traffic and speed characteristics on two-lane highways: field study

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Traffic and speed characteristics on two-lane highways: field study 1 Yasser Hassan Abstract: Many models have been developed to evaluate the operating speeds on two-lane rural highways. However, provided information usually lacks details essential to assess their applicability at locations other than where they were developed. This paper presents a procedure to interpret raw data collected on three horizontal curve sites of different two-lane rural highway classes in Ontario. The speed observations were categorized into three vehicle classes (passen- ger car, light truck, and multi-axle heavy truck) and four light condition categories (day, night, and two transition peri- ods). The minimum headway and percentile value to define the operating speed were examined, and a revision of the current practice deemed not warranted. The findings also indicated that operating speeds do not depend on the time or vehicle class. Finally, the horizontal alignment affects the operating speed, but the speeds of the two travel directions on a horizontal curve may differ even with little contribution of the vertical alignment. Key words: highway geometric design, operating speed, traffic composition, traffic counters, ambient light, acceleration, deceleration. Résumé : Plusieurs modèles ont été développés pour évaluer les vitesses maximales réalisables sur les routes rurales à deux voies. Cependant, l’information fournie ne présente habituellement pas les détails nécessaires pour évaluer les possibilités de les appliquer à d’autres endroits que ceux pour lesquels ces modèles ont été développés. Cet article pré- sente une procédure pour interpréter les données brutes colligées provenant de trois sites de courbes de tracé en plan de différentes classes de routes rurales à deux voies en Ontario. Les vitesses observées étaient catégorisées en trois classes de véhicules (automobile, véhicule utilitaire léger et fardiers à essieux multiples) et en quatre conditions d’illumination (jour, nuit, et deux périodes de transition). L’espacement minimum entre les véhicules et le percentile servant à définir la vitesse maximale réalisable ont été examinés, et il ne s’est pas avéré nécessaire de réviser les prati- ques actuelles. Les conclusions indiquent également que les vitesses maximales réalisables ne dépendent ni du temps de la journée ni de la classe du véhicule. Finalement, le tracé en plan affecte les vitesses maximales réalisables, mais les vitesses dans les deux directions de voyagement sur une courbe horizontale peuvent différer même si la contribution de la composante verticale est faible. Mots clés : conception géométrique des routes, vitesse maximale réalisable, composition de la circulation routière, compteur des véhicules, lumière ambiante, accélération, décélération. [Traduit par la Rédaction] 1054 Hassan Introduction In the highway geometric design process, a designer is re- quired to set an appropriate value of the highway design speed. North American designers have traditionally set the design speed based on the highway classification. Then, by setting a speed limit that is lower than the selected design speed, it has been presumed that the resulting design is a safe one. This belief had been implied in the traditional defi- nition of design speed in the U.S.A. design guide, com- monly known as the Green Book, as “the maximum safe speed that can be maintained over a specific section of high- way when conditions are so favourable that the design features of the highway govern” (AASHTO 1994). Similarly, it was stated in the earlier version of the Geometric Design Guide for Canadian Roads (TAC 1986) that “design speed … is sometimes considered to be the highest continuous speed at which individual vehicles can travel with safety on a road when weather conditions are so favourable and traffic den- sity is so low that the safe speed is determined by the geo- metric features of the road.” The application of this definition of design speed has resulted in a design practice referred to as the design-speed concept (Krammes 2000). In- creasing concerns about the design-speed concept have been widely expressed. For example, Krammes et al. (1995) stated that “growing numbers of geometric design research- ers and practitioners recognize that the design-speed concept as applied in the United States is not able to guarantee con- Can. J. Civ. Eng. 30: 1042–1054 (2003) doi: 10.1139/L03-033 © 2003 NRC Canada 1042 Received 5 November 2002. Revision accepted 31 March 2003. Published on the NRC Research Press Web site at http://cjce.nrc.ca on 2 December 2003. Y. Hassan. Department of Civil and Environmental Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada (e-mail: [email protected]). Written discussion of this article is welcomed and will be received by the Editor until 30 April 2004. 1 This article is one of a selection of papers published in this Special Issue on Innovations in Transportation Engineering.

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Page 1: Traffic and speed characteristics on two-lane highways: field study

Traffic and speed characteristics on two-lanehighways: field study1

Yasser Hassan

Abstract: Many models have been developed to evaluate the operating speeds on two-lane rural highways. However,provided information usually lacks details essential to assess their applicability at locations other than where they weredeveloped. This paper presents a procedure to interpret raw data collected on three horizontal curve sites of differenttwo-lane rural highway classes in Ontario. The speed observations were categorized into three vehicle classes (passen-ger car, light truck, and multi-axle heavy truck) and four light condition categories (day, night, and two transition peri-ods). The minimum headway and percentile value to define the operating speed were examined, and a revision of thecurrent practice deemed not warranted. The findings also indicated that operating speeds do not depend on the time orvehicle class. Finally, the horizontal alignment affects the operating speed, but the speeds of the two travel directionson a horizontal curve may differ even with little contribution of the vertical alignment.

Key words: highway geometric design, operating speed, traffic composition, traffic counters, ambient light, acceleration,deceleration.

