Performance Database Creation for Cessna Citation X

Performance Database Creation for Cessna Citation X Aircraft in Climb Regime using an Aero-Propulsive Model developed from Flight Tests

Georges Ghazi Ph.D Student ETS - Laboratory of Applied Research in Active Controls, Avionics and AeroServoElasticity Montreal, Quebec, Canada

Ruxandra Mihaela Botez Full Professor ETS - Laboratory of Applied Research in Active Controls, Avionics and AeroServoElasticity Montreal, Quebec, Canada

Magdalena Tudor M.A.Sc. Student ETS - Laboratory of Applied Research in Active Controls, Avionics and AeroServoElasticity Montreal, Quebec, Canada

ABSTRACT During aircraft development, several mathematical models are created from our knowledge of fundamental physical laws. Those models are used to gain our knowledge in order to take decisions in all aircraft development phases. In this paper, a methodology to design an aero-propulsive model for the well-known business fastest Cessna Citation X in climb regime from flight test to model identification and validation is presented. The aircraft‟s model was built by identifying a general aircraft mathematical model in climbing flight. A professional level D flight simulator was used as a flight test aircraft and a total of 70 flight tests were performed at different flight points within the aircraft flight envelope. The obtained aero-propulsive model was next interpolated to provide a Performance DataBase model within the whole aircraft flight envelope. Results showed that the proposed methodology gives an excellent estimation of the aircraft performance with a success rate of 100% for both identification and validation process.

ATAG EOM FMS IAS ISA PDB

̇

NOTATION

INTRODUCTION 

= = = = = =

Air Transport Action Group Equation of Motion Flight Management System Indicated Airspeed International Standard Atmosphere Performance Database

= = = = = = = = = = = = = = = =

Acceleration factor Aircraft aspect ratio Drag and lift aerodynamic coefficients Oswald efficiency factor Fuel burn Aircraft gross weight Aircraft altitude Horizontal distance traveled Dynamic pressure Aircraft reference wing area Engine thrust force Specific fuel consumption coefficient Aircraft true airspeed Aircraft weight Engine fuel flow Aircraft center of gravity position

In 2014, around three billion passengers boarded an aircraft somewhere on earth (Ref. 1). On one hand, such a global mobility is obviously a very significant benefit on the development of the global economy and the increasingly multi-cultural society (Ref 2). However, on the other hand, global mobility has also a direct impact on the environmental degradation. According to the Air Transport Action Group (ATAG), in Ref. 3, the 2012 airline operations produced around 2% of carbon dioxide (CO2) global emissions. Although this percentage is relatively low compared to others transports, the aerospace industry is conscious of aviation‟s environmental impact and has committed to reduce by 2050 the net carbon footprint by 50% with respect to the global emissions recorded in 2005 (Ref. 1). Recently, several studies based on flight tests have demonstrated that a 20% reduction in airplane drag leads to an 18% reduction in fuel consumption (Ref 4). Based on these observations, several manufacturers such as Bombardier, Airbus or Boeing have developed great interest in the development and application of winglets wingtip devices on existing commercial airplanes (Ref. 5, 6). According to Boeing, this improvement led to increase the

