Buzz Blog

Physicist Uses Math to Beat Traffic Ticket

Tuesday, April 10, 2012

Here's a practical application for your physics education: using math to successfully beat a traffic ticket in court. Dmitri Krioukov, a physicist based at the University of California San Diego, did just that to avoid paying a fee for (purportedly) running a stop sign.

Krioukov not only proved his innocence, but he also posted a paper detailing his argument online on the arXiv server. The succinct abstract for his paper certainly distinguishes itself from other research papers:
"A way to fight your traffic tickets. The paper was awarded a special prize of $400 that the author did not have to pay to the state of California."

After thinking Krioukov ran through a stop sign, a nearby police officer pulled him over and issued him a citation. According to Krioukov's paper, however, three physical phenomena combined at just the right time and misled the officer.

When Krioukov drove toward the stop sign the police officer was approximating Krioukov's angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects.

Trains, for instance, appear to be moving very slowly when they are far away, but they speed past when they finally reach us. Despite these two different observations at different distances, the train maintains a roughly constant velocity throughout its trip.

In Krioukov's case, the police cruiser was situated about 100 feet away from a perpendicular intersection with a stop sign. Consequently, a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer's perspective.

Similarly, if a car approaches the stop sign with constant velocity but brakes quickly before reaching the sign, the angular velocity will rapidly increase before stopping momentarily. To illustrate this point, Krioukov created two graphs: one for the case of constant linear velocity through a stop sign (illegal) and another for a quick stop at the sign before accelerating back up to speed (legal).

If you look at the graph on the right, you'll notice three lines with different colors, and each line corresponds to a different deceleration at the stop sign. The blue line with the biggest spikes represents a 10 m/s^2 deceleration -- about the highest deceleration for the kind of car he was driving.

This line mimics what actually happened best according to Krioukov because he had a terrible cold that day, and one sneaky sneeze caused him to slam on the brakes hard as he approached the stop sign.

The crux of Krioukov's argument is that this rapid, legal deceleration can appear very similar to the case described in the graph on the left. But the left graph actually represents a car cruising through the stop sign at a constant velocity exceeding 20 miles per hour. So surely an officer would still be able to tell the difference, right?

Not when another car partially obstructs his view, according to Krioukov. When another car partially blocked the officer's view of Krioukov's car momentarily, the officer could have missed the brief yet crucial timing of his stop. At least, that's Krioukov's version of the case.

Either way, his argument appeared to work: "The judge was convinced, and the officer was convinced as well," Krioukov told PhysicsCentral.

This physical description swayed the judge, or maybe she was simply impressed by the sheer dedication Krioukov put into avoiding this ticket.

You can peruse the paper here if you want to devise your own plan to get out of traffic tickets. Leniency in court, however, is not nearly as reliable as mathematical proofs.

Now, Krioukov has a challenge for our readers: "I want to ask the readership to please find the flaw in the argument."

Mathematical figures courtesy Dmitri Krioukov. Top stop sign image courtesy Infrogmation via Wikimedia commons.

Posted by Hyperspace


Anonymous said...

No complicated physics involved. But a Yaris would have a hard time accelerating at the same rate that it could decelerate under maximum braking force. FWD, little economy cars are not known for acceleration. Also, from a practical standpoint, the stop indicated by the graph is not enough time for the human brain to observe the intersection and determine that it is safe to proceed. This is just one more flaw to add to the bag, not THE flaw, just one more.

Friday, April 10, 2015 at 9:26 PM

spsh said...

The field you are referring to has been tested to death. First off, Maxwell's equations are lorentz invariant to begin with. Each term was painstakingly constructed from experiment, all of which you can reproduce from scratch if you like. Once they are built, the model is intrinsically invariant under the Lorentz transform. The point is that reality told us this, it wasn't cooked into the equations.

