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Investigation of fuel savings for an aircraft due to optimization of the center of gravity

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Abstract

The aircraft's center of gravity (CG) has a significant influence on the safety and efficiency, which are determined to a large degree by keeping the CG position within the forward and aft limits. Improper loading reduces the aerodynamics efficiency of an aircraft, resulting in higher flight drag. This paper focuses on the theoretical analysis of the influence of variable CG parameter on the fuel consumption. A new model is developed to predict the fuel consumption rate for an aircraft with it's CG at different position. The numerical result indicates that a more aft CG position produces less drag and, in turn, requires less fuel consumption.
IOP Conference Series: Materials Science and Engineering
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Investigation of fuel savings for an aircraft due to optimization of the
center of gravity
To cite this article: Yitao Liu et al 2018 IOP Conf. Ser.: Mater. Sci. Eng. 322 072018
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SAMSE IOP Publishing
IOP Conf. Series: Materials Science and Engineering 322 (2018) 072018 doi:10.1088/1757-899X/322/7/072018
Investigation of fuel savings for an aircraft due to
optimization of the center of gravity
Yitao Liu1,*, Zhenbo Yang1, Junxiang Deng1, and Junjie Zhu2
1School of Aircraft Maintenance Engineering, Guangzhou Civil Aviation College,
Guangzhou, China
2College of Aerospace Engieering, Nanjing University of Aeronautics and
Astronautics, Nanjing, China
*Corresponding author e-mail: liuyitao@caac.net
Abstract. The aircraft’s center of gravity (CG) has a significant influence on the safety
and efficiency, which are determined to a large degree by keeping the CG position
within the forward and aft limits. Improper loading reduces the aerodynamics
efficiency of an aircraft, resulting in higher flight drag. This paper focuses on the
theoretical analysis of the influence of variable CG parameter on the fuel consumption.
A new model is developed to predict the fuel consumption rate for an aircraft with it’s
CG at different position. The numerical result indicates that a more aft CG position
produces less drag and, in turn, requires less fuel consumption.
1. Introduction
Today’s and tomorrow’s air transport industry is faced with numerous challenges: safety improvement,
fuel saving, emission reduction, noise minimization and cost decrease. Airlines need meticulous
management to respond to these challenges. Various optimization strategies, which range from flight
management to flight operation and aircraft maintenance, are used to decrease the civil aircraft fuel
consumption. [1]
There have been a large number of papers concerned with aircraft fuel savings, especially in the
field of trajectory optimization. Various modeling and simulation methods are used to develop and
evaluate the fuel burn prediction system for different aircraft types [2-4]. But a very limited amount of
research is focusing on optimization of the center of gravity (CG) control for an aircraft.
Weight and balance are two important parameters in the design and operation of an aircraft, and
need to be properly controlled to perform the safety and efficiency of the aircraft. For a certain gross
weight, the balance depends on the control of the CG.
Aircraft is not allowed to fly overweight, nor is it allowed to fly beyond the CG limits. In addition
to the safety factors, the CG also is an important factor in determining the fuel efficiency of the
aircraft. If an aircraft is extremely nose down, resulting from too far forward CG position, the tail will
need to deflect up more to produce higher downward trim force to maintain the aircraft in level flight.
This requires a higher angle of attack (AOA) to generate more lift to balance the aircraft, so additional
drag is produced due to the higher AOA, in turn, higher engine thrust is required. [5]
This paper focuses on the theoretical analysis of the influence of variable CG parameter on the fuel
consumption. A new model is developed to predict the fuel consumption rate for an aircraft with it’s
CG at different position. This model is implemented for Boeing 737-800 aircraft and the numerical
result is validated with the Performance Engineers Manual’s data.
2
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SAMSE IOP Publishing
IOP Conf. Series: Materials Science and Engineering 322 (2018) 072018 doi:10.1088/1757-899X/322/7/072018
2. Theoretical Analysis
2.1. Description of CG
The same as the definition of the CG of other objects, the CG of an aircraft is the point at which the
total aircrafts gravity exerts. The location of CG depends on the distribution of the load on the aircraft.
Any weight change of any part on the aircraft can cause the CG to shift, and the CG always moves
towards the direction where the weight increases. For a certain gross weight, balance control refers to
the control of the CG position.
On large aircraft, the CG is expressed in terms of %MAC, which is a percentage of the length of
the mean aerodynamic chord (MAC), as shown in Figure 1. The equation for calculating the position
of CG, %MAC, can be written as [5]:
%100%
MAC
T
L
X
MAC
(1)
where XT is the distance of CG behind the leading edge of the MAC, and LMAC is the length of
MAC.
