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ScienceDirect Transportation Research Procedia 17 (2016) 244 – 252

11th Transportation Planning and Implementation Methodologies for Developing Countries, TPMDC 2014, 10-12 December 2014, Mumbai, India

Study of Acceleration Behaviour of Motorized Three Wheeler in India Dr. P.S.Bokare∗ a , Dr. Akhilesh Kumar Maurya b a Principal,

RSR Rungta College of Engineering and Technology, Bhilai, 490024, Chhattisgarh, India. Professor, Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039. India. b Associate

Abstract Acceleration behaviour of vehicles is important for various applications. The delay caused while leaving the signalized intersection, depends on acceleration capability of a vehicle, among others factors. Acceleration of motorized three wheelers merits attention since though they accommodate passengers similar to car; they accelerate differently as compared to car. Therefore, objective of this study is to understand the acceleration behaviour of Motorized Three Wheelers. It is observed in this study that acceleration rates of Motorized Three Wheeler differ from reported acceleration rates in literature. The maximum acceleration rate, speed at maximum acceleration and distance travelled during acceleration maneuver are found to be sensitive to maximum speed achieved during acceleration maneuver. On finding existing acceleration models to be insufficient to explain the acceleration behaviour of Motorized Three Wheelers, new models are proposed and validated. c 2016 2015The TheAuthors. Authors.Published Publishedby byElsevier ElsevierB.V. B. V. © This is an open access article under the CC BY-NC-ND license Selection and peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay Keywords: Acceleration Models; GPS; Maximum and Mean Acceleration; Dual Regime Model.

1. Introduction otorized Three Wheelers form a significant (10%) proportion of traffic composition in India Arasan and K.Krishnamurthy M [4]. Since the performance and operating characteristics of these vehicles are different as compared to other vehicles in traffic stream at signalized intersection, their presence poses a considerable resistance to movement of other vehicles. The time taken by vehicles to clear the intersection and the delay caused, depends on number of vehicles at intersection at a given point of time, type of vehicles and their acceleration capabilities. The existing signal cycles are designed on the basis of assumed acceleration rates of Motorized Three Wheelers, Haas et al. [10]. ∗ Corresponding

author. Tel.: +91-788-6459564/65 ; fax: +91-788-2286481. E-mail address: [email protected]

2352-1465 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay doi:10.1016/j.trpro.2016.11.088

P.S. Bokare and Akhilesh Kumar Maurya / Transportation Research Procedia 17 (2016) 244 – 252

Maini and Khan [12] studied the discharge characteristics of vehicles in heterogenous traffic at signalized intersection in India and reported that though the acceleration capabilities of motorcycles and cars is significantly more than Motorized Three Wheelers and buses, variation in clearing speed for different vehicle types is low. This suggests that the performance of higher capacity vehicles is limited by performance of lower capacity vehicles. These authors emphasized the need to quantify the effect of individual vehicles on platoon speed. Rahman et al. [14] conducted the study on movement of heterogenous traffic at signalized intersection in Dhaka, Bangladesh. They concluded that the presence of Motorized Three Wheelers in the mixed flow conditions adversely affect the capacity of signalized intersections. They related the proportion of Motorized Three Wheelers in mixed traffic with their PCU. Prasanna Kumar and Dhinakaran [13] estimated the delay caused due to presence of different vehicle types at signalized intersection. They reported that the characteristics of heterogenous traffic in India are different as compared to that in China and other Asian countries. Contrary to Maini and Khan [12], they observed that the mixed traffic at signalized intersection does not move as a platoon but there is a significant lateral movement. They reported that the Level of Service (LoS) of signalized intersection is adversely affected due to presence of vehicles like Motorized Three Wheelers. Arasan and K.Krishnamurthy [4] studied acceleration characteristics of Motorized Three Wheelers for simulation of heterogenous traffic. They reported that the acceleration characteristics of various vehicle types are different. They reported, average maximum acceleration value for Motorized Three Wheelers for different speed ranges. For speed range of 0 − 20 km/h, 20 − 40 km/h, and for speed > 40 km/h they reported the average maximum acceleration as 1.01 m/s2 , 0.58 m/s2 and 0.34 m/s2 , respectively. This indicates that as speed goes on increasing, the acceleration goes on decreasing. A similar observation was also reported by Bham and Benekohal [5]. Though the acceleration of vehicles is studied by many authors, they mainly included acceleration of cars. Also, the data collection methods used by these authors were out of date and prone to errors. Hence, this study aims at studying the acceleration behaviour of Motorized Three Wheelers replicating conditions of queue leaders at signalized intersection, using modern device like Global Positioning System. 2. Methodology This section presents methods used for data collection and analysis. 2.1. Experimentation Method Vehicles use their maximum acceleration capability at signalized intersection to clear it as quickly as possible. However, due to presence of vehicles with different operating conditions and engine capacity, the maximum acceleration capability of vehicles is seldom exhibited. Therefore, to study the maximum and normal acceleration behaviour of a vehicle, one needs to observe the vehicles at some other location, where such constraints is not prevalent, but full acceleration envelope of queue leaders can be observed, replicating signalized intersection behaviour. Earlier researchers, too, resorted to such study approach El-Shawarby et al. [8], Rakha et al. [17]. Therefore, the present study is also conducted over selected stretch of road under controlled conditions, replicating queue leaders at signalized intersection. An access controlled stretch of road having free flow traffic, with straight geometry and smooth road surface to have constant effect of geometry and rolling resistance respectively, was chosen for this study. A 1.5 km long two lane Nagpur-Mumbai Highway on outskirts of Wardha Town, about 70 km from Nagpur (India) satisfying above conditions was chosen for study. Motorized Three Wheelers are used for plying short distance of 15 km to 20 km on this stretch of road. GPS device with 1 Hz data logging (data logged once in a second) is used to collect speed and position data of Motorized Three Wheelers. All the drivers were asked to speed up vehicles from stop condition to achieve their desired speed (maximum speed at which driver feel safe for a given road geometry and environmental condition; hereafter referred as maximum speed) as early as possible. After cruising at the maximum speed they were asked to stop. This replicated movement of queue leaders at signalized intersection. The weight to horsepower ratio of observed Motorized Three Wheelers was 100 lb/hp (61 kg/kW). During study period, 116 such vehicle acceleration events were observed.

