The story of the guy that used physics to fight a traffic ticket is super popular right now. I am not a big fan of reporting news - it's just not what I do. Instead, let me see what I can do with this problem.
First, what is the deal? Basically, the guy (Dmitri Krioukov) was issued a traffic ticket for failing to stop at a stop sign. His defense was that he stopped with a high acceleration AND the view of his stop was partially blocked another car. On top of this, he claimed that the law enforcement officer was looking at his angular speed and not his actual speed. Since the apparent angular speed depends on the distance to the observer, as he approached the stop sign a slowing down car doesn't look that much different from a constant speed car. This plot from his arXiv paper titled: The Proof of Innocence.
From this you can see that the angular speed of a constant velocity car (red line) and a stopping and starting car (blue) line are similar.
My Analysis
What would I add? How about we model this motion in VPython? Should be pretty easy, right? From the paper, I have the following values:
- Starting velocity of 10 m/s.
- Car length (Toyota Yaris) of 3.81 meters.
- Blocking car length of about 4.8 meters.
- Yaris acceleration of either 10, 3, or 1 m/s2.
- Observer distance of 10 meters.
Here is my first animation. This shows the case of the Yaris with an acceleration of +/- 10 m/s2. For a comparison, I put a constant speed car (speed of 8 m/s) above the stopping Yaris.
What if I change the acceleration of the car to just 3 m/s2? Here is the same plot but with a different acceleration.
For the lower acceleration, the difference between constant speed and stop-start seems to be more obvious. Ok, what if I add the "view-blocking" car? Here is an animation showing three cases in a row. Case 1: blocking car with a constant speed Yaris that doesn't stop. Case 2: blocking car with a stopping Yaris with an acceleration of 3 m/s2. Case 3: blocking car with Yaris stopping with 10 m/s2 acceleration.
Oh, before I forget - the line perpendicular to the road is just there to make sure the "camera" is in the right location. That line is 10 meters long. But what does this video say about the whole angular speed argument? Well, if I was hired to prosecute this guy I would point out that stopping with an acceleration of 10 m/s2 could be mistaken for not stopping at all. However, stopping with a more reasonable acceleration of 3 m/s2 doesn't look like this.
Is This Even a Realistic Acceleration?
Andrew Morrison (@achmorrison) makes a great point about this whole "physicist dominates the law with math" story. First, the story was posted on April 1. You know you should never post real stuff on April 1, right? The other big point is the unrealistic value of acceleration. Fine, maybe a car could stop with an acceleration of 10 m/s2 but a Yaris can not speed up with that acceleration. A Yaris can maybe have an acceleration of 3 m/s2 (based on 0-60 mph in 9 seconds). Finally, Andrew points out that the paper shows the angular speed for constant acceleration 10 seconds before and after the stop. Accelerating for 10 seconds means that the car would get up to 100 m/s - that is crazy.
Is the paper fake? I would say, it is not really fake. It is a paper. It presents an argument. Was this argument used to actually get out of a ticket? Who knows? I imagine someone could track down and see if he actually got a ticket. I don't have any problem believing that Krioukov presented this as a defense. It seems like it could at the very least intimidate the court with maths.
After writing this (but obviously before posting it), Andrew put together some more thoughts on the stopping car problem:
In this second post, Andrew first looks at angular velocity plots for more realistic cases of acceleration. He also brings up a good point, should someone have investigated this story a little bit more before it became so popular? My feeling is that this is just the way things happen on the internet.
First, Andrew states there was no fact-checking. I agree that it seems no one bothered to even see if the cost of failing to stop is what was claimed in the original story. Who should do the fact checking on something like that? Perhaps it is no one's responsibility. I certainly didn't do it because I am not really a journalist. Instead of reporting what happened, I like analysis what happened or what could happen. Other bloggers have other views of what they do. Some of them do try to report the story as a journalist would, but this is the great thing about blogs - everyone can do their own thing.
Now, what about the story? Is this good for science? I don't think it is bad. Like I said, even if it is fake it could be used as a plausible defense in the court of law. It does encourage people to think about cars in a different (physics-like) point of view.
Homepage photo: Nomadic Lass/Flickr
