The Use of Seasonal Wind Forecasts
in Airline Schedule Development
P.] Robinson
Department of Geography
University of North Carolina
Chapel Hill, NC, USA
[Original manuscript received 27 February 1987; in revised form 20
July 1987]
ABSTRACT
Airlines currently use climatological average seasonal winds to create the estimates of
flight times needed for schedule development. Even in mean wind conditions, however,
day-to-day windspeed fluctuations make some wind induced delays inevitable. The
delay frequency is likely to change when wind conditions for a particular season depart
from the mean. In order to assess the potential benefit of seasonal wind forecasts to the
airlines, the potential impact of such changes was determined. A model, developed to
isolate the effect of windspeed fluctuations from other factors influencing flight times,
indicates that in mean conditions daily windspeed fluctuations create delays for more
than 5% of flights only on routes with lengths greater than 1100 n.m. Commonly
occurring seasonal anomalies may reduce this distance to about 800 n.m. The majority
of U.S. domestic flights are shorter than this, so that the significance to the airlines, and
thus the benefit offorecasts, is marginal. For the much longer transcontinental and
transoceanic routes the frequencies of delay can rise rapidly in adverse wind conditions,
and climatological forecasts of seasonal wind can have considerable benefit.
RESUME
Les compagnies aeriennes utili sent couramment les vents saisonniers de vitesse
moyenne pour evaluer les temps de vol necessaires au developpement des horaires.
Cependant, meme dans des conditions de vent moyennes, les fluctuations de la vitesse
du vent au jour Ie jour occasionnent des delais inevitables. II est fort probable que la
frequence des retards change lorsque les conditions de vent pour la saison en question
s'ecartent de la moyenne. Pour mesurer Ie benefice eventuel des compagnies aeriennes a
prevoir les vents saisonniers, l'impact possible de ces changements a ete determine. Un
modele, cree pour isoler I'influence des changements de vent des autres facteurs influant
sur les temps de vol, indique que, dans des conditions moyennes, les variations
journalieres de la vitesse du vent causent des retards sur plus de 5% des vols, mais
seulement sur des itineraires de plus de 1100 milles marins. Des anomalies saisonnieres
courantes peuvent reduire ceUe distance a800 milles marins environ. La plupart des
vols nationaux americains sont cependant plus courts que cela, ce qui implique pour les
compagnies aeriennes que les benefices et Ie sens de ces previsions sont limites. Pour les
itineraires beaucoup plus longs, transcontinentaux ou trans oceaniques, la frequence
P.]
Robinson / Seasonal Wind Forecasts
23
des retards peut s'accroitre rapidement dans des conditions de vent defavorables, et les
previsions de vent saisonnieres s'averent alors avantageuses.
1.
INTRODUCTION
Of the many potential effects of atmospheric events on airline operations, the
most pervasive is the impact of winds peed on flight times. Flight times for any
route will vary daily as a result of winds peed variations. However, airlines must
publish and use schedules which have temporal stability. Hence schedules must
be developed using mean windspeeds but must allow for daily variability. The
result, obvious from even a brief perusal ofthese published schedules (e.g. the
Official Airlines Guide), is that the time for flights between a given city pair
depends on the direction of travel. Further, most airlines develop two basic sets
of schedules, one for winter and one for summer, again reflecting the
climatological conditions.
Competitive and economic pressures dictate that an airline
produce for a particular route a schedule time sufficiently long to minimize the
number of late arrivals but fast enough both to meet competition from other
airlines and to minimize the time an aircraft is idle at a terminal. In schedule
development many non-climatic factors, such as passenger demand, available
gate space, and air traffic control considerations, must be considered, and
allowances made for unforeseen events ranging from equipment failure to
snowstorms at airports. Nevertheless, en-route wind conditions remain the
single most important variable for developing flight schedules for a particular
route and scheduling period.