Résumé : Plusieurs modèles ont été développés pour évaluer les vitesses maximales réalisables sur les routes rurales àdeux voies. Cependant, l’information fournie ne présente habituellement pas les détails nécessaires pour évaluer lespossibilités de les appliquer à d’autres endroits que ceux pour lesquels ces modèles ont été développés. Cet article pré-sente une procédure pour interpréter les données brutes colligées provenant de trois sites de courbes de tracé en plande différentes classes de routes rurales à deux voies en Ontario. Les vitesses observées étaient catégorisées en troisclasses de véhicules (automobile, véhicule utilitaire léger et fardiers à essieux multiples) et en quatre conditionsd’illumination (jour, nuit, et deux périodes de transition). L’espacement minimum entre les véhicules et le percentileservant à définir la vitesse maximale réalisable ont été examinés, et il ne s’est pas avéré nécessaire de réviser les prati-ques actuelles. Les conclusions indiquent également que les vitesses maximales réalisables ne dépendent ni du tempsde la journée ni de la classe du véhicule. Finalement, le tracé en plan affecte les vitesses maximales réalisables, maisles vitesses dans les deux directions de voyagement sur une courbe horizontale peuvent différer même si la contributionde la composante verticale est faible.

Mots clés : conception géométrique des routes, vitesse maximale réalisable, composition de la circulation routière,compteur des véhicules, lumière ambiante, accélération, décélération.

[Traduit par la Rédaction] 1054

HassanIntroduction

In the highway geometric design process, a designer is re-quired to set an appropriate value of the highway designspeed. North American designers have traditionally set thedesign speed based on the highway classification. Then, bysetting a speed limit that is lower than the selected designspeed, it has been presumed that the resulting design is asafe one. This belief had been implied in the traditional defi-nition of design speed in the U.S.A. design guide, com-monly known as the Green Book, as “the maximum safespeed that can be maintained over a specific section of high-way when conditions are so favourable that the design featuresof the highway govern” (AASHTO 1994). Similarly, it was

stated in the earlier version of the Geometric Design Guidefor Canadian Roads (TAC 1986) that “design speed … issometimes considered to be the highest continuous speed atwhich individual vehicles can travel with safety on a roadwhen weather conditions are so favourable and traffic den-sity is so low that the safe speed is determined by the geo-metric features of the road.” The application of thisdefinition of design speed has resulted in a design practicereferred to as the design-speed concept (Krammes 2000). In-creasing concerns about the design-speed concept have beenwidely expressed. For example, Krammes et al. (1995)stated that “growing numbers of geometric design research-ers and practitioners recognize that the design-speed conceptas applied in the United States is not able to guarantee con-

Can. J. Civ. Eng. 30: 1042–1054 (2003) doi: 10.1139/L03-033 © 2003 NRC Canada

1042

Received 5 November 2002. Revision accepted 31 March 2003. Published on the NRC Research Press Web site at http://cjce.nrc.caon 2 December 2003.

Y. Hassan. Department of Civil and Environmental Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada (e-mail:[email protected]).

Written discussion of this article is welcomed and will be received by the Editor until 30 April 2004.

1This article is one of a selection of papers published in this Special Issue on Innovations in Transportation Engineering.

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sistent alignments.” Many countries have, therefore, revisedtheir design practices and adopted an alternative practice re-ferred to as the operating-speed concept (Krammes 2000).

However, the implicit safety guarantee in the design-speedconcept has been struck out in the latest revisions of the Ca-nadian and U.S.A. design guides (TAC 1999; AASHTO2001), where the definition of design speed has been revisedto “a speed selected as a basis to establish appropriate geo-metric design elements for a particular section of road”. Ageneral guideline for selecting design speed has been in-cluded in the Green Book is that “highways should be de-signed to operate at a speed that satisfies nearly all drivers”(AASHTO 2001). The Canadian guide, in accordance withthe latest research recommendations, presents a more quanti-tative guideline that “design speed should be chosen to re-flect the 85th percentile desired speed” (TAC 1999).However, a procedure to predict the 85th percentile desiredspeed, commonly referred to as the operating speed, is gen-erally lacking from the Green Book. On the other hand, theCanadian guide has adopted one of the early models devel-oped in the U.S.A. (Krammes et al. 1995; Ottesen andKrammes 2000).

Considerable research, nonetheless, has been documentedworldwide on the prediction of operating speed on two-lanehighways — for example, refer to the reviews by Gibreel etal. (1999), Hassan et al. (2001), and Fitzpatrick andWooldridge (2001). Extensive recent and on-going researchon operating speed on two-lane rural highways has also beencarried out as part of the development of the InteractiveHighway Safety Design Model (IHSDM) by the U.S.A. Fed-eral Highway Administration (FHWA) (Fitzpatrick et al.2000a; 2000b; Krammes et al. 1995). Among the differentmodels developed for operating speeds on rural highways,two models by Morrall and Talarico (1994) and by Gibreelet al. (2001) are more relevant to Canadian conditions. How-ever, the published documentation on these two models isshort on the details of the data collection procedure, the pro-cedure for interpretation of collected raw data, size of aspeed sample on each curve, or how representative the se-lected curves are to the two-lane rural highway network —shortcomings shared by almost all models.

Thus, this paper was set up with the main objective of de-tailing a procedure that can be used to collect and interpretspeed and traffic data collected using pneumatic-tube auto-matic traffic counters–classifiers. As shown in this study,these counters are capable of collecting a large and reliablesample of speed and traffic data at relatively low cost. How-ever, some processing would be needed to convert the col-lected data into a usable form. The study uses the datacollected on three horizontal curve sites on three differentclasses of two-lane rural highway in Ontario. In the follow-ing sections, the collected data are first described in detail,followed by the interpretation of the data, the statistical anal-ysis performed, and the main findings.

