Under a Gibbous Moon

At least in Ohio. James Barnes received a ticket for ticket for going 84 in a 65 zone along interstate 75. His speed was not acquired by either laser or radar but by calculations made by an Ohio State Highway Patrol airplane (yes, there’s a great use of taxpayer money). In short:

The pilot testified that in Barnes’ case, on the day in question, he first observed a white vehicle, later determined to be driven by Barnes, halfway through the first marked quarter-mile section. As this vehicle entered the second quarter-mile section, meaning the moment the front bumper/grill portion of the white vehicle met the second white epoxy mat, he began timing the vehicle with his two stop watches. At the end of the second section, the pilot noted that 10.68 seconds had elapsed, giving him a speed of 84 miles per hour. He also timed the vehicle through the third and fourth quarters, ascertaining the elapsed time at 10.66 seconds and 11.61 seconds, respectively, giving him speeds of eighty-four miles per hour for the third quarter and seventy-seven miles per hour for the fourth quarter.

The pilot also claims there were no other white vehicles along that stretch of interstate at that time, a claim I find dubious, if not ludicrous.

Barnes, though, thought he was lucky because his employer tracked his whereabouts and speed via GPS, just to make sure that he was being a good boy. Barnes pulled the company logs which showed him going 50 mph. Unfortunately, since GPS is such a new and untested technology (first GPS satellite launched in 1978 and fully operational by 1995) the judge rejected this evidence.

Barnes testified that his speed was detected through his Verizon Wireless cellular phone. He testified that his employer utilizes a GPS program to detect the location and speed of its employees when traveling through their cellular phones and that this program actually sends alerts to his employer if one of its employees is speeding. As previously noted, he submitted downloaded documents regarding his speed and location when the troopers stopped him on March 17, 2009. These documents reflected a rate of speed of 50 miles per hour at the time the troopers purported that he was traveling at 84 miles per hour. However, Barnes did not have an independent recollection of his speed at that time. In addition, Barnes testified that the GPS provided the average of his speed over a two-minute time frame. In other words, the GPS did not give his specific speed at a specific time, but an average speed over two minutes.

The judges complaint is, that since Barnes GPS report didn’t give instantaneous speed, it doesn’t count. My favorite part of this is the judges lack of mathematics. Barnes GPS gave an average speed over a time period of two minutes (120 seconds). It is also given that, according to Barnes GPS, he never exceeded the posted speed limit, otherwise he would have been flagged by his employer.

According to the police airplane, we can account for 32.95 seconds of that time. Now we must assume that Barnes GPS speed covers at least part of the time that the ticket was issued for, otherwise it would have simply been thrown out for being irrelevant.

First we’ll look at a best case scenario for the defendant. This assumes that the 32.95 seconds that he was timed by the pilot fit within a full two minutes of his GPS average time. This leaves 87.05 seconds unaccounted for. The average sample time of the pilot is just a hair under 11 seconds giving us 11 roughly equal time samples.

The average speed for three time samples is 81.67 mph ( (84 + 84 +77) /3 ). Now the article says he was charged with 84 in a 65 but we’ll run with the average. The GPS states that in a 120 second period, Barnes averaged 50 mph.

Given 11 samples, a value of 550 must be obtained to average 50 ( SUM(data) / 11 = 50 therefore SUM(data) must equal 550). For the known time samples we have 84 + 84 + 77 = 245. Subtract 245 from 550 and you are left with 305. The SUM(unknown) must equal 305 in order to make a 50 mph average.

The fun part about this, is the higher we speed we make any of the given unknown points, the lower the rest must go to make up the average. The best possible solution, then, is to simply give the average of the remaining data points (305 / 9 = 33.89). So yes, in order for him to be going 81.67 mph for 32.95 seconds he would have to have been averaging 33.89 mph either before or after (or both) the sample period.

Next, for the worst case scenario. That is were only a single sample period falls within Barnes 120 second average. We’ll take the lowest, 77 mph for 11.61 seconds. Whether we round up to 12 time periods or down to 11 time periods, the difference is almost identical so I’ll round up since it gives Barnes as having a faster average.

12 time periods must equal 600 ( SUM(data) / 12 = 50). 600 – 77 = 523. Since we only had one sample this time, we  are left with 11 unknown points. Given that for each high data point another data point must be reduced to total to our remaining 523, we take the average and arrive at 523 / 11 = 47.55. So, once again, whether before, after, or both, Barnes was averaging 47.55 mph.

In the first scenario, for the pilot to have been correct, Barnes was going only 41.5% of the speed he was alleged to have been going out side of the sample period and 58.2% in the second scenario.

In either case, he apparently suddenly increased his speed rather radically increased his speed for a very brief period of time (32.95 seconds), was “clocked” by an aerial observer, and then returned to a slower speed.

Math calls bullshit.

Related (maybe) posts:

1. Woman crashes car while shaving privates
2. Blockbuster.com and the problems I’ve had
3. Police road rage
4. It just keeps getting worse
5. And no, Linux is still not ready for prime time