
Pop a cheap Android phone on a tripod, and with the right software (or even just taking a video), you have a decent approximation of photo finish equipment.
(I say 'trivial', because a smartphones with the required capabilities are basically free, if you take an old, used one.)
Yes indeed. And I have to admit that my race days are more than 10 years ago before smartphones were commonplace. The fancy organizers had camcorders for this purpose, others audio recorders and some others just pen and paper.
About 15 years ago as a teenager I was at a nerdcamp where amongst other things we did lots of physics experiments.
Eg measure how fast bubbles rise in honey at various temperatures to calculate its viscosity. Or: drop various big blobs of water from a height and analyze what happens. Or, figure out at what windspeed candles blow out.
Relatively simple things, but not usually covered in high school physics classes.
Anyway, it was amazing how many experiments became so much more feasible than even a few years prior, because cheap digital cameras were available.
Oh, this also reminds of how ufo and Loch Ness and Yeti sightings have become so much rarer these days, because people demand proof.
Transponders are very common in club level racing now, and the accuracy available is good enough for the grassroots level of competition in pretty much every discipline (except, possibly, track sprint).
Still, I think there will always be a place for a stone-faced commissaire with a clipboard, freezing their ass off in the finish-line rain, watching the bunch draw near.
I worked in this field, posted elsewhere on this page about working photo finish at Amstel Gold in the past. Around that time we also experimented with transponders, maybe even at an Amstel Gold Race, else at the Netherlands Tour (or Eneco Tour). The accuracy, at high speed, of transponders, didn't quite solve for the close finishes. A bigger problem were the practical issues: transponders gone missing in crashes, bike switches, transponders being mounted in the wrong place (enough to matter). It's not a substitute for photo finish. It is, though, a great substitute for reading bib numbers off of a poorly lighted photo finish. They're complementary.
Would you be so kind to provide a short high level summary on how the transponder tech works?
I always assumed the transponders were mostly used for GC timekeeping in multi-day stage races and maybe help automate the initial results shown on TV post-finish.
The live telemetry (wattage, speed, heartrate) we've seen in some races the last few years are also very interesting. But that's probably a different tech stack from transponders used for timekeeping.
Most transponders in competitive sports, and certainly most pro cycling events, will be an active type, i.e. they include their own power source. The timing mats are relatively simple EM trigger loops that induce the transponder to wake up, yelp its identity (typically on UHF frequencies) to the trackside receivers that will actually record the passing time, then go back to sleep. Such systems generally remain reliable even in large passing groups. Commercial prices vary, but the trackside equipment (mat, decoder, laptop, software) typically costs a few thousand dollars, and the transponders ~$100 each with a lifespan of 5 years.
Some manufacturers claim millisecond accuracy, which is plenty for (say) counting laps in cyclo-cross, or for timing many BMX events; but they're not enough to distinguish the places in a >70km/h field sprint for the finish line.
Some mass participation events like public marathons may use low-cost/disposable passive transponders e.g. ones embedded in the bib number; these are more like a typical RFID chip, having a longer (and rather jittery) wake-up time, in part because they draw power from the mat itself, and a much lower transmission energy. They're more easily disrupted by environmental conditions, or when passing in large groups, or even by sweat & skin contact.
Telemetry from onboard bike computers and sensors is indeed a completely separate stack, and can be anything from a bluetooth relay by phone app over cellular, to a dedicated vendor-specific box with its own SIM card and a short-range radio to signal the team car. The onboard sensors are generally using ANT or BTLE to talk to the head unit aka "bike computer" that aggregates, records, displays, and relays the data. Speed may be calculated by GPS/GLONASS/etc, or sensed by wheel rotations e.g. using a spoke magnet or even hub-based rate ticker, in which case the necessary measure of precise wheel diameter may still be calibrated by the head unit using GPS. Power is not measured directly but inferred e.g. by integrating a dynamometer within the crankarm to compute power from strain & cadence. Some units also capture barometric pressure to estimate altitude, and this may be considered more accurate than GPS right up until you ride through a pressure front and it goes bananas. Some bicycles e.g. those with electronic/wireless shifting may also report their current chainring & sprocket selection, and finally you can overlay all this excruciating near-real-time detail onto the Gopro video feed from your handlebars/seatpost cameras and livestream it over cellular networks and thence to the world-wide peanut gallery.
