Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways (2023)

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93   Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections This appendix presents the equations used for computations in the sightline and reliability analysis model developed in the research. The model objectives, input data, and output results are presented in Chapter 4 of this report. The application of the model is discussed in Chapter 5 of this report. This appendix documents the details of the model computations. B.1 Variables Defined The variables listed and defined in the following table are used in the procedure detailed in this document. A P P E N D I X B Variable Definition a "a" term in quadratic equation α angle between x-axis and departure tangent measured in x-y plane (degrees) b "b" term in quadratic equation β angle between x-axis and length of right-turning vehicle measured in x-yplane (degrees) c "c" term in quadratic equation cminlnx capacity of minor-road lane x (veh/h) dcl-edge distance from major-road centerline to rightmost edge of traveled way (ft) Δ horizontal curve deflection angle (degrees) Δi angle between major-road approach and minor-road approach (degrees) deye-stop distance from driver's eye to stop line in x-y plane parallel to minor-road centerline (ft) dISD length of intersection sight distance (ft) dRT-eye distance from beginning of RTL taper to driver's eye at stop line in x-yplane measured along major-road centerline (ft) dRT-PC distance from beginning of RTL taper to horizontal curve point of curvature measured in x-y plane along major-road centerline (ft) dRT-VPC distance from beginning of RTL taper to vertical curve point of curvature measured in x-y plane along major-road centerline (ft) dstop-edge distance from rightmost edge of traveled way to minor-road stop bar (ft) e horizontal curve superelevation (%) EEi position of right-turning vehicle measured in x-y plane along major-road centerline from origin to right front bottom corner of vehicle (ft) EEI,r,s distance from origin to intersection point associated with right-turning vehicle corner r and through vehicle plane s measured in x-y plane along major-road centerline (ft) EEinc analysis incremental length (ft) G vertical grade of major road approaching intersection when no vertical curvature present (%)

94 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Variable Definition lvc length of vertical curve (ft) m slope of line in x-y plane that intersects the driver's eye and right-turning vehicle corner r (ft/ft) p percent of hour minor-road driver is present and has blocked view for all vehicles across all minor-road lanes pblocked,minlnx,minvehx percent of hour that any vehicle stopped in a particular minor-road approach lane of a particular vehicle type Peff,THveh,h effective percentage of height of through vehicle to be seen φ angle between x-y plane and line formed by right-turning vehicle points RFB and RRB (degrees) Plat,eye lateral placement of minor-road vehicle in minor-road lane (%) Plat,RTveh lateral placement of right-turning vehicle in RTL (%) pminlnx percent of hour minor-road driver is present and has blocked view for a particular minor-road lane pminlnx,minvehx percent of hour minor-road driver is present and has blocked view for a particular vehicle type in a particular minor-road lane pqueue,minlnx percent of hour a driver is present at the stop line in a particular minor-road lane pqueue,minlnx,minvehx percent of hour a driver is present at the stop line for a particular vehicletype in a particular minor-road lane R horizontal curve radius (ft) R' turning radius of right side of right-turning vehicle (ft) Rcr curb return radius (ft) So operating speed of major-road through lanes (ft/s) tblocked total length of time through lane is blocked by right-turning vehicle at all increments i (s) tblocked,i length of time through lane is blocked by right-turning vehicle at a specific increment i (s) tblocked,TH,combined total length of time all through lanes are blocked, adjusted for lane utilization (s) tblocked,TH,RT,combined total length of time all through lanes are blocked, adjusted for lane utilization and right-turning volume (s) tblocked,TH1 total length of time through lane 1 is blocked by right-turning vehicle(s) t'blocked,TH1 total length of time through lane 1 is blocked by right-turning vehicle adjusted for lane utilization(s) tblocked,TH2 total length of time through lane 2 is blocked by right-turning vehicle(s) t'blocked,TH2 total length of time through lane 2 is blocked by right-turning vehicle adjusted for lane utilization(s) tblocked,TH3 total length of time through lane 3 is blocked by right-turning vehicle(s) t'blocked,TH3 total length of time through lane 3 is blocked by right-turning vehicle adjusted for lane utilization(s) tblocked,TH4 total length of time through lane 4 is blocked by right-turning vehicle(s) t'blocked,TH4 total length of time through lane 4 is blocked by right-turning vehicle adjusted for lane utilization(s) θ portion of horizontal curve deflection angle that occurs after the origin (degrees) UTH1,percent percent of major-road through volume in major-road through lane 1 G1 vertical grade approaching vertical curve (%) G2 vertical grade departing vertical curve (%) γ angle between x-y plane and line formed by right-turning vehicle points RFB and LFB (degrees) GRT vertical grade of RTL at EEi (%) GRT,initial initial values used in the calculation of GRT heye driver's eye height (ft) hRTveh height of vehicle in major-road RTL (ft) hTHveh height of vehicle in major-road through lane (ft) lc length of horizontal curve (ft) lero length of superelevation runoff (ft) lparallel length of parallel portion of RTL (ft) lRTveh length of vehicle in major-road RTL (ft) ltaper length of tapered portion of RTL (ft) ltro length of tangent runout (ft)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 95   Variable Definition wmedian width of minor-road median (ft) wminln1 width of minor-road lane 1 (ft) wminln2 width of minor-road lane 2 (ft) wminln3 width of minor-road lane 3 (ft) wortb width of offset right-turn buffer (ft) wrt width of RTL (ft) wRTveh width of vehicle in major-road RTL (ft) wth,1 width of major-road lane 1 (ft) wth,2 width of major-road lane 2 (ft) wth,3 width of major-road lane 3 (ft) wth,4 width of major-road lane 4 (ft) wTHveh width of vehicle in major-road through lane (ft) xeye x coordinate of driver's eye position (ft) xI,r,s set of x coordinates for set of intersection points xIi x coordinate of intersection point i xLFB x coordinate of left-front-bottom corner of major-road right-turning vehicle xLFT x coordinate of left-front-top corner of major-road right-turning vehicle xLRB x coordinate of left-rear-bottom corner of major-road right-turning vehicle xLRT x coordinate of left-rear-top corner of major-road right-turning vehicle xr x coordinate of right-turning vehicle corner r (ft) xRFB x coordinate of right-front-bottom corner of major-road right-turning vehicle xRFT x coordinate of right-front-top corner of major-road right-turning vehicle xRRB x coordinate of right-rear-bottom corner of major-road right-turning vehicle xRRT x coordinate of right-rear-top corner of major-road right-turning vehicle xslope,EE cross slope of RTL at point EE (%) xslope,lt cross slope of roadway left of centerline (%) xslope,rt cross slope of roadway right of centerline (%) yeye y coordinate of driver's eye position (ft) yI,r,s set of y coordinates for set of intersection points yIi y coordinate of intersection point i yLFB y coordinate of left-front-bottom corner of major-road right-turning vehicle yLFT y coordinate of left-front-top corner of major-road right-turning vehicle yLRB y coordinate of left-rear-bottom corner of major-road right-turning vehicle yLRT y coordinate of left-rear-top corner of major-road right-turning vehicle yr y coordinate of right-turning vehicle corner r (ft) yRFB y coordinate of right-front-bottom corner of major-road right-turning vehicle yRFT y coordinate of right-front-top corner of major-road right-turning vehicle yRRB y coordinate of right-rear-bottom corner of major-road right-turning vehicle yRRT y coordinate of right-rear-top corner of major-road right-turning vehicle yrt,base distance measured in x-y plane between the front right bottom corner of right-turning vehicle and major-road centerline (ft) yth distance from edge of through vehicle to roadway centerline (ft) zadj factor used to adjust for roadway elevation at point EE taking into account roadway cross slope (ft) zEE,I,r,s elevation of roadway surface associated with intersection point Ii zeye z coordinate of driver's eye position (ft) zLFB z coordinate of left-front-bottom corner of major-road right-turning vehicle UTH2,percent percent of major-road through volume in major-road through lane 2 UTH3,percent percent of major-road through volume in major-road through lane 3 UTH4,percent percent of major-road through volume in major-road through lane 4 vEE,i speed of right-turning vehicle at analysis point EE,I (ft/s) ventry speed of right-turning vehicle entering the RTL (ft/s) vmin hourly volume of minor-road approach (veh/h) vminlnx hourly volume of minor-road lane x (veh/h) vminlnx,minvehx hourly volume of minor-road vehicle type x in minor-road lane x (veh/h) vRT hourly volume of major-road right turn (veh/h) vturn speed of right-turning vehicle turning onto minor road (ft/s) wexit width of minor-road departing lane (ft) wlnmin width between minor-road centerline and driver's eye projected onto major-road centerline (ft)

96 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways B.2 Determine Origin Condition The origin of the 3-D coordinate system is located on the roadway surface at the centerline where the right-turn taper begins. Based on input to the spreadsheet tool, the following equations determine the numerical condition that corresponds with the roadway alignment at the origin. d ld and0 RT PC cRT PC # #- - (B-1) d ld and0 RT PC vcRT VPC V# #- - (B-2) B.3 Calculate Distance from Origin to Driver’s Eye Along Centerline Prior to calculating the distance from the origin to the driver’s eye along the centerline, an intermediate variable is calculated to account for which minor approach lane is being analyzed: Minor approach lane 1: cos sin dw P w d,lnmin minln Istop edge I lat eye eye stop 1 D D= + +- -` j (B-3) Minor approach lane 2: cos sin w dw P w d, minlnlnmin minln Istop edge I lat eye eye stop 2 1 D D= + + +- -` j Minor approach lane 3: sin cos tan sin w P w w w d d d l l R w w w 2 , lnmin minln minln minln lnmin I lat eye eye stop stop edge I RT eye taper parallel cr I I exit median 3 2 1 D D D D = + + + + = + + + + + - - - ` j (B-4) Origin Location Applicable Equations 1 On tangent Equations B-1 and B-2 are FALSE 2 On horizontal curve Equation B-1 is TRUE and Equation B-2 is FALSE 3 On vertical curve Equation B-1 is FALSE and Equation B-2 is TRUE 4 On horizontal and vertical curves Equations B-1 and B-2 are TRUE Condition Variable Definition zLFT z coordinate of left-front-top corner of major-road right-turning vehicle zLRB z coordinate of left-rear-bottom corner of major-road right-turning vehicle zLRT z coordinate of left-rear-top corner of major-road right-turning vehicle zr z coordinate of right-turning vehicle corner r (ft) zRFB z coordinate of right-front-bottom corner of major-road right-turning vehicle zRFT z coordinate of right-front-top corner of major-road right-turning vehicle zRRB z coordinate of right-rear-bottom corner of major-road right-turning vehicle zRRT z coordinate of right-rear-top corner of major-road right-turning vehicle

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 97   B.4 Determine Driver’s Eye Condition The following equations determine the alphabetical condition that corresponds with the road- way alignment at the driver’s eye position: d d dand ld RT RT PC RT eyeceyeRT PC # $+- - - - (B-5) d d and d l dRT VPC RT eye RT VPC vc RT eye# $+- - - - (B-6) Condition Eye Location Applicable Equations A On tangent Equations B-5 and B-6 are FALSE B On horizontal curve Equation B-5 is TRUE and Equation B-6 is FALSE C On vertical curve Equation B-5 is FALSE and Equation B-6 is TRUE D On horizontal and vertical curves Equations B-5 and B-6 are TRUE The origin and eye conditions can be combined to represent a unique layout that represents the site being evaluated (i.e., “1D” is a site where the origin is on tangent, but the driver at the stop line is at a point along the major-road centerline that is on horizontal and vertical curves). It is possible, with some of these alphanumeric conditions, for there to be horizontal and/or vertical curves between the origin and the driver’s eye. These conditions are represented by lowercase Roman numerals using the following equations: d d d dandd an ld0 >> <RT RT PC RT PC RT eyeeyeRT PC c+- - - - - (B-7) d and d d and d l d0> > <RT VPC RT eye RT VPC RT VPC vc RT eye+- - - - - (B-8) Condition Between Origin and Eye Applicable Equations i Tangent only Equations B-7 and B-8 are FALSE ii Horizontal curve Equation B-7 is TRUE and Equation B-8 is FALSE iii Vertical curve Equation B-7 is FALSE and Equation B-8 is TRUE iv Horizontal and vertical curves Equations B-7 and B-8 are TRUE B.5 Compute Driver’s Eye Coordinates The driver’s eye coordinates are calculated based on the alphanumeric origin-eye condition derived in the previous sections. Each condition has a unique set of equations for determining the coordinates of the eye position. The following subsections address each of these conditions individually. Condition 1Ai dx RT eyeeye = - (B-9) sind ddy 0eye edge Istop eye stopcl edge D= - - -- - - (B-10) , z G d xslope rt y h 100 100eye RT eye eye eye = - - +- ` j (B-11)

