Methodology for Estimating Bicyclist Acceleration and Speed Distributions at Intersections

Methoology for Estimating Bicyclist Acceleration an Spee Distributions at Intersections Miguel Figliozzi, Nikki Wheeler, an Christopher M. Monsere As cities across North America install infrastructure to accommoate a growing number an variety of bicyclists, installation of bicycle-specific traffic signals is a common esign element. A recent survey showe a lack of consistency in esign an timing. In particular, minimum green signal timing is highly epenent on the assume acceleration an spee performance of bicyclists, but no etaile methoology exists to estimate these performance values. Recently, AASHTO, the California Department of Transportation, an the National Association of City Transportation Officials issue ocuments that require the provision of an aequate clearance interval an recommene that, in the etermination of this minimum interval fiel, an investigation of bicyclist spee be conucte. Even if etaile vieo trajectories are available, the etermination of a value for fiel spee an acceleration is not trivial, because values of spees an accelerations are a function of time an iniviual bicyclist performance. The purpose of the research reporte here was to evelop an apply a general methoology to estimate bicyclist acceleration an spee for traffic signal timing applications. With the use of physical equations of motion, this research analytically erive expressions that coul be use to classify an iniviual bicyclist s performance as a function of the observe acceleration profile. The analysis inicate that four basic acceleration profiles were possible an that the profiles coul be obtaine with a parsimonious fiel ata collection metho. The methoology was applie successfully to two intersections in Portlan, Oregon. A etaile statistical analysis showe that the results were intuitive an that the methoology successfully categorize bicyclist performance variations as a result of topography or emographic characteristics. Many cities in North America are making significant investments in bicycling infrastructure to improve cycling conitions. These investments are motivate in part by research that inicates that, to grow bicycle riership, facilities nee to be esigne to accommoate all riers, particularly those emographic groups that might not otherwise choose to cycle in the typical urban setting because to o so woul be a stressful experience (. Most bicycle vehicle crashes in urban areas occur at intersections (. Thus, traffic signal timing plays a significant role in the M. Figliozzi an C. M. Monsere, Department of Civil an Environmental Engineering, Portlan State University, P.O. Box 75, Portlan, OR 9707-075. N. Wheeler, Massachusetts Department of Transportation, 66 West Street, Apartment 4, Northampton, MA 0060. Corresponing author: M. Figliozzi, figliozzi@px.eu. Transportation Research Recor: Journal of the Transportation Research Boar, No. 387, Transportation Research Boar of the National Acaemies, Washington, D.C., 03, pp. 66 75. DOI: 0.34/387-08 effort to make cycling a safe an attractive option for city travel. The setting of many timing parameters involves a elicate balance, because urban intersections must accommoate motor vehicles, peestrians, an cyclists, an the performance of these users varies between an within groups. If movements are separate by users (e.g., a bicycle-specific phase it becomes important to have fielobserve performance values for safety an efficiency. For example, unnecessarily long minimum green times to accommoate cyclists can lea to excessive elays an increase emissions from motor vehicles. Yet inaequately short bicycle-specific minimum green times can create stressful, uncomfortable, an even unsafe bicycle environments (3. Because there may be performance ifferences associate with cycling emographics, it is possible that only strong or high-performance bikers may be capable of the acceleration an spee necessary to clear an intersection safely in situations in which clearance an green time may be minimal. A user that requires more time to cross comfortably (e.g., chil, oler cyclist may be caught miway through an intersection when opposing traffic receives a green. Not only is such a situation unsafe, it also can be a eterrent to bicycling as a viable alternative moe. To meet the nees of bicycle riers an other intersection users aequately, it is vital to unerstan the performance of bicycle riers. Extensive literature an reports on the basis of professional experience escribe operational strategies an esign issues with respect to traffic signals for motorize vehicles an peestrians. In contrast, the literature an reports on engineering