Data collection

Three horizontal curve sites were selected for this study torepresent the three main classes of two-lane highways in On-tario:

• Highway 41: a south–north segment of King’s highwaysouth of the junction to Highway 132.

• Highway 43: an east–west segment of a county road be-tween the junction to Highway 31 and the intersectionwith County Road 1.

• Highway 12: a south–north segment of a secondary roadbetween the intersection with Highway 43 and CountyRoad 9.The first site is under the jurisdiction of the Ontario Min-

istry of Transportation (MTO), while the other two sites areunder the jurisdiction of the United Counties of Stormont,Dundas and Glengarry (SD&G). The as-built alignment datawere collected from the Engineering and Title Records ofMTO (Highway 41) and the final project plans of SD&G(Highways 43 and 12).

Alignment dataAs mentioned earlier, the horizontal and vertical align-

ment data for the selected sites were collected from MTOand SD&G and are presented in Fig. 1. As shown in the fig-ure, the horizontal curves on Highways 41 and 43 have thesame radius (R = 388.08 m), and both curves have spiraltransitions. The horizontal curve on Highway 12, on theother hand, is a simple curve without spiral transition buthas a flatter radius (R = 698.55 m). The vertical alignmentson all three sites are composed of spline grades and weremanually digitized into elevations at discrete stations. Thefigure clearly shows that the sites at Highways 43 and 12have mild slopes, with a 2.34 m elevation differential over304.00 m distance and a 1.27 m elevation differential over508.00 m distance, respectively. These elevation differentialsare equivalent to 0.8% and 0.2% average grade on High-ways 43 and 12, respectively. On the other hand, the site atHighway 41 has a relatively steep grade caused by 17.90 melevation differential over a 410.00 m distance, which isequivalent to 4.4% average grade (downgrade for the north-bound (NB) lane and upgrade for the southbound (SB) lane).

The horizontal alignment before the curve on Highway12, for the NB lane, is a relatively long tangent (993.67 m).After the curve, there is a 388.74 m tangent followed by avery flat curve (R = 873.19 m). For the curve on Highway41 and considering the NB lane, the horizontal alignmentbefore the curve consists of a 239.01 m tangent preceded bya short horizontal curve with spiral (R = 388.08 m). On theother hand, the departure tangent for the curve considered inthis study is 49.04 m long followed by a flat curve with spi-ral (R = 582.13 m). However, the relatively long spirals pro-vide total transition lengths of 360.93 and 170.96 m betweenthe circular curves of the curve considered in this study andthe ones before and after the curve, respectively. Finally, thehorizontal alignment before the curve on Highway 43, forthe eastbound (EB) lane, has a very flat and short simplehorizontal curve (R = 6985.50 m) and a 294.78 m transitiontangent. However, the departure tangent is 170.85 m longand is followed by a curve with spiral that has a radius R =388.08 m. Again, the spirals provide a total transition afterthe curve that is 292.77 m long. In summary, tangents beforeand after each of the three curves provide long enough tran-sitions to be classified as independent tangents that wouldnot affect the operating speed on the circular part of the hor-

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izontal curve or acceleration and deceleration on the tan-gents (Lamm et al. 1988).

Speed and traffic dataThe main focus of this study was to collect and analyze

detailed speed data on the three sites. Five pneumatic-tubetraffic counters–classifiers were used simultaneously at eachsite to collect the speed data at five points. Depending on thehighway orientation (south–north or east–west), the fivepoints were (i) the north or east tangent (TN or TE), (ii) thenorth or east beginning of the circular part of the horizontalcurve (BCN or BCE), (iii) the middle of the horizontal curve(MC), (iv) the south or west end of the horizontal curve(ECS or ECW), and (v) the south or west tangent (TS orTW).

Figure 2 shows the typical arrangement of these fivepoints on a horizontal curve without spiral with an east–west

orientation. The five points can also be classified as ap-proach tangent (AT), beginning of curve (BC), middle ofcurve (MC), end of curve (EC), and departure tangent (DT).It should be noted that each tangent point can be classified

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1044 Can. J. Civ. Eng. Vol. 30, 2003

Fig. 1. Horizontal and vertical alignments of selected test sites (SB = southbound; NB = northbound; EB = eastbound; WB = west-bound; R = horizontal curve radius): (a) Highway 41, (b) Highway 43, and (c) Highway 12.

Fig. 2. Positioning traffic counters–classifiers on horizontalcurves (PC = point of curve; PT = point of tangent; and PI =point of intersection).

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as AT for one direction of travel and DT for the opposingdirection. Similarly, each of the two points at the extremitiesof the curve can be classified as BC and EC for the two op-posing travel directions. In this paper, discussions on speedand traffic characteristics will use the second point designa-tion.

Based on the recommendations of the manufacturer of thecounters, the counters were set up to work in a directional“raw mode” using two tubes per counter. With both tubesstretched across the full width of the road, the counter woulddetermine the direction of travel and calculate the speed,length, number of axles, and axle spacing of each vehicle.The counters were installed on each curve in the morning ofa working day and retrieved on the following morning, thuscollecting a complete set of data for nearly 24 h at each site.To ensure maximum safety during counter installation andretrieval and to minimize traffic disruptions, a four-memberfield crew worked on the data collection. While two crewmembers were responsible for the installation of the coun-ters, the other two were in charge of the traffic control usingSTOP–SLOW traffic signs and traffic cones. Finally, a rainlogger was installed at the MC point to monitor the rainfallduring the speed data collection.

