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Braking distance refers to the distance a vehicle will travel from the point when its
brakes A brake is a mechanical device that inhibits motion by absorbing energy from a moving system. It is used for slowing or stopping a moving vehicle, wheel, axle, or to prevent its motion, most often accomplished by means of friction. Backgroun ...
are fully applied to when it comes to a complete stop. It is primarily affected by the original speed of the vehicle and the coefficient of friction between the
tire A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...
s and the
road surface A road surface (British English), or pavement (American English), is the durable surface material laid down on an area intended to sustain vehicular or foot traffic, such as a road or walkway. In the past, gravel road surfaces, hoggin, cob ...
, and negligibly by the tires'
rolling resistance Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy ...
and vehicle's
air drag In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
. The type of brake system in use only affects trucks and large mass vehicles, which cannot supply enough force to match the static frictional force. The braking distance is one of two principal components of the
total stopping distance Braking distance refers to the distance a vehicle will travel from the point when its brakes are fully applied to when it comes to a complete stop. It is primarily affected by the original speed of the vehicle and the coefficient of friction be ...
. The other component is the reaction distance, which is the product of the speed and the perception-reaction time of the driver/rider. A perception-reaction time of 1.5 seconds, and a
coefficient of kinetic friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...
of 0.7 are standard for the purpose of determining a bare baseline for accident reconstruction and judicial notice; most people can stop slightly sooner under ideal conditions. Braking distance is not to be confused with stopping sight distance. The latter is a road alignment visibility standard that provides motorists driving at or below the design speed an assured clear distance ahead (ACDA) which exceeds a safety factor distance that would be required by a slightly or nearly negligent driver to stop under a worst likely case scenario: typically slippery conditions ( deceleration 0.35 g) and a slow responding driver (2.5 seconds).American Association of State Highway and Transportation Officials (1994) ''A Policy on Geometric Design of Highways and Streets'' (Chapter 3) Because the stopping sight distance far exceeds the actual stopping distance under most conditions, an otherwise capable driver who uses the full stopping sight distance, which results in injury, may be negligent for not stopping sooner.


Derivation


Energy equation

The theoretical braking distance can be found by determining the work required to dissipate the vehicle's
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...
. The kinetic energy is given by the formula: :E=\fracmv^, where is the vehicle's mass and is the speed at the start of braking. The work done by braking is given by: :W=\mu mgd, where is the coefficient of friction between the road surface and the tires, is the
gravity of Earth The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quant ...
, and is the distance travelled. The braking distance (which is commonly measured as the skid length) given an initial driving speed is then found by putting , from which it follows that :d=\frac. The maximum speed given an available braking distance is given by: :v=\sqrt.


Newton's law and equation of motion

From
Newton's second law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in mo ...
: :F=ma For a level surface, the frictional force resulting from coefficient of friction \mu is: :F_=-\mu mg Equating the two yields the deceleration: :a=-\mu g The d_f(d_i,v_i,v_f) form of the formulas for constant acceleration is: :d_f=d_i + \frac Setting d_i, v_f =0 and then substituting a into the equation yields the braking distance: :d_f=\frac=\frac


Total stopping distance

The total stopping distance is the sum of the perception-reaction distance and the braking distance. :D_=D_+D_=v t_+ \frac A common baseline value of t_=1.5 s, \mu=0.7 is used in stopping distance charts. These values incorporate the ability of the vast majority of drivers under normal road conditions. However, a keen and alert driver may have perception-reaction times well below 1 second, and a modern car with computerized anti-skid brakes may have a friction coefficient of 0.9--or even far exceed 1.0 with sticky tires.An investigation of the utility and accuracy of the table of speed and stopping distances
Experts historically used a reaction time of 0.75 seconds, but now incorporate perception resulting in an average perception-reaction time of: 1 second for population as an average; occasionally a two-second rule to simulate the elderly or neophyte; or even a 2.5 second reaction timeā€”to specifically accommodate very elderly, debilitated, intoxicated, or distracted drivers. The coefficient of friction may be 0.25 or lower on wet or frozen asphalt, and anti-skid brakes and season specific performance tires may somewhat compensate for driver error and conditions. In legal contexts, conservative values suggestive of greater minimum stopping distances are often used as to be sure to exceed the pertinent legal burden of proof, with care not to go as far as to condone negligence. Thus the reaction time chosen can be related to the burden's corresponding population percentile; generally a reaction time of 1 second is as a preponderance more probable than not, 1.5 seconds is clear and convincing, and 2.5 seconds is beyond reasonable doubt. The same principle applies to the friction coefficient values.


