Warrants for Left-Turn Lanes

Transportation Kentucky Transportation Center Research Report University of Kentucky Year 1982 Warrants for Left-Turn Lanes Kenneth R. Agent University of Kentucky, ken.agent@uky.edu This paper is posted at UKnoledge. https://uknoledge.uky.edu/ktc researchreports/785

Research Report UKTRP-82-19 WARRANTS FOR LEFT-TURN LANES by Kenneth R. Agent Chief Research Engineer KentJJCky Transportation Research Program College of Engineering University of Kentucky Lexington, Kentucky offered for publication to the Transportation Quarterly The contents of this report reflect the vies of the author ho is responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official vies or policies of the KentuckY Department of Transportation nor of the University of Kentucky. The report does not represent a standard, specification or regulation. October 1982

WARRANTS FOR LEFT-TURN LANES by K. R. Agent ABSTRACT Warrants for the installation of separate lefttum lanes ere developed. Literature as revieed, and policies and practices in other states ere surveyed. Accident analyses of locations ith and ithout separate left-turn lanes ere conducted. Computer simulation as used to determine relationships among traffic delay. load factor, traffic volume, percent left-turns, cycle length, and cycle split. The relationship beteen left-turn acc1dents and confl1icctisrrrs--irrv1'si:ig2rte1:!:-------------------------- Warrants ere developed involving the folloing three general areas: (1) accident experience, (2) volumes (based on delay), and (3) traffic conflicts.

INTRODUCTION A vehicle stopped in the traffic stream to turn left creates an accident potential and impedes the flo of through traffic. The addition of left-turn lanes alays provides an improvement in the traffic flo; hoever, left-turn lanes cannot be built at all locations, and arrants have not been established for determining hen the need for left-turn lanes becomes critical. In this study, arrants or guides ere developed for installing separate left-turn lanes. Computer simulation as used to determine the relationships beteen traffic delay and such variables as percentage left-turns, traffic volume, and cycle length. Accident data ere compared at locations ith and ithout left-turn lanes, and the average number of left-turn accidents for approaches ith no leftturn lane as determined. The relationship beteen left-turn accidents and conflicts as also investigated. Using these sources of input, criteria for determining need for left-turn lanes ere derived. Before data collection and analysis started, both a revie of literature and a survey of arrants or guides used in the other states ere conducted. Fe states used numerical arrants for the installation of left-turn lanes, but most used some guidelines. Those guidelines ere based primarily on either accidents, volume, or delay (1). PROCEDURE ACCIDENT DATA The data base consisted of five years of accident analyses of intersections in Lexington, Kentucky. Accident rates at locations ith and ithout left-turn lanes ere calculated. This as done using volume counts at intersections for a 12-hour period (7 a.m. to 7 p.m.). The assumption as made that 8 percent of the volume occurred in this 12-hour period. Those volumes ere then multiplied by 1.25 to obtain the 24-hour volume. Using the same data base, the average number of left-turn accidents for the approaches ith no left-turn lanes as calculated. The average number of accidents as used to calculate a critical number of left-turn accidents. TRAFFIC VOLUME Computer simulation as used to relate traffic delay and load factor to traffic volume, percentage left-turns, cycle length, and cycle split. TI1e simulation program as the UTCS-1 Netork Simulation Model developed for the Federal Highay Administration (2). An isolated intersection as input into the program. Simulation runs ere made assuming both stop-sign control and signal control. When a signal as specified, the cycle length and cycle split ere given. During peak hours, volumes on the side street of a semi-actuated signal ould be so heavy that a fixed cycle ould be approximated. Data ere simulated for an intersection on a four-lane and on a to-lane street. Equal volumes ere input for both main street approaches. The percentage of leftturns ere varied on one approach

hile the other approach had 1 percent of its volume going straight. Cycles of 6, 9, and 12 seconds ere used. Cycle splits of 7/3 (7 percent of the cycle devoted to the main street), 6/4, and 5/5 ere used. A free-flo speed of 45 mph (2 m/s) as used. The average delay and the load factor ere obtained for the left-turn approach. Load factor is defmed as the ratio of the total number of green-signal intervals fully utilied by traffic during the peak hour to the total number of green intervals for that approach during the same period (3). The maximum value is one. Graphs ere dran relating the variables to critical delay and load factors. The critical delay as 3 seconds, found using a procedure given in another report (4). In that study, engineers ere asked for their opinion of hat constituted maximum tolerable delay for a vehicle controlled by a traffic signal. A mean value of 73 seconds as found. A criterion that 85 percent of all the left-turn approach vehicles be delayed less than this maximum of 73 seconds as then used. Assuming the distribution of delays become approximately normal during peak-flo conditions, the folloing formula can be used: 85th percentile= X+ 1.44 a in hich 85th percentile value of delay of the 85th percentile of the normal distribution (73 seconds), X = mean value of delay, and a standard deviation of the distribution. It as assumed that the standard deviation as approximately equal to the mean. Substituting these values gave a value of 3 seconds for the mean delay. TI1irty seconds as used as the minimum averv age delay necessary because this value constituted the loer bound of excessive delay. A critical load factor of.3 as used because it represents the upper bound of level of service C (3), the upper limit of stable flo. Level of service D represents a one of increasing restriction approaching instability. An additional procedure as used for simulation of non-signalied intersections. One hundred per cent of the volume on one approach turned left hile I percent of the volume on the opposing approach ent straight through the intersection. Volume on the left-turn approach as held constant hile the opposing volume as changed. This permitted a plot of left-turn delay as a function of the left-turn and opposing volumes. Data ere simulated for an intersection on four-lane and to-lane streets. CONFLICT DATA Conflict counts involving left-turn vehicles ere taken at several intersections and related to the number of left-turn accidents and trafflc volumes. l11c conflicts ere classified into several categories (5). Basically, there ere four types of left-turn related conflicts. 1l1e first occurred hen a left-turning vehicle crossed directly in front of or blocked the lane of an opposing through vehicle (opposing left-turn conflict). The second as caused by a vehicle aiting to turn left (rear-end type). A third as a eave resulting hen a vehicle, evading a left-turning vehicle ahead, veered into the path of another vehicle. TI1e fourth involved running the red light. An attempt as made to classify the conflicts according to severity. HoWever, in the analysis, no distinction by severity is made because of inconsistency of data taken by different observers.

