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Road User Sampling Rate 4-2 Road User Information Database for Making Decisions 4-3 Where: t = time Ît = sampling interval Sight Distance Stopping Sight Distance (SSD) Design Values 5-4 Where: tRT = perception-reaction time V = design speed, km/h a = deceleration level, m/s2 Where: tRT = perception-reaction time V = design speed, mi/h a = deceleration level, ft/s2 US Customary: 1.075 2 SSD Vt V a RT= +1 47. Metric: 0.039 2 SSD Vt V a RT= +0 278. Sight Distance Distance traveled while Di= + stance traveled while 5-2 driver perceives, makes the driver completes decisions about, and initiates an appropriate action in response to maneuver (MT) roadway element (PRT) Information(t) Information(t-1) changes= + during tÎ Sampling rate (user, operations, highway,= f environment) 27-1 C H A P T E R 27 Equations
HFG EQUATIONS Version 2.0 27-2 Decision Time A t = 3.0 s Metric: Where: 5-8 V = design speed (km/h) a = driver decel. (m/s2) B t = 9.1 s US Customary: Where: V = design speed (mi/h) a = driver decel. (ft/s2) Metric: Where: C t = 10.2 â 11.2 s d = 0.278Vt d = 0.278Vt D t = 12.1 â 12.9 s US Customary: Where: E t = 14.0 â 14.5 s d = 1.47Vt V = design speed (mi/h) Procedures for Determining Curve Advisory Speed Limits Variables R = Curve Radius (m) O = Offset Distance from center of the lane to the obstruction (m) Tr = Driver Reaction time (seconds) d = Braking Coefficient V = Vehicle Speed (km/h) SDstop = Stopping Sight Distance SDacc = Sight Distance Vacc = Desirable maximum speed limited by lateral acceleration (km/h) Vsight = Desirable maximum speed limited by sight distance (km/h) Yellow Timing Interval Time Plus the Red Clearance Interval Time Metric Values English Values CP t V a Gg [ ] = + + : 2 2 + +W L V 11-6, 22-38 3 127 4 1 V R lateral acc erelevation SF = +( )_ . sup 6-6 = + â = 1 0 03476 0 00004762 4 2 127 2. . . V V V R latera acc l acc SF erelevation SD Racc _ . cos +âââ â â â = sup 5 1 2 â ââ ââ â â â = = + 1 5 2 3 6 R O R SD SD T V V stop acc r sight . . a sight sight r r d V d T T 2 254 5 2 127 3 6 3 6 . . . b = â + âââ â â â + â â ââ â â ââ 2 4 254 SD d acc d Vt V a t = +1 47 1 075. . d Vt V a t = +0 278 0 039. .
27-3 HFG EQUATIONS Version 2.0 Metric: a = deceleration, m/s2 (typically 3.1 m/s2) G = gravity @ 9.8 English: a = deceleration, ft/s2 (typically 10 ft/s2) G = gravity @ 32.2 Where: CP = non-dilemma change period (Change + Clearance Intervals) t = perception-reaction time (nominally 1 s) V = approach speed, m/s [ft/s] g = percent grade (positive for upgrade, negative for downgrade) a = deceleration, m/s2 (typical 3.1 m/s2) [ft/s2 (typical 10 ft/s2)] W = width of intersection, curb to curb, m [ft] L = length of vehicle, m (typical 6 m) [ft (typical 20 ft)] Gate Delay and Gate Interval Times Where: t = driver perception-reaction time (PRT, s) v = approach speed (m/s) a = deceleration rate on level pavement (m/s2) G = acceleration resulting from gravity (m/s2) g = grade of approach lanes (percent/100) D = distance between stop bar and gates (m) L = length of the vehicle (m) Wght = distance between entry and exit gates (m); for calculation see below Where: Wght = distance between entry and exit gates (m) Wt = width of railroad track (m) Wh = width of approaching lane of the highway (m) Wg = distance from track edge to gate (m) Î± = crossing angle (degrees) For 90Î± Î± Î± > = â( ) + â( ) +Â° : W W Wght t h sin tan180 2 180 2Wg sin 180â( )Î± For 90Î± Î± Î± Î± â¤ = + +Â°: W W W Wght t h g sin tan sin 2 2 Gate s v W Lghtinterval time ( )= +( )â¡â£â¢ â¤ â¦â¥ 1 Gate operation time Gate delay Gate interva= + l time 14-8 Gate delay s t v a G g D v ( ) = + +( ) + â¡ â£ â¢ â¤ 2 â¢ â¦ â¥
HFG EQUATIONS Version 2.0 27-4 Contrast Ratio (light-emitting CMS) Where: Luminancemax = luminance emitted by the area or element of greatest intensity (text) Luminancemin = luminance emitted by the area or element of least intensity (background) Display Time for Phases of Dynamic Messages Signs Where: T = total time available to read the message x = number of information units in phase 1 y = number of information units in phase 2 B = blanking time between phases Luminance Contrast Where: Lstripe = the luminance of the pavement marking Lpavement = the luminance of the pavement CIE Veiling Luminance Model Where: Iglare = luminous intensity of glare source Î¸ = glare angle A = driver age L I Aveil glare = + â¡ â£â¢ â¤ â¦â¥ + âââ â â â â¡ â£ 10 5 1 62 53 2 4 Î¸ Î¸ i . â¢ â¤ â¦ â¥ 21-2 Luminance contrast = âL L L stripe pavement pavement 20-10 T B t tâ¥ + +1 2 Time for phase t x Time for phase t 1 2 2 1 2 ( ) = ( ) = 2y T s ft d ( ) = ( )Legibility Distance Traveling Spee ft s( ) 19-10 Contrast ratio max min = Luminance Luminance Optimal contrast ratio range - 19-4= 8 12
27-5 HFG EQUATIONS Version 2.0 Sight Distance Where: d = required sight distance V = velocity of the vehicle(s) tprt = PRT tman = MT dmanV = distance required to execute a maneuver at velocity V k = a constant to convert the solution to the desired units (feet, meters) Reading Time (Sign Comprehension) Reading Distance (Sign Placement) Where: x = the number of critical words/numbers in the message y = the number of critical symbols in the message Reading Time (Complex Signs in High-Speed Conditions) Reading distance is obtained by multiplying the reading time by the travel speed Information Presence Distance (Sign Placement) Legibility Distance (Sign Placement) Minimum Letter Height (Signs) Minimum Letter Height in. Legibility Dist( ) = ance ft Legibility Index ft in. -41 ( ) ( ) 22 Legibility Distance Information Presentatio= n Distance Advance Placement -41â 22 Information Presentation Distance Reading= Distance Decision Distance Maneuver Distan + + ce -4122 Reading Time s Number of Familiar Wor( ) = 0 31. ds 22-40( ) +1 94. Base Reading Time (BRT): BRT s x y -3( ) = +0 5 1 22. 9 Reading time seconds number of symbols( ) = ( )1 + ( )0 5 22. number of words and numbers -32 d kVt kVt where maneuver time is iSD prt man= + , nput or d kVt d where maneuver diSD prt manV= + , stance is input -222
Abbreviations and acronyms used without definitions in TRB publications: AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACIâNA Airports Council InternationalâNorth America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA Air Transport Association ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S.DOT United States Department of Transportation