= Aircraft climb path angle = ISA deviation = Time to climb

1

new Boeing 737 MAX fuel efficiency by 1.8%. More recently, a high interest has also appeared for the development of morphing wing solutions. As shown in Refs. 7-9, morphing wing techniques can be used to improve the aerodynamic characteristics of an airfoil by actively modifying the aircraft wing shape. The main advantage of this technique is the capability of finding an optimal (or suboptimal) shape for the wing for specific flight phases. Improving engine efficiency is also an ongoing effort of the engine manufacturer. For example, the A320 NEO has been equipped with two latest-generation engines PW1100G-JM and LEAP-1A. According to Airbus, these improvements result in 20% fuel saving per seat with respect to the current engine option aircraft (Ref. 10). Another important way to reduce CO2 emissions is the use of biofuel. Recently, flight tests performed with several aircrafts have shown that biofuel is a very promising alternative (Ref. 11). All these examples highlight the efforts provided by the aerospace industry to reduce the carbon dioxide emission footprint. However, although these techniques are promising, they are unfortunately very difficult to implement on aircraft that are currently in service. It is therefore necessary to find other alternatives. This is the reason why during these last years, the aerospace industry and several researchers have focused on alternative solutions such as aircraft trajectories optimization (Refs. 12-19). Accordingly to Jensen et al. (Refs. 20, 21), most of aircraft in the United States do not fly at their optimal trajectories in terms of altitudes and speeds. Therefore, optimizing the vertical profile could be a very good alternative to reduce fuel consumption as shown in various studies (Refs. 15, 16, 18, 19). Trajectory optimization in vertical profile is the pivotal function of the Flight Management System (FMS) (Ref. 22). The FMS is an airborne device that manages each flight and computes the optimal profiles aimed at minimizing the flight costs defined in terms of flight time and total fuel burned. To predict the optimal trajectory, the FMS needs an aircraft‟s mathematical model in order to estimate the aircraft flight cost (Refs. 23-26). The most common way to describe the behavior of an aircraft is to use a set of nonlinear equations called Equations of Motion (EoM) as proposed by Ghazi in Ref. 27 or by Vincent et al. in Ref. 28. However, as the FMS is a device with limited processing capacity, it cannot support or emulate a model based on EoM. For this reason, another type of model, which is more adapted to the FMS‟ architecture, is preferable. Sibin et al. in Ref. 29 described a methodology to build an aircraft performance model for FMS using data of a flight simulator prototype. The obtained model provided good performance data such as aerodynamic forces or engine thrust, and can be therefore used to describe the aircraft behavior within its flight envelope. However, as some aircraft manufacturers are conservative to provide complete

aero-propulsive data, having access to the aircraft data required to create such a model can be very difficult. Murrieta et al. in Ref. 30 presented a methodology to create an aircraft Performance Database (PDB) using a Citation X Level D flight simulator. Based on several flight tests, the aircraft fuel flow was sampled during the cruise phase for different constant altitudes and speeds. The aircraft mass was also considered constant. The results were next prepared and formatted into lookup table in order to be used by an in-house algorithm that can predict the fuel burn during cruise. However, the methodology proposed by Murrieta et al. did not provide enough information about the aircraft aerodynamic parameters, which are usually necessary for aircraft performance analysis or for flight control system design purpose. Gong and Chan in Ref. 31 showed a technique to obtain an aero-propulsive model from available time-to-climb data that can be found in aircraft flight manuals. The model was tuned using a Boeing 737-400 for which time-to-climb and aero-propulsive data were known. In this paper, the engine thrust force was estimated using an existing engine model available for their research on the Boeing 737-400. The obtained model was next adapted by scaling the engine and applied to a Learjet 60 to predict the aircraft trajectories. Comparison between the predicted trajectories and radar track revealed very good results. However, the proposed methodology did not take into account the engine fuel flow (or the fuel burn). This model was therefore not adequate enough to solve problems related to trajectory optimization. Moreover, engine models are not always available from the literature, and the obtaining of such models from engine manufacturers can be really complicated. Similarly, Baklacioglu and Cavcar in Ref. 32 used a genetic algorithm to obtain a aero-propulsive model from the flight manual data of a transport aircraft. Contrary to Gong and Chan, the propulsive model used in their studies was developed based on a semi-empirical equation. A methodology was performed to identify the engine model coefficients that fit well the engine data of a Pratt & Whitney JT9D-7A turbofan for different altitudes and Mach numbers. According to the authors, the consideration of the thrust dependency with respect to altitude and Mach number in the propulsive model was observed to be a more practical approach than the other approaches. Comparisons between predicted time to climb with the aero-propulsive model and the flight manual data have shown good results. The main objective of this paper is to provide an aeropropulsive model of the Cessna Citation X that would be very efficient for the research needs of the Laboratory of Applied Research in Active Control, Avionics and AeroServo-Elasticity (LARCASE) team. Such a model could be useful to support the researchers to validate their algorithms for trajectory optimization (Refs. 24-26) and/or flight control system (Refs. 33-36). The aero-propulsive model was 2

developed using flight tests performed on a professional Cessna Citation X level D aircraft research flight simulator designed and manufactured by CAE Inc. According to the Federal Aviation Administration (FAA, AC 120-40B), the level D is the highest certification level for the flight dynamics modeling.