RESULTS ACCIDENT WARRANT Accident Rates at Intersections ith and ithout a Left-Turn Lane --Using the Lexington data base, accident rates (left-turn accidents per million left-turning vehicles) ere calculated for intersections ith and ithout!eft-turn lanes (Table!). Left-turn related accidents ere based on the folloing definitions: (I) hen a!eft-turning vehicle turned into the path of an oncoming vehicle, (2) hen a!eft-turning vehicle as struck in the rear hile aiting to turn, or (3) hen a vehicle eaving around a vehicle stopped to turn left as involved in an accident. The left-turn accident rate dropped significantly for intersections ith left-turn lanes. For unsignalied intersections, the left-turn accident rate as 77 percent loer. The rate as 54 percent loer at signalied intersections. At signalied intersections, the rate dropped even loer hen left-turn phasing as added. Critical Left-Turn Accident Number --Using the Lexington data, the average number of left-turn accidents for the approaches ith no left-turn lanes as calculated. Separate averages ere calculated for intersections ith and ithout signals. Using the average number of left-turn accidents, the critical number of accidents as also determined. For unsignalied intersections, the average number of accidents as.8 left-turn accidents per approach per year. This corresponded to an average of 1.2 at signalied intersections. The difference as probably due to higher volumes at signalied intersections. TI1e formula used to determine the critical number of accidents as derived from a formula for the average critical accident rate (6): in hich Nc=Na+KVNa+O.S Na K critical number of accidents, average number of accidents, and constant related to level of statistical significance selected (for P =.95, K = 1.645; for P =.995, K = 2.576). For P =.995, the critical number of left-turn accidents in 1 year for an approach as four at an unsignahed mtersechon and live at a signalied intersection. VOLUME WARRANT Excessive Delay at a Signalied Intersection - TI1c computer simulation as used to determine the delay on an approach as a function of the opposing volume, percentage left turns on the subject approach, cycle length, cycle split, and number of opposing lanes. While all other variables ere held constant, the percentage left turns as increased, resulting in relationships shon in Figure 1. The delay per vehicle on the left-turn approach increased as the percentage of left turns increased. The critical delay as found previously to be 3 seconds. As shon in Figure l, this critical delay as reached at various percentage left turns as a function of the opposing volume. For this example, the critical delay as reached at three per-

---------"b"m"a""tl""o"ils-. cent left turns for an opposing peak-hour volume or!. oo vehicles. This compared to the critical Lie lay at about 2 percent left turns hen the opposing peak-hour volume as 8 vehicles. The points at hich delay become excessive ere taken from data such as shon in Figure 1 and plotted as best-fit lines. One of the relationships found is in Figure 2. Given the cycle length and split and the total peak-hour main-street volume (peak hour, both directions), the percentage left turns on an approach necessary to create excessive delay could be found. In Figure 2, for a main-street volume of 1,6 vehicles and a 6/4 cycle split, 19 percent left turns ould be the point at hich delay becomes excessive. Plots, such as Figure 2, ere dran for 6-, 9-, and 12-seeond cycle lengths for to- and four-lane highays. These figures are given in the Appendix. The total main-street volume as used because the volumes on both the left-turn and opposing approaches ould be factors in determining here delay becomes excessive. Equal volumes ere input for both approaches. This as done since it ould have taken a prohibitive number of computer runs to consider all possible combinations of volumes. An analysis of data indicated that using equal volumes on both approaches gives a reasonable approximation of the delay that ould result from different volume com- :Mots saclr as llta t shon-in-figtt-rerhieal-ve-l-j:hth3---wa-h a:h-t--fu.t:-a-le. t..tm:.j+-.wl-"--<"--'1-------- signalied intersection based on excessive delay. Excessive Load Factor - The critical load factor used as.3, representing the upper bound of level of service C, hich is the upper limit of stable flo. The same procedure as used to relate the critical load factor to the variables under consideration as as used for excessive delay. Percentage left turns ere increased hile holding all other variables constant, giving relationships such as plotted in Figure 3. For this example, the critical load factor as reached at 3.5 percent left turns for an opposing peak-hour volume of 1,2 vehicles. TI1is compared to the eriticalload factor at 22.5 percent left turns hen the opposing peak-hour volume as 8 vehicles. It should be noted that the volumes necessary to exceed a load factor of.3 ere slightly higher than those necessary to exceed the critical delay. Data such as plotted in Figure 3 ere-plotted as best-fit lines to produce relationships as shon in Figure 4. The graphical procedure relating an excessive load factor to the variables considered as identical to that used hen excessive delay as considered. In Figure 4, for a main-street peak-hour volume of I,6 vehicles and a 6/4 cycle split, 23 percent left turns ould be the point at hich the load factor becomes excessive. Plots such as Figure 4 ere dran for 6-,9-, and 12-second cycle lengths for toand four-lane highays (1 ). Those plots provide a critical-volume arrant for a left-turn lane based on an excessive load factor. Unsignalied Intersection --Critical-volume arrant curves based on excessive delays using a procedure similar to that for signalied intersections are given in Figure 5 for a four-lane highay (curves for a to-lane highay ere developed ( 1 )). The excessive delay criterion used for signalied intersections as 3 seconds. It ould be logical that a loer delay ould constitute excessive delay at an unsignalied intersection. Therefore, a curve representing a delay criterion of 2 seconds is included. Hoever, there as only a small difference in the to curves. Higher volumes are necessary to create a critical condition at an unsignalied site compared to a signalied site.

