Trans. JSASS Aerospace Tech. Japan Vol. 15, No. APISAT-2016, pp. a45-a51, 2017

Optimal Top of Analysis in Respect to Wind Prediction Errors and Guidance Strategies*

By Adriana ANDREEVA-MORI and Tsuneharu UEMURA (5mm) Aeronautical Technology Directorate, Japan Aerospace Exploration Agency, Tokyo, Japan

(Received January 31st, 2017)

Modern airliners use the profiles calculated by the onboard management system (FMS) to execute safe and efficient descents. Since the wind often varies greatly between the cruising altitude and the end-of-descent altitude, the FMS uses both predicted and measured wind to determine the descent profile. Even so, the actual wind encountered along the descent changes the profile. When a constant descent speed is maintained at idling thrust, the deviates from its path and needs to either fly an additional steady level flight segment to the metering fix or deflect speed brakes to ensure the speed constraints at the metering fix are met. This research analyses the optimal in respect to such wind prediction error and fuel burn. Numerical simulations for the Boeing 767-300 are done and it is shown that an early descent of 0.5 nm would save, on average, 0.9 lb of fuel for an idling descent from 30,000 ft to 10,000 ft and at a constant speed of 280 kt, and decrease the number of cases where the necessary deceleration could not be achieved due to lack of enough lateral distance by 77%, thus improving safety and easing operations.

Key Words: Top of Descent, Flight Management System, VNAV-SPEED, Wind Disturbances, Fuel Optimal

1. Introduction newly developed time and energy managed operations (TEMO) concept with a typical flight management system and Current flight management systems (FMSs), with which argue that TEMO’s performance in terms of arrival time most modern airliners are equipped, can compute a relatively control is superior to existing systems. optimal descent profile based on information available Here, the authors approach the problem from a different onboard the aircraft, such as aircraft weight and performance perspective. The goal of this research is to evaluate how wind model, and information available from the ground, such as prediction errors influence the pre-calculated descent wind predictions. However, despite all technological advances, flightpath using current FMS functions, especially the Top of the prediction errors cannot be fully nullified, so the wind that Descent (ToD) from the perspective of fuel burn. We attempt an aircraft encounters along its descent is always slightly to adjust the ToD to compensate for the inefficiency, thus different from the one predicted. As a result, even though the proposing a more robust descent path calculation. This FMS plans an idle-thrust descent, wind disturbances cause the research models real descent control operations based on the aircraft to either add more power, fly an additional level piloting experience of one of the authors. We consider only segment or deflect speed brakes in order to comply with the the vertical path disturbances, assuming that the aircraft flies a operational constraints along the way. This results in a less predefined lateral path. efficient descent than the one originally calculated by the FMS, that is some extra fuel is burnt to compensate for external 2. Typical Descent Path Calculation disturbances. The descent time from cruising altitude to metering fix also changes due to the difference between Modern aircraft are equipped with an FMS that provides predicted and actual wind. Most researchers consider such valuable guidance for safe and efficient . During the wind prediction errors to set accuracy limits and constraints on descent phase, the role of the FMS is to calculate an efficient descent paths calculated by the FMS. Therefore, much profile at idling or close to idling thrust, which complies with research is being done on eliminating or minimizing the all performance and operational constraints imposed by the effects of wind prediction errors by introducing new hardware airspace, for example. In other words, the FMS calculates the and software solutions that enable timely accurate continuous descent profiles based on and altitude restrictions, as descents. Lenz et al. 1) presented a concept involving an iPad well as on the end-of-descent (here, the metering fix) device that allows the aircraft to meet its predicted time of waypoint. Furthermore, the system requirement of future arrival with an accuracy of 10 sec. Dalmau et al. 2) compared FMSs is to enable the aircraft to fly a 4D trajectory accurately, where the aircraft should be able to compute and execute the © 2017 The Japan Society for Aeronautical and Space Sciences. *Presented at the 2016 Asia-Pacific International Symposium on most fuel-optimal trajectory with an error of less than 10 s Aerospace Technology (APISAT-2016), Oct. 25-27, 2016, Toyama, Japan from the ToD to the runway 3). Little information is publicly available regarding the control laws and logic used in the FMS.