Normally, for a modern large aircraft with acceptable flight characteristics, the range of the
parameter %MAC is usually between 20% and 30%. Obviouslythe greater %MAC is, the more aft
position the CG locates.
Figure 1. Schematic of CG and MAC.
When the CG coincides with the aircraft’s center of lift, the gravity of the aircraft is all balanced by
the lift. If this were the case, there is no vertical aerodynamic force on the tail, resulting in zero
horizontal trim drag. But this perfectly condition could not happen due to the restriction of stability
and safety. The CG of an aircraft must be located within the forward and aft limits for safe flight.
2.2. Flight Aerodynamics
An airplane must be designed to have stability to ensure that it can recover from the interfere of the air
flow with hands off the controls. It is important to note that, for fixed wing aircraft the CG is slightly
forward of the center of lift, as shown in Figure 2. Because of this architecture, the lift always turns the
aircraft nose-down, so nose-up aerodynamic force whose direction is downward has to be produced on
the horizontal tail surfaces to balance the aircraft. In a short period of time, the weight of the aircraft is
assumed constant. Then the wing's lift is a fixed force independent of airspeed, while the tail's nose-up
force varies directly with the airspeed.
For a balanced aircraft in cruise phase (Figure 2), the balance equations, including force balance
and moment balance, can be expressed as follows:
tail
FGL
(2)
321 lFGlLl tail
(3)
where L, G, and Ftail represent the lift produced by wings, the gravity produced by aircraft gross
mass, and the aerodynamic force produced by horizontal tail, respectively; l1, l2, and l3 denote the
3
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SAMSE IOP Publishing
IOP Conf. Series: Materials Science and Engineering 322 (2018) 072018 doi:10.1088/1757-899X/322/7/072018
corresponding arms of L, G, and Ftail .
Figure 2. Schematic of aircraft balance.
The lift is produced by wings, with the direction perpendicular to the relative wind, and it’s
magnitude is determined by a number of parameters, including the airfoil shape, air density, air speed
and the angle of attack (AOA) of the wing. The lift be expressed as [6,7]:
(4)
where CL,
, VTAS and S are the lift coefficient, the air density, the true airspeed, and the wing
reference area, respectively.
The lift coefficient, CL, is mainly determined by the airfoil shape and the AOA. Using Eq. (2) and
(4), the lift coefficient is given by:
SV
Fmg
C
TAS
tail
L2
)(2
(5)
The drag coefficient, CD, need to be determined before calculating the drag. Under nominal
conditions, CD is expressed as:
2
21 LD CCCC
(6)
where C1 is parasitic drag coefficient (dimensionless), and C2 is induced drag coefficient
(dimensionless)
Then the drag force can be determined using the drag coefficient, similarly as the lift expression:
2
2SVC
DTASD
(7)
2.3. Fuel Consumption
Many factors, such as distance, gross weight, engine performance, cruising speed, altitude, wind, and
atmospheric environment, will affect a specific flight fuel consumption. Also, the differences in
aircraft configuration and age, as well as the differences in pilots' operation will affect the level of
aircraft fuel consumption. As our focus is the average fuel consumption level of the aircraft, the
influence of wind on the fuel consumption level is not considered in this model.
The thrust specific fuel consumption, η (kg/(min·kN)), varies depending on the engine type. For
gas-turbine engines, η is expressed as [7]:
)1(
2
1
f
TAS
fC
V
C
(8)
where Cf1 is the 1st thrust specific fuel consumption coefficient, kg/(min·kN); Cf2 is the 2nd thrust
specific fuel consumption coefficient, knots; VTAS is the true airspeed, knots.
As a product of two values, the thrust specific fuel consumption and thrust, THR, the expression of
the nominal fuel flow, fnom (kg/min), can be written as:
Gravity
Datum
l1
l2
l3
Nose-up
Force
Lift
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SAMSE IOP Publishing
IOP Conf. Series: Materials Science and Engineering 322 (2018) 072018 doi:10.1088/1757-899X/322/7/072018
HRnom Tf
(9)
With necessary corrections, the cruise fuel flow, fcr (kg/min), can be expressed as:
fcrHRcr CTf
(10)
where Cfcr is the cruise fuel flow correction factor, which varies with aircraft types and flight
parameters and provides a more accurate description of the fuel consumption. In this paper the factor
is considered as a function of the CG, air speed, grass mass, and altitude.