To sum up, there's an awful lot of 2.4GHz activity going on in the pro peloton, and I hereby deny ever having paired a second bike computer with the HR strap and power meter of my nemesis in order to know when the bastard was too tired to follow my attack, no sir
sportsmanlike is when you lose by a hair, you congratulate the winner and don't feel too bad about it. What you're suggesting is a test of competence, not a race.
Or have a tiebreaker. It would be testing something slightly different (more endurance) than what they'd train for, but there would likely be an easier call the second time, statistically if nothing else.
One other possibility is that the camera was positioned in the correct place, but was angled slightly to the left with respect to the line, rather than being exactly parallel with the line. I don't know how they set up these cameras to ensure they're parallel with the line, but this seems at least as likely as aligning the camera parallel but in the wrong place. I'm not sure how you'd be able to tell from the images though, but it would make a much bigger difference to the actual result.
Interviewer: Is it possible that the photo was taken a wee bit before the black line?
Photo operator: I doubt it... I doubt it because we really took a good look if it's all been set up correctly.
I operated the photo finish at the Amstel Gold Race for a few years, in the early 2000s, as well as at many other races in the Netherlands, Belgium and Germany. We weren't a constant presence at that event, as the association liked it better to either bring in their own people, or rather full-time professionals like the company that does La Tour de France. My boss at that time later sold his timing business to the guy who operated the photo finish this year (the one being interviewed).
While all folks involved here take great pride in their work, the alignment of the camera just never got the attention it clearly deserved. No one ever did the math and they just assumed the difference wasn't significant. Also, people just liked it better to align the camera on the white part of the finish line, since it greatly improves the contrast of the capture. I am sure the equipment has improved, but for a long time, the only thing you were concerned about was contrast, a sudden change in weather (lighting) was known to, at times, render the entire operation useless. Particularly since we were a small operation with only one (photo-finish) camera. Plenty of times I had to climb up ladders and vans to make eleventh hour adjustments to the equipment, with the contestants already in sight.
I feel super bad for the guy. To his defense, the responsibility lies with the UCI officials. To their defense, they do not check up on details like this. Until now, that is.
I remember at least one other time where the broadcast camera (they also tend to have one exactly on the finish line) seemed in disagreement with our "official" photo finish results. That time, a simple shrug did the trick: "hey, photo finish, you know".
Hi Sverhagen, thanks for such an interesting insight. I do feel bad for the guy too, tough gig to have the cycling world analysing you just trying to do your job - especially when there are so many variables he'd have to account for.
And 99.9% of the time it wouldn't make a difference, he's just very unlucky that this time it may have (or may not have, but either way it's brought a focus to the camera position).
I see you're now a software engineer. How did you end up moving from photo-finish operations to software?
The photo finish thing was part of the family business of my neighbors, where I grew up. I did it as a side gig to going to school/college, where I studied electronics, then software engineering. The software I wrote during all that, for the results processing of these cycling events, and of which I sold a few copies around the world, was the reference to get me my first programming (day) job: https://www.totaalsoftware.com/products/stagerace
Edit: looks like the Amstel Gold guy is still using a copy of my software, he has it on his website, neat!
Great research! But van Aart is the right winner. The photo finish picture is stated s the official result. Every athlete knows that, despite alignment errors of the equipment.
Very interesting write up. Given the price of photo-finish cameras, I wonder if there’s a solution with slow motion cameras which could provide some margin for error as well as a better spectacle for viewers?
Slow mo camera's produce too much data to run continuously. These camera's are used to determine the entire finishing order. They need to be running constantly.