Most airlines currently rely on climatological mean winds for each
season for schedule production. However, the advent of climatological
forecasting suggests that more efficient scheduling might well be achieved by
using forecast wind conditions for a particular season rather than the
climatological mean. In order to test this potential application of climatological
information it is necessary to determine if seasonal windspeed anomalies are
sufficient to have a significant effect on airline operations. In the present paper
the wind impact is first isolated from other factors affecting flight times and
then related to potential on-time performance in order to test the overall
significance of the impact.
2.
DAT A
The approach adopted for isolating the impact of wind conditions depends
greatly on data availability. The direct approach relating wind to flight times
for individual flights cannot be used since flight time data are not publicly
available. For similar reasons analysis of the impact through analyses of the
scheduling technique used by the airlines is not possible. However, an indirect
approach which isolates the impact in general terms without being confined to
24
Climatological Bulletin / Bulletin climatologique 22(1) 1988
specific routes or airlines is possible using two readily available data sources:
average route wind speeds and actual schedule times.
The actual schedule time, ST, is that published by the airlines in
sources such as the Official Airlines Guide (1985). ST represents,
approximately, the time between departure from the originating gate and
arrival at the destination gate. It thus includes taxi-times as well as the airborne
phase. However, for long-term averages over a number of routes this taxi-time
can be regarded as constant. Hence it can be assumed that any schedule which
is developed reflects the influence of mean route windspeed on the airborne
phase. By analysis of the schedule time for a variety of routes and their
associated windspeed, the windspeed impact can be estimated.
Aircraft performance is influenced by both the direction and speed ofthe
wind (Figure J). The appropriate wind vector, the equivalent wind, W, is given
(Sawyer, 1950) by:
W=p_(q2+S2j2Jj2A
(I)
where p and q are the components of the actual wind vector V parallel and
normal to the aircraft track respectively, s is the standard vector deviation of
the actual wind and A is aircraft airspeed. W is calculated as a spatial average
along the route. The short-term variability of the equivalent winds for a
particular route has a normal distribution about the climatological mean
value, so that the complete wind distribution is specified by the mean and
standard deviation as published by Boeing (1975a, 1975b).
TRACK
/'
p
A - - HEADING
FIGURE I. Wind vector relationships for determination of equivalent winds.
(after Boeing, 1975a)
RJ. Robinson j Seasonal Wind Forecasts
25
3.
WIN D S PEE DIM PAC TON I N D I V I D U A L R 0 UTE S
The impact of wind on individual routes was obtained by a regression analysis
of variation of ST with W for a variety of routes, seasons and aircraft types.
The relationship was initially established for flights of Boeing 727 Series
aircraft, assuming a 30,000 ft flight altitude, to and from Atlanta and
Dallas-Fort Worth airports in both summer and winter conditions. The
relationship was then tested for other aircraft types and routes, but no
statistically significant differences emerged from these tests. The general
relationship obtained was:
ST =·22.934 + (0.142
x
D) - (0.017
x
D
x
W), (r2 = 0.99)
(2)
where D, the interairport distance, is in nautical miles and ST is in minutes. W
is in knots, with headwinds being negative (Boeing, 1975a). Although these are
not standard international scientific units, they are the only ones currently
"acceptable" for the U.S. domestic airline industry and hence must be used if
the results are to have any practical application. Physically the first term of (2)
is a constant combining airport taxi times and the safety factors incorporated
into the schedule to compensate for unanticipated delays. The second term is
the influence of flight distance without wind effects, while the last term is the
wind effect itself, which in turn depends on the distance over which it acts. The
strong dependence on D, and the relatively weak one on W, is clear. Although
there are physically based underpinnings for the formulation, it is essentially a
statistical relationship. Hence it can be used to analyse the influence of wind
fluctuations on various routes. However, it cannot be used, for example, as a
basis for the development of new schedules.
