“Braking distance”的意思、由来-开放百科全书

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,{{#tag:ref |The average friction coefficient (µ) is related to the tire's Treadwear rating by the following formula:

See HPwizard on Tire Friction|group="Note" |name="Treadwear Rating"}} 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]{{#tag:ref |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.|group="Note" |name="Effect of brake and vehicle type"}}

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]{{#tag:ref | 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|group="Note" |name="NCHRP change"}}) 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]

where {{math|m}} is the vehicle's mass and {{math|v}} is the speed at the start of braking.

where {{math|μ}} is the coefficient of friction between the road surface and the tires, {{math|g}} is the gravity of Earth, and {{math|d}} is the distance travelled.

The braking distance (which is commonly measured as the skid length) given an initial driving speed {{math|v}} is then found by putting {{math|1=W = E}}, from which it follows that

Newton's Law and Equation of Motion

For a level surface, the frictional force resulting from coefficient of friction

is:

Total stopping distance

This is a very simplistic and conceptual theoretical model for how to calculate braking distance. It assumes that the only parameters for the friction force are {{math|μ}} (coefficient of friction) and {{math|g}} (gravity of Earth), which is not the case in real world scenarios. For example, for rubber (car, plane, truck and so on), {{math|μ}} actually decreases as the mass of the car increases. Additionally, {{math|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.^[11]

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,^[12] and a modern car with computerized anti-skid brakes may have a friction coeficient of 0.9--or even far exceed 1.0 with sticky tires.^[13]^[14]^[15]^[16]^[17]

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;{{#tag:ref| 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. |group="Note" |name="TRB"}} or even a 2.5 second reaction time—to specifically accommodate very elderly, debilitated, intoxicated, or distracted drivers.^[13] 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.^[16]^[18]{{#tag:ref| 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.|group="Note" |name="Speed at which braking distance equals perception-reaction distance"}} 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^[19] 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.^[20]^[21]^[22] 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.^[23]

See also

Notes

1. ^{{cite journal |last1=Fricke |first1=L. |title=Traffic Accident Reconstruction: Volume 2 of the Traffic Accident Investigation Manual |publisher=The Traffic Institute, Northwestern University |year=1990}}
2. ^¹{{cite journal |last1=Taoka |first1=George T. |title=Brake Reaction Times of Unalerted Drivers |journal=ITE Journal |volume=59 |issue=3 |pages= 19–21 |date=March 1989 |url=http://www.ite.org/membersonly/itejournal/pdf/jca89a19.pdf}}
3. ^The National Highway Traffic Safety Administration (NHTSA) uses 1.5 seconds for the average reaction time.
4. ^The [https://archive.is/20130731201913/http://www.vcu.edu/cppweb/tstc/crashinvestigation/ Virginia Commonwealth University’s Crash Investigation Team] typically uses 1.5 seconds to calculate perception-reaction time
5. ^¹{{cite web |url=http://law.lis.virginia.gov/vacode/46.2-880/ |title=Tables of speed and stopping distances |publisher=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. ^{{cite book |title=NCHRP Report 400: Determination of Stopping Sight Distances |author=National Cooperative Highway Research Program |publisher=Transportation Research Board (National Academy Press) |page=I-13 |year=1997 |isbn=0-309-06073-7 |url=http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_400.pdf}}
8. ^American Association of State Highway and Transportation Officials (1994) A Policy on Geometric Design of Highways and Streets (Chapter 3)
9. ^{{Cite book |url=http://www.dot.ca.gov/hq/oppd/hdm/hdmtoc.htm |title=Highway Design Manual |publisher=California Department of Transportation |volume=6th Ed. |year=2012 |page=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. ^{{cite web|last1=Tomita|first1=Hisao|title=Tire-pavement friction coefficients|url=http://www.dtic.mil/dtic/tr/fulltext/u2/705987.pdf|website=Defense Technical Information Center|publisher=Naval Civil Engineering Laboratory|accessdate=12 June 2015}}
12. ^{{cite web|url=http://biae.clemson.edu/bpc/bp/Lab/110/reaction.htm#Mean%20Times |title=A Literature Review on Reaction Time |author=Robert J. Kosinski |publisher=Clemson University |date=September 2012 |deadurl=yes |archiveurl=https://web.archive.org/web/20131010194942/http://biae.clemson.edu/bpc/bp/Lab/110/reaction.htm |archivedate=2013-10-10 |df= }}
13. ^¹An investigation of the utility and accuracy of the table of speed and stopping distances {{webarchive|url=https://web.archive.org/web/20120927004530/http://www.virginiadot.org/vtrc/main/online_reports/pdf/01-r13.pdf |date=September 27, 2012 }}
14. ^Tire friction and rolling resistance coefficients
15. ^THE GG DIAGRAM: sticky tires exceed 1.0
16. ^¹{{cite book |title=Theory of ground vehicles |volume=2nd ed. |author=J.Y. Wong |year=1993 |page=26 |url=https://books.google.com/books?id=Blp2D1DteTYC&printsec=frontcover&dq=theory+of+ground+vehicles&hl=fr&ei=lumPTM2TN4L58Ab_qbC3DQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDMQ6AEwAA#v=onepage&q&f=false}}
17. ^{{cite book |author=Robert Bosch GmbH |title=Automotive Handbook |volume=4th ed |page=335 |year=1996 |url=https://books.google.com/books?id=zsRHPwAACAAJ&dq=automotive%20handbook%20bosch&hl=fr&source=gbs_book_other_versions}}
18. ^Frictional Coefficients for some Common Materials and Materials Combinations and Reference Tables -- Coefficient of Friction {{webarchive|url=https://web.archive.org/web/20090308124246/http://engineershandbook.com/Tables/frictioncoefficients.htm |date=2009-03-08 }}
19. ^Tire Test Results
20. ^Warning Signs and Knowing When to Stop Driving {{webarchive|url=https://web.archive.org/web/20080527023158/http://www.helpguide.org/elder/senior_citizen_driving.htm |date=2008-05-27 }}
21. ^{{cite journal |first1=S |last1=Jevas |first2=J. H. |last2=Yan |title=The effect of aging on cognitive function: a preliminary quantitative review. |journal=Research Quarterly for Exercise and Sport |volume=72 |page=A-49 |year=2001}} 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
22. ^{{cite journal |first1=G. |last1=Der |first2=I. J. |last2=Deary |year=2006 |title=Age and sex differences in reaction time in adulthood: Results from the United Kingdom health and lifestyle survey. |journal=Psychology and Aging |volume=21 | issue = 1 |pages=62–73. |doi=10.1037/0882-7974.21.1.62}}
23. ^{{cite web |url=http://www.fhwa.dot.gov/publications/research/safety/humanfac/01103/ |title=Highway Design Handbook for Older Drivers and Pedestrians |publisher=Publication Number: FHWA-RD-01-103 |date=May 2001}}