Another pro;cdurc as also uscj Cor simulating delays at a nonsignalicd intersection. In this pro* cedure, the computer input specified that 1 percent of the volume on the left-turn approach turned left hile 1 percent of the opposing volume ent straight through. Delay to the left-turn vehicles as determined as the left-turn volume as held constant hile increasing the opposing volume (Figure 6). The point at hich left-turn delay started to increase drastically represents the point at hich a left-turn lane should be considered. Sum of Left-Tum and Opposing Volumes-- The minimum sum of peak-hour left-turn and opposing volumes, hich resulted in a critical left-turn delay, as determined (Table 2). The previously developed figures ere used to obtain this table. This table represents a simpler volume arrant that may be used to determine if further investigation is needed. 111e volumes there ould tend to be loer than those given in the previous figures; they represent the minimum volumes necessary to create a left-turn delay problem. Of course, a minimum number ofleft-turns, such as 5 left turns per hour, ould be necessary. TRAFFIC CONFLICTS WARRANT Traffic conflicts at 25 intersection approaches not havmg a separate left-turn lane ere o------- for three peak hours at each approach. In most instances, th-e data collection periods consisted of one morning rush hour (7:3 to 8:3a.m.) and to afternoon rush hours (3:3 to 5:3p.m.). 1l1e peak hours ere found from traffic volume counts and varied from location to location. Data ere recorded on forms developed for conflicts studies (5 ). All conflict types ere recorded: hoever, only those relating to left-turn accidents ere considered in the analysis. Those conflicts included in the analysis ere as follos: (1) opposing left-turn, (2) eave (involving left-turning vehicle), (3) sloed-for-left-turn (4) previous-left-turn, and (5) ran-red-light (turning left). The sum of these five conflicts as referred to as the total left-turn-related conflicts. The 25 intersection approaches ere divided into to groups based on hether they met the previously developed accident arrant. Seven approaches did. The number of accidents used as the highest yearly number of accidents at a particular approach. The average number of left-turn-related conflicts as determined for the to groups of locations. Six of the approaches ere at unsignalied intersections. Those approaches ere not analyed separately because there ere very fe conflicts directly involving the traffic signal (ran-red-light conflict). Also, six of the approaches ere on to-lane streets. Tlse approaches ere not analyed separately since eave conflicts ere not a high proportion of the total. A summary of the number of conflicts at locations that did and did not meet the accident arrant is given in Table 3. For each conflict type, the averages of the numbers of conflicts in the highest hour as ell as all three hours for each approach ere summaried. Also, the 95th-percentile confidence interval as calculated for each average value.

The sloed-for-left-turn conflict occurred most often. It as follov,. ed in frequency by the previous-left-turn and opposing-left-turn conflicts. There as a smaller number of eave conflicts and a very small number of ran-red-light conflicts. The number of conflicts as substantially higher at locations that met the accident arrant. Hoever, there as a very large range in the data, as shon by the confidence intervals. An interesting comparison can be made beteen the upper bound of the confidence interval for the locations that did not meet the accident arrant and the average value at locations that did meet the accident arrant. With the exception of the ran-red-light conflict, the average value for locations meeting the arrant as above the upper bound of the confidence interval for locations not meeting the arrant. This indicates that using these average values as a guideline ould not identify locations ith a lo accident potential. Hoever, some potentially high-accident locations could be missed. A determination of hich conflicts to usc in a traffic-conflicts arrant must also be made. To benefit from all data available, it ould be logical to include the total of all related conflicts in any arrant or guideline. In addition, any one type of conflict found to relate more to the accident potential should be included. Most accidents involved a left-turning vehicle turning into the path of an opposing vehicle. Therefore, the opposing left-turn conflict could be used as a guide. To determine hich conflicts related most directly ith accidents, equations of the bestfit lines relating left-turn accidents and left-turn-related conflicts ere determined. When each approach as treated as a separate point, very poor relationships ere found. The equations shoed that the total conflicts and opposing-left-turn conflicts related best to accidents. The locations ere then grouped by the number of accidents and related to conflicts. Five accident groupings ere used. There ere four locations having no accidents, four ith one, seven ith to, four locations ith three through five accidents, and six ith six or more accidents. Much better relationships ere found hen this procedure as used. Substituting the number of accidents necessary to arrant a signal into the equations provided another procedure for determining critical traffic conflict numbers. Five accidents ere used as input into the equations. Almost identical results ere obtained for both groups of equations. A summaiy of seveutl alteruate metflocls ef clevelopihg traffie eohfligt arr:u1ts or guidli11es is give11 in Table 4. Those methods give similar results. Using both total conflicts and opposing-left-turn conflicts as guidelines ould provide a suitable procedure. The total left-turn-related conflicts provide maximum input; on the other hand, opposing-left-turn conflicts are the most severe and are the most representative of the type of accidents that have occurred. Based on these sources of input, the folloing arrant as developed: add a left-turn lane hen a conflict study shos an hourly average of 3 or more total left-turn-related conflicts or 6 or more opposing-left-turn conflicts in a 3-hour study period during peak-volume conditions. Also, consider adding a lane if 45 or more total left-turn-related conflicts or 9 or more opposing-left-turn conflicts occur in any 1- hour period.

SUMMARY AND CONCLUSIONS 1. Fe states usc numerical arrants fllr the installation of left-turn lanes; hoever, most use some type of guideline. The guidelines ere usually based on either accidents, volume, or delay. 2. Left-turn accident rates ere found to be significantly loer at intersections having left-turn lanes compared to those ithout left-tum lanes. This finding applied to both signalied and unsignalied intersections. 3. The critical number ofleft-turn accidents in one year necessary to arrant installation of a lefttum lane as four at an unsignalied intersection and five at a signalied intersection. 4. Critical-volume arrant curves for a left-turn lane at a signalied intersection ere developed on the basis of excessive delay. Using a critical delay of 3 seconds per vehicle, plots ere developed giving percentage leftturns necessary to create excessive delay as a function of total main-street volume. Plots ere dran for various cycle lengths and cycle splits for to-lane and four-lane highays. 5. Figures similar to those cited above ere developed to give a critical-volume arrant for a leftturn lane based on an excessive load factor. A critical load factor of.3 as used. 6. TI1e volumes necessary to arranleft-turn la1te ere slightl-y-h ig;ll'!,effr'"v1m +--------- bascd on an excessive load fa-ctor than hen based on excessive delay. 7. Critical-volume arrants based on excessive delays ere developed for unsignalied intersections. 8. An alternative type of volume arrant as based on the minimum sum of peak-hour left-turn and opposing volumes necessary to create a critical left-turn delay. Those volumes represent the loer bounds of the volumes necessary to create a!eft-turn delay problem and may be used to decide if further investigation is needed. 9. Traffic conflict studies ere conducted at intersection approaches that did not have a separate left-turn lane. The data shoed that the average number of left-turn-related conflicts as higher at locations that had a higher number of left-tum-related accidents. Hoever, there as a very large range in the data, as shon by the confidence intervals hich ere found. 1. Equations of the best-fit lines relating left-turn accidents and left-turn conflicts ere determined. \.Vhen each approach as treated as a separate point, very poor correlations ere found. Hoever, much better correlations ere found hen the locations ere grouped by number of accidents. A arrant based on conflicts as developed. RECOMMENDATIONS The addition of left-turn lanes alays provides an improvement in the traffic flo; hoever, leftturn lanes cannot be built at all locations. It is recommended that the folloing arrants be used as guidelines to aid in determining hen the need for left-turn lanes becomes critical: I. Accident Experience -- Install a separate!eft-turn lane if the critical number of!eft-turn-related accidents (as defined in the text) has occurred. For one approach in 1 year, four left-turn accidents at an unsignalied intersection and five at a signalied intersection are critical.

