# Analytical Model for Enhancing the Adoptability of Continuous Descent Approach at Airports
## 6 Numerical Results to Illustrate the Model  
This section illustrates the application of our model through the use of industry standard data (e.g., minimum separation distance rules) and a stream of aircrafts arriving for landing at a mid-sized international airport during an afternoon level of demand. In particular, we used actual flight data from flights operated at Nashville International Airport (BNA) from 1200 to 1759 local time, on 17 June 2015. Using BNA flight data and standard industry data, we calculated the probability of blocking for each type of descent profile, namely, CDA and SDA. These probabilities are denoted as \(P_{kCDA}\) and \(P_{kSDA}\). \(P_{kCDA}\) is the probability of blocking if all the aircrafts in the stacking space will conduct CDA, and \(P_{kSDA}\) is defined as the probability of blocking if all the aircrafts in the stacking space will conduct SDA. As previously mentioned, the probability of blocking is the percentage of time an aircraft request to embark on CDA is denied for safety considerations and due to the stacking space being congested and busy and similarly the faction of time an aircraft landing with SDA would need to enter a holding pattern. The relevant parameters in building the model are described as follows. The rate of aircrafts arriving per time period, \(\lambda_{ss}\), is determined based upon the actual number of arrivals at BNA within each of the 24 15-min time periods analyzed. The stacking space, \(S_{p}\), was estimated by visually examining the data and assuming its value as a constant value throughout the six hours. The wind speed, \(W_{s}\), is the average value at BNA during each time period. The aircraft approach speed, \(V_{app}\), is determined based on averages, across all arriving aircrafts, of their initial approach velocity and final approach velocity. The fleet mix of heavy-, medium-, and light-weight aircrafts arriving in each time period and their sequence of arrivals is determined from what actually occurred in each time period. The minimum separation distances under SDA and CDA assumptions, \(d_{SDA}\) and \(d_{CDA}\), respectively, were chosen based on ICAO's wake turbulence application [36] and matrix model to calculate the separation distance between a mix of aircrafts proposed in [35] in each time period. As mentioned previously, these distances vary based on the wake turbulence categories of the leading and trailing aircrafts and, thus, depend on the fleet mix in each time period. Furthermore, the values of \(d_{SDA}\) and \(d_{CDA}\) are identical when the leading and trailing aircrafts have the same weight class and differ otherwise. Figure 7 shows the values of the aircraft arrival rate, \(\lambda_{\text{ss}}\), over time for BNA. Consistent with Equation (17), we calculated the number of aircrafts that can fit in the stacking space if CDA is used, \(k_{CDA}\), and the number of aircraft that can fit in the stacking space if SDA is used, \(k_{SDA}\), as follows:  
\[k_{CDA}=S_{p}/\text{d}_{CDA} \tag{23}\]  
\[k_{SDA}=S_{p}/\text{d}_{SDA} \tag{24}\]  
Those values of \(k_{CDA}\) and \(k_{SDA}\) for BNA are shown in Figure 8. This figure may be provided as systematic output for the air traffic controllers, thus enabling them to know the bounds on the maximum number of aircrafts that may be permitted within the stacking space for each descent method. Because the minimum separation distances for CDA are longer than with SDA, the value of \(k_{CDA}\) is always lower than \(k_{SDA}\), while the difference between the two varies due to the varying fleet mix and arrival sequences in each period.