98 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Condition 1Aii Horizontal curve to the left approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - + - - - - - - - - - ` j (B-12) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - + - - - - - - - - - - - ^ ^h h (B-13) Horizontal curve to the right approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - - - - - - - - - - - ` j (B-14) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - - - - - - - - - - - - - - ` `j j (B-15) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-16) d d l l<RT eye RT PC c ero- -- -` j (B-17) Runoff/Runout Condition AA , sinz G d xslope rt d d d h 100 100 0eye RT eye cl edge stop edge eye stop I eyeD= - - - - +- - - - (B-18) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d d d d d d l h e l 100 100 01 eye RT eye RT eye RT cl edge stop edge eye stop I cPC eye ero D = - - - - - - - + - - - - - - J L K K N P O O (B-19) Horizontal curve to the right approaching the intersection: If , , l d d l e e xslope rt > ero RT eye RT PC c- - -- - then use Equation B-18. Otherwise, use Equation B-20: Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-16 is TRUE BB Superelevation runoff Equation B-17 is TRUE CC Tangent runout Equations B-16 and B-17 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 99   | | | | | , | , , sin z G d l e e xslope rt d d l e xslope rt xslope rt d d d h 100 100 1 1 0 eye RT eye ero RT eye RT PC c cl edge stop edge eye stop I eyeD = - - - - - - + - - - + - - - - - - J L K KK ^ N P O OO h R T S S SS V X W W WW (B-20) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d xslope rt l d d l l d d d h 100 100 0 eye RT eye ro RT eye RT PC c ero cl edge stop edge eye stop I eye t D = - - - - - - - + - - - - - - d n (B-21) Use Equation B-18 if the horizontal curve to the right is approaching the intersection. Condition 1Aiii dxeye RT eye= - (B-22) sind d dy 0eye edge Icl edge stop eye stop D= - - -- - - (B-23) , z G d G l G G l G d d l xslope rt y h 100 100 200 100 100 eye RT VPC vc vc RT eye RT VPC vc eye eye 1 1 2 1 2 = + + - + - - - + - - - ^ ^ h h< F (B-24) Condition 1Aiv Horizontal curve to the left approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - + - - - - - - - - - ^ h (B-25) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - + - - - - - - - - - - - ` `j j (B-26) Horizontal curve to the right approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - - - - - - - - - - - ^ h (B-27) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - - - - - - - - - - - - - - ` `j j (B-28) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-29) d d l l<RT eye RT PC c ero- -- -` j (B-30)

100 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Runoff/Runout Condition AA , z G d G l G G l G d d l xslope rt d d d h 100 100 200 100 100 0 sin eye RT VPC vc vc RT eye RT VPC vc cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - + - - - - - - ` ` j j R T S SS V X W WW (B-31) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: z G d G l G G l G d d l e l d d l d d d sin h 100 100 200 100 100 1 0 eye RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - - - - + - - - - - - - - J L K K ` ` N P O O j j R T S SS V X W WW (B-32) Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-31. Otherwise, use Equation B-33: , , , sin z G d G l G G l G d d l l e e xslope rt d d l e xslope rt xslope rt d d d h 100 100 200 100 100 1 1 0 eye RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - - - + - - - + - - - - - - - - J L K K KK ` ` ` N P O O OO j j j R T S SS R T S S S SS V X W W W WW V X W WW (B-33) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d G l G G l G d d l xslope rt l d d l l d d d h 100 100 200 100 100 0 eye RT VPC vc vc RT eye RT VPC vc tro RT eye RT PC c ero cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - - - - + - - - - - - - - J L K K ` ` N P O O j j R T S SS V X W WW (B-34) Use Equation B-31 if the horizontal curve to the right is approaching the intersection. Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-29 is TRUE BB Superelevation runoff Equation B-30 is TRUE CC Tangent runout Equations B-29 and B-30 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 101   Condition 2A l l d c c RT PCa D= + - (B-35) Horizontal curve to the left approaching the intersection: cos sinsin sind d lR d d dx 0RT eye RT PC c cl edge stop edge eye stop Ieye a a aD= + - - + - - -- - - - -` j (B-36) cos sin sin cosd d lR R d d dy 0RT eye RT PC c cl edge stop edge eye stop Ieye a a aD= - + - - - - - -- - - - -` `j j (B-37) Horizontal curve to the right approaching the intersection: sin cos sin sinx R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= + - - - - - -- - - - -` j (B-38) cos sin sin cosy R R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= - - - - - - - - -- - - - -` `j j (B-39) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c ro erot- - +- -` `j j (B-40) d d l l<RT eye RT PC c ero- -- -` j (B-41) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-40 is TRUE BB Superelevation runoff Equation B-41 is TRUE CC Tangent runout Equations B-40 and B-41 are FALSE Runoff/Runout Condition AA , sinz G d d d d h xslope rt 100 100 0eye RT eye cl edge stop edge eye stop I eyeD= - - - - +- - - - (B-42) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sinz G d e l d d l d d d h 100 100 1 0eye RT eye ero RT eye RT PC c cl edge stop edge eye stop I eyeD= - - - - - - - +- - - - - - J L K K N P O O (B-43)

102 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-42. Otherwise, use Equa - tion B-44: , , , sin z G d l e e xslope rt d d l e xslope rt xslope rt d d d h 100 100 1 1 0 eye RT eye ero RT eye RT PC c cl edge stop edge eye stop I eyeD = - - - - - - + - - - + - - - - - - J L K K KK ` N P O O OO j R T S S S SS V X W W W WW (B-44) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin d xslope rt l d d l l d d d h z G 0 100 100RT eye tro RT eye RT PC c ero cl edge stop edge eye stop I eye eye D = - - - - - - - + - - - - - - J L K K N P O O (B-45) Use Equation B-42 if the horizontal curve to the right is approaching the intersection. Condition 2Aiii Horizontal curve to the left approaching the intersection: sin cos sin sinx R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= + - - + - - -- - - - -` j (B-46) cos sin sin cosy R R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= - + - - - - - -- - - - -` `j j (B-47) Horizontal curve to the right approaching the intersection: sin cos sin sinx R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= + - - - - - -- - - - -` j (B-48) cos sin sin cosy R R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= - - - - - - - - -- - - - -` `j j (B-49) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-50) d d l l<RT eye RT PC c ero- -- -` j (B-51) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-50 is TRUE BB Superelevation runoff Equation B-51 is TRUE CC Tangent runout Equations B-50 and B-51 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 103   Runoff/Runout Condition AA , z G d G l G G l G d d l xslope rt d d d h 100 100 200 100 100 0 sin eye RT VPC vc vc RT eye RT VPC vc cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - + - - - - - - ` ` j j R T S SS V X W WW (B-52) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d G l G G l G d d l l d d l d d d h e 100 100 200 100 100 01 eye RT VPC vc vc RT eye RT VPC vc ro RT eye RT PC c cl edge stop edge eye stop I eye e 1 1 2 1 2 D = + + - + - - - - - - - - - + - - - - - - - - J L K K ` ` N P O O j j R T S SS V X W WW (B-53) Horizontal curve to the right approaching the intersection: If , , l d d l e e xslope rt > ero RT eye RT PC c- - -- - then use Equation B-52. Otherwise, use Equation B-54: , , , sin z G d G l G G l G d d l l e e xslope rt d d l e xslope rt xslope rt d d d h 100 100 200 100 100 1 1 0 eye RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - - - + - - - + - - - - - - - - J L K K KK ` ` ` N P O O OO j j j R T S SS R T S S S SS V X W W W WW V X W WW (B-54) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d G l G G l G d d l xslope rt l d d l l d d d h 100 100 200 100 100 0 eye RT VPC vc vc RT eye RT VPC vc tro RT eye RT PC c ero cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - - - - + - - - - - - - - J L K K ` ` N P O O j j R T S SS V X W WW (B-55) Use Equation B-52 if the horizontal curve to the right is approaching the intersection. Condition 3A x deye RT eye= - (B-56) siny d d d0eye cl edge stop edge eye stop ID= - - -- - - (B-57)

104 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways , z G d l G G d G l G G l G d d l xslope rt y h 100 200 100 200 100 100 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc eye eye 1 2 1 2 1 2 1 2 = - + - + + - + - - - + - - - -` ` ` j j j R T S SS V X W WW * 3 (B-58) Condition 3Aii Horizontal curve to the left approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - + - - - - - - - - - ` j (B-59) cos sin sin cosy R R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop ID D D D= - + - - - - - -- - - - -` `j j (B-60) Horizontal curve to the right approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - - - - - - - - - - - ` j (B-61) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - - - - - - - - - - - - - - ` `j j (B-62) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c ro erot- - +- -` `j j (B-63) d d l l<RT eye RT PC c ero- -- -` j (B-64) Runoff/Runout Condition AA , sin z G d l G G d G l G G l G d d l xslope rt d d d 100 200 100 200 100 100 0 eye RT VPC vc RT VPC vc vc RT eye RT PC vc cl edge stop edge eye stop I eyeV 1 2 1 2 1 2 1 2 D = - + - + + - - - - - - - - - - - - - h+ - +` ` ` j j j R T S S S V X W W W * 4 (B-65) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-63 is TRUE BB Superelevation runoff Equation B-64 is TRUE CC Tangent runout Equations B-63 and B-64 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 105   Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d l G G d G l G G l G d d l e l d d l d d d h 100 200 100 200 100 100 1 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - + - - - - - - - - - + - - - - - - - - - J L K K` ` ` N P O Oj j j R T S S S V X W W W * 4 (B-66) Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-65. Otherwise, use Equa- tion B-67: , , , sin z G d l G G d G l G G l G d d l l e e xslope rt d d l e xslope rt xslope rt d d d h 100 200 100 200 100 100 1 1 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - + - - - - - - - - + - - - + - - - - - - - - - J L K K KK ` ` ` ` N P O O OO j j j j R T S S S R T S S S SS V X W W W V X W W W WW * 4 (B-67) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d l G G d G l G G l G d d l xslope rt l d d l l d d d h 100 200 100 200 100 100 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc tro RT eye RT PC c ero cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - + - - - - - - - - - + - - - - - - - - - J L K K` ` ` N P O Oj j j R T S S S V X W W W * 4 (B-68) Use Equation B-65 if the horizontal curve to the right is approaching the intersection. Condition 4A Horizontal curve to the left approaching the intersection: sin cos sin sinx R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= + - - + - - -- - - - -` j (B-69)