The data files produced by the counters are ASCII textand were retrieved into a notebook computer. A typical filecontained information about the site, recording time, lanesbeing monitored using a lane designation, and the spacingamong the tubes. In this study, Lane 1 designation was al-ways assigned to the eastbound (EB) or southbound (SB)lane, while Lane 9 was the westbound (WB) or northbound(NB) lane. Detailed data were recorded for the passage ofeach vehicle that included the travel direction (using lanedesignation), time of passage (to the nearest second), instan-taneous speed (kilometres per hour), number of axles, vehi-cle length (centimetres), and axle spacing (centimetres). Itshould be noted, however, that as the counters use the airpulse resulting from the passage of a vehicle axle, the calcu-lated vehicle length is actually the vehicle wheelbase.Finally, the data retrieved from the rain logger showed no re-cord of rain on any of the sites considered in this study.

Analysis

Based on the objectives of this study, which were statedearlier, a detailed statistical analysis was carried out usingStatistical Package for the Social Sciences Release 10.1.0.(SPSS®) to examine the traffic and speed characteristics onthe selected field sites as collected by the traffic counters.More specifically, the analysis was carried out to answer thefollowing questions:• How can the counter observations be categorized to differ-

ent vehicle classes?• What headway value would correspond to a free operating

speed condition?• What factors significantly affect the operating speed?• What is the rate of drivers’ deceleration and acceleration

before and after a horizontal curve?

GeneralBefore a meaningful analysis of the collected data can be

carried out, the data had to be screened to isolate the datathat had potential disturbances resulting from factors otherthan the traffic or the road. Although the traffic counterswere set up to start collecting the data at the same time afterall five counters had been installed, initial disturbances maybe reflected in the collected data if the field crew were stillat the site after the counters had started collecting the data.Similarly, end disturbances would result from the fact thatone traffic counter was being removed at a time while therest of the counters were still collecting data. Therefore, thefirst and last 30 min of data at each site were excluded fromthe analysis. The numbers of observations available after thisexclusion were 5 494, 14 258, and 8 371 on Highways 41,43, and 12, respectively, with only 20 vehicles for which thecounters could not calculate the speed or vehicle data wererecorded as “sensor miss”. The distribution of all observa-tions on the different hours of the day is shown in Fig. 3.

Vehicles classificationOperating-speed research in the literature has traditionally

been concerned with the speed of passenger vehicles that are

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Fig. 3. Frequencies of speed observations on the test sites.

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generally presumed to travel at higher speeds than other ve-hicle types. Compared with the use of automatic trafficcounters, manual speed measurements by human observersprovide the distinct advantage of accurate vehicle classifica-tion, and thus the operating speed of passenger vehicleswould be readily available. On the other hand, use of auto-matic traffic counters allows the collection of considerablylarger data samples at the different times of day and at a rel-atively low cost. Automated speed measurements have theother advantage of eliminating the natural tendency of driv-ers to reduce their speed because of the presence of human

observers equipped with radar guns. Furthermore, speed andtime observations are generally more accurate, especially inrecording the exact time of passage needed to calculate thetime headway. Therefore, after the data have been collectedusing the automatic traffic counters, there is a need to cate-gorize the vehicle observations as recorded by the countersinto a number of more uniform vehicle classes.

Figures 4a and 4b present two pie charts for the composi-tion of observed traffic based on the number of axles andwheelbase as determined by the traffic counters for all threesites combined. Clearly, the number of axles can be the firstcriterion for vehicle classification, where heavy trucks (HT)can be easily identified as the multi-axle vehicles. Althoughsome of these multi-axle vehicles might have been passengercars towing some type of trailers, their performance shouldbe closer to that of trucks than passenger cars. As shown inFig. 4a, multi-axle vehicles (number of axles > 2) repre-sented 10.8% of all the observed traffic on the three sites.On the individual sites, this percentage was 19.6, 10.1, and6.7% on Highways 41, 43, and 12, respectively. One should,however, be more careful about interpreting the data of two-axle vehicles. Although the majority of two-axle vehicleshad a wheelbase in the range of 2.00 to 4.00 m (Table 1), thefact that some two-axle vehicles had very low speeds(11 km/h) and very low or very large wheelbase (0.98 or6.00 m) suggests that not all the two-axle vehicles can beclassified as passenger cars (PC). Alternative possible classi-fications in such cases are motorcycles, light trucks (LT), oreven bicycles. However, as only the PC and LT vehicleclasses can affect the geometric design of rural roads, the ve-hicle classification will focus only on identifying observa-tions that fall into one of these classes.

To identify the observations that were most probably PC,the web sites of the major car makes available in Canadawere surveyed to check the range of wheelbase of two-axlevehicles. Specifically, the survey covered• Toyota (http://www.toyota.ca)• Lexus (http://www.lexus.ca)• Honda and Acura (http://www.honda.ca)• Mazda (http://www.mazda.ca)• Nissan and Infiniti (http://www.nissan.ca)• Chevrolet, Oldsmobile, Pontiac, Buick, Cadillac, Saturn,

Chevy Trucks, and GMC (http://www.gmcanada.com)• Ford and Lincoln (http://www.ford.ca)• Chrysler, Dodge, and Jeep (http://www.daimlerchrysler.ca)• Volkswagen (http://www.vw.com)

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Fig. 4. Traffic composition categories and percent frequencies inthe recorded observations: (a) number of axles, (b) wheelbase,and (c) vehicle type. Number of axles

Wheelbase 2 3 4 ≥5 Total

<2 m 315 8 — — 3232 – 2.99 m 17 887 48 — — 17 9353 – 3.99 m 6 115 24 17 — 6 1564 – 4.99 m 483 12 7 — 5025 – 9.99 m 284 900 326 48 1 55810 – 14.99 m — 13 132 250 395≥15 m — — 26 1 208 1 234Total 25 084 1 005 508 1 506 28 103

Table 1. Distribution of vehicle wheelbase by number of axles.