2. Volume --Install a separate left-turn lane hen volumes meet the criteria given in the criticalvolume arrant graphs as shon in Figure 2 and the Appendix for signalied intersections. For signalied intersections, the number of lanes, cycle length, cycle split, total m.:1in-street volume (peak hour), and percentage left-turns must be knon. For unsignalied intersections, the number of lanes, total main-street volume (peak hour), and percentage left-turns must be knon. It is recommended that the curve representing a critical delay of 2 seconds be used for unsignalied intersections. Also, the volumes given in Table 2 representing minimum sums of peak-hour left-turn and opposing volumes giving critical left-turn delays may be used as a guideline to determine if further investigation is needed. 3. Traffic Conflicts -- Consider adding a separate left-turn lane hen a conflict study shos an hourly average of 3 or more total left-turn-related conflicts or 6 or more opposing-left-turn conflicts in a 3-hour study period during peak-volume conditions. Also, consider adding a lane if 45 or more total leftturn-related conflicts or 9 or more opposing-left-turn conflicts occur in any!-hour period. L Agent, K. R.; Development of WaiTants for Left-Turn Lanes, Research Report 526, Division of Research, Kentucky Department of Transportation, July 1979. 2. Netork Flo Simulation for Urban Traffic Control System- Phase II. Volumes 1-5, Federal Highay Administration, March 1974. 3. Highay Capacity Manual, Special Report 87, Highay Research Board, 1965. 4. Traffic Signal Warrants, KLD Associates, KLDTR No. 17, prepared for the National Cooperative Highay Research Program, November 1973. 5. Zegeer, C. V.; Development of a Traffic Conflicts Procedure for Kentucky, Research Report 49, Division of Research, Kentucky Department of Transportation, January 1978.' 6. Agent, K. R.; Development of Warrants for Left-Turn Phasing, Research Report 456, Division of Research, Kentucky Department of Transportation, August 1976.

9 8 - oc I. 27 2 u > 6 _J:I: uu - <:t 5 :I:o Wt:<: >n. o:"- <:t: 4 Q.Z >- «" _J 3 e- OLL _J 2 :I: f-,a oo eoo 6 1 5 1 15 2 PERCENT LEFT TURNS ON THE LEFT APPROACH 25 Figure I. Relationship of Approach Delay to Opposing Volume and Percentage Left Turns (Four-Lane Highay, 9-Second Cycle, 6/4 Cycle Split). => 1 9 eo 7 f- f- 6 LL _J u 4 Q_ ;o CYCLE SPLIT EQUATION '2 7/3 y= 942 ;21X.97 -.228X 6/4 y=73le 99 5/5 y=ll66e -.32X,99 2 1 o L.L_L L_l._L _L l l l.l _L L L_L l j_::::::c=±-!..::j':::i::n=::t:::;:::;=-_j 2 4 6 8 1 12 14 16 18 2 22 24 26 28 3 TOTAL MAIN STREET VOLUME (PEAK HOUR} Figure 2. Percentage Left-Turns When Delay Becomes Excessive (Four-Lane Highay, 9-Second Cycle).

9 " 8 " 7 r ' 4 Q > ".6 > " I- 5 u 1i' ;3A,o -" 3 2-1 15 o PERCENT LEFT TURNS Figure 3. Relationship cf Load Factor to Opposing Volume and Percentage Left Turns (Four-Lane Highay, 9-Second Cycle, 6/4 Cycle Split). 1 9 8 CYCLE SPLIT EQUAl 1 N,, -196X 7/3 y757e 99 y727e -.216X 6/4.99 5/5 yl377e -.34X.98 : " I- I- "- -" u : a. 7 6 4 3 2 1 2 4 6 8 1 12 14 16 18 2 22 24 26 2BOO 3 TOTAL MAIN STREET VOLUME (PEAK HOUR) Figure 4. Percentage LeftTums When Load Factor Becomes Excessive (Four-Lane Highay, 9-Second Cycle).

1 9 8 EXCESSIVE DELAY CRITERION EQUATION r2 3 SECONDS 2 SECONDS y=l625e -.225X y 1893 ;.244X 97.9 8 7 " => 1-1- 6 "- _J 1-5 u " 4 a. 3 2 1 2 4 6 8 1 12 14 16 18 2 22 2'1 "26 28 3 TOTAL MAIN STREET VOLUME {PEAK HOUR) Figure 5. Percentage LeftTums When Delay Becomes Excessive (Four Lane Highay, No Signal). 9 u; 8 " 7 u 6 _J! 5 > " 4 " 1-1- ' "- 3 _J 1- >- _J 2 1-6 7 8 9 1 OPPOSING VOLUME (PEAK HOUR) 11 12 Figure 6. Left-Turn Delay as a Function of Opposing and Left-Tum Volume (Nonsignalied Intersection, Four Lanes).