Atmosphere) temperature deviation, while the outputs of interest are mainly the fuel burn and the horizontal distance travelled. Therefore, the PDB can be represented in a mathematical form by the following equation: [

]

(

)

(1)

where is the fuel burn, is the horizontal distance, is the gross weight, is the center of gravity position, is the indicated airspeed, is the altitude, is the temperature deviation and is a mathematical representation of the PDB. Problem Statement and Model Restrictions This paper is intended to use an aircraft aero-propulsive model of the Cessna Citation X in order to obtain a PDB in climb regime. Therefore, the main objective of this paper can be summarized as follows: Figure 1. Level D Citation X Flight Simulator This paper is organized as follows. The first section of this paper describes the PDBs structure and the problem statement. The second section details the methodology used to build the aero-propulsive model. The third section presents the results of a case study in which the methodology was applied to predict the aircraft performance of the Cessna Citation X during climb. Finally, the paper ends with conclusions and future work remarks.

THE PERFORMANCE DATABASE AND PROBLEM STATEMENT This section first introduces a brief description of the performance database. Then, based on this description, the problem statement and the objectives, along with the assumptions considered in this paper are presented in details. Performance Data Base Definition Basically, the Performance Data Base (PDB) is a simplified numerical model of the aircraft which includes precise information on the main phases of the flight. As illustrated in Figure 2, the PDB can be compared to a black box with multiple inputs and outputs.

Figure 2. Aircraft PDB Inputs and Outputs The choice of the inputs and outputs depends on the study of interest. For example, in trajectory optimization problems, the main parameters that affect the aircraft behavior are the gross weight, the center of gravity position, the altitude, the speed and the ISA (International Standard

„„Identify an aero-propulsive model from flight tests and build a PDB to predict the Cessna Citation X performance in the climb regime.‟‟ To reach this goal, the study has been divided in two parts. Firstly, an aero-propulsive model of the Cessna Citation X has been identified from flight tests using system identification methods. Secondly, once the aero-propulsive model obtained, a PDB for the Cessna Citation X in climb regime was built by reformatting the aero-propulsive model data into a lookup table. Moreover, to simplify the study and reduce the number of flight tests, some restrictions have been considered. These restrictions are listed as follows: i. The aircraft flies in a wind-free environment, ii. The temperature is standard (no ISA deviation), iii. The aircraft engines are operational, iv. The aircraft climbs at a constant IAS. After the definition of objectives and limitations, the next section presents the methodology used to identify a model from flight tests.

SYSTEM IDENTIFICATION METHOD AND FLIGHT TEST DESCRIPTION System identification methods have been widely used by the aerospace industry (Refs. 37, 38). Since the 60s, improvements in aircraft parameters estimation technique have led to a better understand of flight dynamics principles. During recent years, new techniques of system identification have been highly applied on many different aircraft (Refs 39-46). System identification can be defined according to Zadeh as in Ref. 47: “System identification is the determination, on the basis of observation of input and output, of a system

3

within a specified class of system to which the system under test is equivalent” In other words, system identification includes the model structure definition based on mathematical equations and the estimation of parameters defining the model. A more schematically representation of system identification concept is given in Figure 3.

