# Analytical Model for Enhancing the Adoptability of Continuous Descent Approach at Airports
## 2 Preliminaries and Process Description
### Description of the Aircraft Descent and Approach Process at Airports
#### 2.2.1 Descent and Approach Operations  
Aircraft descent could be initiated to attain an optimal profile from the cruise altitude all the way down to landing to minimize fuel burn, emissions, and noise exposure. However, due to Air Traffic Control (ATC) restrictions and aircraft performance limitations, an optimal descent profile may not be attained all the time. For an aircraft operating at typical cruise altitudes, descent will normally initiate at 100 to 130 nautical miles (nmi) from the destination airport. This distance varies primarily due to ATC service restrictions, aircrafts' equipment and performance capabilities, and weather conditions. The controller may issue crossing restrictions during the descent, as part of a Standard Terminal Arrival Route (STAR) or as a requirement for traffic sequencing. These crossing restrictions are generally issued to the cockpit crew in terms of altitude over a fix, and they may include a speed restriction as well [30].  
A stabilized descent requires minimum control adjustments by the pilot in maintaining the planned descent path; more specifically, excessive corrections or control inputs indicate that the descent was improperly planned. Thus, planning the descent from cruise altitude is important because descending early results in more of the flight at a low altitude with increased fuel consumption and noise impacts, and starting the descent late results in problems with controlling both airspeed and descent rates later in the approach phase.  
Prior to flight, pilots need to compute the fuel, time, and distance required to descend from the cruising altitude to the approach gate (an imaginary point used by the controller to provide headings (i.e., vectoring) for aircraft arrivals to the final approach course), with the objective of determining the most economical distance from the airport to begin descent.  
This distance is referred to as the Top of Descent (TOD) point. The computations for the TOD point could be done manually prior to flight or automatically during flight using the Flight Management System (FMS). Conversely, in flight prior to the descent, pilots plan the descent from cruise by reviewing and verifying landing weather to include winds in their consideration, since tempestuous weather at the landing airport can cause slower descents. Furthermore, pilots need to know the cruise altitude and approach gate altitude (otherwise known as the initial approach fix (IAF) altitude), descent rate, and ground speed during descent.  
Based on aircraft performance, approach constraints, aircraft weight, and weather data (such as winds, temperature, and icing conditions), the vertical component of the flight plan, which referred to as the Vertical Navigation (VNAV), is computed. Usually, the VNAV approach is computed from the TOD point down to the waypoint at which the descent ends, which is generally the runway or the Missed Approach Point. There are only two types of VNAV paths that the FMS uses: the performance path or geometric path. The performance VNAV path is computed using an idle or near-idle thrust from the TOD point to the first constrained waypoint, which is constrained by speed and/or altitude and represents a typical CDA. The geometric VNAV path is computed from point-to-point between two constrained waypoints or when a vertical angle is assigned, which may represent a typical SDA, as it is shallower than the performance VNAV path and is typically using a non-idle thrust. Detailed descriptions of SDA and CDA are presented in the following subsections.