Capture conditions for merging trajectory segments to model realistic aircraft descents

Zhao, Yiyuan; Slattery, Rhonda

doi:10.2514/3.21639

Cited by 12 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 2 and Table 4 present a typical climb profile. In connecting two segments in a profile, a certain monotonic variable during the first segment is declared a capture variable 22 . When this variable reaches a certain threshold, the second segment begins.…”

Section: A Flight Segments and Profilesmentioning

confidence: 99%

“…In comparison, the cruise phase can be characterized by segments of level flight with a specified Mach or true airspeed, or cruise climb with constant speed and constant lift coefficient at its optimal value. Summarizing these different cases, a generic vertical flight segment can be described by specifying two objectives out of the five variable groups that use different trajectory controls 22 , presented in Table 3. The guidance law order in Table 3 refers to the order of closedloop guidance laws, as discussed below.…”

Section: A Flight Segments and Profilesmentioning

confidence: 99%

See 1 more Smart Citation

Optimization and Sensitivity Analysis of Climb and Descent Trajectories for Reducing Fuel Burn and Emissions

Zhao

2011

11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference

Self Cite

View full text Add to dashboard Cite

This paper studies and compares optimal climb and descent trajectories that conform to the Air Traffic Control (ATC) procedures and minimize fuel consumption, emissions, flight time, and/or flight distance. Tradeoffs among these different performance criteria are examined. In addition, closed-loop sensitivities are used to evaluate the likely variations of fuel burns, emissions, and flight times when optimized trajectories are tracked in actual flights. In this paper, a point-mass model of conventional commercial aircraft is used, together with available models of aircraft performance and emissions. Aircraft vertical profiles in the ATC system are described through a series of flight segments. The segment parameters are optimized to minimize fuel burn, emissions, flight time, flight distance, and/or their linear combinations, subject to aircraft equations of motion, aircraft performance limitations, and appropriate boundary conditions. A gradient method is devised for numerical solutions. In calculating the closed-loop sensitivities, the method of feedback linearization is used to model aircraft guidance strategies. NOMENCLATURE c tsfc = Thrust specific fuel consumption (C D , C L ) = (Drag, Lift) coefficient C D 0 = Parasite drag coefficient (D, L) = (Drag, Lift) force g = Acceleration of gravity H = Humidity correction h = Geometric altitude h b = Baro-corrected altitude p h = Pressure altitude K = Induced drag factor, feedback gains, weighting coefficients m = Aircraft mass n = Load factor M = Mach number p = Pressure p amb = Ambient pressure in psia p sat = Saturation vapor pressure in mbar R = Specific gas constant s = Path distance S = Aircraft wing area T = Engine thrust CAS V = Calibrated airspeed 1 Ph.D. candidate, 2 V g = Ground speed t V = True airspeed W = mg = Aircraft weight W h = Vertical wind speed W f = Weight of consumed fuel ! W f = Fuel flow rate W NO x = Weight of NOx emissions W CO 2 = Weight of CO2 emissions ẑ = Measured/estimated value of z ! = p / p SL = Pressure ratio ! = Relative humidity a γ = Air-relative flight path angle ! = Engine throttle setting ! = Humidity ratio in kg water / kg dry air ! = Air density ! = ! / ! SL = Temperature ratio ! = Air temperature ! amb = Ambient temperature in R ! ambc = Ambient temperature in C ( ) SL = Sea-level value ( ) 0 = Initial value ( ) f = Final value ( ) min , ( ) max = Minimum, maximum value ( ) c = Command, related to climb phase ( ) d = Related to descent phase ( ) cr = Related to cruise conditions

show abstract

Section: A Flight Segments and Profilesmentioning

confidence: 99%

Section: A Flight Segments and Profilesmentioning

confidence: 99%

Optimization and Sensitivity Analysis of Climb and Descent Trajectories for Reducing Fuel Burn and Emissions

Zhao

2011

11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference

Self Cite

View full text Add to dashboard Cite

show abstract

“…1 is defined by setting constant two out of the following three control variables: thrust, speed, and vertical rate. 16 Idle-thrust descent at constant Mach or calibrated airspeed (CAS) is the most frequently employed procedure by jet-engine aircraft. Pilots set the throttle to idle and maintain a constant Mach until a desired CAS is captured.…”

