Baseline Test No Wind or Initial Spacing Error

For these tests, the wind and start time (initial spacing) standard deviations were set to zero (“Constants” file) to effectively turn off the random terms. In addition the commanded spacing time (“Setup” file) was set to zero to disable IM operations. The resulting nominal operation is depicted in Figure 67Figure 67 through Figure 76.

The altitude profile is shown in Figure 67. The aircraft maintains an altitude of 37,000 feet until arriving at the Top of Descent (TOD). Figure 68 shows the progression of the flight as subsequent segments are completed. For this particular aircraft example, the TOD occurs at approximately 1000 seconds into the simulation run and the aircraft arrives at the reference waypoint at approximately 2300 seconds into the simulation run.

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Figure 69 and Figure 70 show the indicated airspeed and Mach number, flown by the aircraft, respectively. Based on the flight plan described earlier, the aircraft must maintain M=0.8 until arriving at the BGEST waypoint. However, during descent, the indicated airspeed increases. Upon reaching a nominal airspeed value specified in the aircraft limit file (in this case 310 Knots), the flight control system limits the commanded speed to maintain the specified indicated airspeed. This behavior is shown in the indicated airspeed (Figure 69) and Mach number (Figure 70) plots. The constant Mach number is maintained beyond the TOD (approximately 950 seconds into the run) while the IAS increases. Shortly after reaching the nominal maximum IAS of 310 Knots (approximately 1200 seconds into the run), the flight plan calls for a reduction of IAS to 240 Knots. The guidance and control systems decelerate the aircraft and maintain the commanded IAS. The acceleration and deceleration are performed at the specified rate of 0.05 g’s referenced to the inertial speed of the aircraft.

The true airspeed achieved using the specified Mach/IAS speed profile is shown in Figure 71. As expected, during descents, the true airspeed linearly varies between waypoints. The true airspeed signal along with measured wind magnitude and direction, as shown in Figure 72, are used to compute the ground speed for the aircraft. The wind profile shown does not include any added uncertainty. It is the forecast winds at each waypoint location and altitude, and is linearly interpolated between waypoints. The ground speed signal is depicted in Figure 73, showing the nearly linear variation of ground speed from one waypoint to the next as the aircraft progresses through the flight plan.

Although the ground speed generally varies linearly between waypoints, during certain portions of the descent, there are significant differences between the planned and actual velocity profile due to IAS limiting. The TTG estimator currently implemented in the simulation model accounts for the linearly varying ground speed, but it does not fully account for the possible large speed differences. During certain long segments of the flight plan, a difference between the planned speed profile and actual speed profile will result in substantial Estimate Time Enroute (ETE) error for that segment. This introduces significant problems in the interval management since the total TTG is based on the summation of individual segment ETE. These problems will be addressed later in this section.

The rate of climb profile is shown in Figure 74. Although the change in altitude and resulting total energy change is fairly smooth (as shown in Figure 67), the change in air-relative and inertial velocities during descent requires fairly noticeable change in the rate of climb while performing this continuous descent.

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Figure 67 Altitude Profile

Figure 68 Flight Segment Completion Histories

TOD Landing Arrival at BGEST Arrival at CRDNL (reference point) TOD Landing

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Figure 69 Indicated Airspeed Profile

Figure 70 Mach Number Profile

TOD

Landing TOD

Landing Arrival at BGEST

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Figure 71 True Airspeed Profile

Figure 72 Measured Wind Magnitudes and Direction

TOD

Landing Arrival at BGEST

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Figure 73 Resulting Ground Speed

Figure 74 Rate of Climb Profile

The navigation module within each aircraft model computed the instantaneous along-track distance to the waypoint for each segment of the flight plan. This output is shown in Figure 75. This shows the distance flown for each waypoint as a function of simulation run time. The

TOD

Landing TOD

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along-track distance is adjusted to account for initial and final turns from the previous segment track and to the next segment track.

Figure 75 Along-Track Distance to Go for Current Segment

The estimated TTG is depicted in Figure 76. Ideally, the TTG signal is smooth with a slope of - 45 degrees. However, as shown in this figure, any difference between the planned ground speed and actual ground speed will result in “kinks” in the TTG curve. The TTG from the current waypoint k to the reference waypoint n is computed using the ETE for the current segment and all the future segments.

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In the current implementation of the TTG estimator, ETEs for all future segments are computed based on planned speeds and forecast winds. The current segment ETE uses the current measured ground speed of the vehicle and assumes that the aircraft will linearly decelerate to the planned speed at the waypoint. As a result of this assumption, variations in the achieved speed at the waypoint will result in a vertical shift in the TTG curve as shown in Figure 76 at 1200 and 1700 seconds into the run. The significant jumps shown at the point of crossing the PRINC and BGEST waypoints are due to larger differences between the planned and actual ground speeds and the length of segments associated with these speeds.

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Figure 76 Computed TTG for Nominal Case

The achieved spacing for the baseline case with no wind uncertainty and no start time error is 50±1 seconds, which is the nominal start time offset. The resolution of the simulation data is 1 second.