## Appendix A
### Modelling of Safety Potential Field
In real-world situations, a vehicle approaching a target vehicle from behind faces a significantly higher safety risk than when approaching from the side. Assuming the vehicle's centre of mass is (\(x_{0}\),\(y_{0}\)), the distance \(k\) from a point in space to the vehicle is as follows (not accounting for the target vehicle changing lanes and considering \(s_{0}\) as the minimum gap):  
\[|k|=\sqrt{\Big{[}(x-x_{0})\frac{s_{0}}{e^{v}}\Big{]}^{2}+[(y-y_{0})s_{0}]^{2}}, \tag{2}\]  
The vehicle potential field model is designed to enable vehicles to respond to the potential fields of nearby vehicles, maintain a safe distance, and adapt their driving strategies based on the potential field distributions. The target vehicle's potential field impactssurrounding vehicles only within a certain distance. Consequently, this paper constructs a vehicle potential field model that incorporates the vehicle's own attributes and motion state parameters:  
\[U_{v}=M\lambda\frac{e^{-acost\theta}}{|k|}\frac{k}{|k|},\] (A4)  
where \(\lambda\) denotes the vehicle potential field strength coefficient, and \(\theta\) represents the angle between a point \((x,y)\) around the target vehicle and the spatial coordinates of the vehicle's centre of mass. Utilising the vehicle potential field model parameters outlined in Table A2, this study generated 3D potential field and contour projection maps of vehicles under various driving states. Figure A2 graphically represents the potential fields for stationary and uniform motion, as well as acceleration and deceleration phases. In these scenarios, the inner ring of the potential field, centred around the vehicle's position, tends toward infinity. This suggests that any vehicle entering this inner ring is likely to collide, posing an inevitable safety hazard. Furthermore, the intensity of the potential field progressively decreases with increasing relative distance between vehicles. Figure A2a illustrates a scenario where the target vehicle is stationary, with speed and acceleration zero. Here, the stationary vehicle acts as an obstacle, posing an equal level of risk to other vehicles approaching from any angle. Consequently, the potential field in this scenario assumes a circular shape. Figure A2b depicts a vehicle moving at a constant speed of 10 m/s, with zero acceleration; its motion is aligned along the \(x\)-axis. In this case, owing to the absence of velocity along the \(y\)-axis, the intensity of the vehicle's potential field remains unchanged in that direction, irrespective of speed variations. Figure A2c,d illustrate scenarios of acceleration and deceleration at a vehicle speed of 10 m/s, with acceleration rates of 1.5 m/s\({}^{2}\) and \(-1.5\) m/s\({}^{2}\), respectively. In the acceleration case, the potential field shows a pronounced forward tilt, indicating a greater influence on vehicles ahead of the target vehicle than those behind it. In contrast, in the deceleration scenario, the potential field exhibits a notable  
backward tilt, implying a lesser impact on vehicles in front compared to those behind the target vehicle. Figure 14a,b reveal that the intensity of the vehicle potential field increases with the target vehicle's speed. This suggests that the range of driving risk for other vehicles affected by the target vehicle's potential field expands at higher rather than at lower speeds. CAVs are capable of obtaining status information about the preceding and following vehicles during transit. By adapting to the actual potential field values of these vehicles, CAVs can maintain, accelerate, or decelerate their speed within safe limits. This capability significantly enhances the stability of vehicle convoys and optimises road capacity for smoother traffic flow. The visualisation of the multi-vehicle-following traffic scenario and the vehicle potential field in Figure A4 enables an intuitive assessment of the impact of various traffic factors on driving-safety, with the field strength represented in different colours.