106 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways cos sin sin cosy R R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= - + - - - - - -- - - - -` `j j (B-70) Horizontal curve to the right approaching the intersection: sin cos sin sinx R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD= + - - - - - -- - - - -` j (B-71) cos sin sin cosy R R d d l d d d0eye RT eye RT PC c cl edge stop edge eye stop Ia a aD=- - - - - - - - -- - - - -` `j j (B-72) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-73) d d l l<RT eye RT PC c ero- -- -` j (B-74) Runoff/Runout Condition AA , sin z G d l G G d G l G G l G d d l xslope rt d d d 100 200 100 200 100 100 0 eye RT VPC vc RT VPC vc vc RT eye RT PC vc cl edge stop edge eye stop I eyeV 1 2 1 2 1 2 1 2 D = - + - + + - - - - - - - - - - - - - h+ - +` ` ` j j j R T S S S V X W W W * 4 (B-75) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d l G G d G l G G l G d d l e l d d l d d d h 100 200 100 200 100 100 1 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - + - - - - - - - - - + - - - - - - - - - J L K K` ` ` N P O Oj j j R T S S S V X W W W * 4 (B-76) Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-75. Otherwise, use Equation B-77: Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-73 is TRUE BB Superelevation runoff Equation B-74 is TRUE CC Tangent runout Equations B-73 and B-74 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 107   , , , sin z G d l G G d G l G G l G d d l l e e xslope rt d d l e xslope rt xslope rt d d d h 100 200 100 200 100 100 1 1 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - + - - - - - - - - + - - - + - - - - - - - - - J L K K KK ` ` ` ` N P O O OO j j j j R T S S S R T S S S SS V X W W W V X W W W WW * 4 (B-77) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d l G G d G l G G l G d d l xslope rt l d d l l d d d h 100 200 100 200 100 100 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc tro RT eye RT PC c ero cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - + - - - - - - - - - + - - - - - - - - - J L K K` ` ` N P O Oj j j R T S S S V X W W W * 4 (B-78) Use Equation B-75 if the horizontal curve to the right is approaching the intersection. Condition 1B Horizontal curve to the left approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + + - - -- - - - (B-79) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-80) Horizontal curve to the right approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + - - - -- - - - (B-81) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-82) sinz G d e d d d h 100 100 0eye RT eye cl edge stop edge eye stop I eyeD= - - - - +- - - - (B-83) Condition 1Biii Horizontal curve to the left approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + + - - -- - - - (B-84) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-85)

108 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the right approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + - - - -- - - - (B-86) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-87) z G d G l G G l G d d l d d d h e 100 100 200 100 100 0 sin eye RT VPC vc vc RT eye RT VPC vc cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - + - - - - - - ` ` j j R T S SS V X W WW (B-88) Condition 2B Horizontal curve to the left approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= + - - -- - - (B-89) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-90) Horizontal curve to the right approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= - - - -- - - (B-91) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-92) z G d e d d d h 100 100 0 sineye RT eye cl edge stop edge eye stop I eyeD= - - - - +- - - - (B-93) Condition 2Biii Horizontal curve to the left approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= + - - -- - - (B-94) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-95) Horizontal curve to the right approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= - - - -- - - (B-96) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-97) sin z G d G l G G l G d d l d d d h e 100 100 200 100 100 0 eye RT VPC vc vc RT eye RT VPC vc cl edge stop edge eye stop I eye 1 1 2 1 2 D = + + - + - - - - - - + - - - - - - ` ` j j R T S SS V X W WW (B-98)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 109   Condition 3B Horizontal curve to the left approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + + - - -- - - - (B-99) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-100) Horizontal curve to the right approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + - - - -- - - - (B-101) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-102) sin z G d l G G d G G G l G d d l e d d d h 100 200 100 200 100 100 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - - - - - - - - + - - - - - - - l+ + + ` ` `j j j R T S S S V X W W W * _ ` a bb b (B-103) Condition 4B Horizontal curve to the left approaching the intersection: sinsin sinx R d d d0eye cl edge stop edge eye stop Ia aD= + - - -- - - (B-104) cos sin cosR R d d dy 0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-105) Horizontal curve to the right approaching the intersection: sin sin sinR d d dx 0eye cl edge stop edge eye stop Ia aD= - - - -- - - (B-106) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-107) sin z G d l G G d G l G G l G d d l e d d d h 100 200 100 200 100 100 0 eye RT VPC vc RT VPC vc vc RT eye RT VPC vc cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + + - - - - - - - + - - - - - - - + ` ` `j j j R T S S S V X W W W * _ ` a bb b (B-108) Condition 1C x deye RT eye= - (B-109)

110 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways siny d d d0eye cl edge stop edge eye stop ID= - - -- - - (B-110) , sin G G d d xslope rt d d d h z G d G d d 100 0 100 100 200 RT eye RT VPC cl edge stop edge eye stop I eye eye RT VPC RT eye RT VPC 2 11 1 D = + - + - - - - - - + - - - - - - - - ` ` ` j j j R T S SS V X W WW (B-111) Condition 1Cii Horizontal curve to the left approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - + - - - - - - - - - ` j (B-112) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - + - - - - - - - - - - - ` `j j (B-113) Horizontal curve to the right approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - - - - - - - - - - - ` j (B-114) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - - - - - - - - - - - - - - ` `j j (B-115) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-116) d d l l<RT eye RT PC c ero- -- -` j (B-117) Runoff/Runout Condition AA , sin z G d G d d G G d d xslope rt d d d h 100 100 200 100 0 eye RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop eyel 1 1 2 1 D = + - + - - - - - - + - - - - - - - - ` ` ` j j j R T S SS V X W WW (B-118) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-116 is TRUE BB Superelevation runoff Equation B-117 is TRUE CC Tangent runout Equations B-116 and B-117 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 111   Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d G d d G G d d e l d d l d d d h 100 100 200 100 1 0 eye RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT PC c cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - - - - + - - - - - - - - - - J L K K ` ` ` N P O O j j j R T S SS V X W WW (B-119) Horizontal curve to the right approaching the intersection: If ,xslope rt l d d l e e > ero RT eye RT PC c- - -- - , then use Equation B-118. Otherwise, use Equation B-120: , , , sin z G d G d d G G d d l e e xslope rt d d l e xslope rt xslope rt d d d h 100 100 200 100 1 1 0 eye RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT PC c cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - - - + - - - + - - - - - - - - - - J L K K KK ` ` ` ` N P O O OO j j j j R T S SS R T S S S SS V X W W W WW V X W WW (B-120) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d G d d G G d d d d d h xslope rt l d d l l 100 100 200 100 0 eye RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye tro RT eye RT PC c ero 1 1 2 1 D = + - + - - - - - - - - - + - - - - - - - - - - J L K K ` ` ` N P O O j j j R T S SS V X W WW (B-121) Use Equation B-118 if the horizontal curve to the right is approaching the intersection. Condition 2C Horizontal curve to the left approaching the intersection: cos sin sin sin d d d x R d d l 0 cl edge stop edge eye stop I eye RT eye RT PC ca a aD = + - - + - - - - - - - - ` j (B-122) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = - + - - - - - - - - - - - ` `j j (B-123)

112 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the right approaching the intersection: sin cos sin sin x R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = + - - - - - - - - - - - ` j (B-124) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = - + - - - - - - - - - - - ` `j j (B-125) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. l l ld d >c tro eroRT eye RT PC- - +- -` `j j (B-126) l ld d <c eroRT eye RT PC- -- -` j (B-127) Runoff/Runout Condition AA , sin z G d G d d G G d d xslope rt d d d h 100 100 200 100 0 eye RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - + - - - - - - - - ` ` ` j j j R T S SS V X W WW (B-128) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d G d d G G d d e l d d l d d d h 100 100 200 100 1 0 eye RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT PC c cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - - - - + - - - - - - - - - - J L K K ` ` ` N P O O j j j R T S SS V X W WW (B-129) Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-128. Otherwise, use Equation B-130: , , , sin z G d G d d G G d d e e xslope rt d d l e xslope rt xslope rt d d d h l 100 100 200 100 1 1 0 eye RT VPC RT eye RT VPC RT eye RT VPC RT eye RT PC c cl edge edge eye stop I eye ero stop 1 1 2 1 D = + - + - - - - - - - - + - - - + - - - - - - - - - - J L K K KK ` ` ` ` N P O O OO j j j j R T S SS R T S S S SS V X W W W WW V X W WW (B-130) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-126 is TRUE BB Superelevation runoff Equation B-127 is TRUE CC Tangent runout Equations B-126 and B-127 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 113   Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d G d d G G d d xslope rt l d d l l d d d h 100 100 200 100 0 eye RT VPC RT eye RT VPC RT eye RT VPC tro RT eye RT PC c ero cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - - - - + - - - - - - - - - - J L K K ` ` ` N P O O j j j R T S SS V X W WW (B-131) Use Equation B-128 if the horizontal curve to the right is approaching the intersection. Condition 3C x deye RT eye= - (B-132) siny d d d0eye cl edge stop edge eye stop ID= - - -- - - (B-133) , sin z G d l G G d G d d G G d d xslope rt d d d h 100 200 100 200 100 0 eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 D = - + - + - - - - - - - + - - - - - - - - - + 2 ` ` ` ` j j j j R T S S S V X W W W * _ ` a bb b (B-134) Condition 3Cii Horizontal curve to the left approaching the intersection: sin sin cossinx d d d d R d d l 0 eye cl edge stop edge eye stop I RT PC RT eye RT PC cD D D D = + + - - + - - - - - - - - - ` j (B-135) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - + - - - - - - - - - - - ` `j j (B-136) Horizontal curve to the right approaching the intersection: sin cos sin sin x d R d d l d d d0 eye RT PC RT eye RT PC c cl edge stop edge eye stop I D D D D = + + - - - - - - - - - - - - ` j (B-137) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I D D D D = - - + - - - - - - - - - - - ` `j j (B-138) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye.

114 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-139) d d l l<RT eye RT PC c ero- -- -` j (B-140) Runoff/Runout Condition AA , sin z G d l G G d G d d G G d d xslope rt d d d h 100 200 100 200 100 0 eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - - - - - - - + - - - - - - - - -+ ` ` ` ` j j j j R T S S S V X W W W * _ ` a bb b (B-141) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: sin z G d l G G d G d d G G d d e l d d l d d d h 100 200 100 200 100 1 0 eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - - - - - - - - - - + - - - - - - - - - - - + J L K K ` ` ` ` N P O O j j j j R T S S S V X W W W * _ ` a bb b (B-142) Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-141. Otherwise, use Equation B-143: , , , sin z G d l G G d G d d G G d d l e e xslope rt d d l e xslope rt xslope rt d d d h 100 200 100 200 100 1 1 0 eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT VPC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - - - - - - - - - + - - - + - - - - - - - - - - - + J L K K KK ` ` ` ` ` N P O O OO j j j j j R T S S S R T S S S SS V X W W W V X W W W WW * _ ` a bb b (B-143) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-139 is TRUE BB Superelevation runoff Equation B-140 is TRUE CC Tangent runout Equations B-139 and B-140 are FALSE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 115   Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , sin z G d l G G d G d d G G d d xslope rt l d d l l d d d h 100 200 100 200 100 0 eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC tro RT eye RT PC c ro cl edge eye stop eye stop I eye e 1 2 1 2 1 2 1 2 D = - + - + - - - - - - - - - - + - - - - - - - - - - - + J L K K ` ` ` ` N P O O j j j j R T S S S V X W W W * _ ` a bb b (B-144) Use Equation B-141 if the horizontal curve to the right is approaching the intersection. Condition 4C Horizontal curve to the left approaching the intersection: sin cos sin sin x R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = + - - + - - - - - - - - ` j (B-145) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = - + - - - - - - - - - - - ` `j j (B-146) Horizontal curve to the right approaching the intersection: sin cos sin sin x R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = + - - - - - - - - - - - ` j (B-147) cos sin sin cos y R R d d l d d d0 eye RT eye RT PC c cl edge stop edge eye stop I a a aD = - - - - - - - - - - - - - - ` `j j (B-148) It is necessary to check to see whether the superelevation runoff or tangent runout is present at the point along the centerline that corresponds with the location of the driver’s eye. d d l l l>RT eye RT PC c tro ero- - +- -` `j j (B-149) d d l l<RT eye RT PC c ero- -- -` j (B-150) Runoff/Runout Condition Description Applicable Equations AA No runoff or runout Equation B-149 is TRUE BB Superelevation runoff Equation B-150 is TRUE CC Tangent runout Equations B-149 and B-150 are FALSE