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2.2. Analysis Method The collected speed and position data was analysed for acceleration (refer Equation 1). at2 =

v2 − v1 t2 − t 1

(1)

where, at2 is acceleration at time t2 and v1 and v2 are the speeds at time t1 and t2 respectively. It is assumed that acceleration process ended when the increment in speed between two successive data points is less than 0.1 m/s, for next five seconds, Wang et al. [19]. The speeds were averaged over every second. The average speed profile so obtained was termed as idealized speed profile. For acceleration modelling, idealized acceleration-speed data were obtained by averaging acceleration values over 1 m/s speed interval. This idealized acceleration-speed data is used to develop the acceleration model. Developed acceleration models were evaluated using various statistical methods.

3. Data Analysis

12

12

10

10

Average speed m/s

Speed, m/s

Scatter plot of speed-time for all observed Motorized Three Wheeler trips is presented in Figure 1a. Further speed values are averaged over every second to get the idealized speed-time relationship and is presented in Figure 1b. It

8 6 4 2

8 6 4 2 0

0 0

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Time, s

(a) Scatter plot

40

50

60

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10

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30

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60

Time, s

(b) Idealized plot

Fig. 1: Scatter and idealized speed plots for motorized three wheeler during acceleration manoeuver is observed from Figure 1a that most of the trips start from the rest (speed zero). Few trips do not seem to start from rest. This is because the GPS equipment could not capture their start within one second interval. The trips started somewhere between zero and first second. Next, the maximum speed achieved by three wheelers ranges from 5.47 m/s to 11.85 m/s (19.69 km/h to 42.66 km/h). This maximum speed observed is in agreement with the speeds reported by earlier researchers, Arasan and K.Krishnamurthy [4]. The time taken to achieve maximum speed ranges from 29 s to 51 s. Slope of speed time scatter is more in the beginning of acceleration maneuver and less at the end of acceleration maneuver. This indicates higher acceleration at the beginning of acceleration maneuver and lower accelerations at the end of acceleration maneuvers. The speed-time scatter during acceleration maneuver indicates that the time taken to complete acceleration maneuver is different for different trips. Also, it is observed that the maximum speed varied in each trip. Obviously, the slope of speed time scatter varies in each trip, indicating the variation in rate of acceleration of trip. Samuels and Jarvis [18] reported that the parameters like acceleration time and distance, maximum and mean acceleration rates and speed at maximum acceleration (referred hereafter as critical speed) are sensitive to maximum speed of trip. Therefore, the trips are segregated as per their maximum speed range and these parameters are evaluated within each range of maximum speed. Table 1 presents these parameters during acceleration manoeuver. It is observed from Table 1 that during acceleration manoeuver, acceleration time and distance increase with increase in maximum speed (driver desired speed) in all speed ranges. This is because with more speed, driver needs more time to achieve maximum acceleration rate. A similar observation is reported by RaiChowdhury and Rao [15] for passenger car.