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The wheelbase of over 200 vehicles of different makesand models were reviewed from their 2003 catalogues andthe results are shown in Table 2. As shown in the table, thewheelbases of the vast majority of passenger vehicles, sportscars, passenger minivans, and sports utility vehicles wereless than 3.00 m (most of the minivans in Table 2 over3.00 m wheelbase are cargo minivans). On the other hand,the wheelbases of light trucks and cargo minivans were gen-erally greater than 3.00 m but less than 4.00 m. Therefore, areasonable classification of observed two-axle vehicles canbe PC (2.00 m ≤ wheelbase < 3.00 m) or LT (3.00 m ≤wheelbase < 4.00 m). Following this guideline, Fig. 4cshows the composition of observed traffic by vehicle class.As shown in the figure, a very small percentage of the obser-vations could not be classified as PC, LT, or HT and weregiven the designation NA (Not Applicable).

Defining operating speedThe second issue to be addressed in interpreting the col-

lected data is the definition of free operating speed condi-tions. Traditional practice in highway geometric designconsistency research is to use the 85th percentile speed ofvehicles with a 5 s minimum headway. In other words, aproper definition of operating speed requires an examinationof the appropriate headway and the percentile speed.

Operating speed – minimum headwayFigure 5 shows the aggregate frequencies of different

headway observations at the different hours of the day on allthree sites. As shown in the figure, the vast majority of ob-servations at all hours of the day had headway values of 5 sor more. This trend was valid also during the morning andafternoon rush hours (as shown in Fig. 5) and on each of thefive points on each of the three sites (frequency bar chartsare not shown here). With relatively few observations withheadway values less than 5 s (18.5%), further reexaminationof the minimum headway for free operating speed conditionsdoes not seem justified.

Operating speed – percentile valueAs for the appropriate percentile of speed, Fig. 6 shows

the differences (Vi – V85) on the different points of the threesites, where V85 is the 85th percentile value of the daytimePC free-flow speed and Vi is the corresponding 70th, 80th,90th, or 95th percentile value depending on the value of i(exact definition of daytime in this study is provided later).As shown in the figure, V95 can be considerably higher thanthe traditional definition of operating speed (V85), where thedifference can be over 10 km/h. On the other hand, differ-ences between V90 or V80 and the traditional operating speedare relatively small (in the general order of ±3 km/h). Simi-

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Vehicle class

Wheelbase (m)Passengervehicle

Sportscar Minivan

Sportsutility

Lighttruck Total

2.200–2.399 1 1 — 2 — 42.400–2.599 8 6 — 6 — 202.600–2.799 31 14 1 21 2 692.800–2.999 23 2 9 10 6 502.000–3.199 1 1 7 3 8 203.200–3.399 1 — 4 4 8 173.400–3.599 — — 3 1 5 9≥3.600 — — 1 — 10 11Total 65 24 25 47 39 200

Table 2. Distribution of wheelbase by vehicle class of major vehicle makes and models.

Fig. 5. Observation frequencies by hour of day and headway.

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larly the difference between V75 and V85 is relatively small(in the range of 3 to 4 km/h). In addition, the differences ingeneral increase at the tangent points, which do not affectthe design of horizontal curves. Therefore, using a percentilevalue in the range 75 to 90 does not seem to have a signifi-cant effect on the operating speed, and further reexaminationof the most appropriate percentile value is not justified.

Finally, by comparing the differences (Vi – V85) on thethree curve sites, it can be observed that these differencestend to increase in the order of Highway 41, Highway 43,and Highway 12. By comparing the horizontal alignments ofthe three curve sites, it can be shown that the greatest differ-ences of (Vi – V85) correspond to the site on Highway 12 thathas the largest radius. The large radius, compared with thesites on Highways 41 and 43, might have encouraged themore aggressive drivers to adopt higher speed than that se-lected by most drivers. On the other hand, by comparing thevertical alignments, it seems that the differences among thespeed percentiles tend to get larger, and in turn the disper-sion of individual speeds tends to increase, as the overlap-ping vertical grades get flatter. It should be noted that suchdispersion of speed is an indicator of lower design consis-tency. Theoretically, this trend of dispersion should havebeen reflected in speed variance, but was not evident in thevalues of speed standard deviation calculated in this study

that showed no specific trend. Therefore, the results of thethree sites in this study suggest that while the higher speedpercentiles may indicate a trend for speed dispersion, it maynot be reflected in the standard deviation of the entire speedsample. Such a contradiction might have contributed to therejection of the hypothesis that the standard deviation ofspeed can be used as an indication of the presence of a de-sign inconsistency (Collins et al. 1999; Fitzpatrick et al.2000b).

Factors affecting operating speedThe operating speed on a specific segment of a road has

been traditionally determined for passenger cars driving atdaytime. This practice has been the result of the conven-tional belief that passenger cars can and generally do drivefaster than the heavier trucks as well as speeds at daytimeare generally greater than those at nighttime, though someresearch carried out by German researchers and summarizedby Lamm et al. (1999) showed that there was no significantdifference between operating speeds at day and night. In thissection, statistical analysis on the effect of the different fac-tors that may affect the operating speed is presented.