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The research presented here assumes a standard FMS not updated once the descent is initiated. Therefore, we assume necessarily equipped with high-accuracy 4D functions. The that the wind prediction error at the ToD is zero since the main reason is that the authors wanted to analyze descents and current wind is accurately measured; however, further along develop robust ToD proposals applicable to present-day the descent path, a wind prediction error exists. Only the airliners, thus focusing on short-term rather than long-term vertical plane motion is considered here. The vertical motion guidance strategies. Additionally, considering the lifecycle of is controlled by the so-called VNAV-mode. The main modes an aircraft is usually longer than 20 years, it is safe to say that are VNAV-PATH (path-managed descent) and some of the aircraft in production now will still be flying in VNAV-SPEED (speed-managed descent). In a VNAV-PATH 2035,. Therefore air traffic management should be able to mode, the aircraft follows its calculated path at idling thrust accommodate them along with more modern aircraft. Here, and disturbances such as wind prediction errors are we assume that once the descent trajectory is planned, it is not compensated by speed adjustments. Thrust is only added when recalculated. Assuming idling thrust, the ideal descent profile the speed deviation allowed exceeds a certain margin. In a from cruising altitude to the metering fix consists of several VNAV-SPEED mode, on the other hand, the aircraft segments, as shown in Fig. 1. The aircraft starts its descent at maintains its target speed at idling thrust, but might deflect the ToD, following a constant Mach number profile until the from its calculated path due to external disturbances. This crossover altitude, where it switches to a constant calibrated research considers VNAV-SPEED guidance only, that is the airspeed descent (constant CAS descent). This descent target CAS is maintained regardless of the wind encountered continues until a certain altitude, in most airspaces around along the way. 10,000 ft, where speed constraints are enforced. In reality, the Details on the dynamics assumptions and constraints are aircraft decelerates gradually following a shallow glide slope shown in the next section. path. However, for simplicity and clarity of the simulation, we consider a level segment idle-thrust deceleration (shown in 3. Aircraft Flight Dynamics Assumptions and Profile purple). The end of this deceleration segment is the metering Constraints fix, which is the end of the numerical simulation considered in this research. Some researchers refer to this part of the descent The flight dynamics model used in most FMSs is a as a “performance path” 4). Later, the descent continues at a simplified point mass performance model 5). The same model lower CAS where the aircraft profile is determined based on in also used in EUROCONTROL’s BADA ver. 3.11 aircraft published procedures and specific airspace constraints. Further performance model 6), applied in the numerical simulations down, lift devices are deployed for the final drag developed during this research. In this section, we first configuration, allowing the aircraft to approach and land provide a brief description of the point mass model simplified safely. for movement in the vertical plane only then present the performance assumptions that need to be added in order to Top of Descent describe the control strategy simulated here. Next, we show Const. Mach Top of Descent No. Descent the constraints on trajectory and flight profile under which the Crossover Altitude simulations have been performed, and finally discuss the wind Const. CAS Const. CAS Descent Descent prediction error model used.

