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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 between the tires and the road surface, [Note 1] and negligibly by the tires' rolling resistance and vehicle's air drag. 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. [1] [Note 2]
The braking distance is one of two principal components of the total stopping distance. 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, [2] [3] [4] and a coefficient of kinetic friction of 0.7 are standard for the purpose of determining a bare baseline for accident reconstruction and judicial notice; [5] 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) [6] 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 0.35g [7] [Note 3] ) and a slow responding driver (2.5 seconds). [8] [9] 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.
The theoretical braking distance can be found by determining the work required to dissipate the vehicle's kinetic energy. [10]
The kinetic energy E is given by the formula:
where m is the vehicle's mass and v is the speed at the start of braking.
The work W done by braking is given by:
where μ is the coefficient of friction between the road surface and the tires, g is the gravity of Earth, and d is the distance travelled.
The braking distance (which is commonly measured as the skid length) given an initial driving speed v is then found by putting W = E, from which it follows that
The maximum speed given an available braking distance d is given by:
From Newton's second law:
For a level surface, the frictional force resulting from coefficient of friction is:
Equating the two yields the deceleration:
The form of the formulas for constant acceleration is:
Setting and then substituting into the equation yields the braking distance:
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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. [2] However, a keen and alert driver may have perception-reaction times well below 1 second, [11] 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. [12] [13] [14] [15] [16]
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; [Note 4] or even a 2.5 second reaction time—to specifically accommodate very elderly, debilitated, intoxicated, or distracted drivers. [12] 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. [15] [17] [Note 5] 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.
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 [18] 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. [19] [20] [21] 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. [22]
For rubber tyres on cars, the coefficient of friction (μ) decreases as the mass of the car increases. Additionally, μ 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. [23]
In a non-metric country, the stopping distance in feet given a velocity in MPH can be approximated as follows:
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 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 ) 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 are quoted in Rule 126 as: [24]
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal.
In physics, mean free path is the average distance over which a moving particle travels before substantially changing its direction or energy, typically as a result of one or more successive collisions with other particles.
Tribology is the science and engineering of understanding friction, lubrication and wear phenomena for interacting surfaces in relative motion. It is highly interdisciplinary, drawing on many academic fields, including physics, chemistry, materials science, mathematics, biology and engineering. The fundamental objects of study in tribology are tribosystems, which are physical systems of contacting surfaces. Subfields of tribology include biotribology, nanotribology and space tribology. It is also related to other areas such as the coupling of corrosion and tribology in tribocorrosion and the contact mechanics of how surfaces in contact deform. Approximately 20% of the total energy expenditure of the world is due to the impact of friction and wear in the transportation, manufacturing, power generation, and residential sectors.
Aquaplaning or hydroplaning by the tires of a road vehicle, aircraft or other wheeled vehicle occurs when a layer of water builds between the wheels of the vehicle and the road surface, leading to a loss of traction that prevents the vehicle from responding to control inputs. If it occurs to all wheels simultaneously, the vehicle becomes, in effect, an uncontrolled sled. Aquaplaning is a different phenomenon from when water on the surface of the roadway merely acts as a lubricant. Traction is diminished on wet pavement even when aquaplaning is not occurring.
Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses, and permanent (plastic) deformation of the object or the surface. Note that the slippage between the wheel and the surface also results in energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because it is due to the applied torque to the wheel and the resultant slip between the wheel and ground, which is called slip loss or slip resistance. In addition, only the so-called slip resistance involves friction, therefore the name "rolling friction" is to an extent a misnomer.
Brake fade is the reduction in stopping power that can occur after repeated or sustained application of the brakes of a vehicle, especially in high load or high speed conditions. Brake fade can be a factor in any vehicle that utilizes a friction braking system including automobiles, trucks, motorcycles, airplanes, and bicycles.
An adhesion railway relies on adhesion traction to move the train, and is the most widespread and common type of railway in the world. Adhesion traction is the friction between the drive wheels and the steel rail. Since the vast majority of railways are adhesion railways, the term adhesion railway is used only when it is necessary to distinguish adhesion railways from railways moved by other means, such as by a stationary engine pulling on a cable attached to the cars or by railways that are moved by a pinion meshing with a rack.