Table 1: Various parameters corresponding to different maximum speed ranges of Motorized Three Wheeler during acceleration manoeuver Serial Number

1 2 3 4

Max. Speed Range km/h (m/s)

Accel. Time

Accel. Distance

Critical Speed∗ (m/s)

Max. Accel. Rate (m/s2 )

Mean Accel. Rate (m/s2 )

(sec)

(m)

15-25 (4.17-6.94) 25-32 (6.94-8.88) 32-36 (8.88-10.0) 36-43 (10.0-11.94)

27 36 40 50

94.50 156.24 220.80 308.50

2.04 2.30 2.35 2.53

0.54 0.45 0.60 0.64

0.21 0.22 0.22 0.20

Max.: Maximum, Accel: Acceleration, ∗ : Speed at maximum acceleration

The speed at which the maximum acceleration rate occurs (referred as critical speed) varies with maximum speed range. The critical speed range is 1.53 m/s to 2.53 m/s for motorized three-wheeler. However, exact correlation between critical speed and maximum speed range couldn’t be observed, though such relationship was reported by Wang et al. [19]. It can be observed from Table 1 that the maximum acceleration rate varies with maximum speed range of vehicle. The maximum and mean acceleration rates are higher at higher maximum speed, in majority of cases. Arasan and K.Krishnamurthy [4], however, reported maximum acceleration of 1.01 m/s2 , 0.58 m/s2 and 0.34 m/s2 in speed range of 0−20 m/s, 20−40 m/s and > 40 m/s, indicating that the maximum acceleration rate goes on reducing with increase in maximum speed range. The observation in present study does not match with this. The reason is that these studies computed acceleration using travel time measured manually over a particular distance, which may be prone to errors.

4. Acceleration Models This section presents the acceleration models for Motorized Three Wheelers. Exponential smoothing Rakha and Ding [16] method is used to remove the anomalies in distance and time data. The resulting speed data for all trips is further used to compute acceleration as per Equation 1.

4.1. Evaluation of existing models Existing models such as polynomial model reported by Wang et al. [19], linear model reported by Dey and Biswas [7] and dual regime model reported by Bham and Benekohal [5] are evaluated and their suitability to data collected in present study is verified. The acceleration data yielded from Wang’s single regime polynomial model, Wang et al. [19] and Dey’s single regime linear model, Dey and Biswas [7] is found to have a different probability distribution (indicated by |t| values exceeding tα/2 ) and continuous distribution function (indicated by h = 1, in K-S two sample test),Freund et al. [9, Page No. 186], as compared to acceleration computed from speed data, collected in present study. Hence, null hypothesis cannot be accepted in this case. However, the acceleration computed using Bham’s dual regime linear model had a closest match with acceleration computed from observed speed data, in present study (null hypothesis cannot be rejected). Hence, the dual regime linear model is evaluated in detail, in this study. Bham and Benekohal [5] reported that while modelling acceleration of vehicles, speed is preferred over distance since speed provides better fit than distance. Distance is a cumulative measure and hence errors accumulate over time. Small initial error in distance profile magnifies over time. This results in not so good fit and errors are unrealistic. Therefore, appropriate model selection becomes difficult. Bham and Benekohal [5] also found that shape of distance profile of vehicle look similar for different speed models. Moreover, many authors Akelik and Besley [3], Bham and Benekohal [5], Long [11] reported that vehicle acceleration changes over the vehicle speed; at lower speed, acceleration is high and at higher speed acceleration is low, indicating strong relationship between acceleration and speed. Hence, in this study also, the acceleration speed relationship is evaluated.

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4.2. Acceleration-speed model The acceleration-speed scatter plot is presented in Figure 2a. For modeling purpose, the acceleration is averaged over a speed range of 1 m/s, Wang et al. [19], and idealized acceleration-speed plot is obtained. The idealized acceleration-speed is presented in Figure 2b. 1.2

Acceleration, m/s2

Acceleration, m/s

1.2

0.9

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Regime-I

0.9

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(a) Acceleration-speed scatter plot

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(b) Acceleration-speed idealized plot