experience for bicycle-specific signal esign are newer an relatively scarce. A recent survey inicate a lack of consistency across North American cities with respect to bicycle signal esign, etection, an timing parameters (4. In particular, the survey foun a wie range of assume bicycle spees (from. to 8.7 ft/s across bike signals in North American cities. A relatively wie range of publishe cyclist performance ata (e.g., on perception reaction times, rolling spee, accelerations can guie the selection of basic signal parameters (e.g., minimum green, yellow, an all-re clearance intervals; extension times. AASHTO, the California Department of Transportation (Caltrans, an the National Association of City Transportation Officials (NACTO now require that an aequate clearance interval be provie. Furthermore, they recommen that, in the etermination of the minimum interval, a fiel investigation of bicyclist spees be conucte (5 7. These guies suggest that intervals sufficient for 5th percentile spees shoul be use. Absent fiel ata, the guies suggest that a value of approximately 5 ft/s may be use as a efault spee. AASHTO also recommens that extene crossing times shoul be given to some types of riers [e.g., young riers near schools (5, Sec. 4..4, p. 4-44]. 66

Figliozzi, Wheeler, an Monsere 67 Although these guiance ocuments (5 7 recommen fielobtaine values an 5th percentile spees, no consistent methoology is available to etermine fiel spees or acceleration. As iscusse later in this paper, the etermination of fiel bicyclists acceleration an cruising spee is not a trivial exercise. In the literature, no comprehensive mathematical framework has yet appeare to estimate bicycle rier acceleration an cruising spees at intersections. The purpose an main contribution of the research reporte here was to evelop an apply a general mathematical framework to estimate bicyclist acceleration an cruising spee for traffic signal timing applications to ata that coul be extracte from a simple vieo ata collection proceure. Because the simultaneous estimation of acceleration an cruising spee values is not trivial, the methoology containe in this paper can be use to estimate acceleration an cruising spee istributions in intersections with unique or special characteristics. Through the analysis of physical equations of motion, this research analytically erive expressions that coul be use to classify an iniviual bicyclist s performance as a function of the observe acceleration profile. In turn, the acceleration profile coul be use to classify the iniviual bicyclist s performance at an intersection an the performance given ifferent emographics an acceleration an spee istributions. Finally, recommene minimum green times obtaine from current guiance ocuments were compare with fiel estimations with the use of 85th percentile crossing times. LITERATURE REVIEW The recently release 0 AASHTO Guie for the Development of Bicycle Facilities provies a revise treatment of the information that relates to bicyclist types an minimum green crossing time. The three classes of cyclists (A, B, an C presente in the 999 guie have been replace by two new classes, namely Experience an Confient an Casual an Less Confient (5. The new guie presents timing issues separately for staning an rolling bicyclists. For stoppe bicyclists, the guie presents the equations to etermine the minimum green require for a cyclist to start from stop an clear the intersection with. To estimate minimum green crossing times, acceleration an crossing spees must be known. For a bicycle that starts from a stoppe position, the efault acceleration value is.5 ft/s ; the efault rolling spee is 0 mph or 4.7 ft/s. For rolling cyclists, the guie also presents an equation to etermine the rolling crossing time. A cyclist that enters an intersection just at the en of green shoul have sufficient time to clear the intersection uring the yellow change an all-re clearance intervals. The rolling time is presente as the sum of the braking istance, intersection with, an length of bicycle ivie by the assume rolling spee (suggeste as 0 mph or 4.7 ft/s. The new AASHTO guie states that the yellow interval is base on the approach spees of automobiles, an therefore, shoul not be ajuste to accommoate bicycles (5, p. 4-46. The guie suggests the moification of the all-re time or, if that is insufficient, to use a eicate bicycle etector an controller settings to exten time sufficiently to clear the intersection. A spee of approximately 0 mph (4.7 ft/s is now cite in the latest bicycle esign guies as an assume rolling spee (5 7. The NACTO guie requires that an aequate clearance interval (i.e., the movement s combine time for the yellow an all-re phases shall