Speed, Altitude Speed, Altitude Altitude Altitude Constraint（10,000 ft） Constraint（10,000 ft） 3.1. Aircraft dynamics model Idle Deceleration Idle Deceleration Level Segment Level Segment The numerical simulations presented here are, in general, based on the BADA ver. 3.11 model. We consider the Distance Distance movement of a Boeing 767-300 aircraft (assumed weight Fig. 1. Standard descent profile calculated by the FMS (left). For lower 240,000 lb), defined in body-centered coordinates (x, y, h)， cruising altitude, the crossover altitude exceeds the cruising altitude, so true airspeed VTAS, heading ψTAS, flight path angle in respect the constant CAS segment immediately follows the ToD (right). to the air mass γTAS, bank angle ϕTAS, thrust T, drag D, mass m and wind wx，wy andwz. This research considers only the Since this research considers only the part of the descent vertical movement of the aircraft, so the point mass equations from cruising altitude to the end of the deceleration segment at can be simplified as follows: ẋ = VTAS cos γTAS + wx （1） 10,000 ft (metering fix), the flight profile can be broken down ̇ into two segments: idle-thrust descent from ToD to 10,000 ft h = VTAS sin γTAS （2） and idle-thrust level flight deceleration at 230 ft. Assuming a T − D V ̇ = − g sin γ − ẇ （3） cruise speed of 0.82 Mach and descent speed CAS of 280 kt, TAS m TAS x the crossover altitude is around 34,900 ft. The numerical The drag is defined by Eq. (4), where CD is drag coefficient, simulations presented in this paper consider a cruise altitude ρ is air density, and Sref is reference wing area. of 30,000 ft, an altitude lower than the crossover altitude, so 1 2 D = CD ρVTAS Sref （4） there is no constant Mach No. descent segment (Fig. 1 left). 2 The FMS uses both wind prediction input by the pilot and C is calculated as shown in Eq. (5). Here, C and C current wind measurement to calculate the descent path. In D D0 D2 this research, we assume that the profile calculated is not depend on the aircraft’s configuration. BADA distinguishes

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Trans. JSASS Aerospace Tech. Japan Vol. 15, No. APISAT-2016 (2017) among clean, take-off and configuration, for example. Table 1. Trajectory constraints. Assuming trimmed flight conditions, the lift coefficient can be Value calculated as shown in Eq. (6). Aircraft type Boeing 767-300 2 CD = CD0 + CD2CL （5） Weight 240,000 lb VNAV mode VNAV-SPEED Cruise altitude 30,000 ft 2mg （6） C = Final altitude 10,000 ft L ρV2 S TAS ref Descent speed（CAS） 280 kt

Final speed（CAS） 230 kt This research computes the fuel burn during descent in Wind (baseline) 0 kt order to evaluate the flight efficiency. Therefore, the thrust and fuel flow models need to be shown as well. In BADA 3.3. Wind prediction error model ver.3.11, the descent thrust (corresponding to idling thrust) is Most FMSs allow wind prediction data input for several computed as shown in Eq. (7). CTdes and CTc,1~3 are altitudes from the ToD to the runway. Here, we assume the aircraft-type dependent parameters. wind prediction error at ToD is zero, as the wind can be h accurately measured by aircraft equipment. We set three T = C C (1 − + C h2) des Tdes Tc,1 Tc,3 （7） intermediate altitudes between ToD and 10,000 ft where wind CTc,2 prediction error values are defined randomly and model the For steady level flight, the thrust balances the drag. wind prediction errors at all other altitudes based on linear The fuel flow is determined as follows: functions (see Fig. 2). For each wind profile, normally VTAS distributed random values between -30kt and 30 kt (mean 0) at fnom = Cf,1 (1 + ) T （8） altitudes of 25,000 ft, 20,000 ft, 15,000 ft and 10,000 ft are Cf,2 generated. The reason for the mean being zero is the

proposition that the actual wind can be overestimated and h （9） f = C (1 − ) underestimated in respect to the predicted wind with equal min f,3 C f,4 probability. Furthermore, to reflect realistic wind shear

conditions, all wind prediction error profiles comply with a 10 f = max (fmin, fnom) （10） kt/1000 ft wind shear constraint. The total fuel burn is then determined as follows: τ m = ∫ fdt fuel （11） 0

