Sources: Aeronautical Journal
Amsterdam
University of Applied Sciences
Centre
for Applied Research on Education
Alejandro Murrieta Mendoza
École de Technologie
Supérieure
Ruxandra Mihaela Botez
University
of Quebec
Steven Ford
BACKGROUND
The flight computation is divided into two sections:
1. one section for the aircraft traveled distance and
a 2. second section for the time an aircraft flies under
certain flight modes.
Since this method computes the missed approach fuel
and emissions contribution, it computes the fuel
burn for
a given descent approach for a successful landing, as well as for the same descent approach with a missed approach
procedure followed by a successful
landing.
TWO CASE STUDIES – Approach Landing and Approach
Go-Around
These two landing approaches are verified in a
complete flight to study the missed approach contribution for a conventional
mid-range flight. The results show that a descent with the missed approach
procedure requires 5.7 times more fuel than a normal successful descent.
Flight crews can vary their approach procedures and
flap selections to match the objectives of flight, which include fuel
conservation, noise and emissions reductions.
A practical example was given for the departure of an Airbus
A340-600 to demonstrate how the methodology could help airspace
designers and airport authorities to implement noise-reduction
procedures.
The Continuous Descent Approach (CDA) is a
promising operations procedure to reduce noise
and fuel consumption. The CDA is a descent technique in which,
instead of the conventional step descent that requires engine thrusts,
a constant descent slope is followed, setting the aircraft engines to
the IDLE mode, and thus requiring very little thrust.
Various parameters, such as the Top of Descent
(TOD) location, weight, and wind are required to correctly
execute the CDA. In, a number of 70 descents each in Boeing 757 and Airbus
319/320 aircraft were used to apply multiple regression and estimated the TOD
location as a linear function of the available predictive factors.
Some problems that can cause a landing procedure to be
aborted are:
§ Unexpected traffic in the runway: Aircraft that are
unable to take off on time and are still on the runway, aircraft flying close
to the runaway, more rapid traffic overtaking the landing being performed, etc.
Errors and misjudgements in the approach: Flying too high or too low on the final approach, flying too fast or too slow, overshooting the final approach start point, etc.
Incorrect landing: Excessive bouncing at landing.
Wind effects: A sudden change in the crosswinds, a wind direction or speed different than the expected wind direction and speed, problems with the automatic weather broadcast, etc.
The cloud ceiling below the published minimum altitudes.
Flight visibility below published instrument approach procedures minimums.
This procedure is expensive for airlines as it
normally requires high amounts of fuel.
According to Boeing, the fuel required for a missed approach
procedure can burn up to 28 times the fuel consumed during a normal
landing procedure.
It is clear that executing this procedure increases
the fuel requirements for a given flight which would reduce profits to
operators such as airlines.
A cost calculation methodology in terms of fuel and
emissions that can justify the development of products and services, which
would be implemented in low computation devices such as the Flight
Management System (FMS).
Calculating the cost of a missed approach is needed in
order to optimize aircraft trajectories and save fuel while following a given
missed approach procedure.
Climb/Cruise/Descent (CCD) and Landing to Take-Off
(LTO).
The landing procedure
waypoints and the missed approach waypoints
must be defined in order to utilize this methodology. The waypoints for
a descent are published in the instrument approach procedure charts, which the
pilot should be familiar with to carry out the selected landing sequence.
Each waypoint must have the correct information: altitude,
flight speed, and distance between the current waypoint and the next.
Instrument approach procedure chart for Runway 13R (Current Chart 14R)
Instrument approach procedure chart for Runway 13R (Current 14R) of Boeing field in Seattle.
By definition, the CCD and the LTO modes are separated
at the level of 3,000 ft in altitude.
An airplane is in the CCD mode when it is
located at an altitude equal to or above 3,000 ft.
If the airplane is located at another waypoint below
3,000 ft, then it is in the LTO mode.
The procedure of a missed approach is the following:
The airplane starts to fly in the CCD mode at the
initial waypoint (WPT) of the descent procedure found in the approach plan.
It starts to descend, passing through all the WPTs in the CCD mode, eventually
reaching 3,000 ft; below this altitude, the airplane enters into the
LTO mode and continues to descend until it reaches the point where the
pilot must make a decision to either land
or execute the missed approach procedure.
This “decision point” is considered to be the Missed
Approach Point (MAP) for non-precision approaches or the Decision
Altitude (DA) for precision approaches.
If the pilot judges that a safe landing can be
performed, the airplane lands and the flight ends; otherwise, the missed
approach procedure is executed from that point instead of landing. In this case
new steps are followed to execute the missed approach procedure.