116 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Runoff/Runout Condition AA , z G d l G G d G d d G G d d xslope rt d d d h 100 200 100 200 100 0 sin eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - + - - - - - - + - - - - - - - - - ` ` ` ` j j j j R T S S S V X W W W * 4 (B-151) Runoff/Runout Condition BB Horizontal curve to the left approaching the intersection: z G d l G G d G d d G G d d e l d d l d d d h 100 200 100 200 100 1 0 sin eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - + - - - - - - - - - + - - - - - - - - - - - J L K K ` ` ` ` N P O O j j j j R T S S S V X W W W * 4 (B-152) Horizontal curve to the right approaching the intersection: If , l d d l e e xslope rt > ero RT eye RT PC c- - -- - , then use Equation B-151. Otherwise, use Equation B-153: , , , z G d l G G d G d d G G d d l e e xslope rt d d l e xslope rt xslope rt d d d h 100 200 100 200 100 1 1 0 sin eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC ero RT eye RT PC c cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - + - - - - - - - - + - - - + - - - - - - - - - - - J L K K KK ` ` ` ` ` N P O O OO j j j j j R T S S S R T S S S SS V X W W W V X W W W WW * 4 (B-153) Runoff/Runout Condition CC Horizontal curve to the left approaching the intersection: , z G d l G G d G d d G G d d xslope rt l d d l l d d d h 100 200 100 200 100 0 sin eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC tro RT eye RT PC c ero cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - + - - - - - - - - - + - - - - - - - - - - - J L K K ` ` ` ` N P O O j j j j R T S S S V X W W W * 4 (B-154)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 117   Use Equation B-151 if the horizontal curve to the right is approaching the intersection. Condition 1D Horizontal curve to the left approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + + - - -- - - - (B-155) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-156) Horizontal curve to the right approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + - - - -- - - - (B-157) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-158) z G d G d d G G d d e d d d h 100 100 200 100 0 sin eye RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - + - - - - - - - - ` ` ` j j j R T S SS V X W WW (B-159) Condition 2D Horizontal curve to the left approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= + - - -- - - (B-160) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-161) Horizontal curve to the right approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= - - - -- - - (B-162) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-163) z G d G d d G G d d e d d d h 100 100 200 100 0 sin eye RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 1 2 1 D = + - + - - - - - - + - - - - - - - - ` ` ` j j j R T S SS V X W WW (B-164) Condition 3D Horizontal curve to the left approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + + - - -- - - - (B-165) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-166)

118 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the right approaching the intersection: sin sin sinx d R d d d0eye RT PC cl edge stop edge eye stop Ia aD= + - - - -- - - - (B-167) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-168) z G d l G G d G d d G G d d e d d d h 100 200 100 200 100 0 sin eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - + - - - - - - + - - - - - - - - - ` ` ` ` j j j j R T S S S V X W W W * 4 (B-169) Condition 4D Horizontal curve to the left approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= + - - -- - - (B-170) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - -- - -` j (B-171) Horizontal curve to the right approaching the intersection: sin sin sinx R d d d0eye cl edge stop edge eye stop Ia aD= - - - -- - - (B-172) cos sin cosy R R d d d0eye cl edge stop edge eye stop Ia aD= - - - - - -- - -` j (B-173) z G d l G G d G d d G G d d e d d d h 100 200 100 200 100 0 sin eye RT VPC vc RT VPC RT eye RT VPC RT eye RT VPC cl edge stop edge eye stop I eye 1 2 1 2 1 2 1 2 D = - + - + - + - - - - - - + - - - - - - - - - ` ` ` ` j j j j R T S S S V X W W W * 4 (B-174) B.6 Determine First Analysis Point The first analysis point is needed to know where the right-turning vehicle is positioned in the Cartesian coordinate system for the first iteration of the sightline analysis. The sightline model analyzes the right-turning vehicle in several positions in the RTL and how it obscures each major approach lane. The model analyzes each major approach lane in sequence. For the first run of the model (when the major approach lane equals 1, meaning that the sightline model is only con- cerned with the occlusion cast on major approach lane 1, which is the major approach lane adja- cent to the RTL), it is assumed the right-turning vehicle first occludes the major approach lane when the entire right-turning vehicle has entered the RTL. This assumption is needed because a through vehicle in major approach lane 1 cannot be occluded by the right-turning vehicle until the right-turning vehicle is entirely out of the major approach lane.

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 119   For subsequent runs of the model for the other major approach lanes, the right-turning vehicle could potentially occlude the other major approach lanes even when the right-turning vehicle is still partially in the first major approach lane (i.e., the right-turning vehicle is just entering the right-turning vehicle). Thus, it is assumed the first analysis point is just past the origin point of the Cartesian coordinate system (which the origin is assumed to be the point at which the RTL taper begins). If the major approach lane equals 1, then the analysis of determining whether the right-turning vehicle blocks the sightline of a stopped vehicle on the minor-road approach begins when the back left bottom corner of the right-turning vehicle crosses the right edge of the outermost trav- eled lane. If the major approach lane is greater than 1, then the analysis begins 1 ft after the point at which the RTL taper begins. The variable, EE, is used to represent the distance of the front right bottom corner of the right- turning vehicle to the origin along the roadway centerline. If major approach lane equals 1: tan l w w taper rt ortb1~ = + - (B-175) sin cos cos EE w P w w l w 1 100 1 1 1,rt lat RTveh rt RTveh RTveh RTveh1 2~ ~ ~ = - + + - - J L KK J L KK N P OO N P OO (B-176) If major approach lane is greater than 1: EE 11 = (B-177) B.7 Determine Whether EE Is on Right-Turn Taper, Parallel, or Turning Portion of RTL EE l<i taper (B-178) EE l l>i taper parallel+ (B-179) EE Position Applicable Equations On taper Equation B-178 is TRUE On parallel Equations B-178 and B-179 are FALSE On turn Equation B-178 is TRUE B.8 Calculate Speed of Right-Turning Vehicle at EE If EE is the first iteration: v v,EE entry1 = (B-180) If EE is past the first iteration and not on the turning portion of the RTL: l l EE EEv v v v , ,EE i EE i taper parallel turn entry inc1 2 1 2 2 = + + - - - (B-181)

120 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways If EE is on the turning portion of the RTL: v v,EE i turn= (B-182) B.9 Calculate Coordinates of Right-Turning Vehicle at EE The coordinate of the front right bottom corner of the right-turning vehicle is determined first. The calculation of this coordinate is based on the combination of the position of the right- turning vehicle relative to horizontal and vertical curves and whether the right-turning vehicle is on the taper, parallel, or turning portion of the RTL. The following equations determine the alphabetical condition that corresponds with the road- way alignment at the right-turning vehicle position: dd EE and l EERT PCRT PC i c i# $+- - (B-183) d EE and d l EERT VPC i RT VPC vc i# $+- - (B-184) The origin and right-turning vehicle conditions can be combined to represent a unique layout that represents the site being evaluated (i.e., “1D” is a site where the origin is on tangent, but the right-turning vehicle is at a point along the major-road centerline that is on horizontal and verti- cal curves). It is possible, with some of these alphanumeric conditions, for there to be horizontal and or vertical curves between the origin and the right-turning vehicle. These conditions are represented by lowercase Roman numerals using the following equations: d and EE d and d l EE0> > <RT PC i RT PC RT PC c i+- - - (B-185) d EE d d l EEand and0> <>RT VPC i RT VPC RT VPC c iv+- - - (B-186) A variable, yrt,base, is calculated and used in all subsequent conditional calculations of deter- mining the coordinate of the front right bottom corner of the right-turning vehicle. If EE is on the taper portion of the RTL: y d EE l w w w P w l w w 100 1, , rt base cl edge i taper rt ortb rt lat RTveh rt taper rt ortb 2 = - - + + - + + - J L KK J L K K N P OO N P O O (B-187) If EE is on the parallel portion of the RTL: w P wy d 100 , , ortb lat RTveh rtrt base cl edge= - - -- (B-188) Condition Right-Turning Vehicle Location Applicable Equations A On tangent Equations B-183 and B-184 are FALSE B On horizontal curve Equation B-183 is TRUE and Equation B-184 is FALSE C On vertical curve Equation B-183 is FALSE and Equation B-184 is TRUE D On horizontal and vertical curves Equations B-183 and B-184 are TRUE Condition Between Origin and Eye Applicable Equations i Tangent only Equations B-185 and B-186 are FALSE ii Horizontal curve Equation B-185 is TRUE and Equation B-186 is FALSE iii Vertical curve Equation B-185 is FALSE and Equation B-186 is TRUE iv Horizontal and vertical curves Equations B-185 and B-186 are TRUE

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 121   If EE is on the turning portion of the RTL: R R w P w 100 , cr rt lat RTveh rt= + -l (B-189) y d w P w R lR EE l 100, , rt base cl edge ortb lat RTveh rt paralleli taper 22= - - - - + - - -- l l ` j (B-190) Determine Cross Slope and Grade in RTL at EE The elevation (z-coordinate) of the front right bottom corner of the right-turning vehicle is dependent on the cross slope in the RTL at EE. Also, the pitch of the right-turning vehicle is dependent on the grade of the RTL roadway surface at EE. The following procedure is used to determine the cross slope, xslopeEE, and GRT, which will be used in all subsequent equations. Initially, use Equations B-191 through B-193 to determine GRT. If EEi ≤ dRT−VPC, or no vertical curve is present, then: G G,RT initial 1= (B-191) If EEi ≥ dRT−VPC + lvc, then: G G,RT initial 2= (B-192) If EEi > dRT−VPC and EEi < dRT−VPC + lvc, then: G G l EE d G G, vc i RT VPC RT initial 11 2= + + - - ` j (B-193) ,xslopexslope rtEE = (B-194) d l l EE>RT PC tro ero i- -- (B-195) d l l lEE >RT PC ro eroc ti - - +- (B-196) If Equation B-195 or B-196 is true, then use Equation B-194 to calculate xslopeEE. If Equations B-195 and B-196 are false, then continue below. If EEi > dRT−PC − lero, then EE is on the superelevation runoff prior to the horizontal curve, and use Equations B-197 through B-200 to determine xslopeEE and GRT. Horizontal curve to the left approaching the intersection: xslope l d EE e 1EE ero RT PC i= - --J L KK N P OO (B-197) G l G e y ,,RT RT initial ero rt base= + (B-198)

122 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the right approaching the intersection: If , e xslope rt l d EE e > ero RT PC i- -- , use Equations B-191 through B-194. Otherwise: , , ,xslope xslope EE xslope rt l e e xslope rt d EE rt 1i ero RT PC i EE = + - - - -- J L K K KK ` N P O O OO j (B-199) , , l e e xslope rt EE xslope rt GG y , , ero i RTRT rt base initial= - - + ` j (B-200) If EEi > dRT−PC − lero – ltro, then EE is on the tangent runout prior to the horizontal curve, and use Equations B-201 through B-202 to determine xslopeEE and GRT. Horizontal curve to the left approaching the intersection: ,xslope xslope rt l d l EE EE tro RT PC ero i= - --J L KK N P OO (B-201) , l xslope rt GG y ,, tro RT initialRT rt base= + (B-202) Horizontal curve to the right approaching the intersection: Use Equations B-191 through B-194. If EEi − dRT−PC – lc < lero, then EE is on the superelevation runoff after the horizontal curve, and use Equations B-203 through B-206 to determine xslopeEE and GRT. Horizontal curve to the left approaching the intersection: xslope e l EE d l 1EE ero i RT PC c= - - --J L KK N P OO (B-203) G G l e y, ,RT RT initial ero rt base= - (B-204) Horizontal curve to the right approaching the intersection: If , l d l e e xslope rtEE > ero RT PC ci- - -- , use Equations B-191 through B-194. Otherwise: , , ,xslope xslope xslope rt e xslope rt l e EE d l rt EE 1 ero i RT PC c EE i= + - - - - -- J L K K KK ` N P O O OO j (B-205) , , G e xslope rt EE xslope rt G l e y, ,RT i RT initial ero rt base= - - -` j (B-206)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 123   If EEi − dRT−PC − lero − lc < ltro, then EE is on the tangent runout after the horizontal curve, and use Equations B-207 through B-208 to determine xslopeEE and GRT. Horizontal curve to the left approaching the intersection: ,xslope xslope rt l EE d l l EE tro i RT PC c ero= - - --J L KK N P OO (B-207) , G G l xslope rt y, ,RT RT initial tro rt base= - (B-208) Horizontal curve to the right approaching the intersection: Use Equations B-191 through B-194. Right-Turn Condition 1Ai x EERFB i= (B-209) y y ,RFB rt base= (B-210) z G EE xslope y 100 100 ,RFB i EE rt base= - (B-211) EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL = tan−1 + = 0 = sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-212) tan cos sinxslope G 100 EE RT1c b b = - - (B-213) Right-Turn Condition 1Aii Horizontal curve to the left approaching the intersection: cos sinsin yx d R EE d l ,rt baseRFB RT PC i RT PC cD D D= + + - - +- -` j (B-214) cos sin cosyR R EE d ly ,rt baseRFB i RT PC cD D D= - + - - +-` `j j (B-215) Horizontal curve to the right approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - -- -` j (B-216) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - - - - - +-` `j j (B-217) z G EE xslope y 100 100 ,RFB i EE rt base= - (B-218)

