A formula for perfect parallel parking
Developed by esure and Dr Rebecca Hoyle of Surrey University: April 2003
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Research by internet insurer esure indicates that some £151m of insurance claims each year are caused by collisions during parking and low-speed manoeuvres. esure is concerned that parallel parking - on the main culprits for bumps and scrapes - is only tested during 50% of driving tests. esure has worked with Dr Rebecca Hoyle from the Mathematics Department of the University of Surrey to investigate the trigonometry behind the 'perfect parallel park'. The formula is explained below: |
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In the formula above: w = width of car at widest point c = midpoint between axles f = distance from c to front of car b = distance from c to back of car r = minimum radius of turning circle p = distance from parallel car at outset k = optimal distance to kerb fg = distance from car in front at the end of the manoeuvre |
The initial requirements for a perfect 'S' shaped parallel parking manoeuvre are: 1) the right starting position 2) the size of the gap available, and 3) the correct manipulation and timing of the steering within the available turning circle.  The car must start in a parallel position to the car in from and the starting distance from the adjacent car should be equal to the tightest radius of the inner turning circle minus half your car's width.
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 The gap into which the car is to be reversed must be at least as long as the width of your car plus twice the radius of the tightest inner turning circle plus the distance between the point midway between both axles and the back of your car. In all but a few exceptional cases, this will equate to a minimum space of 150% of your cars length. |
 In addition, the distance from the point midway between both axles to the front of the car must be less than the width of your car plus twice the radius of the inner turning circle minus the maximum gap between you and the car in front at the end of the manoeuvre. |
 During the manoeuvre, reversing should be parallel to the point at which the midpoint between your car's axles lines up with the bumper of the car in front. Reversing should continue at low speed until your car is at exactly 45degrees from the kerb at which point an opposite lock should be applied until the car is parallel once more with the kerb. At this point the distance to the kerb should be optimal ie 'k'. The last part of the formula shows the conditions a driver would need to satisfy to avoid hitting the car in front and the kerb during the manoeuvre. |
The mathematical basis of the manoeuvre has been developed in the simplest terms. It can be expressed in a far more complex manner as a motion control problem using shape change, however the authors recommend that for practical purposes it should be supplemented with some pure practical commonsense, such as using any available reflections in cars opposite to judge your position! To link to the press release related to this formula, please click here. |