Figure 4. Flight Test Procedure Finally, the data recorded during the climb were exported from the flight simulator in the form of .csv files, so they can be used in Matlab® and formatted according to the structure that can be found in any aircraft flight manual as shown in Table 2. Table 2. Sample Climb Data GW: 25,000 lbs || Xcg: 17% || ΔISA = 0

Figure 3. System Identification Principles As illustrated in Figure 3, the identification process is divided in three steps. In a first step, several flight tests have to be performed in order to sample the inputs and outputs required to describe the aircraft performance. Then, in a second step, using a set of equations, a mathematical model of the system of interest (i.e. the aircraft) has to be defined. Finally, a procedure that automatically tunes the parameters defining the model must be developed. Flight Tests Procedure Description To estimate the aircraft performance in climbing flight, 70 flight tests were performed with the flight simulator for different airplane configurations in speeds, altitudes, gross weights and center of gravity positions. Table 1 gives the limits of the flight tests envelope considered in this paper. Table 1. Flight Tests Envelope Limits Parameter Altitude Speed (IAS) Gross Weight Xcg

Min 0 ft 140 kts 25,000 lbs 17%

Fuel Burn (lbs)

Horizontal Distance (nm)

1,000 2,000 3,000 . . 33,000 34,000 35,000

0 25.55 50.76 . . 722.44 743.80 765.42

0 2.29 4.61 . . 96.49 100.27 104.12

It should be noted that all the 70 flight tests were not only used for the identification process. Indeed, flight tests were divided into two categories: identification and validation. The first category aimed to identify the aeropropulsive model, while the second category was used to validate the obtained model. However, to minimize the number of flight tests, the choice of the number of flight tests for the identification process should be done carefully. In this paper, the identification flight tests were selected according to the two following assumptions: i. The influence of the speed and/or the gross weight can be modeled by a quadratic function, ii. The center of gravity position does not affect the aircraft performance in terms of fuel burn and horizontal distance travelled.

Max 35,000 ft 350 kts 33,000 lbs 32%

Each flight test was performed according to the procedure described in Figure 4. As it can be seen in Figure 4, the procedure consists in take-off with the aircraft until 1,000 ft. At this altitude, a level flight was performed allowing the test pilot to trim the aircraft (flaps and landing gears retracted) and maintain it at a certain altitude and airspeed. Once the gross weight was closed to the desired value for the flight test, a climb was performed and the airspeed was maintained constant by controlling the throttle and the aircraft pitch angle.

Altitude (ft)

These assumptions were elaborated from many observations made while performing the flight tests. Thus, only 3 speed configurations (140 kts, 280 kts and 350 kts) and 3 gross weight configurations (25 Klbs, 29 Klbs and 33 Klbs) were selected for the identification process (hence, a total of 9 flights tests). The remaining 61 flight tests were used for the validation process. The structure of the flight tests being defined, the next section presents the set of equations that was used to solve the inverse problem associated to this study. 4

It is known that:

Aircraft Aero-Propulsive Mathematical Model By definition, an aero-propulsive model consists of two submodels. The first sub-model is used to compute the aerodynamic lift and drag forces, while the other sub-model is used to predict the propulsive thrust force and the engine performance. To obtain an aero-propulsive model such as the one in this paper, some mathematical developments based on the general aircraft equations of motion must be done. Aircraft Equations of Motion in Climbing Flight According to Refs. 48-52, an aircraft can be considered as a rigid body submitted to four main forces – lift, drag, thrust and weight – which can be seen in Figure 5,

( )

(6)

By replacing Eq. (6) into Eq. (5), the following Eq. (7) is obtained: (

̇

)

(7)

Finally, from Eq. (7), the rate of climb ̇ can be expressed as follows: ( ̇ where

)

(

(8)

)

is the acceleration factor defined by: (9)

Figure 5. Aircraft in Climbing Flight ) are the inertial and stability axes where ( ) and ( respectively, is the engine thrust force, is the lift force, is the drag force, is the aircraft gross weight, is the acceleration due to gravity, is the aircraft true airspeed and is the aircraft climb path angle.

The Eq. (8) is fundamental because it relates climb performance to aero-propulsive forces. According to Eq. (8), if climb performance (i.e. rate of climb) is known for a specific aircraft, therefore the difference between the two aero-propulsive forces L and D can be determined. Conversely, if the difference between the drag and the thrust is known, therefore the climbing performance can be estimated. In others words, using the sampled climb data in Table 2 for different aircraft configurations, a model for the thrust and drag force can be estimated (i.e. identified). Then, using this same model, the aircraft performance can then be predicted within the aircraft flight envelope.