The fuel flow coefficients Cf,1~4 depend on the aircraft type. Here fmin corresponds to idling descent fuel flow. As discussed in the introduction, when due to wind disturbances along the descent the remaining level flight distance to the metering fix is not sufficient for deceleration, the pilot deflects the speed brakes, thus increasing the drag and shortening the deceleration distance. The BADA model Fig. 2. Sample wind prediction error profiles. does not model such speed brake usage. Therefore, in this research, we increase the value of CD0 in Eq. (5) to account 4. Null-Wind Descent Numerical Simulations for deflected speed brakes. Based on discussions with pilots, we assume that speed brakes can reduce the necessary 4.1. Baseline numerical simulation distance for idle-thrust level flight deceleration by 50%, and The baseline used in the series of simulations presented in this constraint is reflected in the maximum increase in CD0. this paper is a null-wind trajectory calculated according to 3.2. Trajectory constraints assumptions shown in Section 3. The results are shown in In the numerical simulations presented in this paper we Table 2. The aircraft starts its descent 59.8 nm prior to the model a descent from cruise altitude of 30,000 ft at CAS 280 metering fix and, in total, burns 298.5 lb in 584 s. The ToD kt to 10,000 ft, followed by a level segment deceleration to calculated by the FMS is 59.8 nm prior to the metering fix. 230 kt. The final point is the metering fix with predefined Table 2. Baseline (null wind) descent simulation results. coordinates. The FMS calculates the ToD coordinates so that there are no unnecessary level segments, that is the length of Phase Level Flight Fuel burn distance time [lb] the level segment at 10,000 ft is just sufficient for deceleration. [nm] [s] The constraints are summarized in Table 1. Steady level at 30,000 ft 0 0 0 Descent 56.2 540 274.5 Idle deceleration at 10,000 ft 3.6 44 24.0 Steady level at 10,000 ft 0 0 0 Total 59.8 584 298.5

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4.2. Early descent shift is shown in Fig. 3. As seen from the figure, late descents Next, assume the aircraft initiates its descent 1 nm prior to are penalized more than early descents. the baseline ToD, that is 60.8 nm prior to the metering fix. In such a case, the aircraft will save the fuel that would otherwise been burnt during the 1 nm segment at 30,000 ft, but will burn additional fuel at 10,000 ft to cover the remaining 1 nm distance to the metering fix. The fuel burn calculation for the 30,000 ft segment was done for 280 kt cruise speed, whereas the fuel burn calculation for 10,000 ft was done for 230 kt. A summary of the results is shown in Table 3. Compared to the baseline, the aircraft burns 6.9 lb more and reaches the metering fix 6 s later.

Table 3. Early descent simulation results. Fig. 3. ToD shift penalty for null wind (B767-300). Phase Level Flight Fuel distance time burn [lb] [nm] [s] 5. Monte Carlo Wind Prediction Error Simulations Steady level at 30,000 ft (-1) (-8) (-20.9) Descent 56.2 540 274.5 The numerical simulations presented in Section 4 were Idle deceleration at 10,000 ft 3.6 44 24.0 Steady level at 10,000 ft (230 kt) 1 14 27.8 based on null-wind assumptions, that is, there was no wind Total 60.8 590 305.4 prediction error between the actual wind and the one used by the FMS to calculate the descent path. In reality, wind 4.3. Late descent prediction errors lead to speed brake deflection during the Next, assume the aircraft initiates its descent 1 nm after the deceleration level flight segment or an additional steady level baseline ToD, that is only 58.8 nm prior to the metering fix. In flight segment at 10,000 ft. Occasionally, wind prediction such a case, the aircraft will burn extra fuel for the 1 nm errors can result in such a long descent path that the remaining segment at 30,000 ft, but will burn less fuel at 10,000 ft. In distance to the metering fix at 10,000 ft is not enough for order to decelerate until the metering fix, the aircraft will use deceleration to 230 kt. We refer to such cases as “failed its speed brakes to increase the drag and shorten the necessary deceleration.” In reality, when the pilot notices the aircraft is deceleration distance. A summary of the results is shown in flying too high above the calculated flight path, speed brakes Table 4. Compared to the baseline, the aircraft burns 14.1 lb will be deflected during descent, so such a “failed more and reaches the metering fix 4 s earlier. From the results, deceleration” case will not occur. The pilot can also it could be said that the use of speed brakes is inefficient and compensate for wind prediction error by adding extra thrust, cannot compensate for the gains obtained while flying at that is partial power, to the idling thrust. Further details can be higher altitude. The figures obtained during these numerical found in previous work by the authors 7). Here, we assume simulations are highly dependent on the aircraft model. Here, idling descent without any extra power added. we use BADA ver.3.11 parameters for a Boeing 767-300, so 5.1. Ideal ToD calculation all discussions are based on the parameter values provided for Wind prediction error profiles are generated as described in this aircraft. Subsection 3.3. Monte Carlo simulation with a total of 1,000 runs is performed. A summary of the results is shown in Table Table 4. Late descent simulation results. 5. Phase Level Flight Fuel distance time burn [lb] Table 5. Summary of Monte Carlo simulation results. [nm] [s] Steady level at 30,000 ft 1 8 20.9 No. of runs Adjustments at level segment at 10,000 ft Descent 56.2 540 274.5 510 Additional steady level flight segment Idle deceleration at 10,000 ft 2.6 32 17.2 Steady level at 10,000 ft (230 kt) 0 0 0 490 424: Deceleration by speed brakes Total 58.8 580 312.6 66: Failed deceleration