TABLE l. COMPARISON OF ACCIDENT RATES AT LOCATIONS WITH AND WITHOUT LEFT-TURN LANES ACC!OE:'T RATE I LEFT-TURN MILLION LEFT- ' TURN VhHCLESI NO SIGNAL NO LEFT-TURN LANE 5.7 WITH LEFT-TURN LANE 1.3 WITH SIGNAL NO LEFT-TURN LANE 7.9 WITH LEFT-TURN LANE 3.6 WITH LEFT-TURN LANE AND PHASING o.g

TABLE 2. SUM OF LEFT-TURN AND OP PDS IN G VOLUMES DURING THE PEAK HOUR NECESSARY TO CREATE A LEFT-TURN DELAY PROBLEW S IGNALIZECJ INTERSECTION <FOUR-LANE HIGHWAY) CYCLE SPLIT CYCLE LENGTH 7/3 6/4 5/5 12 95 8 6 9 1 85 7 ' 1 n 1nnn fl n SIGNALIZED INTERSECTION!TWO-LANE HIGHWAY) CYCLE SPLIT CYCLE LENGTH 7/3 6/4 5/5 12 6.5 55 4 9 7 6 5 6 75 65 55 NON-SIGNALIZED INTERSECTION FOUR-LANE TrW-LANE DELAY CRITERION HIGHWAY HIGHWAY 3 SECONDS 1 9 2 SECONDS 9 8 ASSUMING A MI NUMUM LEFT-TURN VOLUME sue H AS 5 LEFT-TURNS IN TrlE PEAK HOUR

TABLE 3. COMPARISON OF CONFLICTS AT. LOCATIO\S H ICH DID AND DID NOT MEET THE ACCIDENT WARRANT TOTAL a LOCATIONS MEETING LOCATIONS NOT MEETING ACCIDENT WARRANT ACCIDENT WARRANT CONFIDENCE CONFIDENCE INTERVAL INTERVAL TYPE OF (95TH (95TH CONFLICT AVERAGE PERCENTILE) AVER AGE PERCENTILE) PEAK HOURb 45 l 5-71 27 16-37 AVERAGEc 3 13-45 1 8 1-26 OPPOSING LEFT TURN PEAK HOUR 8.7 2-16 3.2 l - 5 AVERAGE 5.9 1-1 l 1.6 1-3 SLOrJED FOR LEFT TURN PEAK HOUR 23 1-36 l 5 8-22 AVERAGE 15 7-23 l 5-15 PREVIOUS LEFT TURN PEAK HOUR 14 4-24 7.6 4-11 AVERAGE 8 5 - l 1 4.9 2-8 WEAVEd PEAK HOUR 4o4 1-8 1.9 1-3 AVERAGE. 1-3 1.1.6-1.6 RAN RED LIGHTd PEAK HOUR.57-1.3.5.2 -. 8 AVERAGE.19.4 o. 2 8.7 a TOTAL OF LEFT-TURN RELATED CONFLICTS b AVERAGE OF THE HIGHEST NUMBER OF CONFLICTS FOUND IN ONE OF THE THREE PEAK HOURS STUDIED FOR THE LOCATIONS c AVERAGE OF THE NUBER OF CONFLICTS FOR THE THREE PEAK HOURS FOR EACH LOCATION d INVOLVING LEFT-TURNING VEHICLES

TABLE 4. METHODS OF DEVELOPING TRAFFIC f8f CONFLICT WARRANTS OF GUIDELINES CRITICAL TRAFFIC CONFLICT LEVEL FOR GIVEN METHOD UPPER LEVEL OF CONFIDENCE SUB ST ITUT ING AVERAGE VALUE INTERVAL AT FIVE ACCIDENTS AT LOCATIONS LOCATIONS NOT INTO EQUATION TYPE OF MEETING ACCIDENT MEETING ACCIDENT RELATING CONFLICTS CONFLICT WARRANT WARRANT AND ACCIDENTS PEAK HOURb 45 37 38 AVERAGE 3 26 26 OPPOSING LEFT TURN PEAK HOUR 8.7 5 6. AVERAGE 5.9 3 3.8 SLOWED FOR LEFT TURN PEAK HOUR 23 22 2 AVERAGE 15 15 14 PREVIOUS LEFT TURN PEAK HOUR 14 ll 12 AVERAGE 7.9 8 7.3 WEAVEd PEAK HOUR 4.4 3 3.4 AVERAGE 2.2 1.6 1o7 a TOTAL OF LEFT-TURN RELATED CONFLICTS I Ht Hll>Mt I Ul'jt-MUUK NUI'"IDcK Ur l.unrll<.l c AVERAGE NUMBER OF CONFLICTS IN THE THREE PEAK HOURS d INVOLVING LEFT-TURNING VEHICLE

APPENDIX FIGURES GIVING PERCENTAGE LEFT-TURNS WHEN DELAY BECOMES EXCESSIVE (SIGNALIZED INTERSECTION)

1 CYCLE SPLIT EQUATION 9 7/3 y926e -_OQI9X.96 '' 8 6/4 y "1212 e -.236X.98 5/5 y-=iigoe -.268X.99 ::> >- >- "-.J >- u a. 7 6-5 4-3 2 - oo 4 sao sao 1 1oo 14 IGOO IBOO ooo 22 24 soo eoo 3 TOTAL MAIN STREET VOLUME (PEAK HOUR) Figure Al. Percentage LeftMTums When Delay Becomes Excessive (Four-Lane Highay, 6-Second Cycle). 1 9 8 7/3 EQUATION '' y -=942e -_21 X 97 6/4 y = 731e -J228X 99-32X 5/5 y -=11666 99 ::> >- >- "-.J u " a. 7 6 4-3.. 2 1 2 4 6 8 1 12 14(J 16 18 2 22 24 26 28 3 TOTAL MAIN STREET VOLUME (PEAK HOUR) Figure A2. Percentage Left-Turns When Delay Becomes Excessive (Four-Lane Highay, 9-Second Cycle).