In the first missed approach procedure step, the pilot set the engines to Take Off Go Around
(TOGA), which means that the engines will be at their maximum power for the
airplane to gain altitude and arrive at the required altitude in accordance
with the IAP. The airplane will then follow different WPTs in the LTO mode,
with the engines in a normal operation mode. Eventually the airplane will come
back to the CCD mode, until it reaches a safe holding zone. Then, when traffic
conditions allow it, ATC will assign the airplane a return vector and the pilot
will try to land again. The airplane will follow this vector, which is normally
within the limits of the CCD mode. Eventually the airplane will enter the LTO
mode again to begin the landing approach.
Climb/Cruise/Descent CCD mode
In order to perform the required calculations in the
CCD mode, the total distance traveled in this mode must first be
determined. This can be accomplished by verifying all the consecutive WPTs of
the defined trajectory and then calculating the CCD distance travelled.
If two consecutive WPTs exist within the CCD mode
limits, then the distance
value is saved as an accumulative variable. This variable, which will
eventually contain the total distance traveled in CCD mode, will be used to
calculate the parameters of interest such as Fuel burned, Nitrogen
Oxides (NOx), the Emissions Index of Nitrogen Oxide (EINOx), Hydro
Carbons (HC), the Emissions Index of Hydrocarbon (EICH), Carbon
Monoxide (CO) and the Emissions Index of Carbon Monoxide (EICO).
It is important to note that not all of the
consecutive WPTs will be in the CCD mode – for some points will be located in
the LTO mode.
If all the WPTs are within the CCD limits, the total
distance travelled in the CCD mode can also be expressed in the following way:
Total distance in CCD = WPT 1 to WPT 2 distance + WPT 2
to WPT 3 distance + WPT 3 to WPT 4 distance + … so on.
Depending on the total nautical miles traveled in this
mode, an interpolation or an extrapolation of the distance may be needed. If
the CCD distance is greater than 125 nm, an interpolation of the distance
in the tables provided by the EIG is required. This distance of 125 nm was
chosen as the lower limit because it is the smallest distance in CCD mode
given in the EIG consumption tables. Nevertheless, the distance traveled in
the landing approach procedure in the CCD mode is usually less than 125 nm.
Since the EIG tables do not have values below 125 nm,
a vector must be created, for which the first distance is not 125 nm but 0[zero]
nm, and the fuel consumption at 0 nm is considered to be 0[zero]
kilograms (kg). This vector makes it possible to interpolate from 0 nm to
the maximal distance value available in the EIG tables for a specific aircraft.
As an example, for the values of the distance and fuel consumption parameters
of the Boeing 737-400, our vectors of distance and fuel are represented in the
following two equations:
Distance (nm)=[0 125 250 500 750 1000 1500 2000]
And
Fuel consumption (kg)=[0 777.7 1442.6 2787.4 4134.9
5477.2 8362.3 11342.2]
With these vectors, a polynomial of interpolation of a
given order can be used to calculate the fuel consumption as a function of
distance. In this paper, the polynomial of order 8 was selected because 8 was
the lowest order where the real values were almost the same as the interpolated
values.
Polynomial interpolation function versus real data
In Figure above, the polynomial function is traced
versus the real data expressed by equations (1.2) and (1.3). It can be seen
that there is no error, because the polynomial function superposes over the
real data.
To find the values of polynomial coefficients for the
fuel consumption as a function of the distance x, the Matlab function
polyfit was applied. The resultant polynomial Fuel(x) for the Boeing
737-400 is shown below:
(1.4) equation.
The fuel consumption dependency with the distance is
obtained by solving the polynomial function expressed in eq (1.4) for the
distance x value; the fuel (kg) was thus calculated for the CCD mode.
Polynomials of order 8 are found for each parameter of
interest: Fuel, NOx, EINOx, HC, EICH, CO and EICO. The polynomials
created for the variation of these parameters with distance for the Boeing
737-400 are described by the following equations:
Landing to Take-off LTO mode
Three different phases can be identified in the LTO
mode:
®
Approach
Landing,
®
Climb
Out and
®
Take-off
Go Around or TOGA.
All these phases occur during a missed approach
procedure. According to the International Civil Aviation Organization (ICAO), the
three phases of an LTO mode have fixed reference times, given in Table 1.
These reference times are provided in the EIG, in FAA Advisory Circular
34-1B and in the ICAO 2013 Environmental Report among others.
In order to identify in which phase an airplane is
located between two WPTs, the following definitions of these phases must be
considered:
Approach
Landing: The WPT (n-1) is at the
same or higher altitude than the WPT (n)
Climb
Out: The WPT (n-1) is at a
lower altitude than the WPT (n).
Take-off
Go Around TOGA: At the Decision
Altitude (DA), the pilot determines if the landing procedure should be aborted,
therefore the missed approach procedure should start.
