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.
Background ...
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
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 ...
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, 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 nee ...
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 ...
. 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 of 0.7 are standard for the purpose of determining a bare baseline for
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 ...
and
judicial notice
Judicial notice is a rule in the law of evidence that allows a fact to be introduced into evidence if the truth of that fact is so notorious or well-known, or so authoritatively attested, that it cannot reasonably be doubted. This is done upon the ...
;
most people can stop slightly sooner under ideal conditions.
Braking distance is not to be confused with
stopping sight distance
Stopping sight distance is one of several types of sight distance used in road design. It is a near worst-case distance a vehicle driver needs to be able to see in order to have room to stop before colliding with something in the roadway, suc ...
. The latter is a
road alignment visibility standard that provides motorists driving at or below the
design speed
The design speed is a tool used to determine geometric features of a new road or street during road design. Contrary to the word's implication, the design speed of the road or street is not necessarily its vehicle speed limit or maximum safe s ...
an
assured clear distance ahead (ACDA) which exceeds a
safety factor
In engineering, a factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analy ...
distance that would be required by a slightly or
nearly negligent driver to stop under a worst likely case scenario: typically
slippery conditions (
deceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
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
Negligence (Lat. ''negligentia'') is a failure to exercise appropriate and/or ethical ruled care expected to be exercised amongst specified circumstances. The area of tort law known as ''negligence'' involves harm caused by failing to act as a ...
for not stopping sooner.
Derivation
Energy equation
The theoretical braking distance can be found by determining the
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
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 accele ...
.
The kinetic energy is given by the formula:
:
,
where is the vehicle's mass and is the speed at the start of braking.
The work done by braking is given by:
:
,
where is the
coefficient of 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 ...
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 quanti ...
, 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
:
.
The maximum speed given an available braking distance is given by:
:
.
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 motion ...
:
:
For a level surface, the
frictional force
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 ...
resulting from
coefficient of 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 ...
is:
:
Equating the two yields the
deceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
:
:
The
form of the
formulas for constant acceleration
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
is:
:
Setting
and then
substituting into the equation yields the braking distance:
:
Total stopping distance
The total stopping distance is the sum of the perception-reaction distance and the braking distance.
:
A common baseline value of
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
An anti-lock braking system (ABS) is a safety anti-skid braking system used on aircraft and on land vehicles, such as cars, motorcycles, trucks, and buses. ABS operates by preventing the wheels from locking up during braking, thereby maintai ...
may have a
friction coefficient
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 0.9--or even far exceed 1.0 with sticky tires.
[An investigation of the utility and accuracy of the table of speed and stopping distances](_blank)
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
The two-second rule is a rule of thumb by which a driver may maintain a safe trailing distance at any speed. The rule is that a driver should ideally stay at least two seconds behind any vehicle that is directly in front of his or her vehicle. ...
to simulate the elderly or neophyte; or even a 2.5 second reaction timeāto 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
An anti-lock braking system (ABS) is a safety anti-skid braking system used on aircraft and on land vehicles, such as cars, motorcycles, trucks, and buses. ABS operates by preventing the wheels from locking up during braking, thereby maintai ...
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
In a legal dispute, one party has the burden of proof to show that they are correct, while the other party had no such burden and is presumed to be correct. The burden of proof requires a party to produce evidence to establish the truth of facts ...
, 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
Beyond a reasonable doubt is a legal standard of proof required to validate a criminal conviction in most adversarial legal systems. It is a higher standard of proof than the balance of probabilities standard commonly used in civil cases, bec ...
. 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
Highway engineering is an engineering discipline branching from civil engineering that involves the planning, design, construction, operation, and maintenance of roads, bridges, and tunnels to ensure safe and effective transportation of people and ...
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 mathem ...
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 foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg made ...
(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 betwe ...
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:
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 pedestrians, horse riders ...
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
In legal terminology, the assured clear distance ahead (ACDA) is the distance ahead of any terrestrial locomotive device such as a land vehicle, typically an automobile, or watercraft, within which they should be able to bring the device to a ...
*
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.
Background ...
*
Cadence braking
Cadence braking or stutter braking is a driving technique that involves pumping the brake pedal and is used to allow a car to both steer and brake on a slippery surface. It is used to effect an emergency stop where traction is limited to reduce the ...
*
Skid mark
*
Stopping sight distance
Stopping sight distance is one of several types of sight distance used in road design. It is a near worst-case distance a vehicle driver needs to be able to see in order to have room to stop before colliding with something in the roadway, suc ...
*
Threshold braking
Threshold braking or limit braking is a driving technique most commonly used in motor racing, but also practiced in road vehicles to slow a vehicle at the maximum rate using the brakes.
The technique involves the driver controlling the brake peda ...
*
Vehicle metrics
There are a broad range of metrics that denote the relative capabilities of various vehicle
A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, car ...
*
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