Based on the Newton‟s second law, namely

Lift L and Drag D Forces Estimation (2)

where is net force applied to the aircraft and is the aircraft acceleration relative to the inertial frame, the kinetic equations of motion for an aircraft in climbing flight can be written in the stability axes as follows: [ [

( )

]

( )

]

(4)

Equation (3) is rearranged as follows: [

]

(10) (11)

(3)

Equations (3) and (4) have the advantage to describe the complete aircraft longitudinal motion. However, solving this set of equations may be really difficult to be done in the estimation algorithm. Moreover, as the study presented is this paper is only focused on the climb performance, the rate of climb should appear in the system. For this reason, the system defined by Eqs. (3) and (4) must be modified.

( )

According to several references in aircraft flight mechanics (Refs. 48-52), the two components of the aerodynamic forces L and D can be expressed with non-dimensional coefficients CL and CD such as:

where is the dynamic pressure and reference wing area.

is the

The lift force L can be easily obtained from Eq. (4) as follows: ( )

[

]

(12)

Then, by combining Eq. (11) and Eq. (12), the lift coefficient CL can be determined with the next equation: (

(5) 5

( )

[

] )

(13)

Contrary to the lift force, the drag force cannot be estimated directly from Eq. (3) because of the thrust, which is also an unknown variable of the problem. Another way to estimate the drag is to use the drag polar equation of a cambered wing (Refs. 49, 51, 52), which states that:

Parameter Estimation Algorithm The aero-propulsive model is derived by determining a combination of thrust and drag forces that best estimates the rate of climb. In order to do this estimation, the aircraft altitude was divided into N-1 sub-segments separated by ft as shown in Figure 6¸

(14)

√

where is the minimum drag coefficient, is the aircraft aspect ratio, is the Oswald efficiency factor and is the aircraft Mach number. It is important to mention that Eq. (14) is normally applied to a wing only. However, assuming that the lift and drag forces are mainly generated by the aircraft wing, this equation can be extended to the entire aircraft. It should be also noted that there are no theoretical methods for estimating the minimum drag coefficient and the Oswald efficiency factor. Several authors such as Raymer in Ref. 53 or Brandt in Ref. 54, proposed many empirical equations to estimate these two parameters from basic aircraft geometrical parameters. However, although these methods are very helpful in preliminary design phase, they usually have to be optimized to better estimate the aircraft performance during the final phase of the aircraft design. In this paper, the Oswald efficiency factor was estimated from the equation proposed by Raymer in Ref. 53: (

)[

(

)]

Figure 6. Discretized Aircraft Trajectory ⟦ ⟧ are the altitude and the where and , horizontal distance traveled corresponding to the position . For each sub-segment, the climb path angle, the rate of climb, the time to climb and the engine fuel flow were computed using Eqs. (19) to (22):

(15) (

where is aircraft wing leading edge swept angle, and the minimum drag coefficient was assumed to be within the range of [0.01, 0.05] with a nominal value of 0.03 (Ref. 54). ̇

̅

)

(19)

( )

(20)

̇

(21)

Engine Thrust and Specific Fuel Consumption The last part of the aero-propulsive model concerns the engine performance. Using the estimation of the drag force obtained in the previous section, the thrust force can be therefore determined from Eq. (3) such as: [

( )

]

(16)

Finally, the engine specific fuel consumption coefficient can be estimated from Eq. (17), ̇ where

̇ is the engine fuel flow defined by: ̇

and

(17)

(18)

is the fuel burn.

These last equations conclude the aircraft aeropropulsive mathematical model. In the next section, the estimation algorithm used in this paper to identify the parameters of the aero-propulsive model is presented.