In a successful approach, where no missed approach procedure
is executed, the Approach Landing phase is the only phase considered for the
LTO calculation, since in a successful landing; the aircraft is not supposed to
climb or to perform a TOGA. If an airplane needs to climb, that indicates that
either the aircraft is leaving airport A on its way to airport B or that the
airplane is performing a missed approach procedure.
After the LTO mode has been determined, the time
traveled is calculated using the speed of the airplane and the distance between
WPTs. This time is saved as an independent accumulation variable for two LTO
phases: approach landing and climb out.
The Take-off/TOGA time value is always considered to be 0.7 minutes, since
in this acceleration phase it is complicated to determine the exact speed of
the aircraft. The time saved in the accumulation variables is multiplied by the
parameter of interest per minute, determined from the tables using the ICAO
reference times given in Table 1, thereby providing the fuel consumption.
As an example, the quantity of fuel burnt in an
Approach Landing phase of 6 minutes is calculated as follows:
In accordance with Table 1, the reference time for an Approach Landing phase is
4 minutes. Looking at Table 2, regardless of the flight distance, the fuel
burnt during the Approach Landing phase is 147.3 kg for this particular
aircraft. By dividing 147.3 kg by 4 minutes, it appears that the aircraft burns
36.825 kg. of fuel per minute during this phase. Thus, the quantity of fuel
burnt in 6 minutes during the Approach Landing phase can be found by multiplying the quantity of fuel burnt times the total
time in this phase, or 6 minutes times 36.825 kg/min, for a
total of 220.95 kg.
Crossover
calculations
It is important
to note that the crossover concept does
not refer to the typical IAS/Mach speed change due to the altitude, in which the pilot has to change the speed reference from IAS to Mach.
The crossover in this here refers to the changes in the 3,000 ft threshold
that separates the LTO mode from the CCD mode. During the missed approach,
at least three crossover situations are referred to:
1. The zone below 3,000 ft where descent is performed prior to landing;
2. Climb out over 3,000 ft after the abortion of the landing procedure
at the MAP (or DA) to wait in the holding pattern for a returning vector to
land; and
3. Descent again
below 3,000 ft in order to land after coming back from the holding pattern.
It is important
to separate the CCD and the LTO modes during all crossover situations, as in
those described above.
A constant slope is considered in the
descending or ascending path followed during the crossover situation. When the
airplane is at the initial distance Dist (n-1), it is at the WPT
(n - 1) at altitude ALTWPT (n - 1). At the final
distance Dist (n), the airplane is at the WPT (n)
at the altitude ALTWPT (n). Figure 4 shows the variation of the
altitude with the distance while descending.
The number of nautical miles (nm) needed to
travel from the current altitude (ALTWPT (n - 1)) at the WPT (n
- 1) to arrive at the crossover altitude in the LTO or CCD mode is
determined using eq. (1.11). If the aircraft is descending, the distance (nm)
is found in the CCD mode, if the aircraft is in the climbing out stage, the
distance (nm) is found in the LTO mode. Equation (1.11) is valid only when the WPT
(n) altitude is lower than the WPT (n-1) altitude. A
similar equation is used when the WPT (n) is higher than the
altitude of WPT (n-1).
Full
flight cost calculation
A hypothetical
full flight distance from the end
of the LTO mode during
taking off from Airport A to the first
waypoint of the landing approach procedure at Airport B is considered in order to calculate a
missed approach’s additional cost with respect to the entire flight’s cost.
Using the distance of the hypothetical full flight route, the polynomials (1.4)
– (1.10) can be solved for this particular case to find the parameter(s) of
interest.
To calculate the
LTO modes during take-off, the values of interest contained in the EIG tables
and shown above in Table 2 are taken directly from these tables, assuming the
standard reference times given by ICAO and shown above in Table 1. The take-off
and climb out phases are accounted for and it is assumed that the fuel and
emissions values in the EIG are the values of this LTO mode.
Once the distance
of the full flight route cost has been determined and the LTO cost obtained,
these costs are added together to obtain the full flight cost for each
parameter of interest.
Note that the
approach landing phase in the take-off section is assumed to be equal to zero
(0). This value is zero because when the airplane is leaving an airport, it is
not supposed to descend at all, as that would mean the airplane is arriving at
the airport instead of leaving it.
In the CCD mode, three different flight phases are combined into one
phase: climb, cruise and descent. In a normal flight, more fuel is spent during the climb phase than in
cruise mode, and in cruise mode, more fuel is spent than in descent.
The method presented here does not take into account
the differences between these varying levels of consumption and assumes that all
three phases considered in the CCD mode comprise one big phase that is only a
function of distance. These differences are not considered here because of the
lack of that type of detailed data in the literature.