Well, there are slow mo cameras that go well over the 2,000 or 3,500 FPS mentioned in the article. If oriented the same way, they would provide a strict superset of the information of a strip photography camera, since you could recover the strip photo by just extracting one column from successive frames of the video. It doesn’t seem like the price is even particularly different. I’m not an expert, though, just judging based on Google results. Maybe there is some obstacle I’m not thinking of.
Bro, literally all of it. What a great piece. Down to guesstimating the tire sizes, tracking down the line width, accounting for road camber, etc. Really enjoyed this.
I think the distortion of the video-finish camera should be considered when making these estimates. There's quite a lot of it happening in the shot. Narrowing down the specific camera intrinsic parameters may be a challenge. The EXIF data of the original footage might be fruitful.
It might also be possible to undistort using some assumptions on colinear points in the video (i.e., the finish line and signs should have straight lines).
I see on issue with this analysis, the use of the TV camera picture a the reference datum. However, that camera has likely many more issues than the finish line camera. While it looks like the red advertisement is aligned with the camera from that image I don't think this is necessarily the case. It depends on the height of the camera, the angle and possible distortions.
While I've only inCluded that single image in my analysis, having a look at the video of the full race where they pass the finish line many times it is clear the red sign is aligned with the finish line.
That's not what I mean. You assume that the TV camera is perfectly aligned with the finish line, because that's how you determine the position of the advertisement relative to the line. However, if the TV camera is offset from the finish line, depending on height/focal length/orientation and aberrations of the camera, the line would appear offset relative to the advertisement. Therefore you determine the wrong position of the line compared to the advertisement. That would always be the same for the full video of the race, so watching the race will not change this.
I'm deeply familiar with FAT andamera systems in track and field. I often wonder if they are a relic but in track the timing can be trickier due to location of the torso. Wouldn't a transponder on a each headtube in the race potentially work better? They could talk communicate with sensors all around and in the finish line.
I've wondered what you'd get if you put a "photo finish" camera on the side of a car. The perspective would be out of whack (e.g. a 10 m long object 20 m away looks the same length as a 10 m long object 2000 m away) but it would be a much cheaper sensor than what Google uses for street view.
I would be excited to see someone try that, since it would produce an image that is effectively a parallel viewpoint in one axis and a pinhole camera in the other. I doubt it would be cheaper than Google's street view cameras, though, since standard cameras and lenses are commodity equipment.
An ordinary camera would work if mounted rigidly to the car, you could shoot a video and then take out the center line after the fact. 55 miles/hour is about 80 ft/sec so the horizontal resolution is a little bit more than a foot with a 60 fps video, you could make out houses but not read house numbers.
I think most webcams have a low-level interface that would let you read out part of the display without reading the rest so getting a better frame rate could be done at low cost too.
I think I'm going to try taking pictures of clouds first...
There is a whole family of "algorithms" for putting together a sequence of images, for instance, if a camera at the side of the road took a slice of pixels at a 45 degree angle you would get a picture of any car (esp license plate) or person who went by, but you would not get a video showing what they did in any detail.
Panorama mode is trying to make something that looks like "a good image", you would want to keep "tack sharp" if the source material is "tack sharp."
If you have 1000s of photographs of a scene you can reference them to each other and build a 3-d model and then synthesize many images you might want to see but it won't be "tack sharp" it will be a video game.
I believe that is essentially what airborne surveillance cameras (used to) do. They used a line-aperture moving film setup. I don’t know how they accounted for the velocity of the aircraft.
In the case of the car I have the following options:
1. from the diagnostics port under the steering wheel I can get the speed of the car from the car's electronic control unit
2. a hiking or computer GPS could be used, probably anything that isn't marketed as a car GPS is OK, the car GPS probably makes awful tracks because they don't want you asking questions like "how much faster can I do the quarter mile if I wrap the exhaust pipe, load this software patch into the the ECU and, take out the passenger and rear seats, radio, glove box cover, wiper blades, and bumpers?"
