## 4 Dynamic Runway Overrun Risk Model  
### Basic Idea  
Research on the risk of runway overrun for civil aircraft based on QAR data faces the main challenge of defining the risk. This is mainly because real runway overrun accidents are rare, while the QAR device has been widely used only in recent years. Therefore, to enable early warning, researchers tend to focus on flights with a high risk of runway overrun, even if there is no actual runway overrun accident.  
Considering that the risk of runway overrun is mainly determined by the position and ground speed of the aircraft at the moment of touchdown, we develop a risk assessment model for runway overrun based on risk areas. It assumes that, after landing, the aircraft decelerates at a fixed rate until it stops (Runway Excursion Risk Assessment Diagram, [[https://flightsafety.org/files/iass/2011-proceedings/Fabregas.pdf](https://flightsafety.org/files/iass/2011-proceedings/Fabregas.pdf)]([https://flightsafety.org/files/iass/2011-proceedings/Fabregas.pdf](https://flightsafety.org/files/iass/2011-proceedings/Fabregas.pdf)), accessed on 25 August 2023). Specifically, as shown in Figure 5, we first construct a two-dimensional diagram, where the origin point corresponds to the end of the runway, the horizontal axis represents the remaining runway length at touchdown for a specific flight, and the vertical axis represents the ground speed at touchdown. Second, the position and ground speed of the aircraft at the touchdown moment are extracted based on the QAR data. In this way, each flight is represented as a data point \((x,y)\) on the diagram, where \(x\) is the remaining runway length at touchdown and \(y\) is the aircraft ground speed at touchdown, as shown by the circular markers. Then, starting from the origin, a curve with constant acceleration is drawn. The horizontal axis of the curve represents the distance, and the vertical axis represents the speed. Obviously, the red curve in Figure 5 is a quadratic curve of distance with respect to speed. The physical meaning of this curve is as follows. First, if the touchdown point of a  
Figure 4: Trajectory correction based on runway projection and ground speed.  
specific flight is located on the curve, then if the aircraft decelerates at the rate given by the curve it will stop exactly at the end of the runway when its speed reduces to zero. That is, if the touchdown point of a flight is above the curve then decelerating at the rate given by the curve will not allow the aircraft to stop at the end of the runway; the aircraft will run off the runway, resulting in a runway overrun accident. Therefore, the area above the curve indicates that a runway overrun incident may occur, while the area below the curve is safe. The distance between a sample point and the curve reflects the degree of runway overrun risk. Clearly, the smaller the distance is, the greater the risk.  
It is worth noting that this curve is often not fixed and depends on factors such as the runway conditions, the weather conditions, and the aircraft's autobrake level. For example, the deceleration rate on a wet and slippery runway is often smaller, resulting in a larger corresponding risk area for runway overrun. In this section, the risk of runway overrun is studied by drawing inspiration from the above method.