In fluid dynamics, drag, sometimes referred to as fluid resistance, is a force acting opposite to the relative motion of any object, moving with respect to a surrounding fluid. This can exist between two fluid layers, two solid surfaces, or between a fluid and solid surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path.
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 stops rolling and slides or spins on the surface of the road. Skid marks can be analyzed to find the maximum and minimum vehicle speed prior to an impact or incident. Skidding can also occur on black ice or diesel deposits on the road and may not leave a mark at all.
A banked turn is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.
Uniform Tire Quality Grading, commonly abbreviated as UTQG, is a set of standards for passenger car tires that measures a tire's treadwear, temperature resistance and traction. The UTQG was created by the National Highway Traffic Safety Administration in 1978, a branch of the United States Department of Transportation (DOT). All passenger car tires manufactured for sale in the United States since March 31, 1979 are federally mandated to have the UTQG ratings on their sidewall as part of the DOT approval process, in which non-DOT approved tires are not legal for street use in the United States. Light truck tires are not required to have a UTQG. It is not to be confused with the tire code, a supplemental and global standard measuring tire dimensions, load-bearing ability and maximum speed, maintained by tire industry trade organizations and the International Organization for Standardization.
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, such as a pedestrian in a crosswalk, a stopped vehicle, or road debris. Insufficient sight distance can adversely affect the safety or operations of a roadway or intersection.
Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continues today.
Headway is the distance or duration between vehicles in a transit system measured in space or time. The minimum headway is the shortest such distance or time achievable by a system without a reduction in the speed of vehicles. The precise definition varies depending on the application, but it is most commonly measured as the distance from the tip of one vehicle to the tip of the next one behind it. It can be expressed as the distance between vehicles, or as time it will take for the trailing vehicle to cover that distance. A "shorter" headway signifies closer spacing between the vehicles. Airplanes operate with headways measured in hours or days, freight trains and commuter rail systems might have headways measured in parts of an hour, metro and light rail systems operate with headways on the order of 90 seconds to 20 minutes, and vehicles on a freeway can have as little as 2 seconds headway between them.
Road slipperiness is a condition of low skid resistance due to insufficient road friction. It is a result of snow, ice, water, loose material and the texture of the road surface on the traction produced by the wheels of a vehicle.
In the design of fluid bearings, the Sommerfeld number (S) is a dimensionless quantity used extensively in hydrodynamic lubrication analysis. The Sommerfeld number is very important in lubrication analysis because it contains all the variables normally specified by the designer.
The capstan equation or belt friction equation, also known as Euler-Eytelwein formula, relates the hold-force to the load-force if a flexible line is wound around a cylinder.
The geometric design of roads is the branch of highway engineering concerned with the positioning of the physical elements of the roadway according to standards and constraints. The basic objectives in geometric design are to optimize efficiency and safety while minimizing cost and environmental damage. Geometric design also affects an emerging fifth objective called "livability," which is defined as designing roads to foster broader community goals, including providing access to employment, schools, businesses and residences, accommodate a range of travel modes such as walking, bicycling, transit, and automobiles, and minimizing fuel use, emissions and environmental damage.
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. This can be divided into compressive and adhesive forces in the direction perpendicular to the interface, and frictional forces in the tangential direction. Frictional contact mechanics is the study of the deformation of bodies in the presence of frictional effects, whereas frictionless contact mechanics assumes the absence of such effects.
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 halt. It is one of the most fundamental principles governing ordinary care and the duty of care for all methods of conveyance, and is frequently used to determine if a driver is in proper control and is a nearly universally implicit consideration in vehicular accident liability. The rule is a precautionary trivial burden required to avert the great probable gravity of precious life loss and momentous damage. Satisfying the ACDA rule is necessary but not sufficient to comply with the more generalized basic speed law, and accordingly, it may be used as both a layman's criterion and judicial test for courts to use in determining if a particular speed is negligent, but not to prove it is safe. As a spatial standard of care, it also serves as required explicit and fair notice of prohibited conduct so unsafe speed laws are not void for vagueness. The concept has transcended into accident reconstruction and engineering.
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