: " f-, 9 8 7 f- 6 "- -' f- 5 u 4 a_ ' I CYCLE SPLIT EQUATIOI '' -234 X 7/3 y=i67e 98 6/4-263X y B42.e 97 515 y=918e -.37'\X 99 3 2.. l_l_l L i_j L_L_L_L_L::::r::...:::t::::J:::::;::::::;;;;;t;;;;;,;=, j 2 4 6 8 1 12 14 16 18 2 22 24 26 28 3 TOTAL MAIN STREET VOLUME (PEAK HOUR) Figure A3. Percentage Left Turns When Delay Becomes Excessive (Four Lane Highay, 12-Second Cycle). ' r-----------------------------.-----.-------,------------------------, 9 ' :: t :J f- 6 f- "- -' 5 f- 4 : a_ 3 CYCLE SPLIT EQUATION '' -.8X 713 y=522995e.9' 6/4 5/ 5-9X y=2252 e ' y=59782e -.9 X 98 2 2 4 hoo SOC 1 12 TOTAL MAIN STREET VOLUME(PEAK HOUR) I GOO Figure A4. Percentage Left-Turns When Delay Becomes Excessive (To-Lane Highay, 6-Second Cycle).

" >-- >-- "-..J >-- u <L IG :J, I CYCLE SPIT EQUATION -.7X '' 9C 7/3 ye4225e 99 -.OO?X 6/4 Y=2728e I BC 7 6 5 4 f i [ 3 I 2 -.OOBX 5/5 Y=6592e.95 1 [ L l [ [ j j _I l j 2 4 GOO BOO iooo 12 14 I GOO TOTAL MAIN STREET VOLUME( PEAK HOUR) Figure AS. Percentage LeftTums When Delay Becomes Excessive (To-Lane Highay, 9-Second Cycle). IOC 9 CYCLE SPLIT EQUATION,, 713 y =35435 e -.OOBX 1. 6 /4 y=7672e--6x 99 8 5/5 y=l952e -7X.99 >- >-- "-..J u <L 7 6 L 5 4 3 n '" 2 1 _...J _l..l j l l j 2 4 soo 8 1 12 14 'GOO TOTAL MAIN STREET VOLUME( PEAK HOUR) Figure A6. Percentage Left-Turns When Delay Becomes Excessive (To-Lane Highay, 12-Second Cycle).

Research Report UKTRP-82-19 WARRANTS FOR LEFT-TURN LANES by Kenneth R. Agent Chief Research Engineer Kentucky Transportation Research Program College of Engineering University of Kentucky Lexington, Kentucky offered for publication to the Transportation Quarterly The contents of this report reflect the vies of the author ho is responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official vies or policies of the Kentucky Department of Transportation nor of the a standard, specification or regulation. October 1982

WARRANTS FOR LEFT-TURN LANES by K.R. Agent ABSTRACT Warrants for the installation of separate left-tum lanes ere developed. Literature as revieed, and policies and practices in other states ere surveyed. Accident analyses of locations ith and ithout separate left-tnrn lanes ere conducted. Computer simulation as used to determine relationships among traffic delay, load factor, traffic volume, percent!eft-turns, cycle length, and cycle split. The relationship --------------lf4oonfig;arn------------------------------------------ Warrants ere developed involving the folloing three general areas: (!) accident experience, (2) volumes (based on delay), and (3) traffic conflicts.

INTRODUCTION A vehicle stopped in the traffic stream to turn left creates an accident potential and impedes the flo of through traffic. The addition of left-turn lanes alays provides an improvement in the traffic flo; hoever, left-turn lanes cannot be built at all locations, and arrants have not been established for determining hen the need for left-turn lanes becomes critical. In this study, arrants or guides ere developed for installing separate left-turn lanes. Computer simulation as used to determine the relationships beteen traffic delay and such variables as percentage left-turns, traffic volume, and cycle length. Accident data ere compared at locations ith and ithout left-tum lanes, and the average number of left-turn accidents for approaches ith no left-turn lane as determined. The relationship beteeu left-turn accidents and conflicts as also investigated. Using these sources of input, criteria for determining need for left-turn lanes ere derived. Before data collection and analysis started, both a revie of literature and a survey of arrants or guides used in the other states ere conducted. Fe states used numerical arrants for the installation ofleftturn lanes, but most used some guidelines. Those guidelines ere based primarily on either accidents, volume, or delay(j). PROCEDURE ACCIDENT DATA The data base consisted of five years of accident analyses of intersections in Lexington, Kentucky. Accident rates at locations ith and ithout left-turn lanes ere calculated. This as done using volume counts at intersections for a 12-hour period (7 a.m. to 7 p.m.). The assumption as made that 8 percent of the volume occurred in this 12-hour period. Those volumes ere then multiplied by 1.25 to obtain the 24-hour volume. Using the same data base, the average number of left-turn accidents for the approaches ith no left-turn lanes as calculated. The average number of accidents as used to calculate a critical number of left-turn accidents. TRAFFIC VOLUME Computer simulation as used to relate traffic delay and load factor to traffic volume, percentage left-turns, cycle length, and cycle split. The simulation program as the UTCS-1 Netork Simulation Model developed for the Federal Highay Administration (2). An isolated intersection as input into the program. Simulation runs ere made assuming both stopsign control and signal control. When a signal as specified, the cycle length and cycle split ere given. During peak hours, volumes on the side street of a semi-actuated signal ould be so heavy that a fixed cycle ould be approximated. Data ere simulated for an intersection on a four lane and on a to-lane street. Equal volumes ere input for both main street approaches. The percentage of left-turns ere varied on one approach

