Faith looked at the sky for the umpteenth time. She had the impression that this would not look good on her previously squeaky-clean police record. She watched the ambulance drive away with its sirens making their usual racket. It was all a bad dream. It had to be. But it wasn't.
The day had begun well enough, with her and Vernal deciding to drive to
Westgate to watch any movie except ``Titanic". Their plans had sunk when
they passed a parked bus. A young boy - no more than six or seven - decided
to cross the road to meet his mother on the
other side. Faith had promptly slammed on the brakes, but didn't succeed in
missing the boy. After that, everything was hazy.
She directed her eyes to Vernal. She could vaguely make out what her friend was saying to a crowd of passers-by, something about they not having been. Various figures were popping out from the crowd, numbers like 80, 120, 100. She didn't think they were talking about temperatures.
The police arrived. Her heart would have sunk further if it wasn't for the fact that it had already hit rock-bottom. She wondered how handcuffs felt. Who'd pay her bail. Whether she could quit the country while on it. She'd always wanted to go to Fiji. Perhaps she could become a barmaid and sue overzealous customers.
Vernal meanwhile had rushed to the police and begun explaining the situation . Some passers-by did the same. The accounts were far from coherent, but the cops put together an account that was essentially true. Except for the speed of the car. The men in blue didn't seem to mind. They said they could find out.
Vernal wondered if they had a reverse crystal ball in the back of the police van. But they only seemed to have a tape measure, which they used to find the length of the skid marks. Nothing unusual, she thought. She'd seen films where they had done that sort of thing. She asked a cop about it.
``It's really quite simple. Suppose we have a car moving at speed u. It decelerates at a constant rate of a, covering a distance x till it reaches a speed v. According to Isaac Newton's Laws of Motion, the formula connecting these quantities is u2 = v2-2ax."
Vernal's brain cells scurried around trying to locate memories of her high school physics lessons.
``But those laws can only be used for situations where the deceleration is constant. But surely that's not the case here!"
``Actually it is. For when your friend slammed on the brakes, the wheels locked and the car skidded. Since the deceleration then was only due to the friction between the car tyres and the road, it was practically constant.''
``Fair enough. So what you are going to do now is apply that formula you talked about before?"
``Not yet. We still need to know the deceleration of the car. A car always decelerates at the same rate under the same conditions, but different cars can decelerate at different rates, because of tyres and things like that. So we are going to take your car, drive it at a certain speed and then skid it to a stop and see how long the skid marks are. We'll then apply the same formula - in a different form - to get the car's deceleration.''
Vernal didn't bother protesting since the police were entitled by law to do anything they wanted with the car. She watched one of them skid the car as she explained to Faith what was going on. Faith didn't seem to be listening. She seemed to be mumbling something about barmaids.
The test completed, the police carried out their calculations:
Initial velocity of car (u) = 50 kmh-1.
Final velocity of car (v) = 0.
Length of skid marks (s) = 13.68 m.
Acceleration of car (a) = \fracv2-u22s = -7.05 ms-2.
Now for the final calculations to determine whether they had broken the road's speed limit of 60 $kmh^{-1}$ when they hit the boy.
Final velocity of car (v) = 0.
Length of skid marks (s) = 21.68 m.
Acceleration of car (a) = - 7.05 ms-1.
Initial velocity of car (u) = [Ö(v2-2as)] = 62.94 kmh-1.
Vernal wasn't sure what to make of the figures. They had exceeded the speed limit. But had they been speeding?
``No.'' said the policeman, ``There is usually some grace when legally defining speeding. At least five kilometres per hour for us. Since you were going at less than 65 kilometres per hour, the state will not press charges."
``But the boy's parents?"
``That's up to them. But a court would be very unlikely to find your friend guilty of speeding."
The above summarizes, albeit in a rather simplified way, the work of a small group of policemen (yes, you heard me right, policemen, there are no ladies yet!) within the Zimbabwe Republic Police National Highway Patrol. This group, which currently numbers 27 Officers scattered throughout all the country's provinces is dedicated to solving the riddle of road traffic accidents using the scientific laws of motion.
It has long been recognized in some developed countries that evidence left on the scene of an accident can give important clues as to the probable cause of the accident, including the behaviour of the vehicle or vehicles involved prior to a crash.
The actual process of road accident investigation comprises a number of physical, mathematical and engineering principles. When applied carefully, evidence gathered this way is irrefutable in a court of law. The conviction rate for traffic offenders is usually very high. Because the process of gathering evidence this way is time consuming and very expensive, the principles and techniques are usually applied to fatal and serious road accidents, not just any accident. This is so even in developed countries such as the United Kingdom.
Road accident investigation techniques were first introduced in Zimbabwe in 1996. The first group of about 13 ZRP Officers were trained in that year by the Grampian Police from Scotland with the help of the Department of Mathematics at the University of Zimbabwe. Only high calibre students, from the different sections of the ZRP, are accepted into the Road Traffic Accident Evaluation Course (as it is called). These have to sit for an entrance examination in mathematics. This examination is currently pitched at more or less the same level as the A-level mathematics examination. Consequently, you find that most of those who succeed have impressive A'level passes in mathematics.
The initial training is very intensive, lasting for four weeks of theory and practical lessons in many aspects of identifying, protecting and correctly interpreting the evidence obtained from tyre marks at the scene of a road accident. In addition, there are about 36 hours of lectures in mathematics, mainly Newtonian mechanics. The students have a chance to apply the mathematics that they learn in practical situations, and this gives then quite a considerable advantage compared with students who learn the same mathematics at college. They have a deeper understanding of the underlying concepts and principles and generally do well in the final examination.
At the end of the four weeks the students have to pass a number of examinations which apart from mathematics include a theory paper, a practical examination and technical drawing. Failure in any examination paper means that the candidate has failed the whole course. The police simply cannot afford the expensive luxury of incompetent officers.
After graduating, the officers are then deployed to various stations, but that does not mean that they can now relax. A performance appraisal is conducted at the end of each year by the training officers and the Department of Mathematics at the University of Zimbabwe to ascertain that the boys are doing their jobs correctly, dilligently and professionally and also to maintain communication between the officers on the ground and HQ in Harare.
Police officers can obtain a higher qualification, a City & Guilds certificate in Road Accident Investigation. This is the highest qualification in this area, and is much sought-after overseas. Holders of this certificate either readily find jobs with insurance companies or set up their own consulting firms giving advice to individuals and insurance companies who pay huge sums for this. You must remember that insurance companies pay hundreds of millions of dollars in insurance claims annually, a huge portion of which are either fraudulent or undeserved. If an insurance company can prove that you were doing 95km/h on a stretch of road along whose limit is 80km/h, then the company will not pay your claim! Beware.
Further training is required to obtain this qualification and the Grampian Police Force (from Scotland) is currently assisting officers from the ZRP to obtain these qualifications. Unfortunately, no-one has got there yet but that situation won't last long! For at least two officers have made significant progress towards this goal.
In summary, the investigation of road accidents using the scientific laws
of motion is to a large extent, going to replace the usually unreliable
eye-witness accounts of accidents. By being able to calculate the speed
and work out the probable cause of an accident hours after it occurred,
the police will be able to bring to book a larger number of traffic
offenders than has been hitherto possible.
The fear of being found out, and the fact that your insurance company will
not compensate you if found out, should serve as an effective deterrent
to speeding. Hopefully this will help to bring back sanity on the roads
(especially in Harare, ha!) and thus reduce the murder and slaughter of
innocent people on them.