Braking distance

Last updated

Vehicle Stopping Distance
.mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}
Reaction Time Distance - (3/4) second
Passenger vehicle Stopping Distance
Heavy Truck Stopping Distance Vehicle Stopping Distance.webp
Vehicle Stopping Distance
   Reaction Time Distance - (3/4) second
   Passenger vehicle Stopping Distance
   Heavy Truck 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 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]

Contents

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.

Derivation

Energy equation

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:

.

Newton's law and equation of motion

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:

Total stopping distance

Tables of speed and stopping distances [5]
Permitted by good tires and clean, dry, level, pavement.

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.

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 [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]

Rules of thumb

In a non-metric country, the stopping distance in feet given a velocity in MPH can be approximated as follows:

  1. take the first digit of the velocity, and square it. Add a zero to the result, then divide by 2.
  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 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]

See also

Notes

  1. The average friction coefficient (µ) is related to the tire's Treadwear rating by the following formula: See HPwizard on Tire Friction
  2. The coefficient of friction is the ratio of the force necessary to move one body horizontally over another at a constant speed to the weight of the body. For a 10 ton truck, the force necessary to lock the brakes could be 7 tons, which is enough force to destroy the brake mechanism itself. While some brake types on lightweight vehicles are more prone to brake fade after extended use, or recover more quickly after water immersion, all should be capable of wheel lock.
  3. THE 2001 GREEN BOOK revised braking distance portion of equation now based on deceleration ( a ) rather than friction factor ( f ) upon recommendation of NCHRP Report 400
  4. A study conducted by the Transportation Research Board in 1998 found that most people can perceive and react to an unexpected roadway condition in 2 seconds or less.
  5. As speed increases, the braking distance is initially far less than the perception-reaction distance, but later it equals then rapidly exceeds it after 30 MPH for 1 second p-t times (46 MPH for 1.5s p-t times): thus . Solving for v, . This is due to the quadratic nature of the kinetic energy increase versus the linear effect of a constant p-r time.

Related Research Articles

In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.

<span class="mw-page-title-main">Friction</span> Force resisting sliding motion

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.

<span class="mw-page-title-main">Projectile motion</span> Motion of launched objects due to gravity

Projectile motion is a form of motion experienced by an object or particle that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion on Earth, most calculations assume the effects of air resistance are passive and negligible.

<span class="mw-page-title-main">Normal force</span> Force exerted on an object by a body with which it is in contact, and vice versa

In mechanics, the normal force is the component of a contact force that is perpendicular to the surface that an object contacts. In this instance normal is used in the geometric sense and means perpendicular, as opposed to the common language use of normal meaning "ordinary" or "expected". A person standing still on a platform is acted upon by gravity, which would pull them down towards the Earth's core unless there were a countervailing force from the resistance of the platform's molecules, a force which is named the "normal force".

<span class="mw-page-title-main">Rolling resistance</span> Force resisting the motion when a body rolls on a surface

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.

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.

<span class="mw-page-title-main">Skid mark</span> Mark left by any solid which moves against another

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.

<span class="mw-page-title-main">Leadscrew</span> Screw used as a linkage in a mechanism

A leadscrew, also known as a power screw or translation screw, is a screw used as a linkage in a machine, to translate turning motion into linear motion. Because of the large area of sliding contact between their male and female members, screw threads have larger frictional energy losses compared to other linkages. They are not typically used to carry high power, but more for intermittent use in low power actuator and positioner mechanisms. Leadscrews are commonly used in linear actuators, machine slides, vises, presses, and jacks. Leadscrews are a common component in electric linear actuators.

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.

<span class="mw-page-title-main">Uniform Tire Quality Grading</span> Standards for passenger car tires

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.

<span class="mw-page-title-main">Bicycle and motorcycle dynamics</span> Science behind the motion of bicycles and motorcycles

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.