̇

(22)

where ̅ is the average true airspeed along a sub-segment, is the time to climb from to and ̇ is the average engine fuel flow along the sub-segment. In the same way, the acceleration factor and the Mach number were also determined along each sub-segment. As all these values are computed directly using the sampled data in Table 2, they are assumed to represent the real state of the aircraft. In parallel, using a first initialization for the minimum drag coefficient and the Oswald efficiency factor , the drag and the thrust forces were calculated from Eqs. (10), (14) and (16). These results led to the finding of a first estimation of the rate of climb using Eq. (8). A minimization routine based on the Nelder-Mead algorithm (Ref. 55) was next used to adjust the minimum drag coefficient, the Oswald efficiency factor and the thrust in order to minimize the error between the estimated rate of climb obtained with Eq. (8) and the rate of climb computed with Eq. (20). Then, 6

the engine specific fuel consumption coefficient was computed using the optimal thrust and rate of climb resulting from the minimization, and Eqs. (17) and (18) such as: ̇

(21)

where is the difference of fuel burn between two altitudes of a sub-segment.

The procedure shown in Figure 7 was applied to all the 9 flight tests identification presented in section Flight Tests Procedure Description. For each flight test, the difference between the thrust and the drag forces TD, the thrust force T, and the thrust specific fuel consumption Tsfc coefficient resulting from the minimization routine were stored and formatted into different 3-D lookup tables as shown in Figure 8,

The complete procedure of the estimation algorithm applied for one flight test (i.e for one aircraft configuration) is shown in Figure 7. Start

Figure 8. 3D Lookup Table Representation

Select an aircraft configuration.

or in a more mathematically form as follows: [

] [ ] [ ]

Select the first sub-segment: i=1

(

)

(

) (

)

(22)

PDB Creation Determine the climb path angle, the rate of climb, the time to climb and the fuel flow using Eqs. (19) to (22)

The last phase of this study concerns the PDB creation using the aero-propulsive model obtained from the estimation algorithm presented in the previous section. Accordingly to Figure 2 and Eq. (1), two parameters must be computed to create the PDB for a specific aircraft: the fuel burn and the horizontal distance traveled.

Initialize aerodynamic paramaters: minimum drag coefficient and Oswald efficiency factor Eq. (15)

Evaluate aircraft models : T and D using Eqs. (10) to (14) Calculate aircraft rate of climb using Eq. (8)

Adjust parameters with minimization

i=i+1

Since the three aero-propulsive parameters in Eq. (22) are given for discrete values of the gross weight, airspeed and altitude, a 3D linear interpolation was performed for each parameter in order to predict their value within the Cessna Citation X flight envelope. After their interpolation, these parameters were used to estimate the aircraft climbing performance for each sub-segment by the following set of equations obtained mainly from Eqs. (8), (17), and (20):

Compute the rate of climb error

̇ No

Is error < 10-3 ?

Is i = N ?

) ̇ ( ) ̅

( ) ̅̅̅̅ { ̇

Yes

Store the results into lookup tables

(

̅

(23)

( )

where ̅̅̅̅ is the average ground speed for a sub-segment ⟦ ⟧. Finally, the defined by the altitudes and , aircraft horizontal distance HD traveled and the fuel burn FB were determined using an Euler integration method as follows:

Yes

̅̅̅̅

(24)

̇

(25)

End

Figure 7. Parameter Estimation Algorithm

where is the time to climb between two consecutive altitudes as expressed in Eq. (21). 7

RESULTS AND DISCUSSIONS To validate the methodology, 70 flight tests were performed using the level D Cessna Citation X flight simulator. As mentioned in the section Flight Tests Procedure Description, only 9 of the 70 flight tests were selected for the identification process. The remaining 61 flight tests were used to validate the obtained model within the Cessna Citation X flight envelope.

In a general way, same results can be observed for the fuel burn FB estimation. Indeed, as shown in Figure 11(b), the maximum relative error between the experimental fuel burn and the predicted fuel burn is always less than 5%.