124 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − Δ = −Δ = −Δ + sin−1 − ( + ) ′ Right = tan−1 + + Δ = Δ = Δ + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-219) tan cos sinxslope G 100 EE RT1c b b = - - (B-220) Right-Turn Condition 1Aiii x EERFB i= (B-221) y y ,RFB rt base= (B-222) z G d G l G G l G EE d l xslope y 100 100 200 100 100 , RFB RT VPC vc vc I RT VPC vc EE rt base 1 1 2 1 2= + + - + - - - - - ` ` j j R T S SS V X W WW (B-223) EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL = tan−1 + = 0 = sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-224) tan cos sinxslope G 100 EE RT1c b b = - - (B-225) Right-Turn Condition 1Aiv Horizontal curve to the left approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - +- -` j (B-226) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - + - - +-` `j j (B-227) Horizontal curve to the right approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - +- -` j (B-228)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 125   cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - - + - - +-` `j j (B-229) z G d G l G G l G EE d l xslope y 100 100 200 100 100 , RFB RT VPC vc vc RT PVC vc EE rt base i 1 1 2 1 2= + + - + - - - - - ` ` j j R T S SS V X W WW (B-230) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − Δ = −Δ = −Δ + sin−1 − ( + ) ′ Right = tan−1 + + Δ = Δ = Δ + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-231) tan cos sinxslope G 100 EE RT1c b b = - - (B-232) Right-Turn Condition 2A l l d c c RT PCa D= + - (B-233) Horizontal curve to the left approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-234) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - + - - +-` `j j (B-235) Horizontal curve to the right approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-236) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - - + - - +-` `j j (B-237) z G EE xslope y 100 100 ,RFB i EE rt base= - (B-238) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′

126 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways tan sin cosxslope G 100 EE RT1z b b = - - (B-239) tan cos sinxslope G 100 EE RT1c b b = - - (B-240) Right-Turn Condition 2Aiii l l d c c RT PCa D= + - (B-241) Horizontal curve to the left approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-242) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - + - - +-` `j j (B-243) Horizontal curve to the right approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-244) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - - + - - +-` `j j (B-245) z G d G l G G l G EE d l xslope y 100 100 200 100 100 , RFB RT VPC vc vc i RT PVC vc EE rt base 1 1 2 1 2= + + - + - - - - - ` ` j j R T S SS V X W WW (B-246) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-247) tan cos sinxslope G 100 EE RT1c b b = - - (B-248) Right-Turn Condition 3A x EERFB i= (B-249) y y ,RFB rt base= (B-250)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 127   z G d l G G d G l G G l G EE d l xslope y 100 200 100 200 100 100 , RFB RT VPC vc RT VPC vc vc i RT VPC vc EE rt base 1 2 1 2 1 2 1 2= - + - + + - + - - - - - - ` ` ` j j j R T S S S V X W W W * 4 (B-251) EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL = tan−1 + = 0 = sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-252) tan cos sinxslope G 100 EE RT1c b b = - - (B-253) Right-Turn Condition 3Aii Horizontal curve to the left approaching the intersection: sin cos sinx d R d l yEE ,RT PC RT PC ci rt baseRFB D D D= + + - - +- -` j (B-254) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - + - - --` `j j (B-255) Horizontal curve to the right approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - -- -` j (B-256) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - - - - - --` `j j (B-257) z G d l G G d G l G G l G EE d l xslope y 100 200 100 200 100 100 , RFB RT VPC vc RT VPC vc vc i RT VPC vc EE rt base 1 2 1 2 1 2 1 2= - + - + + - + - - - - - - ` ` ` j j j R T S S S V X W W W * 4 (B-258) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − Δ = −Δ = −Δ + sin−1 − ( + ) ′ Right = tan−1 + + Δ = Δ = Δ + sin−1 − ( + ) ′

128 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways tan sin cosxslope G 100 EE RT1z b b = - - (B-259) tan cos sinxslope G 100 EE RT1c b b = - - (B-260) Right-Turn Condition 4A l l d c c RT PCa D= + - (B-261) Horizontal curve to the left approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-262) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - + - - --` `j j (B-263) Horizontal curve to the right approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - --` j (B-264) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - - - - - --` `j j (B-265) z G d l G G d G l G G l G EE d l xslope y 100 200 100 200 100 100 , RFB RT VPC vc RT VPC vc vc i RT VPC vc EE rt base 1 2 1 2 1 2 1 2= - + - + + - + - - - - - - ` ` ` j j j R T S S S V X W W W * 4 (B-266) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-267) tan cos sinxslope G 100 EE RT1c b b = - - (B-268) Right-Turn Condition 1B l dEE c RT PCia D= + - (B-269)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 129   Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-270) cos cosy R R y ,RFB rt basea a= - -` j (B-271) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-272) cos cosy R R y ,RFB rt basea a= - - -` j (B-273) y G e z EE 100 100 ,RFB rt basei = - (B-274) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-275) tan cos sinxslope G 100 EE RT1c b b = - - (B-276) Right-Turn Condition 1Biii l EE d c i RT PCa D= + - (B-277) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-278) cos cosy R R y ,RFB rt basea a= - -` j (B-279) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-280) cos cosy R R y ,RFB rt basea a= - - -` j (B-281) z G d G l G G l G d d l e y 100 100 200 100 100 ,RFB RT VPC vc vc RT eye RT VPC vc rt base 1 1 2 1 2= + + - + - - -- - - ` ` j j R T S SS V X W WW (B-282)

130 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-283) tan cos sinxslope G 100 EE RT1c b b = - - (B-284) Right-Turn Condition 2B l EE c ia D= (B-285) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-286) cos cosy R R y ,RFB rt basea a= - -` j (B-287) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-288) cos cosy R R y ,RFB rt basea a= - - -` j (B-289) z G EE e y 100 100 ,RFB i rt base = - (B-290) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-291) tan cos sinxslope G 100 EE RT1c b b = - - (B-292)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 131   Right-Turn Condition 2Biii l EE c ia D= (B-293) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-294) cos cosy R R y ,RFB rt basea a= - -` j (B-295) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-296) cos cosy R R y ,RFB rt basea a= - - -` j (B-297) z G d G l G G l G d l e yEE 100 100 200 100 100 ,RFB RT VPC vc vc RT VPC vc rt basei 1 1 2 1 2= + + - + - - -- - ` ` j j R T S SS V X W WW (B-298) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-299) tan cos sinxslope G 100 EE RT1c b b = - - (B-300) Right-Turn Condition 3B l EE d c i RT PCa D= + - (B-301) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-302) cos cosy R R y ,RFB rt basea a= - -` j (B-303) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-304)

132 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways cos cosy R R y ,RFB rt basea a= - - -` j (B-305) z G d l G G d G l G G l G EE d l y e 100 200 100 200 100 100 , RFB RT VPC vc RT VPC vc vc i RT VPC vc rt base 1 2 1 2 1 2 1 2= - + - + + - + - - - - - - ` ` ` j j j R T S S S V X W W W * 4 (B-306) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-307) tan cos sinxslope G 100 EE RT1c b b = - - (B-308) Right-Turn Condition 4B l EE c ia D= (B-309) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-310) cos cosy R R y ,RFB rt basea a= - -` j (B-311) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-312) cos cosy R R y ,RFB rt basea a= - - -` j (B-313) z G d l G G d G l G G l G EE d l y e 100 200 100 200 100 100 , RFB RT VPC vc RT VPC vc vc i RT VPC vc rt base 1 2 1 2 1 2 1 2= - + - + + - + - - - - - - ` ` ` j j j R T S S S V X W W W * 4 (B-314)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 133   Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-315) tan cos sinxslope G 100 EE RT1c b b = - - (B-316) Right-Turn Condition 1C x EERFB i= (B-317) y y ,RFB rt base= (B-318) z G d G EE d G G EE d y xslope 100 100 200 100 ,RFB RT VPC i RT VPC i RT VPC rt base EE1 1 2 1= + - + - - -- - - ` ` ` j j j R T S SS V X W WW (B-319) EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL = tan−1 + = 0 = sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-320) tan cos sinxslope G 100 EE RT1c b b = - - (B-321) Right-Turn Condition 1Cii Horizontal curve to the left approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - +- -` j (B-322) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - + - - --` `j j (B-323) Horizontal curve to the right approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - -- -` j (B-324) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - - - - - --` `j j (B-325)

134 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways z G d G EE d G G EE d xslope y 100 100 200 100 ,RFB RT VPC i RT VPC i RT VPC EE rt base 1 1 2 1= + - + - - -- - - ` ` ` j j j R T S SS V X W WW (B-326) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − Δ = −Δ = −Δ + sin−1 − ( + ) ′ Right = tan−1 + + Δ = Δ = Δ + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-327) tan cos sinxslope G 100 EE RT1c b b = - - (B-328) Right-Turn Condition 2C l l d c c RT PCa D= + - (B-329) Horizontal curve to the left approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-330) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - + - - --` `j j (B-331) Horizontal curve to the right approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - --` j (B-332) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - - - - - --` `j j (B-333) z G d G EE d G G EE d xslope y 100 100 200 100 ,RFB RT VPC i RT VPC i RT VPC EE rt base 1 1 2 1= + - + - - -- - - ` ` ` j j j R T S SS V X W WW (B-334) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 135   tan sin cosxslope G 100 EE RT1z b b = - - (B-335) tan cos sinxslope G 100 EE RT1c b b = - - (B-336) Right-Turn Condition 3C x EERFB i= (B-337) y y ,RFB rt base= (B-338) z G d l G G d G EE d G G EE d xslope y 100 200 100 200 100 , RFB RT VPC vc RT VPC i RT VPC i RT VPC EE rt base 1 2 1 1 2 1 2 = - + - + - + - - - - - - - 2 ` ` ` ` j j j j R T S S S V X W W W * 4 (B-339) EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL = tan−1 + = 0 = sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-340) tan cos sinxslope G 100 EE RT1c b b = - - (B-341) Right-Turn Condition 3Cii Horizontal curve to the left approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - +- -` j (B-342) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - + - - --` `j j (B-343) Horizontal curve to the right approaching the intersection: sin cos sinx d R EE d l y ,RFB RT PC i RT PC c rt baseD D D= + + - - -- -` j (B-344) cos sin cosy R R EE d l y ,RFB i RT PC c rt baseD D D= - - - - - --` `j j (B-345) z G d l G G d G EE d G G EE d xslope y 100 200 100 200 100 , RFB RT VPC vc RT VPC i RT VPC i RT VPC EE rt base 1 2 1 2 1 2 1 2 = - + - + - + - - - - - - -` ` ` ` j j j j R T S S S V X W W W * 4 (B-346)

