*3.3. Trajectory Generation*

The basis of the trajectory calculation is flight performance data and a waypoint list with local constraints regarding speed and altitude limits. This trajectory must then be subjected to two screenings. Firstly, whether the trajectory for the aircraft is feasible is tested. This includes, for example, checking the radii of curves with respect to the approach speed planned there. Another test criterion is conflicts with other aircraft. A conflict test with polygons representing severe weather areas is a new addition. Conflict detection is implemented by comparing the planned trajectories and the current or predicted weather areas. If both conditions are met, the estimated landing time can be calculated from the new trajectory.

Several functions are available in 4D-CARMA for calculating descent and reduction rates, which are calculated on the basis of EUROCONTROL's Base of Aircraft Data (BADA) [36]. Therefore, the rates depend also on the current altitudes and speeds of aircraft. Thus, if the calibrated air speed (CAS) is reduced at the same time, the descent rate is reduced by almost 50% compared to a descent rate with a constant CAS to indicated air speed (IAS) ratio. However, there is also the possibility of using correction parameters for the BADA data resulting from simulations and flight tests.

Initiated by the planned target time, the trajectory is calculated backwards starting from the threshold into the air. The forward calculation always begins at the current position of the aircraft. It takes place for at least 25 s from the actual time because it is assumed that no AMAN-advised flight state changes are possible during this short period of time due to the operations of a pilot or controller. However, if advisories that are already displayed to the controller are known, it is assumed that these clearances are also given and executed at the scheduled time.

The reverse calculation is normally carried out from the Final Approach Fix (FAF) in the direction of the current aircraft position to the end point of the forward calculation. It receives the waypoint list until where the forward calculation has been performed as input, with all points between the Final Approach Fix (FAF) and the threshold being removed.

When calculating the trajectory coordinates, it is assumed that the current position and track (flight direction) are known. Furthermore, the 2D route of the aircraft is described with constraints through a list of predetermined waypoints *P*1, ... , *PN*. These constraints are the maximum and minimum values for the flight levels and CAS speeds to be maintained. The waypoint *P*<sup>0</sup> corresponds here to the current aircraft position, and the waypoint *PN* corresponds to the runway threshold. If the position of the aircraft now approaches the next waypoint on the route (*Pi*) by less than the predetermined distance *L* of 2 NM, a track change to the next point (*Pi*+1) with a constant radius is started. Of course, this applies only if the flight to the next waypoint is connected with a significant change in direction. After validation trials with air traffic controllers in different projects, directional changes of more than 0.5 degrees are considered as a significant route change in DLR's AMAN.

In both cases—the forward and the reverse calculation—an attempt is made to place an arc from the current position onto the following segment so that the end of the arc will track in the direction of the following waypoint or the segment that can be flown. If this is not possible, a direction change of a maximum of three degrees per second takes place per integration step until the new track runs directly to the next waypoint. At the end, the track is always flown to the next waypoint, but it can happen that the track then deviates somewhat from the segment between the last waypoint and the next waypoint. This deviation is not critical in most phases of the approach. In this way, however, it can always be ensured that deviations around severe weather areas always take place in a soft arc and thus enable a realistic flight path.