be provie to ensure that bicyclists entering the intersection uring the green phase have sufficient time to safely clear the intersection before conflicting movements receive a green inication. In the etermination of this minimum interval, fiel investigation of bicyclists spee is recommene. The guie suggests that intervals sufficient for 5th percentile spees shoul be use. Absent fiel ata, the NACTO guie suggests that 4 feet per secon (9.5 miles per hour may be use as a efault spee (7. The AASHTO guie provies a formula to estimate minimum green for bicycles from a staning position (5: V ( W + L BMG+ Y + Rclear = PRT + + a V where BMG = bicycle minimum green interval (s, PRT = perception reaction time ( s, Y = length of yellow interval (s, R clear = length of all-re clearance interval (s, W = intersection with (ft, L = typical bicycle length (6 ft, a = bicycle acceleration (.5 ft/s, an V = bicycle crossing spee (4.7 ft/s. The California Manual on Uniform Traffic Control Devices provies etection guiance an provisions on the minimum timing parameters (6. The manual states that, for all phases, the sum of the minimum green, plus the yellow change interval, plus any re clearance interval shoul be sufficient to allow a bicyclist riing a bicycle 6 feet long to clear the last conflicting lane at a spee of 0 mph (4.7 ft/s plus an aitional effective start-up time of six secons, accoring to the following formula: ( W + 6ft Gmin + Y + Rclear > 6s+ 4.7 ft s where G min is the length of the minimum green interval (secons an W is the istance from the limit line to the far sie of the last conflicting lane (feet. The AASHTO an Caltrans formulas estimate similar numbers. With the efault AASHTO values of perception reaction ( s, spee (4.7 ft/s, an acceleration (.5 ft/s, the first two terms of AASHTO Equation are approximately 6 s: v PRT + 6s a Empirical evience inicates that a wie range of acceleration an spee performance may nee to be accommoate on the basis of iniviual locations (8. Most publishe stuies have use ifferent measurement techniques to erive these values. Wachtel et al. conucte one of the first stuies of bicyclists minimum green time, an highlighte that the most common signal timing issue relate to vehicle bicycle collisions: a cyclist lawfully enters an intersection on a yellow phase an is hit by a motorist on the intersecting street, who restarts or accelerates into the intersection upon receipt of a green phase (8. In this situation, the clearance time is not sufficient for a cyclist at cruising spee to travel safely across the intersection. Another signal timing issue can occur at the start of a green phase at an actuate signal. A signal that provies only a minimum green time esigne for motor vehicles (a result of low vehicle eman may not be long enough to accommoate

68 Transportation Research Recor 387 a cyclist s nee to react, accelerate, an traverse the intersection, especially at wie intersections an in situations in which multiple cyclists have forme a queue. A hanful of stuies have measure average spees an accelerations an compare them with the guiance ocuments. Pein measure the average spee an approximate the acceleration of cyclists on multiuse paths an at three-leg intersections (9. Rubins an Hany measure intersection clearance times for cyclists in Davis, California, from stoppe, slowe, an rolling positions across a wie age range (0. A stuy conucte in Portlan, Oregon, foun statistically significant performance ifferences between male an female bicyclists, an also when flat an uphill intersections were compare (. Pein investigate trail users, an collecte ata from active an passive stuy participants on skateboars, kick scooters, tanem cycles, manual an power wheelchairs, electric bicycles, inline skates, an han cycles, among several other emerging trail user vehicle types (9. In his stuy of the cyclist group, Pein foun that, after an initial increase in the acceleration rate, the rate ecrease with increasing spee, which was counter to the AASHTO equation, which assumes a constant acceleration (5, 9. More recently, researchers have use vieo-image an processing software to extract each cyclist s trajectory through an intersection ( 3. The trajectories were synchronize to signal phases an were use to etermine start-up time an cruising spee through intersections. The stuies presente evience that performance varie by intersection population. At a location populate mainly by recreational cyclists an families, spees were foun to be slower than at a location largely mae up of commuting college stuents. Bicyclist emographics o affect performance (, 4, 5. Research by Navin foun that young males achieve higher spees than average when they climbe