Safe following distance
I have always maintained the most important thing on a car is the brakes, not the engine. That is why my family forbids me from driving a motorcar, if you've ever been a passenger you will understand why …
Very basic mechanics this work is on the level of high school physics and mathematics. The note that follows will be on rule-of-thumb for estimating following distance.
First we describe a basic physical model under friction with variables initial speed and stopping distance. A road motor vehicle is travelling at a speed v when the brakes are suddenly applied so that the wheels lock and the vehicle skids resulting in continuous skid marks until it comes to halt.
A physical model might be a block of wood of given mass moving on a smooth level plane plank.
All measures are to be converted to SI Units.
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Let the vehicle's mass be M and the friction coefficient between the tyres for our model on the tar road µ
Thus obtained constants as familiar equations in mechanics,
N = Mg the normal force exerted on the block
F = µN resistant force and frictional coefficient
F = aM acceleration and mass
The normal force (weight) is N = Mg giving total resistant force F = µN = µMg and deceleration a
µN = aM and µMg = aM resulting in a = µg
Appropriate values for µ might be found on tables or experimentally determined, g may be taken as 9.8m/s²
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With Newton's second law, from the familiar equations of motion under constant acceleration with initial speed v and distance s
a = µg we have v² = 2as
giving s = ½ v²/a as braking distance to halt, or v = sqrt( 2as)
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Under conservation of energy the same result may be obtained with the definition E = Fs and formula for kinetic energy,
Ek = ½ mv² = E where E is the work done by the braking system to stop the vehicle,
½ Mv² = Fs and we also had F = µN = µgM
Thus ½ Mv² = µgMs and the same result is obtained,
s = ½ v²/ µg or v = sqrt(2µgs)
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Alternately driving classes, in effect for measuring following distance by approximating time delay, use a simple two second rule irrespective of your actual speed.
In order to obtain it watch vehicle in front pass a point on the highway such as a tar strip or sign or over pass shadow on the road then count to yourself one-thousand , two-thousand, that is two seconds. If you pass the mark before two seconds you are too close.
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We may give a rule-of-thumb as suggested for keeping following distances, as to estimate following distance allow one car length (15ft), for every ten mph, (16km/hr) of speed under normal driving conditions. -
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For adverse road or weather conditions a following distance must be longer.
As well as identifying and compensate for other factors, driving conditions such as road gradient i.e. the slope and road surface. Also for the individual vehicle systems, brakes and condition of tyres etc.
General conditions to be taken in account, are such as visibility, individual driver's such as reflexes alertness and fatigue. The results will for example not be reliable if the vehicle is equipped with ABS brakes.
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These models do not work under higher speed. Further investigation and refinement shows these two rules are approximate, and not quite the same either.
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In practice there is a reaction time from when the driver sees the signal to when the brakes are applied, typically around t = 1.5 seconds.
The total stopping distance is then vt + s with s as before.
The driver must trail the lead vehicle by the total stopping distance, while the maximum stopping distance can readily thus be converted to a trailing time.
Other considerations as evidence on the scene are such as momentum and physical, material or structural damage.
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These are typical of calculations for reconstruction of motor vehicle accidents by a specialist expert witness for legal investigations forensics.