For conditions on an individual route, equation (2) can be
differentiated and expressed in finite difference form to indicate the difference
between the actual flight time, AT, and the scheduled time for a particular
flight as a result of the winds peed effect:
(AT-ST)=O.017 D(W- Wj
(3)
where the prime denotes the actual wind conditions for the flight. Since the
equivalent wind has a normal distribution about the mean, this equation
allows determination of the probabilities of delays of a given magnitude and
frequency on any route. Because equation (2) forces an arrival to be exactly on
time in the mean wind conditions, early and late arrivals are symmetrically
distributed about this schedule time. Note that late arrivals, or "delays", are
defined here entirely in the context of the wind impact. They do not necessarily
constitute a delay of a particular flight as experienced by the passengers.
The distribution of delays is unique for each route since it depends
on both the winds peed standard deviation and the route length. As the
26
Climatological Bulletin / Bulletin climatologique 22( I) 1988
100
90
80
CfJ
l-
70
ri
60
I
~
LL
0
w
50
z~
40
(')
w
a:
w
a.
(.)
30
20
10
0
-12
o
-4
-8
-
Early
MINUTES
4
8
12
Late_
FIGURE 2. Frequency distribution of difference between scheduled and actual flight time with
a mean equivalent headwind of 70kts and standard deviations of (A) 28kts and (B) 38kts. Times
for route lengths of 500 n.m. and 1000 n.m. are shown.
standard deviation increases the distribution curve flattens and the frequency
and length of delays increase, as expected from statistical consideration alone
(Figure 2). Similarly, the curve become Oatter as distance increases.
Consequently, while all route will have some delayed flights as a resuJt of
wind peed fluctua.tions, the frequency and everily, a.nd hence the ignificancc
to the airlines, will vary from route to route.
4.
0 V ERA L LIM PAC T
In order to assess the significance of the windspeed variations on various
routes to overall airline operations, the impacts on flights to and from a single
airport, Charlotte North Carolina, were con idered. Thi airport accounts for
ju t over I% of the totaJ aircraft operations and passenger movements within
lheU .. A. ranking21 slofthe 121 domestic hub (Fed.eraIAviation
Administration, 19 6). Lt is reasonably typical of many United late domestic
hub operation, with a wide range of night distances and directions (Figure 3),
but with a majority of hort-hau! nights (Table I). Winter nights, when higher
mean windspeed ' and landard deviations are likely to produce the maximum
impact were used. The night considered here were tho e available during
mid-February, [985. Alillight are confined to the area of the mid-latitude
westerlies, so that equivalent winds vary with flight direction in a roughly
P.l Robinson
I Seasonal Wind Forecasts
27
N
00
t::tl
EO
~
S·
g.
s·
!:!
o
0-
CS .
.0
~
G
N
N
"""'
.'-'
.~
00
FIGURE 3. Cities served by non-stop service from Charlotte in February 1985, showing the zones of approximately equal equivalent winds. The partial
circles indicate approximate airline distance from Charlotte in increments of 200 n.m.
TABLE I. Number of nights per day, mid-Febru ary, 1985, to and from Charlotte, as a function
of route length.
Route Length (n.m.)
# Flights
0-200
200-400
400-600
600-800
800-1000
> 1000
342
146
108
15
14
8
systematic manner. To allow analysis of the overall impact, the routes were
divided into eight zones each with approximately uniform equivalent wind
conditions (Table 2).
The windspeed impact can be summarized by considering the flight
lengths needed to produce 15-minute delays with frequencies of 1% and 5%. 15
minutes is used by the Federal Aviation Administration to define a delay, and
commonly represents the delay which can be tolerated by an airline before
connecting flights are affected. Delay frequencies of both I % and 5% were used
to investigate the variations in minimum flight length produced by a change in
delay frequency. The former frequency indicates no delay in virtually all
conditions, while the latter can be regarded as a value acceptable to the airlines
given their other scheduling constraints.
The impacts of variations in seasonal wind conditions were
investigated by considering the delay distance for: the mean conditions
themselves (W, ow); an increase in the standard deviation of IOkts without
change in the mean wind (w, 0 w+ 10); an increase in the mean equivalent wind
of IOkts without change in standard deviation (W+ 10, 0 w); and an increase in
both the mean wind and the standard deviation of IOkts (W+IO, ow+lO) (Table
2). Such changes are typical oflikely seasonal variations. The winter of 1984- 5,
for example, had winds at commercial flight altitudes for the southeastern
United States more than 10kts below the mean (Robinson, 1986; Kousky,
1985). In contrast a speed more than IOkts above normal for much of the area
served from Charlotte can be inferred for the winter of 1981 - 2 (Dickson, 1982).