As thrust equals to drag (THR = D) during the normal cruise, replace the THR in Eq. (10) with D in
Eq. (7). Consequently, the equation describing cruise fuel flow becomes:
2
2SVCC
fTASDfcr
cr
(11)
3. Results and Discussion
3.1. Numerical Results
A Simulink model was developed based on the equations previously presented for predict the aircraft
fuel consumption. This model is implemented for B737-800 aircraft. Our interest is the influence of
the CG on the fuel consumption. Figure 3 shows the relationship between drag increase and CG
position. The actual variation in drag due to CG depends on airplane design, weight, altitude and Mach.
Choosing 22%MAC as the reference CG position, the curves in Figure 3 indicate that, at a given
cruise Mach, the drag increases when the value %MAC decreases due to CG position moving forward.
In addition, the greater the value W/δ is, the more obvious this trend appears. Here, W represents the
gross weight of the aircraft and δ is the ratio of flight level ambient pressure to the standard sea level
pressure.
Figure 3. Relationship between drag increase and CG position.
The numerical result is validated with the Performance Engineers Manual’s data. The fuel
consumption prediction differences relative to manual’s data are listed in Table 1, presenting the
minimal, maximal and average errors. The comparison shows that our model is accurate and reliable,
and is a valuable reference for fuel consumption modeling used in aircraft flight manager system. By
modifying the corresponding initial parameters, this model can also be used to predict the fuel
consumption of other aircraft types, considering the CG position.
W/
(kg×106)
0.32
0.30
0.27
0.25
0.23
%MAC%
Lift
Drag Increase (%)
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SAMSE IOP Publishing
IOP Conf. Series: Materials Science and Engineering 322 (2018) 072018 doi:10.1088/1757-899X/322/7/072018
Table 1. Comparison between prediction results and manual’s data.
W/δ
(kg×106)
Min Error
(%)
Max Error
(%)
Average Error
(%)
0.32
0.22
8.6
3.2
0.30
0.31
6.4
4.5
0.27
0.26
7.8
3.6
0.25
0.39
6.3
2.7
0.23
0.17
6.9
4.3
3.2. Discussion
The control of weight and balance is one of the core businesses for the airplane operating control
center. The CG parameter of an aircraft has a significant influence on the flight safety and the
operator’s economic benefits. Improper distribution of the aircraft’s useful load will reduce the flight
efficiency, resulting in higher operation cost.
When the CG moves forward, a greater down fore on the tail is required to maintain level cruising
flight. If the altitude and speed are constant, it requires a higher AOA to produce a higher total wing
lift to overcome to additional downward force on the tail. At the same time, additional drag is
produced due to the higher AOA. In turn, more engine thrust is required, which results in higher fuel
consumption.
When the CG moves aft, the required tail trim fore is less, so the lift is less, allowing for a
smaller AOA. This produces less drag, resulting in less fuel consumption.
In order to achieve the best economic benefits and fulfil the constraint of maneuverability and
stability, the operator should proper load and make the CG located near 24% MAC for the B737-800
aircraft.
4. Conclusion
In order to reduce the fuel consumption for air transport industry, investigation of optimized CG
position control for an aircraft is conducted. We develop an accurate analytical model for cruise fuel
consumption, considering the variable CG position.
Analytical equations are derived and solved. The numerical result indicates that a more aft CG
position produces less drag and, in turn, requires less fuel consumption. In addition, the fuel savings
due to CG shifting aft have a distinct advantage when the flight altitude and/or gross weight increase.
But it is important to note that, for the essential safe flight purpose, CG position must be ahead of aft
CG limit.
References
[1] Information on http://www.flysfo.com.
[2] L. Jin, Y. Cao, and D. Sun, Investigation of Potential Fuel Savings Due to Continuous-Descent
Approach, The Elements of Style, Journal of Aircraft, 2013, 50 (3) :807-816.
[3] B.D. Dancila, R. Botez, and D. Labour, Fuel burn prediction algorithm for cruise, constant speed
and level flight segments, Aeronautical Journal, 2013, 117 (1191) :491-504.
[4] YANG Zhenbo, WANG Yu, LIU Yunfei, and CHAI Xiao, The NextGen aircraft trajectory
optimization based on economy and environment impact, Flight Dynamics, 2017, 35. (in
Chinese).
[5] U.S. Department of Transportation, Federal Aviation Administration (FAA), Aircraft Weight and
Balance Handbook, FAA-H-8083-1, FAA, Washington, DC, 2016.
[6] U.S. Department of Transportation, Federal Aviation Administration (FAA), Pilot’s Handbook of
Aeronautical Knowledge, FAA-H-8083-25B, FAA, Washington, DC, 2016.
[7] EUROCONTPOL, USER MANUAL FOR THE BASE OF Aircraft DATA, European
Organisation for the Safety of Air Navigation, [online database]
http://www.eurocontrol.int/sites/default/files/library/007_BADA_User_Manual.pdf
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