D3.2 Aircraft aspects of the Endless Runway

Transcription

1 D3.2 Aircraft aspects of the Endless Runway This document details the studies that have been made in order to identify the most promising runway cross-section and to design a future aircraft concept tailored for operations on a circular runway. Project Number Document Identification Status Final Version 1. Date of Issue Authors Schmollgruber P.; De Giuseppe A.; Dupeyrat M.; Organisation Classification ONERA

2 Page 2/89 Document Change Log Versio Author Date Affected Sections Description of Change.1 P. Schmollgruber 7/2/213 All Initiation of the document structure.2 P. Schmollgruber A. De Giuseppe 24/8/213 All Methodology and results of the various simulations described..3 M. Dupeyrat 26/8/213 All Review and addition of the chapters regarding the ground clearance of the aircraft elements and runway volume calculation..4 S. Aubry All Review.5 J. Hermetz All Review 1. P. Schmollgruber 3/9/213 All Release version Document Distribution Organisation EC NLR DLR ONERA INTA ILOT Name Ivan Konaktchiev Henk Hesselink, René Verbeek, Carl Welman, Joyce Nibourg Steffen Loth, Franz Knabe, Sandro Lorenz, Paul Weitz Maud Dupeyrat, Sébastien Aubry, Peter Schmollgruber Francisco Mugnoz Sanz, María Vega Ramírez, Albert Remiro Marián Jez Review and Approval of the Document Organisation Responsible for Review Reference of comment documents Date All Organisation Responsible for Approval Name of person approving the document Date NLR H. Hesselink The Endless Runway

3 Page 3/89 Table of Contents Document Change Log 2 Document Distribution 2 Review and Approval of the Document Abbreviations 5 Introduction 7 Simulation environment Simulation environment selection General use of Flight Gear in WP3 1 Feasibility of a conventional configuration Approach Reference aircraft selection Definition of the B747-1 model Aircraft 3D model Aircraft characteristics Engine model Validation of the B747-1 model Take-off performance Calibration of the landing performance Parametric studies Runway shape definition Runway volume calculation Take-off simulations Performance analysis Definition of the take-off and landing distances Linear speed distribution Square root speed distribution Square speed distribution Assessment Square root speed vs. linear speed distribution for a reference width of 14 meters Selection of the reference width Landings B747-1 ground clearance analysis 4 The Endless Runway

4 Page 4/ Conclusions on exchange parameters 41 New aircraft tailored for the Endless Runway Approach ERAC Conceptual Design Mission definition Preliminary requirement analysis ERAC Concepts exploration ERAC sizing Sizing process Engine selection ERAC geometry ERAC weight breakdown Final ERAC sketch ERAC ground clearance analysis ERAC model for Flight Gear Inertial properties Refined aerodynamics study Lift-to-drag ratio verification Complementary aerodynamics coefficients for Flight Gear D model ERAC simulations ERAC performance analysis Take-off Landing Requirements review Conclusion on exchange parameters 72 Conclusion Aircraft aspects for the Endless Runway Perspective References 77 Appendix A Key parameters of the Endless Runway project 78 Appendix B Detail of the calculations 79 Appendix B.1 Calculation of the various runway profiles equations 79 Appendix B.2 Calculation of the runway volume for the linear speed evolution runway profile 81 Appendix B.3 Ground clearance of aircraft critical elements with the Endless Runway 82 The Endless Runway

5 Page 5/89 Abbreviations Acronym α δ a δ e δ r ATM CD ERAC CD i CD Cl CL CL Cm Cn CY CL Flap DLR EIS ER ERAC FAR ft ILOT INTA Ixx ISA kts Definition Angle of attack Aileron deflection Elevator deflection Rudder deflection Air Traffic Management Total drag coefficient of ERAC Induced Drag Coefficient Zero-lift drag Coefficient Rolling moment Coefficient Lift Coefficient Lift Coefficient at zero angle of attack Pitching moment Coefficient Yawing moment Coefficient Side-force Coefficient Changes in Lift Coefficient due to Flap Deutsches Zentrum für Luft- und Raumfahrt Entry Into Service Endless Runway Endless Runway Aircraft Concept Federal Aviation Regulation feet Institute of Aviation Instituto Nacional de Técnica Aeroespacial Moment of Inertia around the X axis International Standard Atmosphere Knots The Endless Runway

6 Page 6/89 LDL m MIT MLW MTOW NLR OEI Onera p q r s T/W TSFC V LO V R W/S Landing Length meter Massachusetts Institute of Technology Maximum Landing Weight Maximum Take-Off Weight National Aerospace Laboratory of the Netherlands One Engine Inoperative The French Aerospace Lab Roll rate Pitch rate Yaw rate second Thrust-to-Weight ratio Thrust Specific Fuel Consumption Lift-off speed Rotation speed Wing loading [kg/m²] The Endless Runway