Statistical analysis of variance (ANOVA) was performedto test the significance of the difference between the meansof two or more independent samples. The null hypothesis

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Fig. 6. Difference between speed percentiles and V85 of passenger cars: (a) Highway 41 SB, (b) Highway 41 NB, (c) Highway 43 EB,(d) Highway 43 WB, (e) Highway 12 SB, and (f ) Highway 12 NB.

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(H0) being tested is that all samples belong to populationswith equal means. Statistical analysis of variance (ANOVA)then calculates an F statistic and a corresponding p-value,assuming that all samples belong to populations that followthe normal distribution. If the calculated p-value is greaterthan a preset level of significance (α), the null hypothesisshould be accepted. Otherwise, variations because of ran-dom sampling cannot explain the differences among themeans of the populations, and the samples belong to signifi-cantly different populations.

Effect of ambient lightTo test the effect of ambient light on the operating speed,

the observations had to be categorized into DAY or NIGHTusing the time stamp the counters gave to each observationand some point of time separating the day and night. Poten-tial candidates for such a point of time include the start andend of civil twilight (defined as the instant in the morningand evening when the center of the sun is at a depression an-gle of 6° below an ideal horizon) or time of sunrise and (or)sunset (defined as the instant in the morning and evening un-der ideal meteorological conditions, with standard refractionof the sun’s rays, when the upper edge of the sun’s disk iscoincident with an ideal horizon). Sullivan and Flannagan(2002), for example, used the start and end of civil twilightto separate day and night driving conditions and to examinethe effect of light conditions on specific types of roadcrashes. However, it should be noted that ambient light con-ditions do not abruptly change from day to night or viceversa. The ambient light at the start and end of the civil twi-light, for example, is still sufficient to see large objects, butno detail is discernible. Therefore, although the use of a spe-cific point of time as a separator between day and night maybe acceptable in some applications, it was decided in thisstudy to create two transition time categories, namely, day-to-night-transition (DNT) and night-to-day-transition (NDT).It should be noted that the objective here is not to define theexact time for change of light conditions but rather is tocompare the operating speed at day and night times. Subse-quently, a conservative approach was taken in defining the

two transition time categories, where DNT and NDT weresubjectively assumed to start 30 min before sunset and startof civil twilight, respectively, and were assumed to end30 min after the end of civil twilight and sunrise respec-tively. Since the difference between the sunrise and sunsetand the start and end of civil twilight for the Ottawa region(central location for all three sites) is approximately 30 min,both DNT and NDT span approximately 90 min. Figure 7shows the split of the collected data into the four time cate-gories: DAY, DNT, NIGHT, and NDT.

The PC operating speeds, defined as the 85th percentilespeed of PC with a 5 s minimum headway, on the five datacollection points on each lane of the three sites are shown inFig. 8, and the summary of ANOVA on effect of ambientlight on the operating speeds is shown in Table 3. It shouldbe noted that the frequencies of HT and LT in the time cate-gories other than DAY were relatively low. Therefore, deter-mination of the 85th percentile speed or testing thedifferences of samples may not be very accurate, and theANOVA results related to LT and HT operating speeds (notpresented in the table) should be cautiously interpreted.

As shown in Fig. 8, the operating speeds at all four timecategories are close to each other at almost all data collec-tion points. Furthermore, the DAY operating speed is ex-ceeded by the speed corresponding to at least one other timecategory on almost all points. As for the statistical signifi-cance, as shown in Table 3, the null hypothesis H0 should beaccepted on most points for a level of significance α = 5%.That is, the difference in operating speeds can be attributedto variations because of random sampling. Since the twotransition categories (DNT and NDT) were subjectively de-fined, the analysis was repeated by comparing the speedscorresponding to DAY and NIGHT only, and the speed dif-ferences were also mostly insignificant. These findings werevalid for the LT and HT vehicle classes, but as mentionedearlier because of the small number of observations for thesetwo vehicle classes at times other than DAY the findingshould be interpreted cautiously. Finally, by cross-referencingFig. 8 and Table 3, it can be shown that the points where theeffect of ambient light may be significant must not always

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Fig. 7. Categorization of speed measurements based on ambient light.

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be interpreted that speeds are higher at daytime than atnighttime.

Effect of vehicle classThe operating speeds of the three vehicle classes identi-

fied earlier (PC, LT, HT) at the different observation pointsof the three sites are shown in Fig. 9. As mentioned earlier,the frequencies of LT and HT observations at the DNT,NIGHT, and NDT time categories are too low for meaningfulanalysis, and therefore only the daytime speeds are shown inthe figure. The ANOVA results for the effect of vehicle classare summarized in Table 3. As shown in the table, whenconsidering all three classes, the differences among themeans are mostly significant, indicating that the differencesin speed related to the vehicle class may not be explained byrandom sampling alone. By referring back to Fig. 9, it be-comes evident that the HT operating speeds are generallylower than those of the PC and LT classes. In addition, mostsignificant differences are observed on the Highway 41 SBlane that has the steepest upgrade.

Table 3 also shows that the analysis was repeated after ex-cluding the HT observations; that is the comparison was lim-ited to the operating speeds of PC and LT. In this case, theresults indicate that the speed difference is mostly insignificant,

indicating that such a difference can be related to randomsampling. Subsequently, the statistical analysis indicates thatthe PC and LT vehicle classes (both are two-axle vehicles)adopt similar operating speeds that are higher than that ofthe HT vehicle class (multi-axle vehicles).

