Four-wheel drive vehicles are responsible for more accidents than any other vehicle. For this reason, we need standards for four-wheel drive ownership: if not used by a building tradesperson, the car must be kept outside the metropolitan area or evidence provided that it has been off-road at least twice a year — this does not include being parked on a verge. Another possible exception is for a family with more than three children. If none of these exceptions apply, the owners of fob-watch tractors must pay a premium based on how the 4WD affects the vision of its driver and other motorists, how many accidents the driver of the 4WD causes, and the time difference between the driver and a cheetah in a 100 metre dash.

Essentially, the higher these values, the higher the premium that the driver pays. Here are the formulae by which the factors are costed.

V = Vision
a. Forward vision
The premium is based upon the clarity of forward vision (Vf) that a driver has when behind a 4WD. Full forward vision means that the road can be seen from 10 metres ahead of the car in front. Partial forward vision means the road can only be seen from 30 metres ahead of the car in front. Nil forward vision means that no road surface ahead of the vehicle in front can be seen closer than 50 metres. If there is nil forward vision, the premium (pVf) will be $100. If there is only partial forward vision, the pVf will be $50. Invariably however, all windows in a 4WD are above a car driver’s line of sight, so there is nil forward vision.

So pVf will be $0 if forward vision = 10m,
$50 if forward vision = 30m, or
$100 forward vision = 50m.

b. Side vision
Using only mirrors to see behind the driver will result in blind spots (Bm). The size of mirrors should be in proportion to the size of the vehicle. If a 4WD only has standard mirrors, the blind spots are slightly larger because of the extra height of the mirror from the ground, as well as the length of the vehicle. This makes the driver less able to see objects that (1) are near the rear wheels, or (2) extend out on a 45° angle.

If the mirrors of the 4WD do not compensate for these larger blind spots (being either convex or a larger size), a premium will be levied. The length of a standard blind spot for a four-metre-long vehicle is about 30 centimetres (7.5 centimetres per metre). For every half-metre that the 4WD is over four metres, the premium will be $10 per side, which is thought to be suitable for the 10% increase in the blind spots. The equation itself is

Bm = ((L – 4 [metres]) / 0.5) x ([$]10 x 2),
where L is the length of the vehicle. So for example, if the vehicle was 5.5 metres long, the premium would be

Bm = ((5.5 – 4 metres) / 0.5)x [$]20. The side vision premium is therefore $60.

c. Rear vision
The height of the rear window (Hr) must also be taken into account. Taken from the lower window sill, the window is usually one-quarter as high off the ground again as that of a normal car (Hr(n)). This thereby decreases rear vision (Vr) by the same amount. So knowing that Vr = -Bh (rear blind spot), we have Bh = Hr(n) + (Hr(n) / 4). This results in a blind spot of about two metres (where Hr(n) is about 1.6 metres). As the height of the 4WD cab from the ground is approximately twice that of a normal car, we may use the simple formula of Bh = Vf / 2.

So the complete formula for the 4WD vision premium (pV) is
pV = Bw = Vf + Bh + Bm =>
= {$0, $50, $100} + (Vf / 2) + (((L – 4) / 0.5) x (10 x 2)).

A = Accident
Accidents may be caused by bad drivers of any type of vehicle. Therefore the accident (A) values are taken as the difference between the annual average of accidents, and those for which the rubber-soled glory box is clearly responsible.

When the ratio of accidents between normal cars and 4WDs is 1:1.2 or greater, the premium will be that number multiplied by 50. So if Aw is greater than An x 1.2 (denoted by R), then the accident premium will be

Aw > (R = An x 1.2), then
Aw = R x 50, so
pA = Aw

For example, if Aw = An x 2.7 (which will be R), then the accident premium (pA) is
pA = Aw = 2.7 x 50
= $135.

T = Time
The larger the time difference between a cheetah and a 4WD driver in a 100-metre race, the slower the latter is. Slowness indicates lack of fitness; lack of fitness results in a slower response time. A slower response time makes a driver more likely to have, or to instigate, a traffic accident. Therefore the 4WD owner must get fit or pay more for the privilege of driving their internal combustion ego trip.

A cheetah runs at about 80 kilometres per hour in a short burst. It should be able to accomplish a 100 metre dash in about 5 seconds (Tc). The average time for a fit and healthy person to complete the same distance is is approximately 12.5 seconds (Tp). For every half-second that a person is slower than Tc x 2.25, the 4WD premium is increased by, let’s say, $50 per half-second. So

pT = ((Tc x 2.25 – 12.5) / 0.5) x [$]50.

But why bother with the cheetah at all, you ask? First, for the sake of fairness, it matches the person and the cheetah by comparative age. Secondly, it’s more fun for the spectators.

Finally then, the total premium for city dwelling 4WDs is calculated by:
p = pV + pA + pT

To see how this premium in practice, here is an example. A 4WD is measured and gives these values:
1. Vf (partial vision) = $50;
Bh (partial vision) = $25;
Bm (4.5 m) = $20.
Bw = Vf + Bh + Bm
= $120.
= pV, therefore
pV = $120.

2. The driver’s Aw is 2.7 that of the average An, so:
Aw = 2.7 x 50
= 135
= pA, therefore
pA = $135.

3. The driver’s time is 16.3 seconds; the cheetah’s was 6.7. So
Tp = ((6.7 x 2.25 – 12.5) / 0.5) x 50
= ((15.075 – 12.5) / 0.5) x 50
= (2.575 / 0.5) x 50
= pT, therefore
pT = $257.50

The 4WD premium is thus
$120 + $135 + $257.50, giving a total of $512.50 payable per year.

Happy motoring!

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Appendix A

Summary of calculations:

pV
pV = Bw = Vf + Bh + Bm =>
= {$0, $50, $100} + (Vf / 2) + (((L – 4) / 0.5) x (10 x 2))

pA
pA = Aa(w) = R x 50
If Aa(w)  (R = Aa(n) x 1.2) then

pT
pT = Tp = ((Tc x 2.25 – 12.5) / 0.5) x 50

copyright Troy Grisgonelle 2006.

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