Available via license: CC BY 3.0

Content may be subject to copyright.

IOP Conference Series: Materials Science and Engineering

PAPER • OPEN ACCESS

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

View the article online for updates and enhancements.

This content was downloaded from IP address 181.214.101.76 on 29/03/2018 at 13:59

1

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution

of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Published under licence by IOP Publishing Ltd

1234567890‘’“”

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

1234567890‘’“”

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 aircraft’s 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%. Obviously，the 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

1234567890‘’“”

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]:

2

2SVC

LTASL

(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

4

1234567890‘’“”

SAMSE IOP Publishing

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 (%)

5

1234567890‘’“”

SAMSE IOP Publishing

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