hile the other approach had 1 percent ofits volume going straight. Cycles of 6, 9, and 12 seconds ere used. Cycle splits of 7/3 (7 percent of the cycle devoted to the main street), 6/4, and 5/5 ere used. A free-flo speed of 45 mph (2 m/s) as used. The average delay and the load factor ere obtained for the left-turn approach. Load factor is defmed as the ratio of the total number of green-signal intervals fully utilied by traffic during the peak hour to the total number of green intervals for that approach during the same period (3). The maxhnum value is one. Graphs ere dran relating the variables to critical delay and load factors. The critical delay as 3 seconds, found using a procedure given in another report (4). In that study, engineers ere asked for their opinion of hat constituted maximum tolerable delay for a vehicle controlled by a traffic signal. A mean value of 73 seconds as found. A criterion that 85 percent of all the left-turn approach vehicles be delayed less than this maximum of 73 seconds as then used. Assuming the distribution of delays become approximately normal during peak-flo conditions, the folloing formula can be used: 85th percentile X+ 1.44 a ---------Jit:l-hich 85th percentile value of delay of the 85th percentile of the normal distribution (73 seconds), X mean value of delay, and a standard deviation of the distribution. It as assumed that the standard deviation as approxhnately equal to the mean. Substituting these values gave a value of 3 seconds for the mean delay. Thirty seconds as used as the minimum average delay necessary because this value constituted the loer bound of excessive delay. A critical load factor of.3 as used because it represents the upper bound of level of service C (3), the upper limit of stable flo. Level of service D represents a one of increasing restriction approaching instability. Ao additional procedure as used for shnulation of non-signalied intersections. One hundred percent of the volume on one approach turned left hile 1 percent of the volume on the opposing approach ent straight through the intersection. Volume on the left-turn approach as held constant hile the opposing volume as changed. This permitted a plot of left-turn delay as a function of the left-turn and opposing volumes. Data ere simulated for an intersection on fourlane and to-lane streets. CONFLICT DATA Conflict counts involving left-turn vehicles ere taken at several intersections and related to the number of left-turn accidents and traffic volumes. The conflicts ere classified into several categories ( 5). Basically, there ere four types of!eft-turn related conflicts. The first occurred hen a left-turning vehicle crossed directly in front of or blocked the lane of an opposing through vehicle (opposing left-turn conflict). The second as caused by a vehicle aiting to turn left (rear-end type). A third as a eave resulting hen a vehicle, evading a left-turning vehicle ahead, veered into tl1e path of another vehicle. The fourth involved running the red light. Ao attempt as made to classify the conflicts according to severity. Hoever, in the analysis, no distinction by severity is made because of inconsistency of data taken by different observers.

RESULTS ACCIDENT WARRANT Accident Rates at Intersections ith and ithout a Left-Turn Lane --Using the Lexington data base, accident rates (left-turn accidents per million!eft-turning vehicles) ere calculated for intersections ith aud ithout left-turn lanes (Table 1). Left-turn related accidents ere based on the folloing definitions: (1) hen a left-turning vehicle tnrned into the path of an oncoming vehicle, (2) hen a left-turning vehicle as struck in the rear hile aiting to turn, or (3) hen a vehicle eaving around a vehicle stopped to turn left as involved in an accident. The left-turn accident rate dropped significantly for intersections ith left-turn lanes. For unsignalied intersections, the left-turn accident rate as 77 percent loer. The rate as 54 percent loer at signalied intersections. At signalied intersections, the rate dropped even loer hen left-turn phasing as added. Critical Left-Turn Accident Number --Using the Lexington data, the average number of left-turn accidents for the apmoaches ith no left-turn lanes as calculated. Separate averages ere calculated for intersections ith and ithout signals. Using the average number of left-turn accidents, the critical number of accidents as also determined. For unsignalied intersections, the average number of accidents as.8 left-turn accidents per approach per year. This corresponded to au average of 1.2 at signalied intersections. The difference as probably due to higher volumes at signalied intersections. The formula used to determine the critical number of accidents as derived from a formula for the average critical accident rate (6): in hich = Nc=Na +KvNa +.5 = = critical number of accidents, average number of accidents, and constant related to level of statistical significance selected (for P =.95, K = 1.645; for P =.995, K = 2.576). For P =.995, the clitical number of left-turn accidents in 1 year for an approach as four at an unsignalied intersection and hve at a signalied mtersection. VOLUME WARRANT Excessive Delay at a Signalied Intersection --The computer simulation as used to determine the delay on an approach as a function of the opposing volume, percentage left turns on the subject approach, cycle length, cycle split, aud number of opposing lanes. While ali other variables ere held constant, the percentage left turns as increased, resulting in relationships shon in Figure 1. The delay per vehicle on the left-turn approach increased as the percentage ofleft turns increased. The critical delay as found previously to be 3 seconds. As shon in Figure I, this critical delay as reached at various percentage left turns as a function of the opposing volume. For this example, the critical delay as reached at three per-

cent left turns for an opposing peak-hour volume of 1,2vehicles. This compared to the critical delay at about 2 percent left turns hen the opposing peak-hour volume as 8 vehicles. The points at hich delay become excessive ere taken from data such as shon in Figure 1 and plotted as best-fit lines. One of the relationships found is in Figure 2. Given the cycle length and split and the total peak-hour main-street volume (peak hour, both directions), the percentage left turns on an approach necessary to create excessive delay could be found. In Figure 2, for a main-street volume of I,6 vehicles and a 6/4 cycle split, 19 percent left turns ould be the point at hich delay becomes excessive. Plots, such as Figure 2, ere dran for 6-, 9-, and 12-second cycle lengths for to- and four-lane highays. These figures are given in the Appendix. The total main-street volume as used because the volumes on both the left-turn and opposing approaches ould be factors in determining here delay becomes excessive. Equal volumes ere input for both approaches. This as doue since it ould have taken a prohibitive number of computer runs to consider all possible combinations of volumes. An analysis of data indicated that using equal volumes on both approaches gives a reasonable approximation of the delay that ould result from different volume combinations. Plots such as th-arslion m Figute 2 give a critical-volume arrant-f-etr--a-lefirtfr--l:ane-at-ac------- signalied intersection based on excessive delay. Excessive Load Factor -- The critical load factor used as.3, representing the upper bound of level of service C, hich is the upper limit of stable flo. The same procedure as used to relate the critical load factor to the variables under consideration as as used for excessive delay. Percentage left turns ere increased hile holding all other variables constant, giving relationships such as plotted in Figure 3. For this example, the critical load factor as reached at 3.5 percent left turns for an opposing peak-hour volume of I,2 vehicles. This compared to the critical load factor at 22.5 percent left turns hen the opposing peak-hour volume as 8 vehicles. It should be noted that the volumes necessary to exceed a load factor of.3 ere slightly higher than those necessary to exceed the critical delay. Data such as plotted in Figure 3 ere plotted as best-fit lines to produce relationships as shon in Figure 4. The graphical procedure relating an excessive load factor to the variables considered as identical to that used hen excessive delay as considered. In Figure 4, for a main-street peak-hour volume of I,6 vehicles and a 6/4 cycle split, 23 percent left turns ould be the point at hich the load factor becomes excessive. Plots such as Figure 4 ere dran for 6-, 9-, and 12-second cycle lengths for toand four-lane highays I 1). Those plots provide a critical-volume arrant for a left-turn lane based on an excessive load factor. Unsignalied Intersection -- Critical-volume arrant curves based on excessive delays using a procedure similar to that for signalied intersections are given in Figure 5 for a four-lane highay (curves for a to-lane highay ere developed I 1 )). The excessive delay criterion used for signalied intersections as 3 seconds. It ould be logical that a loer delay ould constitute excessive delay at an unsignalied intersection. Therefore, a curve representing a delay criterion of 2 seconds is included. Hoever, there as only a small difference in the to curves. Higher volumes are necessary to create a critical condition at an unsignalied site compared to a signalied site.