Effect of highway alignmentThe effect of highway alignment on operating speed can

be investigated through two ANOVA tests: effect of observa-tion point and effect of travel direction. First, significantlydifferent operating speeds at the five observation points ofeach curve (AT, BC, MC, EC, and DT) would result mainlyfrom the horizontal alignment. On the other hand, the effectof vertical alignments, which might have contributed also tothe difference of speed on the observation points, would bemore evident in the difference between the two travel direc-tions on the same curve. As noted earlier, LT and HT obser-vations at the DNT, NIGHT, and NDT time categories aretoo small for a meaningful analysis, and therefore the com-parisons here are limited to daytime speeds.

As shown in Table 4, the null hypothesis regarding the ef-fect of observation point should be rejected for almost allcases. That is the difference in operating speed on the differ-ent points of the horizontal curve could not be explained by

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Fig. 8. Operating speeds of PC categorized based on ambient light: (a) Highway 41 SB, (b) Highway 41 NB, (c) Highway 43 EB,(d) Highway 43 WB, (e) Highway 12 SB, and (f ) Highway 12 NB.

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random sampling only. Subsequently, it can be stated thathorizontal curves affect the operating speeds of all vehicleclasses. Similarly, in most cases, no difference in operatingspeeds of both travel directions of the same curve was seenbecause of random sampling. While such a difference couldbe expected for truck speed on the relatively steep grade ofHighway 41, it was surprising to note a significant differ-ence for the PC operating speeds on the two travel directionsof Highway 12. As mentioned earlier, the site on High-way 12 has the mildest grades of the three sites with a 0.2%average grade. Therefore, although the vertical alignmentdoes affect the operating speed, especially that of heavy ve-hicles, the two directions of travel generally exhibit differentPC speed behaviours even at very mild grades. However,potential factors that might have produced this effect, suchas available sight distance, were not examined in this study.

Acceleration and deceleration rateIn addition to studying operating speed, another important

element in design consistency analysis is the accelerationand deceleration rate in operating speed profile. In the rela-

tively earlier models of operating speed profile, it was as-sumed that drivers adopt a constant deceleration–accelerationrate (on the approach tangent to curve and on the departuretangent after the curve, respectively) of 0.85 m/s2 (Krammeset al. 1995; Ottesen and Krammes 2000; TAC 1999). In ad-dition, both deceleration and acceleration are assumed totake place on the approach and departure tangent, respec-tively. However, a later examination of collected speed on21 curve sites in the U.S.A. showed that the average deceler-ation and acceleration rates on the approach and departuretangents were 0.1143 and 0.0448 m/s2, respectively(Fitzpatrick et al. 2000a). Statistical analysis also showedthat both deceleration and acceleration rates were signifi-cantly lower than the constant rate of 0.85 m/s2. Therefore, anewer model for operating speed profile has adopted differ-ent deceleration–acceleration rates ranging from 0.00 to1.00 m/s2 for deceleration and between 0.00 to 0.54 m/s2 foracceleration, depending on the radius of the curve(Fitzpatrick and Collins 2000; Fitzpatrick et al. 2000a).

The operating speeds on the three sites in this study wereused to calculate the acceleration or deceleration rate between

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p-values — effect ofambient light (PC)

p-values — effect ofvehicle class (DAY)

Highway Lane PointAll timecategories

DAY vs.NIGHT

All vehicleclasses PC vs. LT

41 SB AT 0.199 0.365 <0.001 0.619BC 0.906 0.654 <0.001 0.011MC 0.195 0.403 <0.001 0.916EC 0.306 0.748 <0.001 0.074DT 0.647 0.357 <0.001 0.858

NB AT 0.053 0.101 <0.001 0.165BC 0.604 0.329 0.008 0.061MC 0.239 0.633 <0.001 0.603EC 0.426 0.569 <0.001 0.808DT 0.199 0.476 <0.001 0.729

43 EB AT 0.284 0.874 0.005 0.012BC 0.161 0.028 0.025 0.017MC 0.996 0.908 <0.001 0.016EC 0.153 0.571 0.088 0.660DT 0.051 0.047 0.073 0.933

WB AT 0.082 0.635 0.090 0.770BC <0.001 0.238 0.031 0.065MC 0.024 0.163 0.178 0.073EC 0.001 0.593 0.907 0.643DT 0.003 0.793 0.313 0.114

12 SB AT 0.159 0.369 <0.001 0.293BC 0.080 0.813 0.014 0.944MC 0.593 0.773 0.073 0.509EC 0.320 0.093 0.111 0.786DT 0.096 0.115 0.005 0.897

NB AT 0.015 0.405 0.010 0.062BC 0.024 0.996 0.003 0.782MC 0.871 0.974 <0.001 0.851EC 0.134 0.486 <0.001 0.261DT 0.130 0.807 <0.001 0.828

Note: Bold items highlight the p-values less than the level of significance α = 5%; H0 should berejected.

Table 3. Summary of ANOVA — effect of ambient light and vehicle class.

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each two successive points where speed was measured.Based on the laws of kinematics, the acceleration–decelerationrate, a (metre per second squared), was calculated from therelationship

[1] aV V

d= −2

212

1 225.92 -

where V1 and V2 are the operating speeds at the first and sec-ond point, respectively, (kilometres per hour); d1-2 is the dis-tance between the two points (metres); and a is negative fordeceleration and positive for acceleration.