136 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − Δ = −Δ = −Δ + sin−1 − ( + ) ′ Right = tan−1 + + Δ = Δ = Δ + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-347) tan cos sinxslope G 100 EE RT1c b b = - - (B-348) Right-Turn Condition 4C l l d c c RT PCa D= + - (B-349) Horizontal curve to the left approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - +-` j (B-350) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - + - - --` `j j (B-351) Horizontal curve to the right approaching the intersection: sin cos sinx R EE d l y ,RFB i RT PC c rt basea a a= + - - --` j (B-352) cos sin cosy R R EE d l y ,RFB i RT PC c rt basea a a= - - - - - --` `j j (B-353) - z G d l G G d G d G G EE d xslope y EE 100 200 100 200 100 , RFB RT VPC vc RT VPC RT VPC i RT VPC EE rt base i 1 2 1 2 1 2 1 2 = - + - + - - - - - - - + ` ` ` ` j j j j R T S S S V X W W W * _ ` a bb b (B-354) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 137   tan sin cosxslope G 100 EE RT1z b b = - - (B-355) tan cos sinxslope G 100 EE RT1c b b = - - (B-356) Right-Turn Condition 1D l EE d c i RT PCa D= + - (B-357) Horizontal curve to the left approaching the intersection: sinsinx yd R ,RFB rt baseRT PC a a= + +- (B-358) cos cosy R R y ,RFB rt basea a= - -` j (B-359) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-360) cos cosy R R y ,RFB rt basea a= - - -` j (B-361) z G d G EE d G G EE d y e 100 100 200 100 , RFB RT VPC i RT VPC i RT VPC rt base 1 1 2 1= + - + - - - - - - ` ` ` j j j R T S SS V X W WW (B-362) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-363) tan cos sinxslope G 100 EE RT1c b b = - - (B-364) Right-Turn Condition 2D l EE c ia D= (B-365)

138 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-366) cos cosy R R y ,RFB rt basea a= - -` j (B-367) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-368) cos cosy R R y ,RFB rt basea a= - - -` j (B-369) z G d G EE d G G EE d y e 100 100 200 100 , RFB RT VPC i RT VPC i RT VPC rt base 1 1 2 1= + - + - - - - - - ` ` ` j j j R T S SS V X W WW (B-370) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of R-TL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-371) tan cos sinxslope G 100 EE RT1c b b = - - (B-372) Right-Turn Condition 3D l EE d c i RT PCa D= + - (B-373) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-374) cos cosy R R y ,RFB rt basea a= - -` j (B-375) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-376)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 139   cos cosy R R y ,RFB rt basea a= - - -` j (B-377) - z G d l G G d G d G G EE d e y EE 100 200 100 200 100 , RFB RT VPC vc RT VPC RT VPC i RT VPC rt base i 1 2 1 2 1 2 1 2 = - + - + - - - - - - - + ` ` ` ` j j j j R T S S S V X W W W * _ ` a bb b (B-378) Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-379) tan cos sinxslope G 100 EE RT1c b b = - - (B-380) Right-Turn Condition 4D l EE c ia D= (B-381) Horizontal curve to the left approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + +- (B-382) cos cosy R R y ,RFB rt basea a= - -` j (B-383) Horizontal curve to the right approaching the intersection: sin sinx d R y ,RFB RT PC rt basea a= + -- (B-384) cos cosy R R y ,RFB rt basea a= - - -` j (B-385) - z G d l G G d G d G G EE d e y EE 100 200 100 200 100 , RFB RT VPC vc RT VPC RT VPC i RT VPC rt base i 1 2 1 2 1 2 1 2 = - + - + - - - - - - - + ` ` ` ` j j j j R T S S S V X W W W * _ ` a bb b (B-386)

140 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal Curve Direction EEi on Right-Turn Taper EEi on Parallel Portion of RTL EEi on Turning Portion of RTL Left = tan−1 + − = − = − + sin−1 − ( + ) ′ Right = tan−1 + + = = + sin−1 − ( + ) ′ tan sin cosxslope G 100 EE RT1z b b = - - (B-387) tan cos sinxslope G 100 EE RT1c b b = - - (B-388) Compute Coordinates of Other Seven Corners of Right-Turning Vehicle Right Rear Bottom Corner cos cosx x lRRB RFB RTveh z b= - (B-389) cos siny y lRRB RFB RTveh z b= + (B-390) sinlz zRRB RFB RTveh z= + (B-391) Left Rear Bottom Corner cos sinx x wLRB RRB RTveh c b= + (B-392) cos coswy yRB R B RTvehL R c b= + (B-393) sinwz zRB R B RTvehL R c= + (B-394) Left Front Bottom Corner cos sinx x wRFB RTvehLFB c b= + (B-395) cos cosy y wLFB RFB RTveh c b= + (B-396) sinz z wB R B RTvehFLF c= + (B-397) Right Front Top Corner sin sinx x hR RFB RTvehFT c b= - (B-398)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 141   sin cosy y hR RFB RTvehFT c b= - (B-399) cosz z hR RFB RTvehFT c= + (B-400) Right Front Top Corner sin sinx x hRRB RTvehRRT c b= - (B-401) sin cosyy hRRB RTvehRRT c b= - (B-402) cosz z hRRT RRB RTveh c= + (B-403) Left Rear Top Corner sin sinx x hRT RB RTvehL L c b= - (B-404) sin coshy yRT RB RTvehL L c b= - (B-405) coshz zRT RB RTvehL L c= + (B-406) Left Front Top Corner sin sinx x hT B RTvehLF LF c b= - (B-407) sin cosy y hT B RTvehLF LF c b= - (B-408) cosz z hT B RTvehLF LF c= + (B-409) B.10 Calculate Intersecting Points There are eight sightlines for every point EE. The sightlines originate from the driver’s eye of the vehicle stopped on the minor-road approach and intersect each of the eight corners of the right-turning vehicle. The left and right sides of the through vehicle in each through lane are assumed to be part of vertical planes parallel to the z-axis. In the case of through lanes on horizontal curves, these vertical planes are assumed to be the surface of a cylinder with a central axis parallel to the z-axis. In this section of the procedure, the intersecting points between the sightlines and vertical planes of the through vehicle are calculated. For through lanes with a horizontal curve, the sightline may intersect four planes: a vertical plane associ- ated with the tangent prior to the PC, two intersections with surface of cylinder associated with the horizontal curve, and a vertical plane associated with the tangent after the point of tangency. A variable used in this procedure, yth, is dependent on which major approach through lane is being analyzed and is different for the right and left sides of the through vehicle. For each through lane, intersecting points must be calculated for the right and left sides of the through vehicle separately.

142 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Major Approach Through Lane Vertical Surface Parallel to Right Edge of Through Vehicle Vertical Surface Parallel to Left Edge of Through Vehicle 1 ℎ = − − + ℎ ,1 − ℎ ,1 , ℎ 100 + 0.5 (1 − , ℎ 100 ) ℎ ℎ = − − + ℎ ,1 − ℎ ,1 , ℎ 100 + ℎ − 0.5 (1 − , ℎ 100 ) ℎ 2 ℎ = − − + ℎ ,1 + ℎ ,2 − ℎ ,2 , ℎ 100 + 0.5 (1 − , ℎ 100 ) ℎ ℎ = − − + ℎ ,1 + ℎ ,2 − ℎ ,2 , ℎ 100 + ℎ − 0.5 (1 − , ℎ 100 ) ℎ 3 ℎ = − − + ℎ ,1 + ℎ ,2 + ℎ ,3 − ℎ ,3 , ℎ 100 + 0.5 (1 − , ℎ 100 ) ℎ ℎ = − − + ℎ ,1 + ℎ ,2 + ℎ ,3 − ℎ ,3 , ℎ 100 + ℎ − 0.5 (1 − , ℎ 100 ) ℎ 4 ℎ = − − + ℎ ,1 + ℎ ,2 + ℎ ,3 + ℎ ,4 − ℎ ,4 , ℎ 100 + 0.5 (1 − , ℎ 100 ) ℎ ℎ = − − + ℎ ,1 + ℎ ,2 + ℎ ,3 + ℎ ,4 − ℎ ,4 , ℎ 100 + ℎ − 0.5 (1 − , ℎ 100 ) ℎ m x x y y eye r eye r = - -J L KK N P OO (B-410) Calculate Intersection Points with First Tangent Vertical Plane The following equations calculate the points of intersections between the eight sightlines and the vertical plane that is parallel to the left or right side of the through vehicle on the major-road approach prior to the PC. For eye conditions 1Ai, 1Aii, 1Aiii, 1Aiv, 3A, 3Aii, 1B, 1Biii, 3B, 1C, 1Cii, 3C, 3Cii, 1D, or 3D, use the following equations: x m y mx y 1 , , ,r s th s eye eyeI = + -8 B (B-411) y y, , ,r s th sI = (B-412) For major-road through lanes 2, 3, or 4 and eye conditions 2A, 2Aiii, 2B, 2Biii, 2C, 2D, 4A, 4B, 4C, or 4D, use the following equations:

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 143   Horizontal curve to the left approaching the intersection: tan sec x m R y d mx y R y R y d y 180 180 1 , , , , , , I r s th s RT PC eye eye th s th s RT PC th s r r = + + - - + + - + - - J L K KK a a a N P O OO k k k (B-413) tan secy x R y d R y R y d y 180 180 1, , , , , , , ,I r s I r s th s RT PC th s th s RT PC th s r r = - + - + + - +- - J L K KKa a a N P O OOk k k (B-414) Horizontal curve to the right approaching the intersection: tan sec x m R y d mx y R y R y d y 180 180 1 , , , , , , I r s th s RT PC eye eye th s th s RT PC th s r r = + + - + + + - + - - J L K KK` ` ` N P O OOj j j (B-415) tan secy x R y d R y R y d y 180 180 1, , , , , , , ,I r s I r s th s RT PC th s th s RT PC th s r r = - + - + + - +- - J L K KK` ` ` N P O OOj j j (B-416) Calculate Intersection Points with Horizontal Curve Vertical Surface The following equations calculate the points of intersections between the eight sightlines and the vertical surface that is parallel to the left or right side of the through vehicle on the major- road approach on the horizontal curve. These equations only apply to analyses that include a horizontal curve. Point of Curvature Is at or Before the Origin Horizontal curve to the left approaching the intersection: a m 1 1 2 = + (B-417) b m y m x R 2 2 2eye eye 2 = - + - (B-418) c m y m x y x y R y 2 2 , , eye eye eye eye th s th s2 2 2 2= - + + - (B-419) y a b b ac 2 4 , ,I r s 2! = - - (B-420) m y y xx , , , , I r s I r s eye eye= - + (B-421)

