6. Lateral Placement of Vehicles over Roads of Different Width
6.4 Lateral Gap Maintaining Behaviour of Vehicles from Road Median
groups are extracted and modelled for cars and trucks. This indicates that 95% vehicles maintain larger gap than this. This section is divided into two parts, i) Model development and ii) Validation of Models
6.4.1 Model Development for Minimum Lateral Gap maintained by Cars and Trucks The regression models are fitted for a lateral gap of cars and trucks using each vehicle’s operating speed and size of median as variables. The regression models for the lateral gap are fitted by taking two dummy variables (i.e. width and height of median) and operating speed of the vehicle as independent variable. The simplest case of dummy coding is when the categorical variables have ‘n’ levels and are converted to ‘n-1’ dichotomous variable. The size of median are divided into different groups according to the design guidelines of India (IRC: SP 84, 2014;
IRC: 86, 1983; IRC: SP 73, 2007). The width of medians are divided into four groups. The dummy coding of the categorical variables, width and height of medians are presented in Table 6-11.
Table 6-11 Dummy coding for different groups of height and width of medians
Width of Median Categories W1 W2 w3
i W <1.2 m 1 1 0 0
ii W ≥1.2 m & < 2.5 m 2 0 1 0
iii W ≥2.5 m & < 4.5 m 3 0 0 1
iv W ≥ 4.5 m 4 0 0 0
Height: (Barrier Kerb) Categories H
i H ≥ 200 mm & ≤ 350 mm 1 0
ii H > 350 mm & ≤ 800 mm 2 1
Following Equation 6-6 and 6-7 are the fitted models for minimum lateral gap maintaining behaviour of cars and trucks respectively.
𝐺𝑎𝑝𝑐𝑎𝑟𝑠 (𝑚) = 0.662 + (0.031 ∗ 𝑉) − (0.077 ∗ 𝑊1) − (0.190 ∗ 𝑊2) − (0.028 ∗ 𝑊3) + (0.209 ∗ 𝐻)...6-6
𝐺𝑎𝑝𝑇𝑟𝑢𝑐𝑘𝑠 (𝑚) = 0.716 + (0.010 ∗ 𝑉) + (0.408 ∗ 𝑊1) − (0.173 ∗ 𝑊2) − (0.373 ∗ 𝑊3) + (0.164 ∗ 𝐻)……...6-7
where Gap=Lateral gap maintained from the edge of the median (m), V=Operating speed of the vehicle, W1, W2 & W3 are width groups of median according to design guidelines and H=Height group of median according to design guidelines. The residual plot and normal probability plots indicate a better fit of the predicted model. Figure 6-20 presents the observed and predicted data of cars and trucks with their residual plot and the normal probability plots.
Residual Plots Normal Probability Plots
Figure 6-20 Observed and Predicted data with their residual plots and their normal probability plots
6.4.2 Validation of the Developed Model
The models are validated with a new set of data collected from a different site. The MAPE values are obtained (23.9 for Cars & 22.32 for trucks) for the validation site also. From the MAPE values, it can be concluded a better fit of the model to the data. Figure 6-21 presents the details of the observed and predicted minimum lateral gap maintained by cars and trucks from the median.
Figure 6-21 Observed and Predicted data of lateral gap for the validation site
The minimum lateral gap maintained by cars and trucks from medians with different width and height are obtained and presented below in Figure 6-22. The impact of different width are presented by considering a fixed median height of 0.3m (refer Figure-6-22a & 6-22c).
Similarly, the impact of height is obtained and presented by keeping a fixed median width of 2.5m (Figure 6-22b & 6-22d).
0 1 2 3
0 10 20 30
Cars
Y Predicted Y
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
0 10 20 30
Residuals
Speed(km/h)
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-3 -2 -1 0 1 2 3
Residuals
Normal Scores
0 1 2 3
0 10 20 30
Trucks
Y Predicted Y
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
0 10 20 30
Residuals
Speed(km/h)
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-3 -2 -1 0 1 2 3
Residuals
Normal Scores
0 0.5 1 1.5 2
0 5 10 15 20 25 30
Lateral Gap from Median (m)
Speed (m/s)
Cars
Observed Predicted
0 0.5 1 1.5 2
0 5 10 15 20
Lateral Gap from Median (m)
Speed (m/s)
Trucks
Observed Predicted
(a) (b)
(c) (d)
Figure 6-22 Minimum Lateral Gap maintained by Trucks and cars for different combination of Median Width and Height (a) Cars with different width (b) cars with different height (c) Trucks with different width (d) Trucks with different height
From Figure 6-22a & 6-22b, it can be observed that the lateral gap maintained by cars increases for medians with width, i.e. 2.5m and 4.5m and a height of 0.3m. There is no significant difference is observed between the 2.5m and 4.5m width medians with a standard height of 0.3m. It is observed that for a median width of 1.2m, cars feel safe to move closer to the median, which indicates that with the increase in width of medians for a standard height of 0.3m, vehicles move closer to the median. However, in case of 2.5m and 4.5m width of medians cars shifts away from the median. From the video analysis it is observed that in case of medians with larger widths (2.5m and 4.5m), the plantations are observed. In such cases, though the height of median kerb is lesser i.e. 0.3m, riders perceive the height of median including the plantations height. So, they moves away from the medians due to the safety concern. It is also observed that for a median height of 0.3m, trucks maintain the higher gap for 0.45m width of
0 0.5 1 1.5 2
0 10 20 30
Lateral Gap from Median (m)
Speed (m/s)
Cars
0.45m Width 1.2m Width
2.5m WIdth 4.5m Width
0 0.5 1 1.5 2
0 10 20 30
Lateral Gap from Median (m)
Speed (m/s)
Cars
0.2m Height 0.3m Height 0.45m Height
0 0.5 1 1.5
0 10 20 30
Lateral Gap from Median (m)
Speed (m/s)
Trucks
0.45m Width 1.2m Width
2.5m WIdth 4.5m Width
0 0.2 0.4 0.6 0.8 1 1.2
0 10 20 30
Lateral Gap from Median (m)
Speed (m/s)
Trucks
0.2m Height 0.3m Height 0.45m Height
the median and it decreases with increase in width of median (i.e. 1.2m followed by 2.5m).
However, for 4.5m width of median trucks shifts away from the median. This may be due to the height of plantation inside the median. In case of 2.5m width of median the plantation height was lesser compared to the 4.5m median width. Hence, for 2.5m width, though the car drivers perceive it as obstacles due to the lesser wheel height, the truck drivers does not. However, in case of 4.5m width of median, the larger height plantation works as obstacles at the road side.
Hence the trucks moves away from the median.
Similarly, the impact of median height is also studied for a standard median width of 1.2m. It is observed that as the height of median decreases cars move away from the median. Similar observation is also observed in case of trucks. It is also observed that in all cases, the impact of operating speed has a higher impact on cars for the minimum lateral gap maintaining behavior from median, comparing to trucks.