4.4. ToD shift penalty In 51% of all cases, additional steady level flight segments As seen in the simulations presented above, the fuel burn are necessary to reach the metering fix, that is the descent has differs between the early and late descent profiles: early started too early and the ideal ToD is after the one calculated descent is penalized less than a late one. In the case of a late by the FMS. In 49% of all cases, the descent should have descent, the pilot needs to deflect speed brakes during the idle- started earlier for better efficiency. This ideal descent shift is thrust level deceleration segment in order to meet the speed shown in the histogram in Fig. 4. The minimum ToD shift is -3 constraint of 230 kt at the metering fix. According to the nm and the maximum is 2.9 nm. As seen from the histogram, assumptions discussed in Section 3, speed brakes can shorten the distribution can be roughly approximated to a normal the necessary deceleration distance by only 50%, so the late distribution with a mean of 0.049 and standard deviation 1.140. descent is limited to 1.8 nm. No such performance constraint If the fuel burn penalties for early and late descents were equal, exists for early descent. The fuel burn penalty versus ToD such a normal distribution would mean that, even in view of

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Trans. JSASS Aerospace Tech. Japan Vol. 15, No. APISAT-2016 (2017) wind prediction error uncertainties, the best strategy would be brakes). In Case 3, the ToD shift not only eliminates the use to initiate the descent at the ToD calculated by the FMS. for speed brakes, but also leads to the addition of a steady However, the fuel burn penalty is not symmetrical in respect level flight segment. Occasionally, the ToD shift might just to the ideal ToD, so further investigation is necessary. Since compensate for the speed brakes without causing a steady the penalty for late ToD is higher than the penalty for early level flight segment. However, this particular case can be ToD, it is reasonable to assume that, on average, the optimal considered as a sub-case to either Case 2 or 3, so we do not ToD shift should be in the negative direction, that is, the deal with it explicitly here. aircraft should initiate its descent prior to the ToD calculated. It should be noted here that an early descent will not Such a series of simulations is presented in the next increase the number of “failed decelerations”. On the contrary, subsection. since the distance available for deceleration at 10,000 ft increases compared to the nominal case, some “failed deceleration” runs might actually be executable under the early descent assumptions. Since we assume that wind prediction error depends on altitude only, a lateral shift in the ToD will only shift the descent portion of the flight trajectory laterally without influencing the fuel burnt during the descent. The fuel differences between the nominal case and early descent case will only come from the level flight segments at the 30,000 ft cruise altitude and 10,000 ft deceleration altitude.