In the mean wind conditions for which the schedules are developed
the major factor affecting the flight distance before delays are felt is 0 w. Since
Ow is similar for all directions except south, the distances before delays occur
are similar, being over 800 n.m. before a delay frequency greater than 1% is
reached , and over 1000 n.m. for a 5% frequency. For the southbound routes the
distance is about 100 n.m. greater at both probability levels.
A 10% increase in the standard deviation alone decreases the route
distance needed before the delay frequency reaches the 5% level by about 200
n.m., the corresponding value for the 1% level being 60 n.m. The decrease is
most marked for the southbound flights, where the proportional increase in
standard deviation is the greatest. A 10% increase in mean equivalent wind
alone has a very similar effect. With 10% changes in both Wand 0 w
incorporated, the distance decreases by about 300 n.m. at the 5% level, 200
n.m. at the I % level (Table 2).
P.J Robinson / Seasonal Wind Forecasts
29
TABLE 2. Route distance (n.m.) at which wind induced delays occur with a frequency of 5%
and I % in winter wind conditions.
Direction
W
NW
N
NE
E
SE
S
SW
Wind (kts)
Route Distance
W
(W, uw)
-70
-45
6
55
70
3
-25
-75
w
28
28
30
30
29
30
25
30
(W+IO,uw)
(W, uw+IO)
(W+ 10, uw+ 10)
5%
1%
5%
1%
5%
1%
5%
1%
1175
1175
1100
1100
1125
1100
1285
1100
855
855
815
815
825
815
925
815
945
945
935
935
940
935
995
935
760
760
750
750
755
750
770
750
950
950
910
915
930
910
1035
910
730
730
705
710
715
705
785
705
810
805
795
795
800
795
840
795
660
660
655
655
660
655
670
655
TABLE 3. Percentage of flights to and from Charlotte subject to wind induced delays in various
wind conditions
Delay
Frequency
(w, a w)
(w, a w+lO)
(W+IO, aw)
(W+IO, uw+lO)
5%
1%
0.95
2.52
1.26
3.47
1.26
3.47
3.47
3.47
TABLE 4.
Frequency of wind induced delay as a function of route distance for long routes
Route
TransPacific
From W Coast
TransPacific
From E. Co ast
TransAtlantic
From W Coast
TransAtlantic
From E. Coast
TransContinental
Distance
(n.m.)
Mean Wind
(kts)
Delay Frequency
(percent)
waw
(W, aw)
(W,uw+lO) (w+lO , uw) (W+IO , aw+lO)
4500
-35
7
6
26
42
47
5600
-34
7
9
30
52
54
4800
-25
7
6
27
47
48
3200
-37
9
4
20
25
37
2100
-42
10
10
6
22
Translating these results into the percentage of flights to and from
Charlotte which are likely to be affected by seasonal wind variations, the
overall impact is small (Table 3). Only the long routes to the west coast are
affected in the mean conditions, while the Texas and Colorado routes are
added in the more severe situation. These represent a small portion of the total
operation. Since Charlotte has a typical route structure, the results indicate
that for most domestic carriers the seasonal windspeed fluctuations are likely
to have a rather marginal effect on operations.
30
Climatological Bulletin
I
Bulletin c1imatologique 22(1) 1988
The impact on the longer routes, however, suggests that the wind
effect for transoceanic and transcontinental operations may be more
ignificant. For sucb routes delays were assessed u jog generalized mean wind
condition developed from the data of Boeing ( 1975b) (Table 4). Since here the
emphasis i on the frequency of delays for fixed if omewhat generalized ,
route di tances, tbe re ults are expressed as the frequency with which flight
u ing the pre ent chedule would be delayed in the changed wind condition.