Fig. 2: Scatter and idealized acceleration-speed plots for Motorized Three Wheeler during The maximum acceleration rate observed in this study varies from 0.50 m/s2 to 1.009 m/s2 with average maximum acceleration values as 0.76 m/s2 . The corresponding time taken by the trip to reach maximum acceleration is 3 s to 6 s with an average time is 4 s. The maximum acceleration rate reported for motorized three-wheeler by Arasan and K.Krishnamurthy [4] is 1.01 m/s2 which is slightly higher than acceleration rates observed in this study. It is observed from Figure 2a and 2b that acceleration initially increases with speed till it attains its maximum value. With further increase in speed, the acceleration decreases monotonously. Hence, acceleration-speed idealized plot can be divided in two distinct regimes. Speed corresponding to maximum acceleration can act as a point of divide between two regimes. Regime-I can be defined as before attaining maximum acceleration and regime-II as after attaining maximum acceleration, refer Figure 2b. The speed corresponding to maximum acceleration (which acts as a point of divide) is termed as critical speed. The idealized acceleration-speed plot (i.e Figure 2b) indicates that critical speed is 2.34 m/s. These two regimes can be modeled separately, since they have opposite slopes and are of different spans. A similar dual regime modelling philosophy was also reported by Bham and Benekohal [5]. Akcelik and Biggs [2] suggested that since the acceleration regimes are separated by the point of maximum acceleration, the accelerationspeed should be modeled as dual regime, unlike single regime model reported by Samuels and Jarvis [18] and Rakha et al. [17]. In single regime model, the acceleration profile is in the form of a step function causing vehicle behaviour discontinuous from previous step. In dual regime model, however, there is only one point of discontinuity at the maximum acceleration (separation of regimes). The dual regime model of acceleration-speed offers simplicity and ease of calculations as compared to polynomial model. This results in reduction in simulation time. Hence in this study, the acceleration-speed is modelled as a dual regime.

4.2.1. Strength of acceleration speed relationship To evaluate the strength of relationship between acceleration and speed, the Pearson Product Moment Correlation y) Coefficient value, r , Freund et al. [9, Page No. 354], is computed for both regimes using Equation, r = √(x− x¯)(y−¯ 2 2 (x− x¯) (y−¯y)

(where, x and y are predictor (speed) and response (acceleration) variables respectively and x¯ and y¯ are means of predictor (speed) and response (acceleration) variables respectively.) and found as +0.92 for Regime-I and −0.94 for Regime-II. Values of r for both regimes are close to +1 and −1 indicating that relationship between acceleration and speed is strong. Also the + and − values of r for Regime-I and Regime-II respectively, indicate that slope of relationship is positive (i.e. response increases with predictor) in Regime-I and negative (i.e. response decreases with predictor) in Regime-II.

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4.2.2. Evaluation of various model forms Further, various model forms such as linear, polynomial and exponential are calibrated using linear regression. To choose among various model forms, Residual Sum of Squares (RSS, refer Equation 2), is used, Freund et al. [9]. RS S =

n

2

yi − yˆ

(2)

i=1

where, RSS is Residual Sum of Squares, yi is observed value of response, yˆ is estimated value of response. The RSS values for various vehicle types and various model forms are presented in Table 2 It is observed from Table 2 that Table 2: Residual Sum of Squares (RSS) for various model forms for regime-I and regime-II

Regime-I Regime-II ∗ ∗

Linear a = α + β × v∗

Exponential ∗ a = k1 × e±k2 ×v

Polynomial a = k3 × v2 + k4 × v + k5∗

0.014 0.110

0.023 0.020

0.0004 0.023

a is acceleration at time t, v is speed at time t α, β, k1 , k2 , k3 , k4 and k5 are model parameters

minimum values of RSS are for polynomial form for regime-I and exponential form for regime-II. 4.2.3. Model calibration Linear regression (ordinary least square) is used to formulate the model and obtained relationships for Regime-I and Regime-II are presented in Table 2. Collected field data is used to calibrate the model. Values of model parameters are presented in Table 3. Table 3: Model parameters for Regime-I and Regime-II Regime-I a = k1 × v2 + k2 × v + k3 k1 k2 k3 r2 -0.23 +0.98 -0.295 0.99

Regime-II a = k4 × e−k5 ×v k4 k5 r2 1.471 -0.26 0.95

4.2.4. Model Diagnostic The model presented in earlier sections is based on linear regression technique. The adequacy of model is required to be checked, since it may fail due to various reasons like, ABRAHAM and LEDOLTER [1, pg. 69]; 1. 2. 3. 4.

Its functional form may be incorrect; Errors may not be normally distributed; Errors may be co-related and Variance of error may not be constant.

These assumptions can be tested using residual analysis. Residues are the parts of independent variables unexplained by the designed model. Residues are defined as, 3; e = yi − yˆ

(3)

where, e is residue, yi is observed value of response, yˆ is estimated value of response. Various assumptions stated above can be checked either graphically using residual analysis or numerically using hypothesis test. The graphical analysis include plot of residue against predicted response. For the assumption of independence of errors and constant variance of errors to be true, this plot should show no trend. The plot of accelerations predicted using model and residue is presented in Figure 3a and 3b. Since it does not show any trend the assumption of independent errors and constant variance of errors is satisfied.