Now applying this transform to relativity was indeed a theoretical jump. However, we have tested that formalism better than any other theory in history. That QED predicts the cross sections for electron scattering to something like 13 digits says that we have it right. Every conceivable test of this theory that's been performed has sided with it.

Every competent physist understood the origin of the lorentz transform in relativity. It isn't trickery, you apparently didn't pay attention in those classes you took to get your "MS.C in physics". It's a model built like all models. It's merit is entirely in it's ability to predict reality. How it was developed is besides the point, although the idea that there could be trickery in such development is beyond stupid, it illustrates a completely missunderstanding of both mathamatics, and physics. Frankly, science as well.

If you don't agree with the theory, that's your business. I disaggree with lots of theories. But I have evidence for it. That's how science works. If you want it to change, you provide evidence for it. We've provided evidence that special relativity and the quantum mechanics which now relies on it works excellently. We have 70 years of papers supporting this, including literally as much data as the web occupied just a few years ago. If you want to make a dent in it, you need to provide experimental proof otherwise. IF you did, we'd listen and adjust our theories. That's how science works.

Tuesday, September 24, 2013 at 1:40 PM

spsh said...

Yeah we do. We do it all the time. Myths about what physicists say are propagated by highschool teachers with too much zealotry for the field. Admirable, but pedantic and irrelevent. I'm more concerned with the way that the universe works. If someone adds a prefix 'de' to replace the 'a' to tell me the sign is negative compared to it's current velocity, fine by me.

Tuesday, September 24, 2013 at 1:28 PM

Anonymous said...

The story is the 10th, the paper is dated the 1st.

Tuesday, September 24, 2013 at 7:56 AM

Anonymous said...

This all would have been much easier if he just had a radar detector. They actually use physics, no papers or equations are required. He could have read some radar detector reviews to get information, rather that doing this.

Friday, September 6, 2013 at 9:17 PM

YS said...

Problem is there is no stopping time at the stop sign. From what I remember you are supposed to at least remain at the stop sign for about, 3 seconds? before you can accelerate again. There could also be another issue depending on how fast the other car blocked the view.

Thursday, August 15, 2013 at 3:26 PM

Derek China said...

Your "quick stop" is called a "rolling stop" and it's illegal

Friday, August 2, 2013 at 2:23 PM

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Wednesday, July 10, 2013 at 6:02 PM

Anonymous said...

i think he never stop, anyway good trick

Wednesday, January 2, 2013 at 11:25 AM

DeadParrot said...

It says April 10th not April 1st.

Friday, December 28, 2012 at 2:24 PM

Anonymous said...

To the Anonymous poster who repeatedly used the word
"paean" Please, look it up. I believe the word you're really reaching for is "peon". Your average citizen is not a "A song of praise or triumph." ;)

Tuesday, December 25, 2012 at 1:12 AM

Charles Ramsey said...

Not all parts of an automobile move at the same speed the top of the wheel moves at twice the speed. Radar detectors are exaggerating the speed of motor cycles which have exposed spokes. Traffic cameras detect cross sectional area motor cycles have to get closer to trip the stoplight this leads to more run red lights because the yellow light has a shorter cycle if no traffic is detected. Sensors in the roads detect metal motorcycles have to get closer to trip the sensor this also leads to more run red lights. Bicycles are generally unable to be detected by all three means this leads cyclist getting speeding tickets because the radar detected an automobile behind it or running red light tickets.

Monday, December 24, 2012 at 6:13 PM

Anonymous said...

This is fantastic!!

Monday, December 24, 2012 at 2:56 PM

Anonymous said...

There is a big hole in this argument. If the car that blocked the Officer's view zoomed through the intercection, without stopping, the Officer will still be able to see Dmitri waiting at the stop sign. On the other hand, if the other driver stopped, the Officer would have noticed Dmitri stopped. A stop at a STOP sign will take a minimum of 1 second, looking left and right before proceeding. A car traveling at 20 mph will travel past the STOP sign in a fraction of a second, still leaving enough time for the Officer to see Dmitri stopping at the STOP sign. The Judge was either confussed or impressed by the law breaker.

