### Capacity of a Single Runway (Afcha & Hetteman)

```Kimberly Afcha and Danielle Hettmann


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
Five considerations:
 1. ATC Safety Rule: no Simultaneous Runway Occupancy
(SRO)
 2. ATC Safety Rule: Maintain Wake Vortex Separation
 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 leadfollow 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 leadfollow aircraft fly the approach in pairs and separation

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

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


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 = 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)
Fleet Mix
Probability of Type of
Aircraft
H
.3
L
.2
M
.25
S
.25
MTC = Min ( MTCSRO, MTCWVSDB)
1.
Runway Occupancy Time (ROT)
2.
E[ROT] = Σi (pi * ROTi)
E[ROT] = (.3*80) + (.2*65) + (.25*50) + (.25* 45)
= 60.75
MTCSRO= 3600/ E[ROT]
MTCSRO= 3600/60.75
= 59.26
1.
2.
3.
The
and
The
The
groundspeed of the aircraft (vj)


Inter-arrival time (tij)
Inter-arrvial time matrix T
aircraft
T=
I(H)
2(L)
3(M)
4(S)
Trailing aircraft
1(H)
2(L)
120
188
65
65
50
55
72
83
E[Tij] = ΣiΣj (pij *( Tij))
3(M)
281
96
65
98
4(S)
416
194
204
120
Tij = sij/vj for compression case
Tij = ((r + sij)/vj ) – (r/ vi ) for separation case




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


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 = 3600 seconds/E[tij]
E[tij]= (.09*120)+(.06*188)+…+(.06*120)
=141.9
MCT = 3600 seconds/141.9
= 25.368
MTC = 3600/E[tij]
Where tij = Tij + b
E[tij]= 146.9 seconds
MTC= 3600/ 146.9
= 24.505 arrivals per hour
Recall
MTC = Min ( MTCSRO, MTCWVSDB)
MTC = Min (59.26, 24.505)
= 24.505 arrivals per hour
```