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(a) Acceleration residues versus predicted acceleration, Regime-I

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0.47

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(b) Acceleration residues versus predicted acceleration, Regime-II

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(c) Predicted acceleration versus observed acceleration, Regime-I

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Observed Acceleration, m/s2

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(d) Predicted acceleration versus observed acceleration, Regime-II

Fig. 3: Plot of acceleration residuals

Similarly, for the assumption of normality of errors, the observed acceleration is plotted against predicted acceleration. For the assumption of normality of error to be true, the plotted points shall be clustered along the straight line of 45◦ angle. This is ratified in Figure 3c and 3d. Paired ‘t’ test is used to test the means of observed acceleration and predicted acceleration. Two hypothesis are tested −(i) null hypothesis: μ¯ = μo − μm = 0, where μo and μ p are mean of observed and predicted acceleration respectively and (ii) alternate hypothesis: μ¯ 0. The test statistic is calculated as follows Freund et al. [9], |t| = |

μ¯ √ | sd / n

(4)

where, μ¯ is mean of the difference between observed and predicted acceleration, sd is standard deviation of difference in paired data, n is number of data points. The hypothesis is tested for 95% confidence interval (α = 0.05), where α is significance level. One cannot reject null hypothesis if |t| ≤ tα/2 (= t0.025 ). Table 4 presents values of |t| and tα/2 for various vehicle types. Table 4: Results of Hypothesis Test Regime

|t|

tα/2

Remark

Regime-I Regime-II

0.03 0.99

1.96 1.96

|t| < tα/2 |t| < tα/2

Values of, |t| ≤ tα/2 , hence, null hypothesis that μ = μo − μm = 0 cannot be rejected. This implies that there is no statistically significant difference between means of observed and predicted acceleration values of motorized three wheeler.


4.2.5. Observed and predicted trajectories and speed Further, a comparison of observed and predicted trajectories and speed profiles are carried out and presented in Figure 4a and 4b. Observed trajectory of a vehicle is calculated from observed speed-time data. The modeled trajectory is calculated using modelled acceleration and modelled speed. Trajectory and speed are computed using acceleration and time as per Bokare and Maurya [6]. Paired t-test is used to compare the means of observed and mod500

12 Predicted distance, m

375

Observed speed, m/s Predicted speed, m/s

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Observed distance, m

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Fig. 4: Observed and predicted trajectories and speed eled trajectories and speed profiles. Hypothesis is tested for 95% confidence interval (α = 0.05)− (i) null hypothesis: μ = μo −μm = 0, where μo and μm are mean of observed and modeled values and (ii) alternate hypothesis: μ 0. From the test results it is observed that the test statistic |t| ≤ tα/2 (= t0.025 ). Hence the null hypothesis cannot be rejected. This indicates that proposed models for Motorized Three Wheeler estimate the vehicle’s trajectory and speed with fair accuracy.

5. Conclusions Acceleration behaviour of vehicles is important for various applications like length of yellow light at intersection, determination of sight distances at intersection, determination of length of acceleration lanes, ramp design, traffic simulation modelling, vehicular emission modelling, instantaneous fuel consumption rate modelling, etc. In present study, acceleration behaviour of Motorized Three Wheelers is analyzed. Summary of main findings of this study are presented below; • The rate of acceleration was found to increase from lowest value to maximum value with increase in initial speed. After attaining maximum value, acceleration rate decreased with further increase in speed. • The maximum acceleration rate observed in this study varied from 0.50 m/s2 to 1.009 m/s2 with an average maximum acceleration values as 0.76 m/s2 . The corresponding time taken by the trip to reach maximum acceleration is 3 s to 6 s with an average time is 4 s. The maximum acceleration rate reported for Motorized Three Wheeler by Arasan and K.Krishnamurthy [4] is 1.01 m/s2 which is slightly higher than acceleration rates observed in this study. • The acceleration-speed relationship is modelled as a dual regime relationship (second order polynomial in regime-I, before attaining maximum acceleration and negative exponential for regime-II, after attaining maximum acceleration rate). • Proposed models are statistically evaluated and found fairly accurate in predicting the observed accelerationspeed behaviour. The results of this study can be used to design the interval of green and yellow light at signalized intersection, modelling tailpipe emissions of Motorized Three Wheelers etc. The results can also be used to input values of acceleration of Motorized Three Wheelers in microscopic simulation models.

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