Monday, December 24, 2012 at 11:02 AM

A Bocelli, true event said...

Hey I beat a ticket like this also. I had a red light ticket.
I didnt run the light but the officer claimed I did.
I proved 2 things , 1 he could not see the light controlling my direction of travel to testify what color the light was.
2. he information was incorrect about the lane of travel and position of my vehicle. I big work truck.
Dont ever think a ticket means your guilty unless you know your guilty.

Monday, December 24, 2012 at 10:24 AM

Anonymous said...

As it is physically impossible to keep one's eyes open while sneezing, I suggest that he continued his deceleration right on through the stop sign... only to come to a stop after having passed, ever so slowly, through it.
His perception of events may be flawed, just as he suggests, the citation issuing officer's were.

Monday, December 24, 2012 at 9:30 AM

Alissa Banks said...

That's such an amazing way to get out of traffic tickets! I love this guy!

Monday, December 17, 2012 at 4:41 PM

Anonymous said...

I think I've been a passenger in a car with this exact situation 40 years ago. There is no question that a friend of mine made a quick full stop at stop sign, but was issued a citation for running the stop sign. There was an obstruction, and the officer's position was almost exactly as described.

Saturday, June 9, 2012 at 12:40 AM

Anonymous said...

Well, if correct expression is used instead of (8), where initial velocity is not missed, the resulting observed angular rate would never be misinterpreted ...

Saturday, May 5, 2012 at 3:11 AM

Nessanel said...

I believe that one flaw is as follows: police use Doppler radar to measure the speed of their targets. The Doppler shift is proportional to the dot product of the direction of propagation of the radar wave and the direction of travel. Therefore, if the police was perpendicular to the direction of travel, as is the case in the diagrams, then the Doppler shift will be zero and the police will not measure anything.

Tuesday, April 24, 2012 at 9:50 PM

Anonymous said...

I hereby nominate Dmitri Krioukov for the 2012 Ignobel prize in physics

Tuesday, April 24, 2012 at 4:51 PM

Anonymous said...

OK folks - take this as example of how the internet works. HP and many other sites have posted and reposted this story. Check out the link to the original paper - and pay attention to the publication date before you try to wrap your head around the physics. April 1st. Does that date mean anything to you ???? Yes - this was a gag... now picked up and repeated within the echo chamber of the internet. Yes, I do hold several physics degrees.. But really people - you should not need to check the math on this item to understand what's really happening!

Monday, April 23, 2012 at 3:58 AM

Anonymous said...

Date of publication in the UCSD campus newspaper... April 1.... Think about it !!!!!

Monday, April 23, 2012 at 3:55 AM

samhouch said...

Doesn't this presentation presume and require that car #2 (C2) ran the stop sign while blocking the view of car #1 (C1) which was allegedly stopping? Wouldn't the officer therefore have noticed the C2 vehicle as being the primary offender, esp. since it was closest to the officer and in plain view? Furthermore, wouldn't having the two vehicles side by side offer a comparison opportunity, i.e., if car # 2 blows through the stop sign, then car # 1 would appear to stop as it would be lagging behind car #2 (if indeed car#1 stopped). Similarly, if car #2 was directly witnessed to have stopped, then wouldn't that provide a comparitive to determine similar/different behavior of car #1 behind it? I can see this working if car #2 were turning right from the right lane of C1 and C2's shared street, and therefore blocked the view to C1 while failing to give a relative behavior to compare; especially if car #2 had to pause for an oncoming vehicle before completing his turn. But, I don't see it working of C#2 continued to parallel c#1, and thus offering a relative behavior to go compare.

Monday, April 23, 2012 at 2:26 AM

Anonymous said...

Just a correction to the price of the California ticket. The base fine for 21453 is $404, not $235; however, with fees and assessments, the total comes to $480.

Sunday, April 22, 2012 at 11:20 PM