# Safe Driving Distance and Speed for Collision Avoidance in Connected Vehicles
## 4 Stopping Distance and Braking Dynamics
### Weather Effects on the Stopping Distance  
Figure 13 shows the effects of weather conditions and tire type on the stopping distance of a vehicle. A vehicle with a winter tire traveling at a speed of 100 km/h on wet roads needs a 66 m intervehicle gap and 71 m with summer tires. Meanwhile, on icy roads, traveling at a speed of just 30 km/h needs a stopping distance of 57 m (with winter tires) and 68 m with summer tires.  
We have calculated the maximum speed of the following vehicle for different speeds of the followed vehicle given an initial gap. In the case of dry asphalt, which is the ideal condition, the maximum speed of vehicle A (\(V_{Amax}\)) and the initial gap between the vehicles assuming the reaction time of the driver of 1 s are shown in Figure 14. At around 30 km/h, the initial gap between the vehicles is 10 m, and the maximum speed of almost 180 km/h with a 100 m gap between the vehicles. However, in the case of snow, the friction coefficient becomes very low, and thus the stopping distance increases, which affects the initial ideal gap between the two vehicles. The visibility significantly affects the stopping distance [36; 37]. Thus, in foggy weather, the driver's reaction time is usually increased from 1 s to 8 s [36; 37; 47; 60].  
We calculated the same values in the case of foggy weather, as shown in Figure 15. As it can be seen, the increase in the driver's reaction time significantly increases the stopping distance; hence, the maximum allowed speed of the following vehicle must be decreased. For example, if the followed vehicle is traveling at a speed of 100 km/h and the initial separating distance with the following vehicle is 100 m, then the maximum allowed speed of the following vehicle is 150 km/h in the case of dry asphalt in clear weather while it is only 58 km/h in the case of dry asphalt in foggy weather. When the road condition is bad, such as in the case of snowy roads, the maximum speed in the case of clear weather is 118 km/h, while it is dropped to 76 km/h in the case of foggy weather.  
Figure 13: Effects of weather conditions and tire type.  
Similarly, we calculated the minimum safe driving distance for different speeds of both the following and the followed vehicle when the weather is clear, assuming the driver reaction time is 1 s, and when the weather is foggy, assuming that the driver reaction time is 8 s. Figures 16 and 17 show the obtained results in the two cases, considering the dry asphalt and snowy roads. As shown, the minimum distance between the vehicles is proportional to the speed of vehicle B (the followed vehicle) on both road types, but the minimum distance is longer on snowy roads. For example, the minimum safe driving distance in the case of dry asphalt when the followed vehicle travels at a speed of 120 km/h and the following vehicle travels at a speed of 100 km/h is 52 m and 280 m in the cases of clear and foggy weathers respectively. In the case of snowy roads, for the same conditions, the minimum allowed safe driving distance is 130 m and 370 m, respectively.  
Figure 14: Maximum speed of the following vehicle for different speeds of the followed vehicle for different initial distances between the two vehicles when the driver reaction (\(T_{rA}=1\) s).  
Figure 15: In foggy weather: maximum speed of the following vehicle for different speeds of the followed vehicle for different initial distances between the two vehicles when the driver reaction (\(T_{rA}=8\) s).