7 Page 7/89 1. Introduction According to various publications proposing vision statements for air transportation [1][2], the global traffic could reach 16 billion passengers annually in 25 leading thus to congestion of infrastructure. It is then mandatory for research institutes today to explore innovative airport concepts that present a certain discontinuity in order to achieve a significant step forwards in terms of capacity performance. Today s solutions that have been optimized for decades have indeed only small margins for improvement left. With this objective, the Endless Runway consortium (NLR, DLR, ILOT, INTA, Onera) proposes to investigate a radical solution for airport layouts based on a circular banked runway. The key asset is to offer the possibility to take-off and land in any direction from any point on the circle. In addition, since the airport facilities would be located inside the circle, the expensive land covered by the entire airport would be reduced. Such a global concept not only requires to redesign the complete airport layout but also to analyze in details the air traffic management (ATM) aspects. However, regarding operations on this Endless Runway, it must be noted that an aircraft will move to the outside of the circle during the take-off acceleration because of the centrifugal force. To limit its effects on the aircraft structure and passengers, the runway will be banked. Therefore, at lift-off, the aircraft will be operating in a specific position on the runway with a certain bank angle at a given height. For landing, the aircraft will touchdown in a specific point, with a given speed and a specific bank angle. As the velocity decreases, the airplane will move towards the center of the runway where the bank angle tends to be null. These unconventional maneuvers for take-off and landing require to complete a study (WP3) focusing on aircraft design aspects that will use the Endless Runway. Preliminary discussions within the consortium identified five decisive requirements that shall be achieved during the investigations related to the aircraft aspects of the Endless Runway: To indicate whether it is possible for a 21 civil transport aircraft to take-off and land on a circular runway; To investigate the required changes on a conventional aircraft to use the Endless Runway concept; To calculate the take-off and landing performance of the aircraft; To identify the best suited new configuration for taking-off and landing from a circular runway; To compare the take-off and landing performances of this unconventional aircraft to the ones of a standard aircraft. The completed work will allow the determination of the exchanges parameters (Appendix A) that are necessary for an assessment of the Endless Runway from an airport and ATM point of view. Regarding the level of details needed to take-off and land from an Endless Runway, it is necessary to set-up a complete design and simulation environment. Thus, the first technical section of this report presents such an environment that is based on the free and open-source program Flight Gear. Subsequently, the document details all the work that has been performed to assess the feasibility to take-off and land from a circular runway with an existing aircraft (task T3.1 in the project). Additional information is provided in order to explain the rationale behind the selection of the runway cross section as well as its reference width. Finally, this report details the activities that have been performed in order to design and simulate in Flight Gear an innovative aircraft concept that is tailored to the Endless Runway (task T3.2 in the project). The Endless Runway

8 Page 8/89 2. Simulation environment When looking at the decisive requirements as stated in the introduction, emphasis is given to the performance calculation of today s and tomorrow s aircraft on a circular runway. In aircraft design, the general approach to determine the take-off and landing performance is to make a two-dimension analysis of the aircraft considered as a point mass where different forces are applied: lift, drag, thrust, ground reactions. An example of this approach well suited for classical operations on a flat runway is illustrated in the following figure. Figure 1 : Classical performance analysis for take-off [3] By solving the equations along the X axis, it is then possible to find an analytical solution corresponding to the take-off field length. The method is quick, reliable and it allows taking into account a certain slope of the runway as well as a wind component. However, in the case of the Endless Runway concept, the runway is asymmetric and curved. The take-off and landing phases must then be analyzed in three-dimensions and a numerical method will be required to solve the equations of motion. Another decisive requirement for WP3 stresses the necessity to be able to assess the capability of a current aircraft to take off and land on a circular runway. In this case, a full analysis of the aircraft motion is required and the system to be solved takes into account the three degrees of freedom along (forces) and the three degrees of freedom around (moments) the reference axes and the various associated variables. The figure here below illustrates the different variables to be considered. Figure 2 : Variables to be considered to assess the aircraft motion (ground reactions are not shown) [4] The Endless Runway

9 Page 9/89 The two previous points indicate that in order to analyze the aircraft behavior during take-off and landing and to calculate its take-off and landing performance on a banked runway, a 6 degrees-of-freedom (DOF) simulator will be mandatory. There are several 6DOF simulators available (commercial and free) and all aeronautical research centers developed their own propreterian codes over the years. However, the simulator to be used in the Endless Runway project for WP3 has to meet a number of specific requirements: 1. It must be flexible enough to enable take-offs and landings from circular runways with different bank angles; 2. It must be flexible enough to enable simulations with new aircraft concepts; 3. It must be shared by the different partners; 4. It must be open to modifications by all partners; 5. It must be as reliable as possible. 2.1 Simulation environment selection With the basic requirements of the simulator fixed, a review of the possible options has been carried out. The problem with most of commercial software is their limited flexibility. It is indeed difficult to implement in the simulation a new aircraft with its characteristics as well as a new type of three dimensional runway. However, among these products, X-Plane [5] enables users to build airplanes through the program Plane-maker and it offers also the possibility to design sceneries. Regarding free software, partners all agree that Flight Gear [6] is the key reference in the domain of 6DOF simulations. An important asset for Flight Gear is its large community of contributors since it is a free software. The continuous improvements made over the years resulted in a reliable product. Another reason for its success is its flexibility: Flight Gear offers the possibility to use its different modules independently, to select different flight dynamics models and their associated aircraft characteristics, to add new vehicles and airports layouts. Some 6DOF simulators offer 3D visualizations. They are generally developed in C++ or with Matlab and their outputs are plots of different variables over time. All Endless Runway partners have developed such simulators over the years that could be used (with some modifications) in the project. However, since the software has to be shared and modified by the different contributors, there are complicated intellectual properties issues. There is then the option to develop from scratch such a code that would be tailored to the need of the required analyses. Since there are requirements stipulating that the simulator must be shared and can be modified by all partners, it cannot be affected by proprietary aspects. Regarding commercial software, X-Plane seems to be a good choice given its low price and the positive feedback about its reliability. Flight Gear on the other hand is completely free. In addition, its architecture makes it easy to implement new aircraft and new runway shape with their associated files containing all characteristics. In the end, the remaining two options for the simulation environment are: An especially developed 6-degrees-of-freedom model tailored on the project requirements; Flight Gear (no cost at all with respect to X-Plane). The subsequent qualitative assessment between these two solutions is presented in the following table that summarizes pros and cons of both solutions. The Endless Runway

