The numbers don't add up

by Jesse 27. October 2008 23:21

A friend of mine got pulled over the other day, maybe a half mile behind me.  When I heard the officer gave him a ticket for 78mph, my first response was "no way in hell".  I'm good at math, so I decided to prove it with numbers.  Take notes, you can use this because its math.  Numbers don't lie (if you don't screw up).

Trig teaches us a couple useful things.  First, one of my favorite equations, A2 + B2 = C2 - this tells you the length of sides of a 90' triangle, C being the hypontenuse.  What does this give us?  Everything we need, IDDQD, I win.

When the officer was tagging people, he was outside the far RIGHT lane, not the usual left lane, being head-on with normal, would-be speeders -- this is a fault of the officer I intend to prove with simple math.  There's also a fundamental flaw in lasers - they ONLY measure the velocity of an object realitive to the device, a perfectly straight line (ok, maybe off by a degree or two, but thats neglegable) -- that's why most officers sit in the left side.  I'm going to first establish the area, and some measurements thanks in part to Live Maps.  These are estimates, but a lot safer than actually going out there and measuring Smile

5pm on I71 south bound on the north end is a bit of a mad-house and usually lasts until 6-6:30 (duh, normal rush hour).  People coming out of Polaris heading home, hitting 270/161/etc makes it a bit on the heavy side if you can't get out before 5.  I'd call it modertate traffic - you aren't changing lanes much and when you do, it might take a few seconds to get over.  Not exactly high-speed territory.  More over, the officer isn't going to get a good clean shot to someone that's floating down the highway in the left lane, especially during this time which doesn't play into his favor.

Here's the area.  The officer sits on the far right, he's in the left lane.  He estimates he was about 100yrds ("about a football field") when he got tagged, which considering the traffic volume, I'd say thats possible.  He also estimates he was going around 70, not 78.  Lanes of traffic in that area are about 30 yards wide.  We have our math.  So let's start with using a perfect triangle (which, as you can tell, its not, we'll get to that).

Using our simple math of 1002 + 302 = x2, our math comes out to 105 for X.  So how fast was he going realtive to the 100yard side?  Easy - 78mph / 105 = X / 100.  This number comes out to about 74mph which is a huge thing.  In Columbus (maybe even the entire state), 10 over is two points on your license, under that is only 1 point and that turns out to a difference on your insurance -- they frown on tickets.  Now you could argue he said he was 100 yards away from the officer, and you'd be right, but comes out to about the same, the lower end of 74mph.

But there's a problem.  The road curves off to the left (east) meaning it isn't 30 yards at the base of the triangle.  By my guess, conservatively, it's 50 yards.


 

 

1002 + 502 = X2 comes out to 111.  78 / 111 = X / 100 comes to ~70mph.  Hmm, that's barely over the limit.  And if you again say "well, he said 100 yards" -- comes out to 67.1mph so by my basic, easy math, from where the officer was and the speed he recorded it COULD be anywhere from 74mph to 67.1mph - granted, yes still technically speeding, but NOT 78mph. You could also argue the officer tried to line up the left lane with where he was, which is plasuable, BUT with the heavier traffic ...I don't think that's realisticly possible to aquire a car though the traffic of that volume.  Hmm, maybe I should send this off to mythbusters?

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Like the description says, at my core, I'm a scientist and engineer.  I came from humble beginnings on a 486DX2 Packard Hell playing doom2 on IPX to in a small time retail shop and got into hardware (ISO layers FTW!) and it was all downhill from there.  I'm infinitely curious about almost everything and always wanting to know.

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