Sliding is a type of motion between two surfaces in contact. This can be contrasted to rolling motion. Both types of motion may occur in bearings.

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.

<span class="mw-page-title-main">Capstan equation</span> Relates the hold-force to the load-force if a flexible line is wound around a cylinder

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.

<span class="mw-page-title-main">Geometric design of roads</span> Geometry of road design

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.

References

  1. Fricke, L. (1990). "Traffic Accident Reconstruction: Volume 2 of the Traffic Accident Investigation Manual". The Traffic Institute, Northwestern University.{{cite journal}}: Cite journal requires |journal= (help)
  2. 1 2 Taoka, George T. (March 1989). "Brake Reaction Times of Unalerted Drivers". ITE Journal. 59 (3): 19–21. ISSN   0162-8178.
  3. The National Highway Traffic Safety Administration (NHTSA) uses 1.5 seconds for the average reaction time.
  4. The Virginia Commonwealth University’s Crash Investigation Team typically uses 1.5 seconds to calculate perception-reaction time
  5. 1 2 "Tables of speed and stopping distances". The State of Virginia.
  6. ACDA or "assured clear distance ahead" rule requires a driver to keep his vehicle under control so that he can stop in the distance in which he can see clearly
  7. National Cooperative Highway Research Program (1997). NCHRP Report 400: Determination of Stopping Sight Distances (PDF). Transportation Research Board (National Academy Press). p. I-13. ISBN   0-309-06073-7.
  8. American Association of State Highway and Transportation Officials (1994) A Policy on Geometric Design of Highways and Streets (Chapter 3)
  9. Highway Design Manual. Vol. 6th Ed. California Department of Transportation. 2012. p. 200. See Chapter 200 on Stopping Sight Distance and Chapter 405.1 on Sight Distance
  10. Traffic Accident Reconstruction Volume 2, Lynn B. Fricke
  11. Robert J. Kosinski (September 2012). "A Literature Review on Reaction Time". Clemson University. Archived from the original on 2013-10-10.
  12. 1 2 An investigation of the utility and accuracy of the table of speed and stopping distances Archived September 27, 2012, at the Wayback Machine
  13. Tire friction and rolling resistance coefficients
  14. THE GG DIAGRAM: sticky tires exceed 1.0
  15. 1 2 J.Y. Wong (1993). Theory of ground vehicles. Vol. 2nd ed. John Wiley & Sons. p. 26. ISBN   9780470170380.
  16. Robert Bosch GmbH (1996). Automotive Handbook. Vol. 4th ed. Bentley Publishers. p. 335. ISBN   9780837603339.
  17. Frictional Coefficients for some Common Materials and Materials Combinations and Reference Tables -- Coefficient of Friction Archived 2009-03-08 at the Wayback Machine
  18. Tire Test Results
  19. Warning Signs and Knowing When to Stop Driving Archived 2008-05-27 at the Wayback Machine
  20. Jevas, S; Yan, J. H. (2001). "The effect of aging on cognitive function: a preliminary quantitative review". Research Quarterly for Exercise and Sport. 72: A-49. Simple reaction time shortens from infancy into the late 20s, then increases slowly until the 50s and 60s, and then lengthens faster as the person gets into his 70s and beyond
  21. Der, G.; Deary, I. J. (2006). "Age and sex differences in reaction time in adulthood: Results from the United Kingdom health and lifestyle survey". Psychology and Aging. 21 (1): 62–73. doi:10.1037/0882-7974.21.1.62. PMID   16594792.
  22. "Highway Design Handbook for Older Drivers and Pedestrians". Publication Number: FHWA-RD-01-103. May 2001.
  23. Tomita, Hisao. "Tire-pavement friction coefficients" (PDF). Defense Technical Information Center. Naval Civil Engineering Laboratory. Archived from the original (PDF) on June 14, 2015. Retrieved 12 June 2015.
  24. "Typical stopping distance" (PDF).

Further reading