Next, we run simulations for various values of ToD shift. Fig. 4. ToD shift necessary to eliminate the inefficiency at 10,000 ft. The example below assumes an early shift of 1 nm, that is, the descent is initiated 60.8 nm prior to the metering fix. A summary of the results is shown in Table 7. 5.2. Early ToD shift simulations Table 7. Early ToD (-1 nm) results summary. This subsection presents the results for early ToD in the Case Number Ave. fuel burn “Failed decelerations” 1,000 cases discussed in the Monte Carlo Simulations above. of runs difference [lb] made successful First, early descents are considered, i.e. the ToD shift is Case 1 510 6.4 0 negative. There are three possible cases, as described in Table Case 2 193 -14.0 63 6. Case 3 297 -2.6 0 Total 1000 -0.20 63 Table 6. Early ToD cases overview. The fuel burn difference is calculated as a difference FMS calculated ToD Early ToD between the fuel burn for the FMS calculated ToD trajectory EARLY ToD ToD (FMS calculated) ToD (FMS calculated) under a wind prediction error environment and the early ToD profile under the same wind conditions, not relative to the Case 1 null-wind baseline. This assures a fair and realistic STEADY LEVEL STEADY LEVEL NECESSARY DISTANCE NECESSARY DISTANCE comparison applicable in real operations. As expected, FOR DECELERATION FOR DECELERATION (for wind at 10,000 ft) average fuel burn results show that early ToD is inefficient in (for wind at 10,000 ft) EARLY ToD EARLY ToD Case 1, where the steady level flight segment at 10,000 ft ToD (FMS calculated) ToD (FMS calculated) became 1 nm longer and could not compensate for the fuel

saved from the 1 nm cruise level flight segment at 30,000 ft. Case 2 SPEED BRAKES SPEED BRAKES Several factors contribute to this result. First, at higher altitude, NECESSARY DISTANCE NECESSARY DISTANCE FOR DECELERATION FOR DECELERATION the air density is lower, and thus the necessary thrust and fuel (for wind at 10,000 ft) (for wind at 10,000 ft) flow are also lower. On the other hand, the 230 kt speed is EARLY ToD ToD (FMS calculated) closer to the most efficient maximum L/D than 280 kt. Our wind assumptions set the wind prediction error at cruising Case 3 STEADY LEVEL altitude to 0 kt, while the maximum/minimum wind prediction NECESSARY DISTANCE error at 10,000 ft is 30 kt. The fuel burn for these lower and FOR DECELERATION (for wind at 10,000 ft) upper bounds are shown in Table 8.

Table 8. Case 1 level segment fuel burn. Case 1 corresponds to all 510 runs described in Table 5. When the wind prediction error has led to an additional steady Altitude [ft] CAS [kt] Wind [kt] Fuel [lb] level flight segment at 10,000 ft, an early descent will only 30,000 280 0 20.9 10,000 230 -30 31.3 elongate this segment, as shown in Case 1. Case 2 uses speed 10,000 230 30 25.0 brakes in both cases when the ToD initiates the descent at the FMS-calculated point and when the ToD is early ( i.e., the Even in the case of a tailwind, the fuel burn for the level ToD shift is not enough to eliminate the need for speed segment at 10,000 ft exceeds the one for the segment at