on a grae (5. A UK stuy foun no statistically significant ifference between male an female spees on flat roaways but significantly lower spees (for females on uphill roaways (6. ACCELERATION AND SPEED DETERMINATION The etermination of fiel bicyclist acceleration an spee is recommene by the guiance ocuments as well as through the use of 5th percentile spees. No methoology to etermine fiel spees or acceleration is provie, however. Automate methos to extract object trajectories from vieo ata are possible, although not wiely available (7. Even if etaile vieo trajectories are available, the etermination of a value for fiel spee an acceleration is not trivial, because values of spees an accelerations are a function of time an iniviual bicyclist performance. For example, when a bicyclist starts in a staning position, the initial spee is zero; it takes time t c to reach cruising spee. The change of spee is, in turn, a function of the acceleration a from time zero t 0 (the time when bicyclist movement is imminent to time t c. As expecte from physics an real observations, the value of acceleration is not a constant but tens to ecrease as spee increases (. Many potential acceleration values can be observe in a secon-by-secon trajectory analysis. To compare against guiance acceleration an spee values a consistent methoology is necessary, one erive from funamental physics equations of motion, to obtain representative average acceleration an spee values. Again, it is not trivial to obtain representative average acceleration an spee values. For an iniviual bicyclist, it is possible to observe the time t to cover a given istance from a staning position. If the goal is to obtain an average acceleration, enote a, an a cruising spee v c, an if constant acceleration is assume, the time to reach cruising spee is t c = v c /a. The istance travele is equal to c a t ( vc = ( c = a The time elapse up to the first observations is equal to ( c t = tc + ( t tc = tc + v c Replacement of v c = t c a an c = (v c /a into Equation yiels ( vc vc t = + a a vc vc t = + a v c In Equation, two values are known from measurement (t, an two unknowns, v c an a. Thus the problem is ineterminate. It is not possible to estimate both values simultaneously. This inetermination can be broken if another observation is taken. In aition to (t,, it is possible to obtain a secon pair of observations timing the cyclists time t to cover a given istance from a staning position an a start at time istance (t 0, 0. Without loss of generality, it is assume that t < t an <. With the observations (t, an (t, it is possible to have four acceleration profiles on the basis of the point at which each bicycle rier has finishe acceleration (i.e., the cyclist has reache a cruising spee. These cases are escribe in the following list: Case. The cyclist reaches cruising spee within, at, or before he or she reaches the time istance (t,. Case. The cyclist reaches cruising spee after (t, but before he or she reaches (t,. Case 3. The cyclist reaches cruising spee after (t,. Case 4. The cyclist oes not have a nonecreasing spee profile. To simplify the notation an expressions, the prime symbol is introuce to enote the ifferences. For example, the partial time (t an istance ( between Observations an are enote as t = t t = Similarly, the partial time (t an istance ( between Observations 0 an are enote as t = t t 0 = 0 Determination of Case The cyclist reaches cruising spee within, at, or before the cyclist reaches the time an istance (t,. Thus it is possible to solve the ( (

Figliozzi, Wheeler, an Monsere 69 ineterminacy, because the secon perio is travele at a cruising spee as v c ( = = ( t t t If Equation 3 is replace into Equation, the value of a is obtaine as t t = + at a = t t t vc tc = a (3 (4 This equation is prove because the cruising spee must satisfy v c at (i.e., in Case the cruising spee is assume to be reache in the time interval [t, t ]. For the only potentially feasible root (Expression 9, the feasibility constraint inicates that the cruising spee is reache in the time interval [t, t ] as shown in Expression 0. vc = at ( at a (9 ta v t a (0 c Determination of Case 3 In Case 3, the cyclist reaches cruising spee after (t,. Thus two average accelerations may occur in each perio, a an a : Given that accelerations cannot be negative, Case hols when this obvious inequality is vali as follows: t > t = a ( t a( t = v t + ( ( Determination of Case The cyclist reaches cruising spee after (t, but before he or she reaches (t,. In Case, it is possible to estimate the acceleration in the first perio as follows: a = ( t (5 However, t c an v c are still unknown. In this case, v c is reache in the time interval [t, t ], an