For the e long routes the frequency of delay rise rapidly as the conditions
change. Thi certainly indicate that action by the airlines is required, and
suggests that climatological wind forecasts are potentially very valuable for
schedule development on these longer routes.
The information for the longer routes is presented in generalized
form and should be treated with caution. The model used to relate winds to
schedule time was developed for relatively short routes in an area of the
westerlies where the permissible air lane are closely prescribed . On longer
routes flight paths can be chosen to utilize the rno t advantageou wind
conditions. everal routes are transpolar with some time outside the main line
of the westerlies, and almost all are likely to be at a higher altitude than the
modeled values. Nevertheless, they give a first suggestion of the likely impact of
windspeed and the potential value of climatological forecasts.
5.
CON C L U S ION S
Airline schedules are closely adjusted to climatological mean winds. Major
seasonal wind variations are incorporated by the development of separate
schedules for winter and summer. Within each season, however, occasional
wind induced delays are inevitable because of day-to-day winds peed
fluctuations. In the climatological mean wind conditions of winter, when these
fluctuations are most marked, arrivals more than 15 minutes after the
scheduled time are likely to occur more than 5% of the time only on routes
more than 1100 n.m. long. For most United States domestic airline operations
this involves only about 1 percent of the total flights (Federal Aviation
Administration, 1986). If the same schedule is retained for a season when the
wind conditions depart from the mean, delays will increase in frequency but
are still likely to affect less than 5% of the total flights. This relatively small
impact suggests that the gains which can be achieved by an airline through the
use of seasonal wind forecasts are unlikely to outweigh the extra effort needed
to develop the SChedules.
The situation changes markedly, however, when transcontinental
and transoceanic operations are considered. The longer routes increase the
probability of delays in all wind conditions. Departures from the climatological
mean conditions can lead to delays for a third or more of the flights. Although
on these routes the flexibility in the choice of flight path may decrease the
actual number of wind induced delays, a significant number are still likely to be
P.J Robinson / Seasonal Wind Forecasts
31
affected. Hence for transcontinental and transoceanic operations seasonal
forecasts have the potential to assist airlines in producing efficient schedules.
6.
A C K NOW LED GEM E N T S
Thanks are due to Mr. R. Powell, Vice-President, Piedmont Airlines, for many
helpful di cussions concerning airline operations, and to Mr. R. Fry, Federal
Aviation Administrat.ion Raleigh-Durham Airport, for information on the air
traffic control system and its implications. Support for this work was provided
by the University Research Council, University of North Carolina at Chapel
Hill.
REFERENCES
Boeing, 1975a: Winds on United States domestic routes. Doc. #W341O, Boeing
Commercial Airplane Co., Seattle, Washington.
Boeing, 1975b: Winds on world air routes. Doc. #W3412, Boeing Commercial Airplane
Co., Seattle, Washington.
Dickson, R.R., 1982: Weather and circulation of February 1982, Monthly Weather
Review, 110,446-457.
Federal Aviation Administration, 1986: Statistical Handbook of Aviation: Calendar
Year 1985. U.S. Dept. of Transportation, Federal Aviation
Administration, Office of Management Systems, Washington, D.C. np.
Kousky, Y.E. , 1985: The global climate for December 1984- February 1985: A case of
strong intraseasonal oscillation. Monthly Weather Review, 113,
2158-2172.
Official Airlines Guide, 1985: Official Airline Guide, North American Edition, Official
Airline Guides, Oak Brook, Illinois (semimonthly)
Robinson, P.l. 1986: Windspeed fluctuations and airline operating costs, Preprints,
Conference ofImpacts of 1985 Climate, Asheville, North Carolina,
August 1986, American Meteorological Society, Boston, pp 178-179.
Sawyer, J.S., 1950: Equivalent headwinds: Application o/upper-wind statistics to
air-route planning, Met. Rept., 2, No.6, Meteorological office, 535a, Her
Majesty's Stationery Office, London.
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Climatological Bulletin
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Bulletin climatologique 22(1) 1988