For each flight test, the horizontal distance traveled and the fuel burn were computed from the flight simulator measurements. In parallel, the same flight tests were evaluated using the PDB created from the aero-propulsive model. The fuel burn and the horizontal distance traveled were next compared in order to conclude about the accuracy of the PDB. As there are no specific criteria in the literature to validate a PDB model, a maximum deviation of 5% was considered in this paper. Thus, if the maximum error between the two models was less than 5%, then the flight test was considered as success. To illustrate the way in which each flight test was validated against experimental data, an example of three successful cases is given in Figures 10 and 11. (a) − Altitude VS Horizontal Distance 35 GW = 25,000 lb Xcg = 32% DISA = 0°

Altitude [1000 ft]

30 25

140 kts

200 kts

Figure 11. Estimated Fuel Burn FB

260 kts

These analyses were repeated for all the 70 flight tests. The success ratio obtained and the numbers of flight test realized for both identification and validation processes are summarized in Table 3.

20 15 10 5 0

Experimental data Simulated data 0

10

20

30

40

50

60

70

80

90

Table 3. Success ratio and number of valid flight tests

100

Horizontal distance [nm] (b) − Distance Error VS Altitude 0.35 140 kts 200 kts 260 kts

Relative Error [%]

0.3

Flight Test Category

Number of flight test

Identification

9 (13%)

0.25 0.2 0.15 0.1

Validation

0.05 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Altitude [1000 ft]

Figure 10. Estimated Horizontal Distance HD Figure 10(a) represents the aircraft trajectory in the longitudinal plan, and Figure 10(b) exposes the relative error for each trajectory. As it can be seen, the error for the horizontal distance HD is smaller than 0.35%, which means that the aircraft horizontal trajectory is well predicted by the PDB. The flight tests were performed for three speeds: 140, 200 and 260 knots. Is should be also noted that the error decreases considerably with the altitude. The reason for this decrease is due to the computation of the error with respect to the total distance traveled. This means that as longer the aircraft travels, the more accurate the model is.

61 (87%)

Performance Horizontal Distance (HD) Fuel Burn (FB) Horizontal Distance (HD) Fuel Burn (FB)

Success ratio 100% 100% 100% 100%

As it can be seen, the methodology gives an excellent estimation of the aircraft performance. Indeed, all the criteria imposed in this paper are satisfied with a success rate of 100% for each flight test category (identification and validation). This means that the aero-propulsive model and the interpolation methods used to create the PDB are sufficiently accurate and could be further adapted for their use on other aircraft.

CONCLUSION AND FUTURE WORKS In this paper, an aero-propulsive model and a performance database (PDB) for the Cessna Citation X in climbing flight were created from flight tests. A total of 70 flight tests were 8

performed with a professional level D flight simulator designed and manufactured by CAE Inc., where the level D is the highest certification level for the flight dynamics modeling. A complete mathematical model of the aircraft in climbing flight was presented, and an estimation algorithm was developed to identify the different parameters of the model. The parameters of the identified aero-propulsive model were next formatted into 3D lookup tables in order to allow their interpolation within the whole Cessna Citation X flight envelope. Finally, a PDB was created and several comparisons between the flight tests data and the predictions obtained with the PDB were performed. Results showed that the proposed methodology gave an excellent estimation of the aircraft performance with a success rate of 100% for both identification and validation process. Thus, it has been concluded that the aero-propulsive model and the PDB created in this paper were experimentally validated. In order to improve the results and the methodology presented in this paper, future studies will focus on the development of different PDBs for the cruise, descent, acceleration and deceleration phases to allow a complete flight analysis of the aircraft.

ACKNOWLEDGMENTS This work was performed at the Laboratory of Applied Research in Active Controls, Avionics and AeroServoElasticity research (LARCASE). The Aircraft Research Flight Simulator was obtained by Dr Ruxandra Botez, Full Professor, thanks to the research grants that were approved by the Canadian Foundation of Innovation (CFI) and Ministère du Développement Économique, de l'Innovation et de l'Exportation (MDEIE) and the contribution of CAE Inc. Thanks are dues to CAE Inc. team and its leader Mr Ken Dustin, and to Mr. Oscar Carranza Moyao for their support in the development of the Aircraft Research Flight Simulator at the LARCASE laboratory. Special thanks are also dues to Mrs Odette Lacasse at ETS for her support in the research proposal. Thanks are dues also to the CMC ElectronicsEsterline team, more specifically to Mr Reza Neshat for his interest in this subject.

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