Equation must be written as follows: t vc = + a v ( vc a c Expression of Equation 6 as a secon-orer equation is as follows: tv + = 0 c In its replacement, the following is obtaine: vc = at ± ( at a (7 To obtain real roots, the term insie the square root must be positive as follows: ( at a > 0 t > a From the analysis of Equation 7 only one root may be feasible. This root is infeasible as vc = at + ( at a (8 (6 a a From Equation, the following is known: = ( t (3 From Equation, the following is obtaine: ( att = ( t Because a > 0, a feasibility constraint is that > att, > v t (4 The istance travele in the interval [t, t ] must be longer than the istance that woul be travele if the spee at time t was maintaine (i.e., if a = 0. If this conition oes not hol, the bicyclist is ecreasing spee (i.e., a < 0, an the spee profile is no longer a nonecreasing function of time. This situation is not what is usually expecte from a cyclist that crosses an intersection from a staning position; a bicyclist s intuitive behavior woul be to break to reach a staning position. This latter case naturally brings up the final case. Determination of Case 4 Given a cyclist in a staning position, Cases to 3 have assume a positive acceleration until the cyclist eventually reaches cruising spee (i.e., the spee profile is nonecreasing. However, in Case 4 the cyclist oes not have a nonecreasing spee profile an oes not fit any of the previous cases. For example, the cyclist may accelerate to a maximum spee an then ecelerate to a final cruising spee. Distributions of Acceleration an Spee With the use of two time an istance measurements an the formulas presente in this section, it was possible to classify a bicyclist s

70 Transportation Research Recor 387 for cyclists that travele on Maison Street westboun an crosse Gran Avenue. Because the intersection of Maison Street an Gran Avenue was locate along a popular morning commute route, ata collection took place uring the expecte peak hours of 7 an 0:30 a.m. The secon investigation, referre to here as the grae intersection stuy, took place at the intersection of Northeast Weiler Street an North Vancouver Avenue in Portlan. Crossing-time ata were collecte for cyclists that travele uphill on Weiler Street eastboun an crosse Vancouver Avenue. This intersection was locate along a popular commute route out of owntown Portlan, an the collection perio coincie with the expecte afternoon peak hour perio between 3 an 6:30 p.m. Crossing-time ata were obtaine through vieo footage of the ata collection. For each stuy, a vieo camera was locate at the far sie of the intersection (relative to the irection of bike traffic, on the siewalk ajacent to the bike lane. This position provie a view of the cyclists as they approache the intersection, stoppe at the near sie of the intersection on a re light, an travele through the intersection on a green light. Figure shows the view from the vieo camera at each intersection an a iagram of the fiel setup. For consistency, researchers collecte ata only from the cyclists that (a came to a complete performance case, acceleration, an cruising spee value. This framework was applie to two intersections in Portlan, Oregon, with ata collecte previously (. Each bicycle crossing time was allocate to an acceleration case, an then average acceleration an cruising spee values were calculate for each bicycle rier. Through the aggregation of iniviual rier performance values, it was possible to put together istribution functions of average acceleration an cruising spees. These istributions coul be use to calculate average an 5th percentile values. The spee an acceleration istributions were a function of the intersection with an the chosen values for (,. For the sake of consistency, this research mae use of = in all the case stuies an calculations. Fiel ata escriptions, results, an insights are provie in the following sections. DESCRIPTION OF CASE STUDY This case stuy inclue two intersections. Data were collecte uring the winter an summer, an these particular intersections were chosen because they were locate along popular commute routes an ha goo pavement conitions at the time of ata collection. The first investigation, referre to here as the flat intersection stuy, was conucte at the intersection of Southeast Maison Street an Gran Avenue in Portlan. Crossing-time ata were collecte (a (c (b ( FIGURE Data collection setup an summary: vieo camera perspective of (a level intersection stuy on Maison Street an (b grae intersection stuy on Weiler Street; (c fiel setup iagram with intersection istance measurements; an ( summary of cyclists by group (ist 5 istance; SE 5 southeast; st 5 street; NE 5 northeast; N 5 north; ave 5 avenue.