10 Page 1/89 Table 1: Assets and drawbacks of the possible simulation environments Assets Drawbacks Tailored 6DOF simulator Complete knowledge of the physics behind the simulation Possibility to modify the code in case of a specific issue Possibility to run completely automated take-off and landing segments Significant development time Outputs would be plots Difficulty in the modelling of the circular runway Difficulty to organize the work between the partners Flight Gear Proven simulation software based on a 6 DOF model It is a full simulation tool enabling any user to fly the aircraft A large community developed auxiliary tools to develop the scenery Possibility to model new aircraft concepts Source code available Good visualization possibilities Changes to the original code are risky Physics needs to be validated before use Simulations might require manual inputs decreasing thus the repeatability After weighting all the different options, the WP team decided to use Flight Gear as the simulation environment for the activities of WP3. This choice is consolidated by the fact that this program is widely used in research for simulation developments [7]. However, the associated drawbacks must be taken into account. Therefore, to verify the physics laws implemented in Flight Gear, there is a task in WP3 that is solely dedicated to validate the reference aircraft model. 2.2 General use of Flight Gear in WP3 The goal of this section is to quickly present the structure of Flight Gear and how this simulator will be used in WP3. First, it is important to know that the overall simulation relies on a Flight Dynamics Model (FDM). This is the module that takes into account all pilots inputs, ground reactions during take-off and landing, aircraft properties (aerodynamics, weights, inertia, propulsion ) and determines the behavior of the airplane over time. The aircraft characteristics are stored in.xml files where the FDM will look for specific values. There is then the visualization part: 3D models in the.ac format [8] are integrated in the virtual environment and the user can see its aircraft flying over the newly created airport. For the scope of aircraft studies in the Endless Runway project, the selected Flight Dynamics model is JSBSim [9]. Through this selection, the partners have complete control of the inputs that are transferred to the simulator: JSBSim relies indeed on all the aircraft characteristics that are indicated by the designers in the.xml file. Then, 3D models of both the aircraft and the banked circular runway are integrated in the simulator. At this point, it is possible to manually fly the mission and to assess in a qualitative manner the behavior of the aircraft on the Endless Runway concept. However, the decisive requirements stated in the introduction require a quantitative approach. In order to enable a more refined analysis, the recording of all aircraft parameters during the mission is activated. In this manner, Flight Gear generates a.txt file (called telemetry.txt in the project) that collects all necessary aircraft parameters. Following the approach taken during flight test analyses, the take-off and landing performances are calculated based on the recorded values provided by the simulator. In this first assessment of the aircraft behavior on a circular runway, the simulations are made without the effects of wind. The Flight Gear set-up used in WP3 is illustrated in the following figure: The Endless Runway

11 Page 11/89 Flight Gear Virtual Mission Pilot inputs Flight Dynamics Model : JSBSim Computer Screen Airport 3D model Telemetry.txt.XML file Aircraft 3D model Figure 3 : Flight Gear set-up for WP3 The Endless Runway

12 y x EC DG-RTD Page 12/89 3. Feasibility of a conventional configuration 3.1 Approach The work presented in this chapter corresponds to the activities performed within Task 3.1 Feasibility of a conventional configuration. The objective is to take an existing passenger aircraft and to operate it on an Endless Runway airport to both assess its behavior and define the attainable level of performance. From a practical point of view, the work is divided in two parts. The first one consists in modeling a reference aircraft and validating its take-off and landing performances on a classical dry runway. This stage is mandatory in order to minimize the uncertainty regarding the physics used in the simulator as explained in the previous chapter. The second step focuses on simulations with different banked circular runways. The outcome of these tests is a direct comparison of the aircraft behavior on these different tracks, the determination of the level of take-off and landing performances and the identification of the most promising runway cross section. The approach that has been used in the final part of T3.1 is illustrated here below: Flight Gear Virtual Mission Post Flight Analysis Pilot inputs Flight Dynamics Model : JSBSim Computer Screen Performance analysis Runway cross section selection 3D parametric shapes Reference Aircraft 3D model Telemetry.txt validated.xml file Figure 4 : Approach to be used in the final part of T Reference aircraft selection In such a prospective study, it is important to select the correct reference or baseline in order to draw conclusions on the investigated system. Usually, in aircraft studies, single aisle aircraft (Boeing 787 or Airbus A32) are usually taken as references since they are a key market segment [1][11]. However, in the case on the Endless Runway project, the object under study is the runway and the reference aircraft provides only metrics for the assessment. With the objective of remaining conservative, the baseline aircraft must then correspond to the most challenging case for the design of the Endless Runway. Because of the banking of the runway, it is clear that large wingspans aircraft (and especially with wings in the lower position) may have ground contact issues. This problem is emphasized if engines are located under the wing. These different elements lead to the selection of a 4 engines low-wing twin-aisle aircraft as reference: it would indeed have a large wing area because of the high weight and a lower ground clearance between the track and the outer engines. At this stage, the WP3 Team identified 3 possibilities: The Airbus A34 The Airbus A38 The Boeing B747 The Endless Runway

13 Page 13/89 The next table presents some key characteristics for these airplanes. It is however important to note that the data are presented to provide some references and not to compare the aircraft. They have been indeed designed at different times and the level of technology is not comparable. Table 2 : Key data of 4 engines low wing twin-aisle airplanes Airbus A38-8 Airbus A34-6 Boeing B747-1 MTOW : 56 tons MTOW : 368 tons MTOW : 333 tons Wing area : 845 m² Wing area : 439 m² Wing area : 511 m² Span : m Span : 63.4 m Span : 59.6 m Engine : 4 x 311 kn Engine : 4 x 249 kn Engine : 4 x 197 kn In order to carry out the validation process explained in the previous paragraph, it is necessary to have a large and reliable database on the aircraft characteristics. The A38-8 is a new aircraft and it is the flagship of Airbus. Therefore, it is extremely difficult to have accurate data about it. For the A34-6, more values are available but the aerodynamics characteristics can only be assumed. Boeing provided in 197 a lot of data to NASA for the development of a Jumbo Jet Simulator under the form of a complete report. Today, this report is available [12] and the contents allow the consortium to generate the.xml file of the aircraft for Flight Gear for a B Besides, the B747 is the oldest aircraft between the three possible candidates. Its take-off and landing performances are more conservative from a runway design point of view. For these reasons, the consortium decides to use the Boeing B747-1 as the reference aircraft for the study of aircraft aspects of the Endless Runway. 3.3 Definition of the B747-1 model As described previously, an aircraft model in Flight Gear is based on different files. The most important ones in order to fly a mission are: A 3D model; An.XML file storing all aircraft characteristics; An.XML file storing all engine data. The next paragraphs detail the generation of these three files for the Boeing B The Endless Runway