Section: Delay Absorption Proceduresmentioning

confidence: 99%

Arrival Delay Absorption using Extended Metering with Speed Control

Nikoleris

Chatterji

Almog

et al. 2012

12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis And

View full text Add to dashboard Cite

It is often the case that due to demand-capacity imbalance at an airport, flights are assigned by air traffic controllers an amount of delay that they must absorb before their expected arrival at the airport. This paper investigates the distance needed by aircraft to absorb such delays through a speed reduction of up to 10% with respect to their nominal speed. Thirty five representative days of operations with distinct traffic volume and delay characteristics are considered for the analysis. For each day, a simulation of traffic in the NAS is conducted in the absence of any constraints on sector or airport capacity thereby resulting in delay-free aircraft landing times. Flights are assigned delays due to demandcapacity imbalances at forty major US airports, which are computed through a first-comefirst-served scheduler. Distances from the airport where flights should reduce speed in order to absorb their assigned delay are computed through an aircraft trajectory generator. Analysis focuses on jet aircraft reaching their top-of-climb point at least 250 nautical miles from their destination airport. Out of all aircraft assigned delays, on average 73% were able to absorb that delay entirely through speed control. Of these aircraft, on average 93.5% of flights were able to absorb their assigned delay by reducing speed in either the same or an adjacent Air Route Traffic Control Center (ARTCC) from their arrival airport. ARTCCs that issue the highest number of advisories for speed reduction are Washington (ZDC), Atlanta (ZTL), and Chicago (ZAU). Finally, results are also provided for the specific cases of Las Vegas (LAS) and Phoenix (PHX) airports.

show abstract

“…The trajectory simulation model uses the same aircraft equations as the CTAS and EDA trajectory synthesizer 17,18 . The equations are as follows with variables defined at the beginning of this paper:…”

Section: Trajectory Synthesizer Model a Ctas Trajectory Synthesizermentioning

confidence: 99%

“…, σ represents the unknown true (infinite sample) standard deviation. Then by focusing on the desired accuracy of the sample standard deviation,(17) can be inverted and expressed in terms of a sample standard deviation uncertainty percentage (k % ) that is user selected:Monte Carlo uncertainty tolerance:(18), leads to an expression for the required number of trials N if the sample standard deviation is no greater than k % :Number of Monte Carlo trials:…”

mentioning

confidence: 99%

Effect of Uncertainty on En Route Descent Adviser (EDA) Predictions

Mueller¹,

Bortins²,

Schleicher³

et al. 2004

AIAA 4th Aviation Technology, Integration and Operations (ATIO) Forum

View full text Add to dashboard Cite

The En Route Descent Advisor (EDA) is one of the Center TRACON Automation System (CTAS) decision support tools under development at the NASA Ames Research Center. EDA generates maneuver advisories for arrival aircraft to meet scheduled arrival times at the arrival meter fix, sometimes 20 -25 minutes ahead of the aircraft's scheduled meter fix arrival time. This work determined the sensistivity of the EDA advisories to system uncertainties, including initial condition, environmental, and aircraft performance data errors. Using a Monte Carlo simulation that incorporates a Matlab Trajectory Synthesizer (TS) simulation, the sensitivities of the EDA predicted trajectory to these data error sources were obtained. The key metric is the meter fix crossing time error since this metric directly measures the performance of EDA. This performance analysis involved a minimum of 200 Monte Carlo trials per error parameter. In addition to the single aircraft performance analysis, the impact of aircraft prediction errors on conflict detection between closely-spaced aircraft was also explored. These Monte Carlo performance analyses determined how robust the EDA advisories are to input parameter uncertainties. Nomenclature

show abstract

Capture conditions for merging trajectory segments to model realistic aircraft descents

Cited by 12 publications

References 3 publications

Optimization and Sensitivity Analysis of Climb and Descent Trajectories for Reducing Fuel Burn and Emissions

Optimization and Sensitivity Analysis of Climb and Descent Trajectories for Reducing Fuel Burn and Emissions

Arrival Delay Absorption using Extended Metering with Speed Control

Effect of Uncertainty on En Route Descent Adviser (EDA) Predictions

Contact Info

Product

Resources

About