CENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCHCENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCH1RUNWAY OPERATIONS:Computing Runway Arrival CapacityOR750 /SYST660USE Runway Capacity SpreadsheetSpring 2008Lance Sherry2CATSRCATSRBackground• Air Transportation System Infrastructure is composed of:• Airports– “Airside” (runways, taxiways, ramps, …)– “Landside” (terminals, passenger lounges, access roads, rental cars, busses, parking, • Air Traffic Control– Tower– Terminal Area– En-route3CATSRCATSRRunway Capacity•90% of MTC with good weather MTC•100% of MTC with bad weather MTC• Split in Airport Arrival Rate (AAR) and Airport Departure Rate (ADR)•Number of movements per hour than can be reasonably sustained over period of several hoursSustained Capacity85-90% of MTC•Used for “Schedule Coordination” (in Europe). Sets limit on scheduled arrivals/departures•Number of movements per hour at a reasonable LOS (i.e. delay minutes = 3 min)Declared Capacity80-90% of MTC•Avg of 4 min delay, means some vehciles >> 4 mins•Runway capacity achieved when avg delay = 4 mins•Expected number of movements performed in 1 hour•Delay set to average 4 min delay per vehiclePractical Hourly Capacity (PHCAP)•Does not violate ATC separation rules•Continuous Demand•No limits on delays•Expected number of movements performed in 1 hourMaximum Throughput Capacity (MTC)% of MTCAssumptions and NotesDefinitionSee deNeufville/Odoni (2004) pages 370 to 3744CATSRCATSRRunway Operations• Arriving aircraft land• Departing aircraft takeoff• Runway capacity determined by:• Separation distance between arriving aircraft– Separation Distance Violation• Separation distance between departing aircraft– Separation Distance Violation• Only one aircraft on runway at any time– Simultaneous Runway Occupancy• Separation distance and Runway Occupancy Time (ROT) determined by aircraft type (weight/lift, landing speed, …)• Heavy (e.g. 747-400)• Large (e.g. 777, 767)• Medium (e.g. 737)• Small (e.g. RJ)5CATSRCATSRModel for Runway Arrivalsn – length of final approachi(j) – type of leading (trailing) aircraftVi– ground speed of aircraft type iOi– runway occupancy time of aircraft type iSij– minimum separation distance between two airborne aircraft i and jTij– minimum acceptable time interval between successive arrivals at runway of aircraft type i and type jRunwayn6CATSRCATSRMinimum Time Separation Between 2 Aircraft• Runway can only have single aircraft at a time• Minimum separation distance between arriving aircraft must be maintained at all times• Tij> Oi• minimum acceptable time interval between successive arrivals at runway of lead aircraft type i and follow aircraft type j > runway occupancy time of aircraft type i7CATSRCATSRArrival Two Cases• Lead aircraft of type i is faster than follow aircraft of type j• Case: Expanding Separation• Lead aircraft of type i is slower than follow aircraft of type j• Case: Decreasing Separation8CATSRCATSRExpanding Separation (vi >vj)Tij= Minimum Acceptable Time Interval between successive Arrivalsmax of1. ((n + sij)/vj) – (n/vi)– (time for follow aircraft (j) to fly separation distance plus final approach path) – (time of lead aircraft (i) to fly final approach path)2. oioccupancy time of lead aircraftRunwaynRunwaynsijij> sijn/vi(n + sij)/vjij9CATSRCATSRExpanding Separation (vi >vj)((n + sij)/vj) – (n/vi)nSi,jRwy ThresholdRwy ExitTimeDistanceoiConstant Separation (vi =vj)i jSi,jNOT DRAWN TO SCALESi,j/vjnSi,jRwyThresholdRwy ExitTimeDistanceoii jSi,jSi,j/vj((n + sij)/vj)(n/vi)10CATSRCATSRDecreasing Separation (vi < vj)Tij= Minimum Acceptable Time Interval between successive Arrivalsmax of1. (sij/vj)– (time for faster follow aircraft (j) to fly separation distance) –(time of lead aircraft (i) to fly final approach path)2. oioccupancy time of lead aircraftRunwaynRunwaynsij> sij11CATSRCATSRContracting Separation (vi <vj)nSi,jRwy ThresholdRwy ExitTimeDistanceoiConstant Separation (vi =vj)i jnSi,jRwyThresholdRwy ExitTimeDistanceoii jSi,jNOT DRAWN TO SCALESi,j/vjSi,j/vj((n + sij)/vj)(n/vi)12CATSRCATSRMixed Fleet Arrivals• Average Minimum Acceptable Inter-arrival TimeE[Tij] = Σi to KΣj to Kpij· Tij• K – number of aircraft types• K2– number of aircraft type i followed by aircraft type j (pairs)• pij– probability of aircraft type i followed by aircraft type j • Maximum Capacity Throughput (MCT) = arrivals/hour = 1/E[Tij] • Assumes continuous supply of arriving aircraft• Assumes no arrival queueing delays• Sustained Capacity Throughput (SCT) = arrivals/hour = 1/E[Tij + δ] • δ = 10 secs = additional distance (padding) used by Air Traffic Controllers to avoid violating separation distance13CATSRCATSRExampleAircraft Type i pi vi oiH 0.2 150 70L 0.35 130 60M 0.35 110 55S 0.1 90 50Follow (j)Lead (i) H L M SH 4 5 5 6L 2.5 2.5 2.5 4M 2.5 2.5 2.5 4S 2.5 2.5 2.5 2.5S =δ = 10 secsFollow (j)Lead (i) H L M SH 0.0 4 0.07 0.07 0.02L 0.07 0.1225 0.1255 0.035M 0.07 0.1225 0.1255 0.035S 0.02 0.035 0.035 0.01P =E[Tij] = 116.3 Sustained Capacity Throughput (Arrivals/Hour) = 30.9 aircraft/hours14CATSRCATSRLimitations of Model• Model assumes:• independent runway (no intersections or parallel)• Landing aircraft only• Wind speed and direction• viand oishould be random variables• Separation distance should be random variables15CATSRCATSREND16CATSRCATSRHomework: Runway Operations - ArrivalsUse Runway Operations – Arrival Spreadsheet1. Plot a graph with Max # Arrivals/Hour on y-axis, Aircraft Type (i,j) on the x-axis ( H-H, L-L, M-M, S-S). • What aircraft type pairing generates the highest number of operations?• What aircraft type pairing generates the highest number of operations?• Plot a graph with Total # Seats on y-axis, Aircraft Type (i,j) on x-axis (H-H, L-L, M-M, S-S). Assume seats for aircraft type as follows: H=524, L=304, M=44, S=36. • What aircraft type pairing generates the highest number of seats for arrivals?• What aircraft type pairing generates the lowest number of seats for