Final
calculations
The next step consists of carrying out the calculation
presented above. The costs for a missed landing approach and for a successful
landing approach are generated. Next, each is added to the full flight costs
and the cost difference between these two situations is calculated. The two
flights thus evaluated are:
1) full flight with a missed landing approach followed
by a successful landing, and
2) full flight with a successful landing.
Results
The results shown
here are obtained for the flight plan cost of a short flight with a successful
first attempt landing and the same short flight with a missed approach
procedure followed by a successful landing. The short flight distance from
Take-off to the first approach plate waypoint is 650 nm. The standard atmospheric
conditions are considered.
The
Landing and missed approach procedure
The landing approach
simulated as proposed by our industrial partner is shown in Figure 1. Table 3
shows the waypoints to be followed for a successful landing and Table 4 is the
flight plan (waypoints) for a landing with a missed approach procedure followed
by a successful landing. Altitudes are expressed in Mean Sea Level (MSL). In these tables, the ID refers to the
sequence on which the waypoint was visited, the waypoint name is the name
provided to that waypoint, altitude is the altitude at which the waypoint
should be fly by at, the distance refers to the distance to the next waypoint,
speed refers to the speed at which the aircraft should fly from the given
waypoint, and mode shows the flight mode of considered for that waypoint.
The increased complexity of the flight plan in Table 4
compared to that of Table 3 is obvious; the number of waypoints to be
followed by the aircraft to execute the missed approach procedure increase
substantially. It is interesting to observe that during the execution of a
successful landing sequence (Table 3) the aircraft does not perform any climb.
Table 4 is much more complex. The missed approach procedure is expressed
following the WPTs ID 5: “RNP 0.3” to ID 17 “RWY 13”. Point ID 8 is the safe
holding cruise (4 turns were executed); this is the place where the aircraft
waits for a return vector (a trajectory to intercept one of the points of the
IAP) from ATC.
Once the returning vector is provided, the waypoint
that shows the exit from the holding zone is WPY ID 9: “BLAKO (exit)”. WPYs ID
10: “AUBURN” to ID12: “SEATACII” represent the returning vector. WPT ID 13:
“JUGOK” is the interception of the IAP flight plan. Note that WPTs ID 14:
“JAMRO” to ID 17: “RWY 13” in Table 4 coincides with waypoints ID 3: “JAMRO” to
ID 6: “RWY13” in Table 3.
Fuel
burned and emissions comparison between a conventional landing and a landing
after a missed approach
The first sets of
results in Table 5 and Table 6 present a successful landing procedure following
the flight plan in Table 3. The second set of results show a missed approach
procedure followed by a successful landing; these follow the flight plan in Table
4. The comparison between the two different landing sequences is presented in
Table 7.
In Table 5 and Table 6, some values are not available
and are indicated with “n/a”. These values were impossible to compute due to
the lack of information. For example, in the LTO mode for the phase TOGA, in
Table 5 (row 4, column 4), the speeds for the TOGA during the flight time of
0.7 seconds are not known, therefore it was impossible to calculate the
distance in nm. In the CCD mode of Table 6, the flight time was not calculated
(row 6, column 4) because the cruise speed is unknown, however it was possible
to calculate fuel consumption because this phase is a function of distance.
During the execution of a successful landing without a
missed approach in Table 5, as expected, there were neither climb outs nor TOGA
flight phases because the aircraft should always be descending. However, in
Table 6, the crew needs to climb out to execute the missed approach procedure.
Table 7 is a comparison of landings with and without a missed approach
procedure.
The missed
approach burns 5.7 times more fuel than a successful approach. The extra fuel
burned augments the contaminant emissions of CO2, NOx, HC, EINOx, EIHC, and
EICO. This difference can be explained in terms of the existence of a TOGA and
a climb out phase during the missed approach procedure in Table 6. Both flight
phases consume a great quantity of fuel, especially while flying at low
altitudes. Flying a cruise phase at low altitude was also required. This small
cruise phase was given by ATC in the form of a vector to intercept the landing
path to the runway after the missed approach.
Because the landing is rigidly defined by the IAP, the only opportunity
to reduce the fuel consumed by the procedure has to come from ATC delivering
friendly (and timely) intercepting vectors, and/or by developing speed
controllers to efficiently manage speed to demand the least possible thrust.
It is clear that missing an approach is expensive in
terms of time and fuel for an airline, and that the extra emissions released to
the environment are high -- 4.83 lbs of CO (Table 5, row 4, column 8) for one
particular flight (to specify just one emission). In the hypothetical case
developed above, executing the missed approach costs 5.7 times more fuel (Table
7, row 5, column 2) than carrying out the successful approach, and this cost is
only expressed in terms of fuel. If the Cost Index (determines the flight time
cost) is taken into account, due to the number of extra hours flown and the extra
fuel burnt, the total cost in dollars is even higher.
