# Safe Driving Distance and Speed for Collision Avoidance in Connected Vehicles
## 4 Stopping Distance and Braking Dynamics  
It is essential to understand the braking dynamics to be able to estimate the safe driving speed and the safe driving separation distance or ACDA. In this section, we present the Stopping Distance (SD) affecting parameters and the braking dynamics. As shown in Figure 6, when the driver perceives a danger, he/she takes some time before making the decision to brake; this is known as the thinking time, \(t_{1}\). Once the driver decides to brake, it takes a period to move his/her leg and press on the brake pedal; this period, \(t_{2}\), is called the reaction time. Usually, the braking system does not engage instantaneously, but it takes a few milliseconds to fill up the braking system to create the necessary brake compression; this period is called the brake effectiveness time, \(t_{3}\). During all these periods, the vehicle moves with a constant speed. Once the brake becomes effective, the vehicle decelerates at a constant deceleration, \(j\), until it stops completely; this period is called the braking period, \(t_{4}\). The stopping time \(T_{s}=t_{1}+t_{2}+t_{3}+t_{4}\). According to [26], if the driver is alert, then \(t_{1}=0.5\) s, \(t_{2}=0.2\) s, and \(t_{3}=0.3\) s. Nowadays, some drivers are not alert (e.g., using his/her smartphone while driving), in such a case, the perception time may be more than 1.0 s.  
Figure 5: LiDAR Distance measurement [54]. The braking time \(t_{4}\) is affected by different factors such as the braking force, tire state, tire type, and friction force. \[SD=V.(t_{1}+t_{2}+t_{3})+\frac{V^{2}}{2.g.\ (f\pm s)} \tag{1}\]  
where \(V\) is the vehicle speed, \(t_{1}\) is the thinking time, \(g=9.81\) is the gravity constant, \(f\) is the adhesion coefficient that varies with the road type, as shown in Figure 7, and \(s\) is the slope of the road. Figure 7 shows the adhesive coefficient (\(f\)) for different road types/conditions; it can be seen that Asphalt (Dry) has the highest adhesive coefficient (\(f=0.9\)) whereas Icy road has the lowest adhesive coefficient (\(f=0.1\)). There is also a 10% decrease in the adhesive coefficient of Asphalt (Dry), Pavement (Dry), Asphalt (wet), and Pavement (wet), respectively. An increase in adhesive coefficient results in a sharp decrease in braking distance, as shown in Equation (1). The tire state significantly affects the braking distance. Figure 8 shows the effect of tire state on the braking distance of a moving connected vehicle, provided the speed and nature of the road are constant. As it can be seen, with new tires (8 mm  
Figure 6: Stopping distance dynamics when the driver perceives a danger. Figure 7: Adhesion coefficient (\(f\)) for different road types/conditions. distance is at a minimum (60 m), and worn-out tires (3 mm tread) result in 90 m braking distance (50% increase in braking distance) whereas another surge in braking distance (115 m) is observed when using bald tires with 1.5 mm tread. Deductively, the braking distance increases as the tires wear out over time. Table 3 presents the total stopping distance (in meters) for different road types and for different speeds. As can be seen, Asphalt (Dry) has the least total stopping distance at the lowest speed (3.2 m at 10 km/h) and the lowest stopping distance at the highest speed (138 m at 150 km/h) compared to the other road types. Deductively, the icy road has the longest total stopping distance at the slowest speed (6.7 m at 10 km/h) and the highest stopping distance at the fastest speed (927 m at 150 km/h) compared to Snowy roads and others. Figure 9 presents the extra stopping distance of vehicles traveling on dry and wet asphalt at different speeds. The extra stopping distance for a vehicle traveling on wet asphalt compared to dry asphalt is 1.2 m at 30 km/h. However, the extra stopping distance becomes longer at higher speeds.