144 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Horizontal curve to the right approaching the intersection: a m 1 1 2 = + (B-422) b m y m x R 2 2 2eye eye 2 = - + + (B-423) c m y m x y x y R y 2 2 , , eye eye eye eye th s th s2 2 2 2= - + - - (B-424) y a b b ac 2 4 , ,I r s 2! = - - (B-425) x m y y x, , , , I r s I r s eye eye= - + (B-426) Point of Curvature Is After the Origin Horizontal curve to the left approaching the intersection: a m 1 1 2 = + (B-427) b m y mx m d R 2 2 2 2eye eye RT PC 2 = - + - -- (B-428) c m y m x y y d x x d y R y d 2 2 2 2 , , eye eye eye eye RT PC eye eye RT PC th s th s RT PC2 2 2 2 2= + - + + - + - + - - - (B-429) y a b b ac 2 4 , ,I r s 2! = - - (B-430) x m y y x, , , , I r s I r s eye eye= - + (B-431) Horizontal curve to the right approaching the intersection: a m 1 1 2 = + (B-432) b m y mx m d R 2 2 2 2eye eye RT PC 2 = - - - +- (B-433) c m y m x y y d x x d y R y d 2 2 2 2 , , eye eye eye eye RT PC eye eye RT PC th s th s RT PC2 2 2 2 2= + - + + - - - + - - - (B-434) y a b b ac 2 4 , ,I r s 2! = - - (B-435) x m y y x, , , , I r s I r s eye eye= - + (B-436)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 145   Calculate Intersection Points with Second Tangent Vertical Plane The following equations calculate the points of intersections between the eight sightlines and the vertical plane that is parallel to the left or right side of the through vehicle on the major-road approach after the point of tangency. These equations only apply to analyses that include a hori- zontal curve. Point of Curvature Is at or Before the Origin l l d c c RT PCa D= + - (B-437) Horizontal curve to the left approaching the intersection: tan tan tan x m mx y R y y 2 , , , , I r s eye eye th s th s a a a = - - - - +` j (B-438) mx mx yy , , , ,I r s I r s eye eye= - + (B-439) Horizontal curve to the right approaching the intersection: tan tan tan x m mx y R y y 2 , , , , I r s eye eye th s th s a a a = + - + + +` j (B-440) y mx mx y, , , ,I r s I r s eye eye= - + (B-441) Point of Curvature Is After the Origin Horizontal curve to the left approaching the intersection: tan tan tan x m mx y d R y y 2 , , , , I r s eye eye RT PC th s th s D D D = - - - + - +- ` j R T S S V X W W (B-442) y mx mx y, , , ,I r s I r s eye eye= - + (B-443) Horizontal curve to the right approaching the intersection: tan tan tan x m mx y d R y y 2 , , , , I r s eye eye RT PC th s th s D D D = + - + + + +- ` j R T S S V X W W (B-444) y mx mx y, , , ,I r s I r s eye eye= - + (B-445) Compute z Coordinate The equation for the z-coordinate is the same for all situations of horizontal curve position: z x x y y z z x x y y z, , , , , , I r s r eye r eye r eye I r s eye I r s eye eye2 2 2 2 = - + - - - + - + ` ` ` ` `j j j j j (B-446)

146 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways B.11 Determine EE for Each Intersection Point The associated EE point must be calculated for each intersection point calculated in the previ- ous section. Calculate EE for Intersection Points on First Tangent Point of Curvature Is at or Before the Origin The associated EE point for intersection points on the first tangent prior to the horizontal curve is calculated as follows: Horizontal curve to the left approaching the intersection: sin cos EE d R y R y d x y R y R y d y 180 1 180 , , , , , , , , , , , I r s RT PC th s th s RT PC I r s I r s th s th s RT PC th s 2 2 r r = - - - - + - + - - - - - -- J L K K K J L K KK` ` ` ` N P O OO N P O O O j j j j R T S S S R T S S S S V X W W W V X W W W W (B-447) The intersection point should be discarded if one of the following is true: sin R y d x R y> , , , , th s RT PC I r s th s- - - - ` j (B-448) x x y yx x y y > , , , ,r eye eye eyeI r s I r sr eye 2 2 22 - + - - + -` ` ` `j j j j (B-449) Horizontal curve to the right approaching the intersection: sin cos EE d R y R y d x y R y R y d y 180 1 180 , , , , , , , , , , , I r s RT PC th s th s RT PC I r s th s th s th s RT PC I r s 2 2 r r = - + + - + + + - + - - - -- J L K K K J L K KK` ` ` ` N P O OO N P O O O j j j j R T S S S R T S S S S V X W W W V X W W W W (B-450) The intersection point should be discarded if one of the following is true: sinR y R y d x 180 , , , , I r s th s th s RT PC2 r - + - - ` ` j j (B-451) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-452) Point of Curvature Is After Origin (or No Horizontal Curve Present) The associated EE point for intersection points on the first tangent prior to the horizontal curve (or simply the roadway if no horizontal curve is present) is EEI,r,s = xI,r,s, unless one of the following equations is true:

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 147   EE d>, ,I r s RT PC- (B-453) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-454) Calculate EE for Intersection Points on Horizontal Curve Point of Curvature Is at or Before the Origin Horizontal curve to the left approaching the intersection: sinEE R R y x 180, , , , , I r s th s I r s1 r = - - (B-455) The intersection point should be discarded if xI,r,s ≥ 0 and one of the following is true: sin cos x y y R y R y l d R y R y l d180 1 180 > , , , , , , , , , I r s I r s th s th s th s c RT PC th s th s c RT PC 2 2 2 2 r r + - - - - + - - - -- - J L K K K ` ` a ` ` a ` N P O O O j j j k j j k R T S S SS R T S S S S V X W W WW V X W W W W (B-456) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-457) The intersection point should be discarded if xI,r,s < 0 and one of the following is true: sin cosx y R y R y d R y R y d y 180 1 180 >, , , , , , , , ,I r s th s th s th s RT PC th s th s RT PC I r s 2 2 2 2 r r + - - - - + - - - - - J L K KK` ` ` ` ` N P O OOj j j j j R T S S S R T S S SS V X W W W V X W W WW (B-458) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-459) Horizontal curve to the right approaching the intersection: sinEE R R y x 180, , , , , I r s th s I r s1 r = + - (B-460) The intersection point should be discarded if xI,r,s ≥ 0 and one of the following is true: sin cos x y y R y R y l d R y R y l d180 1 180 > , , , , , , , , , I r s I r s th s th s th s c RT PC th s th s c RT PC 2 2 2 2 r r + - + + - + - + - + -- - J L K K K ` ` a ` ` a ` N P O O O j j j k j j k R T S S SS R T S S S S V X W W WW V X W W W W (B-461) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-462)

148 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways The intersection point should be discarded if xI,r,s < 0 and one of the following is true: sin cosx y y R y R y d R y R y d180 1 180 >, , , , , , , , , I r s I r s th s th s th s RT PC th s th s RT PC2 2 2 2 r r + - - + + + - + - + - - J L K KK` ` ` ` ` N P O OOj j j j j R T S S S R T S S SS V X W W W V X W W WW (B-463) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-464) Point of Curvature Is After Origin The intersection point should be discarded if xI,r,s < dRT−PC. Otherwise, use the following equa- tions to determine the associated EE point for intersection points on the horizontal curve. Horizontal curve to the left approaching the intersection: sinEE d R R y x d 180, , , , , I r s PC th s I r s RT PC RT 1 r = + - - - - - (B-465) The intersection point should be discarded if one of the following is true: sin cosx d y y R y R y 1>, , , , , , ,I r s RT PC I r s th s th s th s 2 2 2 2 D D- + - - + - --` ` ` ` `j j j j j R T SS R T SS V X WW V X WW (B-466) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-467) Horizontal curve to the right approaching the intersection: sinEE d R R y x d 180, , , , , I r s RT PC th s I r s RT PC1 r = + + - - - - (B-468) The intersection point should be discarded if one of the following is true: sin cosx d y y R y R y 1>, , , , , , ,I r s RT PC I r s th s th s th s 2 2 2 2 D D- + - + + - + --` ` ` ` `j j j j j R T SS R T SS V X WW V X WW (B-469) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-470) Calculate EE for Intersection Points on Second Tangent These equations only apply when a horizontal curve is present. Point of Curvature Is at or Before the Origin Horizontal curve to the left approaching the intersection: R y l d180 ,th s c RT PC i r = - - -a ` j k (B-471) n sin ta siny y R yEE l 1 2, , , ,, , I r s th s th sI r s ci i i iD = + - - -` j R T S S V X W W (B-472)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 149   The intersection point should be discarded if one of the following is true: sinx R y, , ,I r s th s# i-` j (B-473) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-474) Horizontal curve to the right approaching the intersection: R y l d180 ,th s c RT PC i r = + - -a ` j k (B-475) tan sin sin EE l y y R y 2 1 , , , , , ,I r s c I r s th s th s i i i iD = + - - +` j R T S S V X W W (B-476) The intersection point should be discarded if one of the following is true: sinR yx , , ,I r s th s# i+` j (B-477) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-478) Point of Curvature Is After Origin Horizontal curve to the left approaching the intersection: tan sin sin EE d l y y R y 2 1 , , , , , ,I r s RT PC c I r s th s th s D D D = + + - - -- ` j R T S S V X W W (B-479) The intersection point should be discarded if one of the following is true: sinx d R y, , ,I r s RT PC th s# D+ -- ` j (B-480) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-481) Horizontal curve to the right approaching the intersection: sin tan sinEE d l y y R y 2 1 , , , , , ,I r s RT PC c I r s th s th s D D D = + + - - +- ` j R T S S V X W W (B-482) The intersection point should be discarded if one of the following is true: sinx d R y, , ,I r s RT PC th s# D+ +- ` j (B-483) x x y y x x y y> , , , ,r eye r eye I r s eye I r s eye 2 2 2 2 - + - - + -` ` ` `j j j j (B-484) B.12 Determine Elevation of Roadway Surface at EEI,r,s The elevation of the roadway is dependent on the position of EEI,r,s relative to the vertical curve (if present) and the superelevation on horizontal curves along with the superelevation runoff and tangent runout. A factor, zadj, is first calculated in the following subsection, which takes into account the cross slope of the roadway.

150 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways Calculate zadj If no horizontal curve is present, then: , , y yz xslope rt 0 100 If then<, ,th s th sadj = (B-485) , , y yz xslope tl 0 100 If then, ,th s th sadj$ = (B-486) If EEI,r,s ≥ dRT−PC and EEI,r,s < dRT−PC + lc, then: yz e 100,th sadj = (B-487) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s > ltro + lero and yth,s < 0, then: , yz xslope rt 100,th sadj = (B-488) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s > ltro + lero and yth,s ≥ 0, then: , yz xslope lt 100,th sadj = (B-489) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s < lero and the horizontal curve is to the left and yth,s < 0, then: yz d EE e l 1 100, , , th sadj ero RT PC I r s= - -- J L K K N P O O (B-490) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s < lero and the horizontal curve is to the left and yth,s ≥ 0 and , l d EE e e xslope lt >, , ero RT PC I r s- -- , then: , z y xslope lt 100,adj th s = (B-491) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s < lero and the horizontal curve is to the left and yth,s ≥ 0 and , l d EE e e xslope lt, , ero RT PC I r s # - -- , then: , , ,z l e e xslope lt d EE xslope lt xslope lt y e1 100 , , , adj ero RT PC I r s th s= - - - - +- J L K K KK ` N P O O OO j R T S S S SS V X W W W WW (B-492)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 151   If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s < lero and the horizontal curve is to the right and yth,s < 0 and , l d EE e e xslope rt >, , ero RT PC I r s- -- , then: , z y xslope tr 100,adj th s = (B-493) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s < lero and the horizontal curve is to the right and yth,s < 0 and , l d EE e e xslope rt, , ero RT PC I r s # - -- , then: , , ,z l e e xslope t d EE e xslope t xslope t y r r r1 100 , , , adj ero RT PC I r s th s= - - - - +- J L K K KK ` N P O O OO j R T S S S SS V X W W W WW (B-494) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s< lero and the horizontal curve is to the right and yth,s ≥ 0, then: z l d EE y e 1 100 , , ,adj ero RT PC I r s th s= - -- J L K K N P O O (B-495) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s ≥ lero and the horizontal curve is to the left and yth,s < 0, then: , z l d l EE y xslope rt 100 , , ,adj ro RT PC ero I r s th s t = - -- J L K K N P O O (B-496) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s ≥ lero and the horizontal curve is to the left and yth,s ≥ 0, then: , z y xslope lt 100,adj th s = (B-497) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s ≥ lero and the horizontal curve is to the right and yth,s < 0, then: , z y xslope tr 100,adj th s = (B-498) If EEI,r,s < dRT−PC and dRT−PC − EEI,r,s ≥ lero and the horizontal curve is to the right and yth,s ≥ 0, then: , z l d l EE y xslope tl 100 , , ,adj tro RT PC ero I r s th s= - -- J L K K N P O O (B-499)