14 Page 14/ Aircraft 3D model One of the key inputs for the simulation visualization is the 3D model of the aircraft. The Flight Gear community developed over the years numerous 3D aircraft models that can be downloaded and used in the simulations. After a review of different digital-mock-ups associated to the Boeing B747-1, the partners identified an accurate 3D model available in [6] and illustrated in the next figure as an option to be used in the Endless Runway project. The model has indeed a lot of details such as high-lift devices and landing gears. Figure 5 : 3D model of the B747-1 In order to validate this model, some verification must be made. The partners have therfore compared various lengths on the 3D model with reference data that are measured on the three-view drawing provided by Boeing [13]. Since no major deviation has been noted, the selected 3D model is used in the project for the planned activities Aircraft characteristics To feed the Flight Dynamics Model (JSBSim in this case), all aircraft characteristics are stored in an.xml file whose name is the aircraft name. The next figure shows the highest level of the file where all systems and disciplines are listed: The Endless Runway

15 Page 15/89 Figure 6 : Highest level of the B747 description file (747-1.xml) Values available in the reference report [12] and data provided by Boeing [13] allow the completion of both the metrics section (storage of geometrical reference lengths) and the mass_balance section (storage of weight and inertial data) in the.xml file: Figure 7 : How inertia data are provided to JSBSim in the.xml file It must be noted that the inertia data (moments of inertia and products of inertia) are in this case fixed. One file describes the B747-1 characteristics in the take-off configuration and a second one provides characteristics for landing. The changes are clearly not negligible (Ixx, the body axis moment of inertia varies from 14e+6 to 19e+6 slug.ft² at MTOW). For ground reactions, landing gear position entered in the.xml file correspond to the values presented in [12] and the rolling friction coefficient is fixed to the average value for a dry concrete surface. Regarding the parameters of the landing gear, the values found in the original.xml file are kept. Moreover, with the objective of checking the possible contacts between the aircraft and the banked runway during the take-off and landing phases, it has been decided to add contact points (23) on the critical area of the aircraft. The contact points are defined by their geometrical location (X, Y, Z coordinates) and very high values for both the static and dynamic friction coefficient. This non-physical value generates such a high friction force that the aircraft cannot move The Endless Runway

16 Page 16/89 anymore. In this manner, if one of these critical points ends up touching the 3D model of the circular track, the simulation is stopped. The user understands then that the cause is a ground contact. Figure 8 : Ground reaction data For the propulsion system, the high level.xml file calls another file where the performances of the engine are described (see section 3.3.3) and provides the location of the 4 engines. To complete the necessary data for the Flight Dynamic Model, the B747-1 aerodynamics must be implemented. Based on curves provided in [12], ONERA generated the lookup table requested by JSBSim. The next figures illustrate the reference curves for the lift coefficient (for different flap settings) and how the data are entered in the.xml file. The Endless Runway

17 Page 17/89 Figure 9 : Lift coefficient data for the B747-1 [12] Figure 1 : Lift coefficient lookup table used in Flight Gear The same procedure is repeated for the other two force coefficients (drag and side-force) and the three moment coefficients (roll, pitch and yaw). The Endless Runway

18 Page 18/ Engine model The engine data are stored in a specific.xml file that has the name of the engine installed on the aircraft. For the B747-1 mode, a file called JTD9D.xml is available. In order to model the engine performance with respect to flight altitude and Mach, the WP3 Team uses the formulas proposed in E. Roux PhD [14]. Part of her work focused on the development of an analytical engine model suited for conceptual design studies. With respect to other models, her approach took into account physical aspects to have more reliable results. In [15], the characteristics of the JT9D-3A are given: Static Thrust : N By-Pass ratio : 5.2 Overall Pressure Ratio : 21.5 Based on these values, the evolution of the installed thrust for each engine as a function of Mach and altitude has been determined. The figure below details the evolution of the installed maximum thrust for the JT9D-3A engine at the take-off. Figure 11 : JT9D-3A installed thrust at take-off 3.4 Validation of the B747-1 model With the B747-1 model completed, the next step is to compare the take-off distance (all engines operative) obtained through Flight Gear simulations and reference values provided in [12] Take-off performance The take-off distance is defined as the distance covered by the aircraft from where the brake-release point to the altitude of 35 ft. Between these two points, the aircraft reaches various speeds related to the certification. The Endless Runway

19 Page 19/89 At V R, the rotation speed, the pilot provides an input to initiate the rotation. At V LO, the aircraft becomes airborne. The distance from the starting point up to V LO is called the ground run. Figure 12 illustrates this critical phase of the mission. H=35 ft Take-off distance Figure 12 : Illustration of the take-off distance (modified picture from [3]) In the Boeing report [12], experimental data of a ground run up to lift-off speed are provided. Since it is difficult to repeat in Flight Gear the same rotation input as in [12], the consortium decided to compare the experimental data to the simulation value up to V R. The next figures show that the simulation is capable of reproducing the real behavior of the aircraft with only limited error margin. Figure 13 : Speed behavior during the ground run The Endless Runway