3. You could add an accelerometer and use a Kalman filter to combine that with other information sources to estimate vehicle position. Consumer accelerometers aren't that good, you are taking $2500 or so for one that car racers use.
I analyzed it to death and came to the conclusion that 1 will be good enough for a project which is the reverse of the camera being described: that is, put a neopixel strip on the side of my car and generate i think high quality images at night if someone happens to be focused at about the right distance but NOT tracking the vehicle.
This was a really good writeup. I thought for sure there would be no way to salvage it after you mentioned how they messed up but then you talked about using the curvature of the spokes and the width of the wheels in the photo finish to figure out how the wheels were spinning and it blew my mind.
Awesome research. I have similar quibbles about photo finish cameras in sports and written about them [0].
There are usually tons of rules in sport about the equipment, the Race course etc . but how exactly the finish needs to be set up is often vague. In this case it was an alignment issue at fault. But the next problem is the arbitrary resolution finish cameras work at. How wide is the pixel slot? This can be the difference between calling a tie or a small margin.
Yeah the UCI rules for photo finish seem very vague, and also don't seem enforced. I haven't used a photo-finish camera myself but it seems to me the tech behind these is quite dated, the shots from the 1960s are almost as good except for the frame rate and number of pixels. Perhaps there is a better way.
In addition to the technological factors here (optics), think about the biological timing of the riders. Wout van Aert picked the right time to accelerate and win -- from the front! He won even with a significant aerodynamic disadvantage.
Wout!!!
> According to UCI regulations, the photo finish verdict is final, because the finish line is what the photo finish says it is.
Nice write-up.
Instead of these photo-finish cameras, would a piezoelectric sensor strip on the road (plus perhaps a regular camera) be a better solution to judge the winner in such cases?
I was thinking about this problem too, and realized that the photo-finish also provides placings for all the other contestants. Some other type of sensor might be able to more accurately place who was first, but could struggle greatly differentiating the pack of contestants behind them.
Any reason why the single pixel wide capture approach is used? Seems very prone to operator setup error. It has to be exact at the finish line and exactly parallel to the line and there's no easy way of knowing if it was setup correctly after the face.
Wouldn't it be better to set up multiple high speed cameras at different angles
High speed cameras produce significantly more output data, which makes them more expensive I'd have to imagine.
Not to mention a high speed camera misaligned on the finish is going to produce similarly skewed results. Anything not happening exactly along the optical axis is getting distorted by perspective. At least a line camera doesn't pretend to have accurate information on anything except the line you aim it at.
Or you could just change the rules and declare that the finish line is wherever the camera is pointed at and what's painted on the ground is just a rough indicator of where the finish line actually is.
It's been maybe fifteen years since I read up on those rules, I assume some things changed, but there weren't much details on this then. Do you have some relevant quotes?
This is also what I thought when reading the rules. It does say the race if you can't tell by the eye is decided by the photo-finish. But from what I read at no point does it say, the finish is where the photo-finish points and the paint is just arbitrary.
https://i.imgur.com/g78YNla.png
Each pixel column is a specific point in time. I added a few landmarks: when the front of the wheel passes the camera view, when the axis of the wheel passes the camera view, and when the end of the wheel passes the camera view. Blue for the top biker (Wout) and green for the bottom biker (Tom).
Every single event happened earlier for Wout. Both wheels are the same diameter. Therefore, the entire period where the wheel intersected the camera view, Wout's wheel was ahead. Including the exact period where Wout passed the actual finish line.
If Tom would have passed Wout, you would expect that the bottom wheel would be more "squeezed" such that the end of Tom's wheel would have passed the camera line earlier than Wout. Same for the other landmark (centre of wheel).
You can add more landmarks if you want (e.g. approximate when the wheel passes for 25% and for 75%), but it should be clear by pure margin that Wout had the lead for the whole duration where the front wheels passed the camera view. Pretty much all the computation in this article was unnecessary.
Amstel gold made the good call, though I agree that it was probably more luck.