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30,000 ft by at least 4.1 lb and 10.4 lb at the most. Therefore, becomes; actually, for some wind prediction profiles, an early early descent in Case 1 would worsen the fuel efficiency of descent of 1.5 nm worsens the fuel burn by as much as 13 lb. the flight profile. The maximum average fuel saving is achieved for 0.5 nm For Case 2, the flight distance at 10,000 ft increases by 1 early ToD shift (0.92 lb), which depending on the perspective, nm, but this distance is flown at idling thrust. For null-wind might be considered insignificant. conditions, the entire deceleration component of 3.6 nm However, the merit of early descent is not limited to fuel requires only 24 lb. Assuming an early descent, an extension savings. As shown in the 1 nm early ToD shift simulation of 1 nm for the level segment at 10,000 ft will only result in a discussed earlier, some “failed decelerations” become fuel burn increase of less than 9 lb, which compared to a executable because more distance becomes available for saving of 1 nm flown less at 30,000, still leads to a deceleration at 10,000 ft. When descent is initiated 1 nm significant fuel burn saving for Case 2. The analysis of Case 3 is not so straightforward. The earlier than originally planned, 63 out of all 66 cases become tradeoff between fuel burn added for idling deceleration and executable (see Table 7). The results of this analysis are steady level flight at 10,000 ft and fuel saved at 30,000 ft shown in Fig. 7. For an early ToD shift of 0.5 nm, a 77% depend on the length of the initial idling deceleration (speed increase in executable decelerations is observed. Since there is brake) segment. Therefore, both positive and negative fuel a tradeoff between fuel savings and successful decelerations burn differences are possible. for early ToD shift between 1.5 nm and 0.5 nm, the choice of Normalized histogram of the simulation results for 1 nm the optimal value should be left to the aircraft operator or pilot early ToD is shown in Fig. 5. The results confirm the analysis in control. shown above. Such a histogram can be obtained for any value of an early ToD shift. The average fuel saving from a 1 nm early ToD shift is 0.2 lb.

Fig. 7. Number of decelerations made possible as a result of early descent.

6. Concluding Remarks

Fig. 5. Normalized histogram of the fuel burn difference for 1 nm early Modern flight management systems provide important ToD and nominal ToD. guidance by calculating optimal descent profiles implementing various operational and performance constraints Next, we ran analogous simulations varying the ToD shift for minimum fuel consumption. Wind predictions and value and considered the average fuel burn differences. The onboard measurements are used to calculate the descent Monte Carlo simulation results are shown in Fig. 6. The profile. Once the descent is initiated, however, wind crosses show the average fuel savings and the vertical line predictions often do not match the actual wind encountered by segments show the standard deviation. the aircraft. Assuming the aircraft maintains idling thrust and speed, such a disturbance causes the aircraft to defer from its calculated path and leads to either an additional steady level flight segment at a lower altitude or speed brake deflection. This research investigated whether shifts in the top of descent can compensate for such inefficiencies. It was shown that an early descent might not only save fuel, but also provide a larger window for the necessary deceleration at lower altitudes, thus increasing the flight safety and supporting easier and more robust pilot control. Future work will include numerical simulations of other aircraft types and descent scenarios.

References Fig. 6. Fuel burn difference for various early ToD shifts. 1) Lenz, H., Kohrs, R.: Just On Time- A Concept for iPad Enabled Timely Accurate Continuous Descent Operations. Paper presented at: AIAA Guidance, Navigation, and Control The earlier the descent is, the larger the standard deviation Conference, 2017; Grapevie, Texas.

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2) Dalmau, R., Verhoeven, R., Gelder, Nd., Prats, X.: 6) Eurocontrol. User Manual for the Base of Aircraft Data Performance Comparison between TEMO and a Typical FMS (BADA) Revision 3.11. 2013. in Presence of CTA and Wind Uncertainties. Paper presented 7) Andreeva-Mori, A., Uemura, T.: Descent Operation Evaluation at: Digital Avionics Systems Conference (DASC), 2016. Based on Analysis of Pilot Strategies (in Japanese). Paper 3) Avery, D.: The Evolution of Flight Management Systems, presented at: 47th JSASS Annual Meeting, 2016; Tokyo. IEEE Software, 28, 1 (2011), pp. 11-13.

4) Bronsvoort, J., Huynh, T., Enea, G.: An Operator-Focused Metric for Measuring Predictability and Efficiency of Descent Operations. Paper presented at: AIAA Aviation, 2016; Washington, D.C. 5) Alonso-Portillo, I., Atkins, EM.: Adaptive Trajectory Planning for Flight Management Systems: AIAA ; 2001. SS-01-06.

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