20 Page 2/89 Figure 14 : Behavior of the model concerning the ground distance These results validate the correct behavior of the B747-1 model in Flight Gear for the take-off phase Calibration of the landing performance For the landing phase, the validation cannot be performed. In the case of the B747-1, there are no clear indications in the available documents about the braking procedures. It has been thus decided to use the FAR (Federal Aviation Regulation) Landing Length presented in [12] to calibrate the static friction coefficient in the B747-1.xml file used for landing simulations as indicated in Figure 15. Figure 15 : FAR Landing length for the B747-1 [12] The Endless Runway

21 Page 21/89 From the previous figure, it can be observed that the B747-1 lands in about 195 m in its maximum landing weight configuration. After several simulations, the team decided to fix the static friction coefficient to.2. This coefficient has been chosen in order to obtain the FAR landing distance with full-brakes activated for the entire ground run. 3.5 Parametric studies The following parametric studies based on simulations aim at identifying the most promising cross section of the runway considering various aspects including take-off performance and subsequently the best width. Landings are tested next on the best shape considering the most advantageous width Runway shape definition Following the preliminary review of circular runway activities in [16], the consortium decided to compare three runway cross-sections. These sections are classified according to the speed variation they provide along the circle radius (x): Linear speed distribution V = K. x Square speed distribution V = K. x 2 Root square speed distribution V = K. x As expressed in [17], the shape of the runway is defined by the following equation (with R the radius of the inner circle, x the radial position and z the runway height): z = 1 x g. R 1 + x dx R V 2 It is then possible to mathematically calculate the runway height depending on the position along the circle radius (see Appendix B.1 for calculation detail): For a linear speed distribution, the height is defined as: z = K2 2 R g 1 X R X + ln 1 + X, with K = R R V mrx W rrrrrr For a square speed distribution, the height is defined as: The Endless Runway

22 Page 22/89 z = K2 R 3 g 3 4R X3 2 3R + X2 X + R 2R ln 1 + X, with K = V mrx 2 R W rrrrrr X4 For a square root speed distribution, the height is defined as: V mrx z = K2 g X R ln 1 + X, with K = R W rrrrrr The first parametric study consists in fixing the reference width to 14 meters and applying the different formulas to calculate the correct cross section. During simulations with the B747-1 on straight runways, the rotation speed was fixed to 16 kts. In order to have a certain security margin, the maximum speed to be achieved on the banked runway is set at 2 kts (12.9 m/s). Knowing that the inner radius of the circular runway is equal to 15 m and that the speed of 12.9 m/s is reached at a width of 14 m, it is possible to draw the complete runway cross section. The figure below shows the different speed distribution and the corresponding shapes. The Endless Runway

23 Page 23/89 Figure 16 : Speed distributions and associated runway profiles With these curves, each runway cross section has been modeled with AC3D. The next figures illustrate the 3D model of a circular runway based on the linear speed distribution: Figure 17 : 3D model of the circular runway (linear speed variation width = 14m) The Endless Runway

24 Page 24/ Runway volume calculation In order to provide additional information for the multi-criteria analysis, it is decided to estimate the required volume of ballast that would be necessary build the banked circular runway. The next figure illustrates the parameters that are used to complete this preliminary calculation: z R = R + W rrrrrr Area A f(x) O x cg R R x Figure 18 - Parameters used for the computation of the runway volume Guldin second theorem tells us that the volume of the runway section is the product of the area A of the section between f(x) and z= by the length of the circle covered by its center of gravity, G, of abscises x G. V = 2πx G A The following formula ([33]) gives the abscissa of the center of mass: The two previous equations combined imply: And finally: x G = 1 A V = 2π 1 A R R R xf(x)dx xf(x)dx A V = 2π R R xf(x)dx The generic formula expressed above is now specifically applied to the linear speed runway profile. In the 2D plan (O, x, z), the runway section profile is defined by F, translation of f(x) of which origin is moved at the center of the circular runway: The Endless Runway

25 Page 25/89, x < R F(x) = K 2 2 R g 1 (x R ) 2 2 x R + ln 1 + x R, R 2 R R R x R At this stage of the project, the outward section of the Endless Runway has not been defined. Therefore, the volume computation will only consider the runway inwards section (up to the highest point). The preceding generic formula becomes: V = 2πK2 R 2 g R x 1 (x R ) 2 2 x R + ln 1 + x R dx 2 R R R V = 2πK2 2 R (R R ) 4 2 (R R ) 3 (R R ) 2 g 8R 6R 2 The detail of the computation is given in Appendix B.2. R + R 2 R R 2 2 ln R R After calculation, we find that for a 15 m inner radius runway, 14 m width, with the external runway circle planned for aircraft speed of 12,9 m.s -1, the volume of ballast is of almost 11 millions of cubic meters. For a 15 m width, it increases to about 13 million and for 13 m, it decreases to 9,7 million. Again, these results do not account for the outward section of the runway, as this has not yet been defined at this stage of the project (WP2 responsibility). Table 3 : Runway ballast volume R W runway Input values 15 m 14 m V T/Omax 12,9 m.s -1 g 9,81 m.s -2 Intermediary values K,735 R' Result 164 m V m Take-off simulations With the circular runway models integrated in Flight Gear, it is then possible to perform take-off simulations with the validated B747-1 model. Figure 19 illustrates the take-off simulation. The Endless Runway