Figliozzi, Wheeler, an Monsere 7 FIGURE Total crossing time for flat intersection (n 5 49. stop at the intersection, (b stoppe at the first crosswalk line an were the first cyclists in a queue, an (c ha at least one foot on the groun. These parameters allowe researchers to capture the reaction an start-up time require for a cyclist from the same reference point, an eliminate cyclists that balance on their bike before they receive a green. Perception an reaction time was not inclue in the following measurements. Each intersection was ivie into two sections: a painte pavement line miway through the intersection that separate Distances an ( an with the notation in the previous section. Distance 3 = + referre to the entire intersection an was the sum of the previous two. During each ata collection, two collectors were present to film an collect rier an bicycle characteristics. Figures an 3 present the total crossing time ( + istributions with the same scale to facilitate comparisons. As shown in the figures, the crossing times were skewe towar the left. Both the flat an grae intersections showe a long tail of cyclists, which fell to the right an ha longer than average crossing times. It was easily observe that the flat intersection ha shorter crossing times an less sprea stanar eviation than the grae intersection. FIGURE 3 Total crossing time for grae intersection (n 5 73.

7 Transportation Research Recor 387 TABLE t-test Between Mean Crossing Times an Noncentral t-test Between 85th Percentile Crossing Times: Flat Intersection Crossing Time a t-test Between Mean Crossing Times (s t-test Between 85th Percentile Crossing Times (s µ female µ male t-statistic p-value µ female,85th µ male,85th t-statistic t 0.05,47 p-value t 3.7 3.6.4.6 E 0 4.05 4.5.43.9 7.95 E 0 t..05 4.9***.00 E 04.45.5 5.60***.34 9.58 E 07 t + t 5.93 5.65 3.07**.40 E 03 6.49 6.3.97** 0.54.0 E 03 a Female versus male. * >95% significance; ** >99% significance; *** >99.9% significance. TABLE t-test Between Mean Crossing Times an Noncentral t-test Between 85th Percentile Crossing Times: Grae Intersection Crossing Time a t-test Between Mean Crossing Times (s t-test Between 85th Percentile Crossing Times (s µ female µ male t-statistic p-value µ female, 85th µ male, 85th t-statistic t 0.05,7 p-value t 4.84 4.39 4.79***.00 E 04 5.65 4.90 7.83*** 4.75 5.4 E 06 t.49.4 6.7***.00 E 04.85.49 6.87***.8.53 E 0 t + t 7.34 6.53 6.59***.00 E 04 8.35 7.39 7.88***.95 6.06 E 0 a Female versus male. * >95% significance; ** >99% significance; *** >99.9% significance. ACCELERATION AND PERFORMANCE TABLE 3 Acceleration Case by Gener Percentage by Case Intersection Group 3 4 Flat Female 98 0 0 Male 8 6 0 Grae Female 45 5 4 0 Male 46 44 0 0 Tables an show results from the statistical analysis of crossing times at the flat an grae intersections, respectively. Comparisons were mae with the unpaire t-test an noncentral t-test, an the female an male emographics were stuie. The comparison of gener groups at the flat intersection (Table shows that the mean an 85th percentile crossing times were statistically significantly ifferent. Females ha a longer crossing time at a significance level greater than 99% only in the secon interval. The comparison of gener groups at the grae intersection (Table shows that the mean an 85th percentile crossing times t, t an t + t were statistically significantly ifferent. Females ha a longer crossing time at a significance level greater than 99.9%. These results suggest that males ten to achieve higher acceleration an spees on graes, which is consistent with previous results in the literature. The results here seeme to inicate that males tene to go faster in the secon perio in the flat intersection an in both perios in the grae intersection. The interpretation of the ifferences between groups was facilitate when the acceleration cases evelope earlier were applie. The results are shown in Table 3. At the flat intersection, males ha a greater tenency to keep increasing their spee in the secon half of the intersection (more Case an 3 types. As expecte, both groups at the grae intersection require more time to