Figure 10 shows the calculated acceleration–decelerationrates for the passenger cars at daytime. As shown in the fig-ure, the deceleration and acceleration rates are generally lessthan 0.85 m/s2. Furthermore, the deceleration does not gen-erally occur on the approach tangent nor does accelerationoccur on the departure tangent. In addition, it can be ob-served that deceleration on the approach tangent (from AT toBC) is generally followed by acceleration from BC to MC,and vice versa. Similarly, acceleration from MC to EC isgenerally followed by deceleration on the departure tangent

(from EC to DT). This trend is most obvious for the SB ofHighway 41, which has the steepest upgrade. While thesteep upgrade might have contributed to the large decelera-tion rate, it could not possibly have contributed to the largeacceleration rate from BC to MC. Therefore, assuming thatspeed selection is not affected by visual misperception of thehorizontal curvature, drivers do not seem to adopt a constantspeed on the horizontal curve but rather continuously correcttheir speed based on information they perceive and processalong the curve. The most likely type of such information isthe lateral acceleration imposed on the drivers while negoti-ating the horizontal curve. Such a continuous correction ofspeed selection could be an indicator of the degree of con-sistency of horizontal curves but could not be examinedwithin the limited number of curve sites considered in thisstudy.

Conclusions

This paper presented the results of a statistical analysiscarried out on speed and traffic data collected on three hori-

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1052 Can. J. Civ. Eng. Vol. 30, 2003

Fig. 9. Daytime operating speeds categorized based on vehicle class: (a) Highway 41 SB, (b) Highway 41 NB, (c) Highway 43 EB,(d) Highway 43 WB, (e) Highway 12 SB, and (f ) Highway 12 NB.

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zontal curve sites, each located on a different class of two-lane rural highways in Ontario. The main findings of thisanalysis are as follows.• Most of the data collected using pneumatic-tube traffic

counters–classifiers can be categorized into an appropriatevehicle class, namely passenger car, light truck, or multi-axle truck. Such classification can be carried out using thenumber of axles and wheelbase of each vehicle. Only asmall percentage of vehicles would not fall in any of theseclasses and should be excluded from the analysis. Owingto the large sample collected, this exclusion should not af-fect the analysis.

• The two main criteria defining operating speed, namelyminimum headway and percentile value, were reexam-ined. By analyzing the collected data, it was shown thatmost vehicles had a headway greater than or equal to 5 s.In addition, very little change in operating speed would beexpected for a percentile value ranging from 75 to 90.Subsequently, it was concluded that a revision of the defi-nition of operating speed as the 85th percentile value ofall passenger car speeds with a minimum headway of 5 sis not warranted.

• Trends of dispersion of the higher speed percentiles werenot reflected in the values of the overall standard devia-tion of the entire sample of free-flow speed. Therefore, al-though speed dispersion may be an indicator of designinconsistency, it might not be detected by examiningspeed standard deviation.

• By dividing the speed data into day, night, and two transi-tion periods, the operating speed of all vehicle classesdoes not seem to depend on the ambient light. However,this general finding should be cautiously applied to lightand heavy trucks, as their observation frequencies duringthe night and transition times were too small for reliablestatistical analysis.

• The operating speed of all two-axle vehicles does not de-pend on the specific vehicle class (passenger cars or lighttrucks). Both of these classes, however, adopt higher oper-ating speed than that of heavy multi-axle trucks.

• The operating speed on a specific segment of a highwaydepends on the positioning of the speed measurement rel-ative to the horizontal curve. In addition, operating speeds

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p-value

Highway Lane Point PC LT HT

Effect of observation point41 SB N/A <0.001 <0.001 0.002

NB <0.001 <0.001 <0.00143 EB N/A <0.001 <0.001 <0.001

WB <0.001 <0.001 <0.00112 SB N/A <0.001 0.001 0.223

NB <0.001 <0.001 0.464Effect of direction of travel41 N/A AT <0.001 <0.001 <0.001

BC <0.001 0.373 <0.001MC <0.001 <0.001 <0.001EC 0.149 0.019 0.038DT 0.630 0.854 0.135

43 N/A AT <0.001 <0.001 <0.001BC <0.001 <0.001 <0.001MC <0.001 <0.001 0.216EC 0.212 0.998 0.309DT 0.321 0.755 0.130

12 N/A AT <0.001 <0.001 0.366BC <0.001 0.009 0.378MC 0.029 0.419 0.118EC 0.031 0.010 0.858DT <0.001 0.001 0.447

Note: Bold items highlight the p-values less than the level of significance α = 5%; H0 should berejected.

Table 4. Summary of ANOVA — effect of highway alignment.

Fig. 10. Acceleration and deceleration rates for passenger cars atdaytime.

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may differ for the two travel directions on the same hori-zontal curve even when the effect of the vertical align-ment is minimal.

• Acceleration and deceleration rates were generally lowerthan the constant rate of 0.85 m/s2 assumed in predictingoperating speed profile. In addition, drivers do not assumea constant speed on the horizontal curve but rather contin-uously update their speed as they get and process differentinformation on the curve such as lateral acceleration. Therate of deceleration–acceleration change may be an indi-cator of design inconsistency and should be examined us-ing data on more curve sites.

Acknowledgments

Financial support for this study was provided by the Natu-ral Sciences and Engineering Research Council of Canadaand Transport Canada. Equipment used in the study was ac-quired through funding by the Canada Foundation for Inno-vation and Ontario Innovation Trust. The author would liketo thank D. Edwards, B. Boutilier (MTO Eastern District Of-fice), and L. Bender (SD&G County) for their assistance indata collection, as well as, P. Misaghi, M. Awatta,O. Ramadan, and M. Rohani (Carleton University) for col-lecting the experiment data.

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