26 Page 26/89 Figure 19 : Take-off simulation with the B747-1 on a circular runway A drawback in the Flight Gear set-up is the obligation to have manual inputs during the take-off phase. To limit the uncertainty regarding the take-off field length and the overall behavior of the aircraft, several simulations are performed. In addition, stripes of alternated colors are mapped of the runway to provide information about the speed to allow more accurate manual manoeuvers in Flight Gear: In the first stripe (from 15 to 152m of radius), the speed should vary between and 28.5 Knots; In the second stripe (from 152 to 158m of radius), the speed should vary between 28.5 and 114 Knots; In the third stripe (from 158 to 161m of radius), the speed should vary between 114 and 157 Knots; In the fourth stripe (from 161 to 164m of radius), the speed should vary between 157 and 2 Knots Performance analysis Before initiating the analysis of the recorded flight data (telemetry.txt), it is mandatory to define the take-off distance to be considered in the performance analysis. Subsequently, the different plots that are reviewed to complete the performance analysis for different runway shapes are presented Definition of the take-off and landing distances As presented in 3.4.1, the take-off distance corresponds to the ground distance that is covered by the airplane up to an altitude of 35 feet. In the case of the Endless Runway project, the performance analyses at this conceptual stage only consider the case when all engines are performing properly. In addition, the take-off distance in the case of a banked and circular runway is defined as the ground distance covered by the airplane up to an altitude that corresponds to the addition of the lift-off height of the runway and the 35 ft obstacle. The following figure illustrates the definition of the take-off distance: The Endless Runway

27 Page 27/89 End of take-off altitude 35 ft obstacle Lift-off height Figure 2 Take-off distance definition for the Endless Runway The same approach is used for the definition of the landing distance. In this case, the altitude corresponding to the start of the landing phase is defined as the runway height at touchdown plus the obstacle height (fixed to 5 ft as indicated in [3]). In the case of the endless runway, more conservative definitions of take-off and landing distances could be used. However, the selected approach is somehow very similar to the existing one for conventional operations and allows thus a reasonable comparison of the performances Linear speed distribution This section will analyze the take-off performance of the B747-1 taking of the Endless runway when a linear speed distribution is used to define the runway cross section. The first plot to be observed is the flight path. This overall view allows to have an idea of the complete take-off path in 3 dimensions and to quickly identify issues during take-off (wrong manoeuver or telemetry recording issues). The break release on the circular runway occurs at (,). The Endless Runway

28 Page 28/89 Flight Path 4 3 z [m] y [m] x [m] Figure 21 : Take-off flight path The second figure to be analyzed facilitates the identification of the rotation speed during the take-off phase on a circular runway. The evolution of the elevator position provides the time at which the pilot commanded the rotation. In this case, it is 51 seconds. At this time, the airspeed is about 165 knots which is close enough to the reference rotation speed provided in [12] to prove validity of the simulation (the difference is about 3%). 2 Airspeed [Knots] t [s] Elevator Position Norm. [-] t [s] Figure 22 : Evolution of both the airspeed and the normalized elevator position over time The Endless Runway

29 Page 29/89 Another key point in the take-off analysis is the identification of the lift-off speed. To note this value, the team reviews the recorded vertical speed data. At t=54 seconds, the vertical speed starts to increase in a constant manner indicating that the aircraft is climbing. It is then considered that lift-off occurs at this time. The corresponding speed at t=54 seconds is 172 knots. Since the reference lift-off speed is 168 kts [12], the validity of the simulation with respect to the take-off procedure is verified. 8 Vertical speed [m/s] t [s] 2 Airspeed [Knots] t [s] Figure 23 : Evolution of both the vertical speed and airspeed over time In a fourth step, it is necessary to study the altitude over time in order to: Verify that the lift-off speed is made at the right height of the circular runway; Find out at which time the 35 ft (1.7 m) obstacle is passed; Measure the take-off distance. According to the formulas presented earlier regarding the cross-section of the runway, for a speed of 172 kts the airplane should be located at a height of 2 meters. By looking at the Altitude plot (Figure 24), it is confirmed that the aircraft position is correct and that the specific procedure associated with the circular runway is well respected. Since lift-off is performed at an altitude of 2 meters, the reference altitude to be considered for the obstacle is not 1.7 meters but about 31 meters. From the altitude plot (Figure 24), it can be determined that this height is reached at t=58 seconds. With this information, it is now possible to directly read the total take-off distance from the ground distance plot (Figure 24). In this illustrated case, the B747-1 took 31 meters to complete its take-off. The Endless Runway

30 Page 3/89 6 Altitude [m] t [s] 4 Ground Distance [m] t [s] Figure 24 : Altitude and ground distance variation over time The last elements to be assessed during the take-off simulation are the required steering to perform the circular movement and the sustained lateral acceleration. The next figure illustrates the value observed with Flight Gear (associated rudder displacement is not shown). Steering [deg] t [s] Acceleration along Y [m/s²] t [s] Figure 25 : Steering and lateral acceleration variation over time The Endless Runway

31 Page 31/89 Regarding steering, the first plot in Figure 25 shows that the circular movement of the aircraft has been achieved with several discontinuous inputs from the pilot. It is interesting to note that the absolute value of these inputs increased over time to achieve the desired trajectory. The consortium agrees that a continuous controlled steering would improve the overall performances as well as lower steering angles. The second plot in Figure 25 identifies the lateral acceleration related to passenger comfort. The idea is to verify that during the circular trajectory during take-off, the sustained accelerations do not exceed 1.2 m/s² [31]. The recorded data show a maximum value of 1 m/s², indicating thus that the performed maneuver would be below discomfort for passengers. For the subsequent multi-criteria assessment, it is decided to take into consideration average values regarding steering and lateral acceleration. In the presented simulation, the calculated values are: Average steering angle : 2.4 deg (for the ground run) Average absolute lateral acceleration :.37 m/s² Square root speed distribution This section will analyze the take-off performance of the B747-1 taking of the Endless runway when a square root speed distribution is used to define the runway cross section. The same plots as described in the previous section are reviewed for take-off simulations performed on a circular runway with a cross section defined by a square root speed distribution. In Figure 26, the aircraft trajectory during take-off is shown (it is important to note that this take-off is completed in the other direction when compared to Figure 26). The circular path is visible as well as the airborne segment that is considered in the analysis. Flight Path 8 6 z [m] y [m] x [m] 1 Figure 26 : Take-off flight path The first step in the analysis focuses on the determination of the rotation speed. With this objective, the elevator position is reviewed to determine the time at which the pilot commanded the rotation. Figure 27 The Endless Runway