Another procedure as also used for simulating delays at a nonsignalied intersection. In this procedure, the computer input specified that 1 percent of the volume on the left-turn approach turned left hile 1 percent of the opposing volume ent straight through. Delay to the left-turn vehicles as determined as the left-turn volume as held constant hile increasing the opposing volume (Fignre 6). The point at hich left-turn delay started to increase drastically represents the point at hich a left-turn lane should be considered. Sum of Left-Turn and Opposing Volumes-- The minimum sum of peak-hour left-turn and opposing volumes, hich resulted in a critical left-turn delay, as determined (Table 2). The previously developed fignres ere used to obtain this table. This table represents a shnpler volume arrant that may be used to determine if further investigation is needed. The volumes there ould tend to be loer than those given in the previous figures; they represent the minimum volumes necessary to create a left-turn delay problem. Of course, a minhnum number ofleft-turns, such as 5 left turns per hour, ould be necessary. TRAFFIC CONFLICTS WARRANT Traffic conflicts at 25 intersection approaches not havmg a separate left-turn lane ere observed for three peak hours at each approach. In most instances, the data colledion periods consisted of one morning rush hour (7:3 to 8:3a.m.) and to afternoon rush hours (3:3 to 5:3p.m.). The peak hours ere found from traffic volume counts and varied from location to location. Data ere recorded on forms developed for conflicts studies (5). All conflict types ere recorded: hoever, only those relating to left-turn accidents ere considered in the analysis. Those conflicts included in the analysis ere as follos: (1) opposing left-turn, (2) eave (involving left-turning vehicle), (3) sloed-for-left-turn ( 4) previous-left-turn, and (5) ran-red-light (turning left). The sum of these five conflicts as referred to as the total left-turn-related conflicts. The 25 intersection approaches ere divided into to groups based on hether they met the previously developed accident arrant. Seven approaches did. The number of accidents used as the highest yearly number of accidents at a particular approach. The average number of left-turn-related conflicts as determined for the to groups of locations. Six of the approaches ere at unsignalied intersections. Those approaches ere not analyed separately because there ere very fe conflicts directly involving the traffic signal (ran-red-light conflict). Also, six of the approaches ere on to-lane streets. Those approaches ere not analyed separately since eave conflicts ere not a high proportion of the total. A summary of the number of conflicts at locations that did and did not meet the accident arrant is given in Table 3. For each conflict type, the averages of the numbers of conflicts in the highest hour as ell as all three hours for each approach ere summaried. Also, the 95th-percentile confidence interval as calculated for each average value.

The sloed-for-left-turn conflict occurred most often. It as folloed in frequency by the previousleftmturn and opposingmleftmturn conflicts. There as a smaller number of eave conflicts and a very small number of ran-red-light conflicts. The number of conflicts as substantially higher at locations that met the accident arrant. Hoever, there as a very large range in the data, as shon by the conm fidence intervals. An interesting comparison can be made beteen the upper bound of the confidence interval for the locations that did not meet the accident arrant and the average value at locations that did meet the accident arrant. With the exception of the ran-red-light conflict, the average value for locations meeting the arrant as above the upper bound of the confidence interval for locations not meeting the arrant. This indicates that using these average values as a guideline ould not identify locations ith a lo accident potential. Hoever, some potentially high-accident locations could be missed. A determination of hich conflicts to use in a traffic-conflicts arrant must also be made. To benefit from all data available, it ould be logical to include the total of all related conflicts in any arrant or guideline. In addition, any one type of conflict found to relate more to the accident potential should be included. Most accidents involved a left-turning vehicle turning into the path of an opposing vehicle. Therefore, the opposing left-turn conflict could be used as a guide. To determine hich conflicts related most directly ith accidents, equations of the bestfit lines relating left-turn accidents and left-tum-related conflicts ere determined. When each approach as treated as a separate point, very poor relationships ere found. The equations shoed that the total conflicts and opposing-left-turn conflicts related best to accidents. The locations ere then grouped by the number of accidents and related to conflicts. Five accident groupings ere used. There ere four locations having no accidents, four ith one, seven ith to, four locations ith three through five accidents, and six ith six or more accidents. Much better relationships ere found hen this procedure as used. Substituting the number of accidents necessary to arrant a signal into the equations provided another procedure for determining critical traffic conflict numbers. Five accidents ere used as input into the equations. Almost identical results ere obtained for both groups of equations. A summarv of several alternate methods of developing traffic conflict arrants or guidlines is given in Table 4. Those methods give similar results. Using both total conflicts and opposing-left-turn conflicts as guidelines ould provide a suitable procedure. The total left-turn-related conflicts provide maximum input; on the other hand, opposing-left-turn conflicts are the most severe and are the most representative of the type of accidents that have occurred. Based on these sources of input, the folloing arrant as developed: add a left-turn lane hen a conflict study shos an hourly average of 3 or more total left-turn-related conflicts or 6 or more opposing-left-turn conflicts in a 3-hour study period during peale-volume conditions. Also, consider adding a lane if 45 or more total left-turn-related conflicts or 9 or more opposing-left-turn conflicts occur in any! hour period.