Actual total stopping distance

The actual total stopping distance may differ from the baseline value when the road or tire conditions are substantially different from the baseline conditions or when the driver's cognitive function is superior or deficient. To determine actual total stopping distance, one would typically empirically obtain the coefficient of friction between the tire material and the exact road spot under the same road conditions and temperature. They would also measure the person's perception and reaction times. A driver who has innate reflexes, and thus braking distances, that are far below the safety margins provided in the road design or expected by other users, may not be safe to drive. Most old roads were not engineered with the deficient driver in mind, and often used a defunct 3/4 second reaction time standard. There have been recent road standard changes to make modern roadways more accessible to an increasingly aging population of drivers. For rubber tyres on cars, the coefficient of friction () decreases as the mass of the car increases. Additionally, depends on whether the wheels are locked or rolling during the braking, and a few more parameters such as rubber temperature (increases during the braking) and speed.


Rules of thumb

In a non-
metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathe ...
country the stopping distance in feet given a velocity in MPH can be approximated as follows: # take the first digit of the velocity, and square it. Add a zero to the result, then divide by 2. # sum the previous result to the double of the velocity. Example: velocity = 50 MPH. stopping distance = 5 squared = 25, add a zero = 250, divide by 2 = 125, sum 2*50 = 225 feet (the exact value can be calculated using the formula given below the diagram on the right). In
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...
the rule of thumb for the stopping distance in a city in good conditions is the 1-second rule, i.e. the distance covered in 1 second should at most be the distance to the vehicle ahead. At 50 km/h this corresponds to about 15 m. For higher speeds up to about 100 km/h outside built-up areas a similarly defined 2-second rule applies, which for 100 km/h translates to about 50 m. For speeds on the order of 100 km/h there is also the more or less equivalent rule that the stopping distance be the speed divided by 2 k/h, referred to as ''halber tacho'' (''half the
speedometer A speedometer or speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. Now universally fitted to motor vehicles, they started to be available as options in the early 20th century, and as standard equipment f ...
'') rule, e.g. for 100 km/h the stopping distance should be about 50 m. Additionally, German driving schools teach their pupils that the total stopping distance is typically: (Speed\div10)\times3+(Speed\div10)^2 In the UK, the typical total stopping distances (thinking distance plus braking distance) used in
The Highway Code ''The Highway Code'' is a set of information, advice, guides and mandatory rules for road users in the United Kingdom. Its objective is to promote road safety. The ''Highway Code'' applies to all road users including pedestrian A pedest ...
are quoted in Rule 12

as: * 20 mph: 40 feet (12 metres) * 30 mph: 75 feet (23 metres) * 40 mph: 118 feet (36 metres) * 50 mph: 175 feet (53 metres) * 60 mph: 240 feet (73 metres) * 70 mph: 315 feet (96 metres)


See also

* Assured clear distance ahead *
Brake A brake is a mechanical device that inhibits motion by absorbing energy from a moving system. It is used for slowing or stopping a moving vehicle, wheel, axle, or to prevent its motion, most often accomplished by means of friction. Backgroun ...
* Cadence braking *
Skid mark A skid mark is the visible mark left by any solid which moves against another, and is an important aspect of trace evidence analysis in forensic science and forensic engineering. Skid marks caused by tires on roads occur when a vehicle wheel ...
* Stopping sight distance * Threshold braking * Vehicle metrics *
Vehicular accident reconstruction Traffic collision reconstruction is the process of investigating, analyzing, and drawing conclusions about the causes and events during a vehicle collision. Reconstructionists conduct collision analysis and reconstruction to identify the cause ...


Notes


References


Further reading

* * * * *


External links


Car Stopping Distance CalculatorBraking Distance CalculatorTables of speed and stopping distancesWikibooks: Sight DistanceThe Highway Code (in English)
{{DEFAULTSORT:Braking Distance Road transport Vehicle braking technologies