(Editor's Note: The following article was contributed by TomMorris, the owner of St. LouisTraffic Accident Reconstruction.)

Eratosthenes was a Greek mathematician who lived in Egypt in the3^rd Century BC. He observed that in Syene, on thelongest day of the year, columns cast no shadows when the sun wasdirectly overhead. However, at the same time, the columns inAlexandria cast a significant shadow. This simple observationled Eratosthenes to conclude that the only way for both columns tocast shadows of differing lengths at the same time was if thesurface of the earth was curved. A few simple geometriccalculations later, he had calculated the circumference of theplanet.

The story of Eratosthenes illustrates that a lack of informationisn't what prevents one from discovering the truth. Everyonecould see the same shadows. However, nobody saw theirsignificance because intuition and daily experience led them toerroneously conclude that the earth was flat. If we look atauto collisions a different way than we normally do, then we mightalso see something that previously went undetected.

Control of the Intersection

This is a common argument used when a vehicle covers asignificant distance within the intersection prior toimpact. Photos show the damages to the right quarter panel andthe police report has the vehicle crossing five lanes oftraffic, almost clearing the intersection. The driver crossingthe intersection claims to have been traveling at the posted limit,entering on a yellow light that turned to red. The otherdriver claims to have accelerated from a stop after his lightturned green. Did anyone see the vehicle run a red light?No.

So the adjuster deftly argues that the law requires a stoppedvehicle presented with a green signal to yield the right of way toany vehicle lawfully within the intersection beforeproceeding. Since the vehicle had crossed five lanes,the driver of that stopped vehicle must have been inattentive priorto starting into the intersection, right? It at least seemsreasonable. After all, look at that distance the vehicletraveled within the intersection before being struck.

Let's take a look at this another way. The one thing thatis missing from this analysis is the consideration of time. Acollision occurs because two vehicles attempt to occupy the samespace at the same time. The impact point gives us a commontime and location for each vehicle.

Because everyone is willing to concede that the vehicleaccelerated from a stop on a green light, we have the means tocalculate our second time. Take a look at the stop bar and thecollision point. How far did the vehicle accelerating from astop travel prior to the collision? The stop bar is about 12feet back from the curb and maybe a half a lane beyond that, or 6feet. Let's figure a total of 18 feet. Before we cancalculate the time, we must calculate how fast the vehicle wasgoing at 18 feet. We use the formula…

The typical acceleration rate for a passenger vehicle from astop is around 0.2g or 6.4 ft/s/s. The initial velocity iszero.

Now that we know the end velocity, we can calculate the timeusing

So now we know that the collision occurred approximately 2.4seconds after the vehicle accelerated. However, we want toknow when things happened in relation to the changing of the light,as it is part of everyone's testimony. Did the vehicleaccelerate at the instant the light turned green? Likelynot. An average driver, according to AASHTO requiresapproximately 1.3 seconds to respond to a green light. Addthat to the acceleration time of 2.4 seconds, and you can now saythat the collision occurred 3.7 seconds after the stopped vehicle'slight turned green.

The next question to answer is “where was the crossing vehiclewhen the light turned green for the stopped vehicle?” How fastdoes this driver claim to be traveling? Was he or she drivingat the posted limit perhaps? At 35 miles per hour or 51 ft/s,we can now calculate its position relative to the impact point.

If the vehicle crossed five lanes at 12 ft per lane, thataccounts for 60 ft. Add the length of the vehicle of 15 ft andthat accounts for 75ft traveled within the intersection. Thensubtract that 75 ft from the total distance to impact of 188.7 ftand it places the crossing vehicle 113.7 ft outside theintersection when the stopped vehicle received the greenlight. Since most electric traffic signals have a conflictmonitor, you can effectively state that under the testimonyprovided, the crossing vehicle was 113.7 ft from the intersectionwhen the light turned red.

Not only did the crossing vehicle enter the intersectionunlawfully through a red light, but it was also a significantdistance from the intersection when the driver decided toproceed. When applying a Monte Carlo analysis to this scenario, we discover that therewas a 0.02 percent chance that the driverentered on a yellow, and a 99.98 percent thatthe driver entered through a red.

Until now, this would just be viewed as a “swearing match,” withno visible means of resolution. A new approach providesanswers that were there the whole time. It could be the righttime to start looking at shadows a littledifferently.