Capacity of a single runway
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Capacity of a Single Runway. Kimberly Afcha and Danielle Hettmann . Maximum Throughput Capacity (MCT). Measure of capacity of the runway Based on the following assumptions: Continuous supply of arrivals and/or departures Air Traffic Control rule – no simultaneous Runway Occupancy (SRO)

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Capacity of a Single Runway

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Capacity of a single runway

Capacity of a Single Runway

Kimberly Afcha and Danielle Hettmann


Maximum throughput capacity mct

Maximum Throughput Capacity (MCT)

  • Measure of capacity of the runway

  • Based on the following assumptions:

    • Continuous supply of arrivals and/or departures

    • Air Traffic Control rule – no simultaneous Runway Occupancy (SRO)

    • Air Traffic Control rule – safe Wake Vortex Separation Distances between two flights

    • Static fleet mix

    • Approach procedure does not change


Mct of a runway

MCT of a Runway

Five considerations:

  • 1. ATC Safety Rule: no Simultaneous Runway Occupancy (SRO)

  • 2. ATC Safety Rule: Maintain Wake Vortex Separation Distance between lead and follow aircraft

  • 3. ATC Controller/Pilot Separation Control Accuracy: ATC/Pilots insert a buffer distance to avoid violating separation rules

  • 4. Fleet Mix: determines the type of aircraft in the lead-follow pairs. The type of aircraft determines the separation distance used. Small aircraft following large aircraft require longer distances than large aircraft following large aircraft.

  • 5. Final Approach Path Distance: the length of time lead-follow aircraft fly the approach in pairs and separation


Modeling mct

Modeling MCT


Maximum throughput capacity for a homogeneous fleet mix

Maximum Throughput Capacity for a Homogeneous Fleet Mix


Mct for homogeneous fleet mix

MCT for Homogeneous Fleet Mix

  • Simultaneous Runway Occupancy (SRO):

    • MCT = 3600 seconds/ROT

  • Wake Vortex Separation Distance

    • Determined by separation distance

    • Wake vortices generated off wing-tips of aircraft

    • Strength of the vortex is governed by the weight, speed, and shape of the wing of the generating aircraft


Minimum separation distance

Minimum Separation Distance

  • MCT = 3600 / (s/v) where t = s/v

    • t = inter-arrival time

    • s = distance between aircraft at runway threshold

    • v = groundspeed of aircraft

    • Example: Heavy following Heavy, t=96 seconds

      • MCT = 36000 / 96 = 37.5 flights/hour


Atc controller separation buffer

ATC/Controller Separation Buffer

  • Separation distance is determined through coordination of ATC and pilot

  • Separation Buffer:

    • MCT = 3600 / ((s/v)+b)

    • t = inter-arrival time

    • s = distance between aircraft at runway threshold

    • v = groundspeed of aircraft

    • b = buffer

    • Example: Heavy following Heavy, t=96 seconds

      • MCT = 36000 / (96 + 10)= 34 flights/hour


Mct for a homogeneous fleet mix

MCT for a Homogeneous Fleet Mix

  • MCT = Min(MCTSRO, MCTWVSD, MCTWVSDB)

    • SRO = Single Runway Occupancy

    • WVSD = Wake Vortex Separation Distance

    • WVSDB = Wake Vortex Separation Distance and Buffer (ATC/Controller Buffer)

  • Simplified to:

  • MCT = Min(MCTSRO, MCTWVSDB)


Maximum throughput capacity for a non homogeneous fleet mix

Maximum Throughput Capacity for a Non-Homogeneous Fleet Mix


Mtc non homogenous fleet mix

MTC-Non Homogenous Fleet Mix

MTC = Min ( MTCSRO, MTCWVSDB)


Mtc simultaneous runway occupancy rule

MTC- Simultaneous Runway Occupancy Rule

  • Runway Occupancy Time (ROT)

  • Probability of lead-follow


Computing e rot

Computing E[ROT]

E[ROT] = Σi(pi * ROTi)

E[ROT] = (.3*80) + (.2*65) + (.25*50) + (.25* 45)

= 60.75


Mtc simultaneous runway occupancy rule1

MTC-Simultaneous Runway Occupancy Rule

MTCSRO= 3600/ E[ROT]

MTCSRO= 3600/60.75

= 59.26


Mtc wake vortex separation rule

MTC-Wake Vortex Separation Rule

  • The separation distance between the lead and the follow (sij)

  • The groundspeed of the aircraft (vj)

  • The probability of a lead-follow pair (pij)


Mtc wake vortex separation rule1

MTC-Wake Vortex Separation Rule

  • Inter-arrival time (tij)

  • Inter-arrvial time matrix T

    E[Tij] = ΣiΣj (pij *( Tij))


Mtc wake vortex separation rule2

MTC-Wake Vortex Separation Rule

Tij = sij/vj for compression case

Tij = ((r + sij)/vj ) – (r/ vi ) for separation case


Compression case

Compression Case

  • Lead slower than Follow

  • Compression distance- additional distance used by Follow as it catches up to Lead

  • Compression Time = r/(Vj – Vi)

  • Cases: H-H, H-L, H-M, H-S, L-L, L-M, L-S, M-M, M-S, S-S


Separation case

Separation Case

  • Lead faster than Follow

  • Separation Distance- additional distance at the runway threshold caused by Lead faster than Follow

  • Separation Time= ((r + sij)/vj ) – (r/ vi )

  • Cases: S-M, S-L, SH, M-L, M-H, H-L.


Mtc wake vortex separation rule3

MTC-Wake Vortex Separation Rule

MTC = 3600 seconds/E[tij]

E[tij]= (.09*120)+(.06*188)+…+(.06*120)

=141.9

MCT = 3600 seconds/141.9

= 25.368


Mtc wake vortex separation rule with buffer distance

MTC-Wake Vortex Separation Rule with Buffer Distance

MTC = 3600/E[tij]

Where tij = Tij + b

E[tij]= 146.9 seconds

MTC= 3600/ 146.9

= 24.505 arrivals per hour


Mtc non homogenous fleet mix1

MTC-Non Homogenous Fleet Mix

Recall

MTC = Min ( MTCSRO, MTCWVSDB)

MTC = Min (59.26, 24.505)

= 24.505 arrivals per hour


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