32 Page 32/89 shows that the input is given at t=53 seconds. At this time, the airspeed is about 161 knots. Since the rotation speed provided in the reference document [12] is 16 knots, the resulting small difference indicates that the simulation is performed correctly. 2 Airspeed [Knots] t [s] Elevator Position Norm. [-] t [s] Figure 27 : Evolution of both the airspeed and the normalized elevator position over time Once this verification about the pilot inputs is made, the subsequent step is the determination of lift-off speed. This value is measured by looking at the recorded vertical speed: 1 Vertical speed [m/s] t [s] 2 Airspeed [Knots] t [s] Figure 28 : Evolution of both the vertical speed and airspeed over time The Endless Runway

33 Page 33/89 From Figure 28, it can be said that lift-off occurs at t=57 seconds. The corresponding speed is about 171 knots which results in a difference of 1.8% with the reference lift-off speed of 168 kts [12]. This negligible alteration confirms the validity of the manual simulation with respect to the take-off procedure. The next step requires the review of the altitude over time in order to: Verify that the lift-off speed is made at the right height of the circular runway; Check at which time the 35 ft (1.7 m) obstacle is passed; Measure the take-off distance. Given the mathematical laws generating the runway cross section for a square root speed distribution, the speed of 171 kts is reached at a height of 26.5 meters. Plots in Figure 29 confirm the aircraft position is correct and that the simulation matches the take-off procedure associated with the circular runway. According to the take-off distance definition in the case of banked and circular runways, the reference altitude to be considered for the obstacle is about 37 meters ( ). In Figure 29, the altitude plot indicates that this height is reached at t=6 seconds. Looking at the corresponding plot of the ground distance, it can be determined that the B747-1 takes 35 meters to complete its take-off. 8 Altitude [m] t [s] 4 Ground Distance [m] t [s] Figure 29 : Altitude and ground distance variation over time As for the simulation on a runway with a cross section providing a linear speed distribution, the last elements to be analyzed are the required steering to perform the circular movement and the sustained lateral acceleration. Figure 3 illustrates these values recorded during the Flight Gear simulation. The Endless Runway

34 Page 34/89 Steering [deg] t [s] Acceleration along Y [m/s²] t [s] Figure 3 : Steering and lateral acceleration variation over time As in section , the steering plot of Figure 3 indicates that the circular path of the B747-1 has been obtained thought discontinuous and increasing inputs from the pilot. Once again, a continuous controlled steering would allow better overall performances as well as lower steering angles. It must be noted that the steering values are in this case negative because of the direction of take-off. The second plot of Figure 3 shows the lateral accelerations that are correlated to passenger comfort. In this case, it can be seen that the value of 1.2 m/s² is never exceeded. A take-off on a circular runway with a cross-section generating a square root speed distribution would then be acceptable from a passenger point of view. The average values obtained for this simulation are: Average steering angle : -3.8 deg (for the ground run) Average absolute lateral acceleration :.38 m/s² Square speed distribution The square speed distribution results in a really radical cross section that is not suitable for taking-off with the B Several attempts have been made but all were unsuccessful. This cross section will therefore not be investigated in this assessment Assessment After completion of the take-off simulations and the associated data analyses, a multi-criteria assessment has been made to identify the best runway cross-section. In a second step, additional points are investigated in order to converge to the definitive runway width. The Endless Runway

35 Page 35/ Square root speed vs. linear speed distribution for a reference width of 14 meters To compare the two possible speed distributions, the assessment has been made concerning the three main performance criteria: The take-off distance; The average absolute lateral acceleration; The average steering angle. Besides, elements related to the runway itself are taken into consideration: The runway maximum height; The runway volume. In addition, a more qualitative element is introduced. It is called Pilot feedback and it corresponds to the user appreciation of the difficulty to perform a take-off in a manual manner. Since taking-off from a straight and flat runway is the easiest option, the value for this, will be indicated as 1. Regarding the linear speed distribution, the manoeuver requires some experience and there is always a risk of touching the ground. A value of 5 is then reported. Lastly, since maneuvering on a runway defined by a square root speed distribution is easier, an appreciation of 7 is given. The following table synthesizes all inputs related to the different cross sections: Table 4 : Summary table to select the runway cross section for a reference width of 14 meters Conventional runway Linear speed distribution Square root speed distribution Take-off distance [m] Average absolute lateral acceleration Average steering angle [m/s²] [deg] Pilot feedback Runway maximum height [m] Runway volume [m 3 ] When looking at the efficiency of an airport, the take-off distance is a key parameter. With regard to this aspect, the square root speed distribution is preferable since the distance with respect to the linear speed distribution is shorter (6.6% increase with respect to the standard runway while the linear speed distribution results in an 8.4% increase). As important as the performance aspect, the cost related to the construction of an Endless Runway is paramount. From this point of view, the linear speed distribution is the best option. Since the Entry Into Service (EIS) of the Endless Runway would be about 25, it can be foreseen that the operations would be fully automated. In this case, the pilot feedback is no more relevant in the comparison. The same can be said about lateral accelerations and average steering: in 25, a specific control system could be installed to allow continuous small actuations decreasing thus the peak values. Therefore, the choice to be made is about performance against cost. The Endless Runway