reach cruising spees. At the flat intersection, both groups tene to achieve a cruising spee in the secon part or even after the intersection. The chi-square tests inicate a significant ifference (>99% between the istribution of acceleration cases at the flat an grae intersections (Case 4 observations were zero an were not inclue in the chi-square test. At the flat intersection, most cyclists reache cruising spee in the first half of the intersection (Case, with a few cyclists in Case, an even fewer in Case 3. However, at the grae intersection most cyclists were ientifie as Case. Compare with what occurre in the flat intersection, a greater percentage of cyclists still accelerate through the secon half of the intersection. Thus the grae must have ha an impact on riers. Cyclists continue to accelerate over a longer istance on a grae. Figures 4 an 5 present histograms of accelerations for the flat an grae intersection stuies. It was clear that the values of the acceleration at the flat intersection were significantly higher than those at the grae intersection. Tables 4 an 5 show that at the flat intersection there was no statistically significant ifference between the male an female cyclist mean an 5th percentile acceleration for both stuy perios. However, the mean cruising velocities showe a statistically significant ifference (with 99.9% significance in both stuy perios; male cyclists achieve greater spee than female cyclists. As inicate previously, this fining suggeste that, although the rate of acceleration was not significantly ifferent, male cyclists continue to accelerate for a longer perio of time than female cyclists an reache a greater cruising spee. This fining was consistent with the fining of acceleration case istributions iscusse previously in which a greater percentage of male cyclists were ientifie as Case an Case 3 at the flat intersection, an who reache cruising spee

Figliozzi, Wheeler, an Monsere 73 FIGURE 4 Accelerations for flat intersection (n 5 49. FIGURE 5 Accelerations for grae intersection (n 5 7. TABLE 4 Unpaire t-tests Between Mean Acceleration an Cruising Spee Level Intersection Grae Intersection Conition a µ female µ male t-statistic p-value µ female µ male t-statistic p-value Winter a 4.90 5.06 0.60 5.5 E 0 3.34 3.78.40*.84 E 0 V c 3.6 5.4 5.8*** 0 4.6 6.3 4.9*** 7.00 E 05 Summer a 5.36 6.5.56.0 E 0.90 3.88 4.40*** 3.00 E 05 V c 3.77 4.87 3.45*** 7.40 E 04 5. 7.7 4.34*** 4.00 E 05 a Female versus male. * >95% significance; ** >99% significance; *** >99.9% significance.

74 Transportation Research Recor 387 TABLE 5 Noncentral t-tests on 5th Percentile Acceleration an Cruising Spee Level Intersection Grae Intersection Conition a µ female,5th µ male,5th t-statistic t 0.05,98 p-value µ female,5th µ male,5th t-statistic t 0.05,86 p-value Winter a 3.76 3.35.5 0.47.76 E 0.49.9.30**.56 9.0 E 03 V c.85 3.64 5.78***.7 5.8 E 07.73 3.70.06*** 0.48.80 E 05 Summer a 3.98 4.05 0.4 0. 5.9 E 0.00.94 4.***.49.54 E 05 V c.50 3.33.6*** 0.8 3.9 E 04.04 4.93 5.03***.37.73 E 05 a Female versus male. * >95% significance; ** >99% significance; *** >99.9% significance. in the secon half of the intersection or beyon. At the grae intersection, there were statistically significant ifferences; male cyclists achieve greater acceleration. This fining seeme to verify the physical impact of the hill on acceleration an cruising spee, which was evient when performance by gener was examine. DISCUSSION OF RESULTS Current AASHTO (5 an Caltrans (6 guielines recommen fiel measurements or an acceleration of.5 ft/s an a bicycle cruising spee of 4.7 ft/s. A recent survey foun that the assume spee was 8.7 ft/s in the timing plans for some bicycle-specific signals (5. In the Portlan case, the application of the AASHTO an Caltrans guielines resulte in 0.6 s an. s for the flat an grae intersections, respectively. The flat intersection ha a with of 6 ft, an the grae intersection ha a with of 70 ft. The fiel measurement of the 85th percentile of crossing times inicate that these values were 6.4 s an 7.8 s, respectively, for the flat an grae intersections. If s for perception reaction time