Establishing an Upper-Bound for the Benefits of NextGen Trajectory ...

Frequency60005154500038864000300027312556Airway routesGCD routesMinimum 7.3 nm 14.6 nmAverage 642.4 nm 612.3 nmMedian 518.3 nm 489.2 nmMode 98.6 nm 60.4 nmMaximum 2,497.4 nm 2,485.1 nmSD 473.3 nm 466.3 nmSum 12,783,583.0 nm 12,184,854.0 nm20792000Flight using airway routesFlights using GCD routes9821000812562335 336 284165180100 300 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500Distance flown when using airway / direct routes (nm)Frequency20000180001600014000120001000080006000400017951MinimumAverageMedianModeMaximumSDSum-7.9 nm30.1 nm17.3 nm0.0 nm1,498.5 nm60.7 nm598,724.8 nmFig. 1. Comparison of histograms of the distances flown using airways anddirect routesdistance is done with the utils.getGCDistanceNM function ofFACETs API. The external program also records the totalnumber of flights in each sector, including all the sector levels,i.e., low, high, and super. Distances and sector loads are writteninto text files for further analyses.A. Distances flownIII. RESULTSFigure 1 compares the histogram of the distance flown whenusing airways to the histogram of the distance flown whenusing direct routes. The figure also includes the descriptivestatistics for the scenarios. When using airways, most ofthe flights travel less than 1,000 nm, with a peak of flightsbetween 200 and 400 nm. Short flights, i.e., less than 200nm are frequent, but not a majority in this input file. Thereis a long tail in the distribution, but the actual number offlights is low compared to the other distances. The flights withlonger distances correspond to flights from Alaska or other USterritories not directly in the continent.When using direct routes, most of the flights travel less than1,000 nm, with a peak of flights between 200 and 400 nm.Short flights, i.e., less than 200 nm are more frequent thanwhen using airways. This is an immediate benefit of usingdirect routes: shorter flown distances. The comparison of thetails shows that their frequencies are similar.The distribution for the scenario of the direct routes isshifted toward the shorter distances. This is evident in thatthe average, median, and mode are smaller in this scenariothan they are in the airways scenario. The standard deviationis also smaller indicating that the distribution is less dispersein this scenario.The figure shows that the input file used in this experimentsis dominated by short to mid distance distance flights. Thisreflects that the input file comes from a database that containsonly data for actual domestic flights in the US. The greaterchanges in the frequencies are observed in the flights from 0to 200 nm, and from 800 to 1,000 nm. This suggests that thebenefits of using direct routes are clearer in short flights or intrans-continental flights.Figure 2 shows the distribution of the differences of distanceflown by corresponding flights in both scenarios, i.e., it is a20000Fig. 2.1093616110 46 10 21 6 18 14 4 5 0 1 2 3-50 50 150 250 350 450 550 650 750 850 950 1050 1150 1250 1350 1450Difference in the distance flown (nm)Histogram of the flight-by-flight difference in the distance flownTABLE IINUMBER OF MINUTES WITH AT LEAST ONE SECTOR SATURATED OR ONTHE VERGE OF SATURATIONNumber of minutes with at leastScenarioone sector on or above(% of the total 2,114 minutes)MAP 80% of MAPFlights using airway routes 689 (32%) 944 (44%)Flights using direct routes 456 (21%) 917 (43%)paired comparison of distances. The figure also includes thedescriptive statistics for the distribution. The 1,093 (5.5%) ofthe differences in the distance flown are negative indicatingthat the direct routes are longer than the airway routes. Thisis mathematically incorrect. This is due to errors in themeasurement of the distance during the simulation. Noticethat the minimum difference is -7.9 nm, and the bin of thehistogram goes from -100 to 0 nm, so the negative differencesare in this 7.9 nm range. The peak of the histogram occurswhen the difference is between 0 and 100 nm, 90% of thedifferences are in this range.A paired two-tail t-test shows that the mean of the differencebetween the distances flown by corresponding flights in thetwo scenarios is significantly different than zero (M=30.1,SD = 60.7, N = 19,900), t = 69.9647 and the two-tail p =0.000. A 95% confidence interval about the mean is (29.2,30.9). This average reduction in the distance flown addsto 598,724.8 nm saved when using direct routes instead ofairways. The reduction in distance flown benefits the airlinesand the environment, through a reduction in fuel burned, i.e.,less pollution and lower costs.B. Sectors over MAPA metric for the load of sectors is a function of time, space,the number of flights, and routes of the flights. The number offlights did not change between scenarios in this experiment.The routes are expected to change significantly when goingfrom flight plans to direct routes. With this change in the typeof route the distribution of sector load through time and spaceis also expected to change.