152 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC > ltro + lero and yth,s < 0, then: , z y xslope tr 100,adj th s = (B-500) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC > ltro + lero and yth,s ≥ 0, then: , y xslope lt z 100,adj th s = (B-501) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC < lero and the horizontal curve is to the left and yth,s < 0, then: y e l EE l d z 100 1 , , , adj th s ero I r s c RT PC= - - - - J L K K N P O O (B-502) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC < lero and the horizontal curve is to the left and yth,s ≥ 0 and , l EE l d e e xslope lt >, , ero I r s c RT PC- - -- , then: , z y xslope lt 100,adj th s = (B-503) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC < lero and the horizontal curve is to the left and yth,s ≥ 0 and , l EE l d e e xslope lt, , ero I r s c RT PC # - - -- , then: , , ,z e xslope lt xslope lt xslope lt y l e e EE l d 100 1 ,, ,adj th s ero I r s c RT PC= - - - - - +- J L K K KK ` N P O O OO j R T S S S SS V X W W W WW (B-504) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC < lero and the horizontal curve is to the right and yth,s < 0 and , l EE l d e e xslope rt >, , ero I r s c RT PC- - -- , then: , z y xslope tr 100,adj th s = (B-505) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC < lero and the horizontal curve is to the right and yth,s < 0 and , l EE l d e e xslope rt, , ero I r s c RT PC # - - -- , then: , , ,z l e e xslope rt EE l d e xslope t xslope t y r r1 100 , , , adj ero I r s c RT PC th s= - - - - - +- J L K K KK ` N P O O OO j R T S S S SS V X W W W WW (B-506)

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 153   If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC < lero and the horizontal curve is to the right and yth,s ≥ 0, then: z l EE l d y e 1 100 , , ,adj ero I r s c RT PC th s= - - - - J L K K N P O O (B-507) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC ≥ lero and the horizontal curve is to the left and yth,s < 0, then: , z l EE l d y l xslope rt 100 , , ,adj I r s c RT PC th s tro ero= - - -- J L K K N P O O (B-508) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC ≥ lero and the horizontal curve is to the left and yth,s ≥ 0, then: , z y xslope lt 100,adj th s = (B-509) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC ≥ lero and the horizontal curve is to the right and yth,s < 0, then: , z y xslope tr 100,adj th s = (B-510) If EEI,r,s ≥ dRT−PC and EEI,r,s − lc − dRT−PC ≥ lero and the horizontal curve is to the right and yth,s ≥ 0, then: , z l EE l d l y xslope tl 100 , , ,adj tro I r s c RT PC ero th s= - - -- J L K K N P O O (B-511) Calculate Roadway Surface Elevation If no vertical curve is present: z GEE z 100, , , , , EE I r s I r s adj= + (B-512) If EEI,r,s < dRT−VPC, then: z z G d EE 100, , , , , EE I r s adj RT VPC I r s1 = - - + -` j (B-513) If EEI,r,s ≥ dRT−VPC + lvc, then: z G d l G G d G l l G G l G EE l d z 100 200 100 200 100 , , , , , EE I r s RT VPC vc RT VPC vc vc vc I r s vc RT VPC adj 1 2 1 2 1 2 1 2 2 = - + - + + - + - - + - - -` ` `j j j R T S S S V X W W W (B-514)

154 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways If EEI,r,s < dRT−VPC + lvc and EEI,r,s ≥ dRT−VPC, then: z G d l G G d G EE d l G G EE d z 100 200 100 200 , , , , , , , EE I r s RT VPC vc RT VPC I r s RT VPC vc I r s RT VPC adj 1 2 1 2 1 2 1 2 = - + - + - + - - + - - - -` ` ` ` j j j j R T S S S V X W W W (B-515) B.13 Determine Length of Blocked Through Lane Associated with EEi For each set of intersection points {x, y, z}I,s associated with EEi, the length of the through lane that is blocked by a right-turning vehicle at point EEi must be calculated. There are at most eight intersection points in each set {x, y, z}I,s. These points need to be transformed into a two-dimensional set of points. The x-coordinate of each point is simply the EEI,r,s value calculated for each point. The y-coordinate of each point is zI,r,s − zEE,I,r,s. Note that this y-coordinate can be thought of as the height of the intersection point above the roadway surface, and the x-coordinate can be thought of as the position of the intersection point along the roadway. For a visual representation of these points, the set can be graphed with EEI,r,s on the x-axis and zI,r,s − zEE,I,r,s on the y-axis. To determine the length of the blocked through lane associated with a right-turning vehicle at point EEi, perform the following steps: Step 1: Begin with intersection point with maximum EEI,r,s. Label this point as I1. Step 2: Determine which of the remaining intersection points produces a line from I1 with the largest azimuth. Label this point as I2. Step 3: Repeat Step 2, labeling points as I3, I4, and so on until the intersection point with minimum EEI,r,s is reached. Step 4: Starting with I1, go to the first point that exceeds P h 100 , ,eff THveh h THveh . If I1, the first point, exceeds this threshold, skip ahead to Step 6. End of Blocked Length x,r s I1= (B-516) Step 5: If this point is after I1, then determine EEr,s (x-axis coordinate) when the line from Ii to Ii+1 equals P h 100 , ,eff THveh h THveh :

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 155   End of Blocked Length x y y P h y x x100, , , r s I I I eff THveh h THveh I I Ii i i i i i 1 1 = - - - - + + J L K K K ` N P O O O j (B-517) Step 6: Continue to step through all Ii points sequentially until point Ii becomes less lower than P h 100 , ,eff THveh h THveh . If the last remaining Ii does not conform to this condition, then: of Blocked Length xBeginning ,r s Ilast= (B-518) Otherwise: Determine EEr,s when the line Ii-1 to Ii equals P h 100 , ,eff THveh h THveh : Beginning of Blocked Length x y y P h y x x100, , , r s I I I eff THveh h THveh I I Ii i i i ii 1 1 = + - - - - - J L K K K ` N P O O O j (B-519) B.14 Length of Time Through Lane Is Blocked Associated with EEi The length of time that the through lane is blocked when a right-turning vehicle is at EEi is dependent on the speed of the right-turning vehicle and the analysis increment: t v EE , , blocked i EE i inc= (B-520) B.15 Determine Final Blocked Lengths and Total Time Blocked Up to this point, blocked lengths on both the left and right edges of the through vehicle that are associated with a right-turning vehicle at EEi have been calculated. Once the right-turning vehicle has been analyzed at all EE points, it is necessary to determine whether the through vehicle is truly blocked, and if so, what portions of the through lane are blocked by multiple positions of the right-turning vehicle (multiple EEi points). A through vehicle is only regarded as truly blocked if both the left and right edges of the through vehicle are within the blocked length region. So, BlockedLengthr,left and BlockedLengthr,right have to be compared to determine where these two lengths overlap. This overlap length, BlockedLengthi, will be blocked for a duration of tblocked,i. For all BlockedLengthi, any portions of the through lane that have multiple BlockedLengthi overlapping will be blocked for a duration equal to the sum of all tblocked,i associated with those overlapping BlockedLengthi. Two checks need to be conducted prior to summing all tblocked,i. The first check is to make sure a portion of the blocked length associated with tblocked,i is within the intersection sight distance influence area of the intersection. This distance is calculated using the following equation: .d S7 5SD oI = (B-521)

156 Assessing the Impacts of Right-Turn Lanes on Rural and Suburban Highways The second check is only for the rightmost through lane. It is necessary to make sure the blocked length associated with tblocked,i occurs at or after the beginning of the RTL taper. The total blocked time is computed as the sum of all tblocked,i for each unique combination of major-road through lanes and minor-road lanes, major-road vehicle types in through lanes, major-road vehicle types in RTLs, and minor-road vehicle types in each minor-road lane. t t ,blocked blocked i=/ (B-522) B.16 Compute Probability of Minor-Road Vehicle Present at Stop Line The two-way stop-controlled methodology from the HCM is used to estimate the probability that a vehicle will be present at the stop line in each minor-approach lane. The capacity for each minor-approach lane is computed using HCM procedures. The probability of a vehicle or queue present at the stop line can be estimated with the following: c v p 1minlnx minlnx minlnx ,queue = - (B-523) The value computed in the previous equation can also be interpreted as the percent of an hour that a minor-road vehicle is stopped in a minor-road lane. This value can be broken down by vehicle type in each minor-road lane: p v p v minlnx minlnx minlnx,minvehx min x, ,, queuequeue ln minvehx = (B-524) pqueue,minlnx and pqueue,minlnx,minvehx are presented on the output report on the line labeled PMRV. B.17 Compute Percent of Hour the View Is Blocked The percent of the hour during which any minor-road driver that might be present at the stop line would have a blocked view is computed separately for each minor-road lane and minor-road vehicle type. Up to this point, the total time blocked was computed for each unique combination of minor and major lane and vehicle types on the minor road, major-road through lanes, and major-road RTLs. First, tblocked is scaled by major-road through lane utilization for each unique combination of minor and major lane and vehicle types on the minor road, major-road through lanes, and major-road RTLs: t t U t t U t t U t t U , , , , , , , , , , , , blocked TH blocked TH TH percent blocked TH blocked TH TH percent blocked TH blocked TH TH percent blocked TH blocked TH TH percent 1 1 1 2 2 2 3 3 3 4 4 4 = = = = l l l l (B-525) Second, tblocked,TH is scaled by vehicle type percentages in each major-road through lane and summed together to compute a combined time-blocked value, taking into account through lane utilization and through lane vehicle type distribution. Note that this combined through lane blocked time is for each unique combination of minor-road lane and vehicle types on minor- road and major-road RTLs.

Procedure for the Sightline and Reliability Analysis Model for RTLs at Minor-Road Stop-Controlled Intersections 157   t t t t t, , , , , ,blocked TH combined blocked TH THveh blocked TH blocked TH blocked TH1 1 3 2 3 4= + + + = l l l l/ (B-526) Third, tblocked,TH,combined is scaled by vehicle type percentages in major-road RTLs and summed together to compute a combined time-blocked value, taking into account RTL vehicle type dis- tribution. This sum represents the time blocked by one major-road right-turning vehicle. So, the summed blocked time value is multiplied by the major-road right-turning volume. This value represents the blocked time for each unique combination of minor-road lane and vehicle types on the minor road. t v t, , , , ,blocked TH RT combined RT blocked TH combined RTveh 1 3 = = / (B-527) Lastly, the percent of hour that any vehicle stopped in a particular minor-road approach lane of a particular vehicle type is computed using the following equation: ,maxp t 3600 1blocked,minlnx,minvehx , , ,blocked TH RT combined= J L KK N P OO (B-528) pblocked,minlnx,minvehx is presented on the output report in the row labeled PBV. B.18 Compute Percent of Hour Minor-Road Driver Is Present and Has Blocked View This final step computes the percent of the hour that a minor-road driver is present at the stop line and that driver’s view is blocked by a right-turning vehicle. This is computed for each unique combination of minor-road lane and minor-road vehicle type: p p pminlnx,minvehx blocked,minlnx,minvehx minlnx,minvehx,queue= (B-529) The value computed in the previous equation can be combined for each minor-road vehicle type to obtain the blocked percentage for all vehicles in each minor-road lane: p pminlnx min minlnx ,minvehx veh 1 3 = = / (B-530) Lastly, an overall blocked percentage for all vehicles across all minor-road lanes is computed in the following equation: vp p v 1 min minlnx minlnx minln 1 3 = = / (B-531) pminlnx and p are presented on the output report on the line labeled PSDL.

Abbreviations and acronyms used without denitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North 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 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 FAST Fixing America’s Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration GHSA Governors Highway Safety Association 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 MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) 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

N C H RP Research Report 1062 Assessing the Im pacts of Right-Turn Lanes on Rural and Suburban H ighw ays Transportation Research Board 500 Fifth Street, NW Washington, DC 20001 ADDRESS SERVICE REQUESTED ISBN 978-0-309-69922-8 9 7 8 0 3 0 9 6 9 9 2 2 8 9 0 0 0 0