was ae (as suggeste by AASHTO, the crossing time was estimate to be 7.4 s an 8.8 s, respectively (Figures an 3. A comparison of the acceleration an spee values from Table 5 an the existing guielines inicate that the biggest ifference was foun in the value of acceleration (higher in the fiel an that the spees in the fiel actually were less than 4.7 ft/s for riers that starte from the stoppe position. The application of an assume spee of 4.7 ft/s (higher than the fiel-observe 5th percentile of 3 ft/s over a wier intersection also helpe to reuce the ifference between calculate an fiel minimum green crossing times. The existing guielines call for 3. an.4 s longer green times for the flat an grae intersections, respectively. The existing guielines a 30% an % more crossing times than the 85th percentile oes for flat an grae intersections, respectively. AASHTO s recommene values are closer to the 98th percentile, but they are still higher than the observe 98th percentile. Aequate yellow an all-re time also is critical to ensure the safety of bicyclists that start to cross the intersection as the signal turns yellow. In the Portlan case, longer green times were not an issue because these intersections ha a high volume of cyclists. It also was clear that the engineer shoul provie signal times that woul be appropriate uner less favorable conitions (e.g., weather, bicycle queuing. In some cases, however, such aitional times, coul have a significant accumulate impact on vehicle elays, fuel consumption, an emissions if the green time was provie at a minor crossing (with no peestrian crossing request an the re was extene for the main congeste arterial. The methoology propose in this paper can be use to estimate fiel istributions of acceleration an cruising spees an to justify longer crossing times when a special type of rier nees special accommoation (e.g., young riers near schools. It is always goo practice to a room for aitional safety through the use of lowerthan-aashto-suggeste acceleration or crossing spee. However, it is recommene that the aitional safety be justifie through fiel estimations of acceleration an spee istributions, especially if safer an more comfortable bicycle traffic signal esigns generate high costs in elays, fuel consumption, an emissions. CONCLUSIONS The research escribe in this paper emonstrates how fielcollecte observations from a basic vieo setup can be use to successfully estimate esign acceleration an spee values with the use of equations of motion. It shows that it is not trivial to obtain istributions of cyclists acceleration an spee istributions. The propose analytical proceure allows for further statistical analysis of cyclist acceleration an cruising spee performance by emographic group an intersection grae (if these ata are collecte, or to justify longer crossing times when a special type of rier nees special accommoation (e.g., young riers near schools; oler riers near a retirement home. Finings from the statistical analysis were intuitive an consistent with the expecte performance of bicycle riers by gener an intersection grae. The existing policy guielines [i.e., AASHTO, Caltrans, an NACTO (5 7] require that an aequate clearance interval be provie, an they recommen that, in the etermination of this minimum interval, bicyclist spees unergo fiel investigation. Clearly, as other work has shown, the performance values erive for a particular intersection crossing location epen on intersection location, the type of cyclist, an the time of the ata collection. Traffic engineers shoul be cognizant of this epenency when they eploy ata collection equipment an reuce ata for analysis. In particular, fiel estimations of acceleration an spee istributions shoul be provie if bicycle traffic signal esigns that excee AASHTOrecommene values result in high costs in terms of elays, fuel consumption, an emissions. ACKNOWLEDGMENTS The authors gratefully acknowlege the Oregon Transportation, Research, an Eucation Consortium, the Oregon Department of Transportation, an FHWA for sponsoring parts of this research.

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