36 Page 36/89 Even if the square root speed distribution is better from a performance point of view, the difference is negligible while differences regarding the size of the runway (and thus cost) are not. For these reasons, the runway cross section following a linear speed distribution is selected as the most promising solution Selection of the reference width With the runway cross-section fixed, simulations are performed with reference widths of 13 meters and 15 meters. From a performance point of view, the differences regarding the take-off distance appear to be negligible. When looking at the runway volume (cost aspects), a width of 13 meters is preferable. Simulations on a runway with a smaller width resulted in high lateral accelerations. Acceleration along Y [m/s²] t [s] Figure 31 : Observed lateral accelerations during a take-off for a reference width of 13 m The previous figure shows that the limit of 1.2 m/s² set in [16] is exceeded during the ground run on the circular runway with a width of 13 meters. Even if future aircraft could be equipped with a control system allowing a better automated trajectory resulting in lower acceleration, a width of 14 meters is to be preferred. Regarding the 15 meters option, no real benefits have been pointed out by the simulation. The consortium fixes then the reference runway width to 14 meters. To conclude the aspects related to the runway width, a complete runway cross section is illustrated in the next figure: Figure 32 : Runway cross section (B747-1 is positioned at the height corresponding to the rotation speed) The Endless Runway

37 Page 37/89 For aircraft that operates on the curved surface, the available width is larger than the reference length. In order to avoid an abrupt end of the runway below the wing tip (asymmetric aerodynamics), a linear portion is added (blue line in Figure 32). Airport designers have to consider this additional part as well as the external shape of the Endless Runway considering safety aspects (dashed line in Figure 32) Landings On a banked circular runway, the pilot has to land on a precise circle at a given speed. Unfortunately, there was no time to implement any assistance to perform the correct manoeuver in Flight Gear. Completing the procedure manually is then a real challenge and differences are observed between the various simulations. In this section, the analysis of one landing simulation is carried out. Note that the.xml file of the B747-1 is specifically modified to operate the aircraft with its maximum landing weight and the corresponding inertia. As for take-off, the first interesting plot is the flight path that gives an overview of the trajectory. In the next figure, it is possible to identify the tangential approach of the aircraft as well as the ground run on the circular track. Flight Path z [m] y [m] x [m] -2-1 Figure 33 : Landing Flight Path The Endless Runway

38 Page 38/89 To point out issues concerning the touchdown point, it is useful to examine the landing gear compression. In Figure 33, it can be seen that the impact with the track occurs at t=6 seconds. At this time, the airspeed is about 137 knots. The difference of 5% with the reference speed provided in [12] is acceptable..4 L.G.2 c ompression t [s] 15 Airspeed [Knots] t [s] Figure 34 : Evolution of the landing gear compression and the airspeed over time According to the runway cross-section formulas, a speed of 137 knots corresponds to a height of 1 meters above the ground. Since the definition of the landing distance requires a clearance over a 15 meters obstacle, it can be said that the landing distance must be calculated from the point where the altitude of the aircraft is 25 meters. In Figure 34, it can be observed that the altitude of 25 meters is reached at t=4 seconds. The ground distance corresponds then to 19 meters. The Endless Runway

39 Page 39/89 6 Altitude (m] t [s] 25 Ground Distance [m] t [s] Figure 35 : Altitude and ground distance evolution over time Regarding the passenger comfort, the plot of the sustained lateral accelerations presented here below shows that the limit of 1.2 m/s² is exceeded several times (red circles). However, the average value of the acceleration is.66 m/s². Acceleration along Y [m/s²] t [s] Figure 36 : Lateral acceleration evolution over time Because of the difficulty of the manual approach used for landing simulations, it is preferable to review other telemetries before defining the performance. Since the previous simulation has a low landing speed, the consortium decided to perform a landing with a higher speed (15 knots). The next figure shows the resulting landing distance knowing that the FAR obstacle is cleared at t=2 seconds. The Endless Runway

40 Page 4/89 3 Ground Distance [m] t [s] Figure 37 : Landing distance measured for another simulation (higher landing speed) In this case, the landing distance is about 24 meters. With data gathered from other simulations, an average value of 22 meters can be defined as the landing distance for the B747-1 on a circular runway B747-1 ground clearance analysis In Figure 37, a front view of the B747-1 ([32]) allows to measure the fixed reference distance d3 as well as the distances d1 and d2 for the critical elements, in this case the wingtips. d1 and d2 are also reported for both the inner and outer engines. d 1 d 2 d 3 Figure 38 - Example of measure taking for the wingtips of the B747-1 The measures are reported in Table 5. The Endless Runway

41 Page 41/89 Table 5 : B747-1 key distances for ground clearance calculation Landing gear d3 6,3 [m] Inner engine d1 1,7 [m] d2 12,3 [m] Outer engine d1 2,5 [m] d2 21,5 [m] Wingtip d1 6,2 [m] d2 3, [m Based on the mathematical formulas developed in Appendix B.3, a routine developed in Python (high-level programming language) computes the distance values and indicates the corresponding position of the aircraft on the linear speed distribution. The results are presented in Table 6. Nominal distance on flat ground (m) Table 6 : B747-1 ground clearance calculations Minimum distance (m) Internal aircraft side Corresponding abscissa of the center of the landing gear (m) External aircraft side Minimum distance (m) Corresponding abscissa of the center of the landing gear (m) Outer engine 2,5 1,18 127,5 1,35 113,8 Inner engine 1,7 1,27 13,9 1,42 128,5 Wingtip 6,2 3,55 12,6 3,68 13,9 As seen in chapter , the B747-1 lift-off speed observed during the simulation is 172 kts (88,5 m.s -1 ). Therefore, according to Figure 16 (Speed distribution), the aircraft will never roll beyond the 162 m radius runway circle. Hence the most critical element, that is to say the downhill outer engine, will actually have a clearance greater than 1,18 meters that occurs on radius 1627,5 m. To conclude, all aircraft elements remain clear from the ground with sufficient margin during the ground roll. 3.6 Conclusions on exchange parameters The simulations performed in Flight Gear on a validated B747-1 model enabled the consortium to define the parameters to operate The Endless Runway: Size of the circle (radius) The first simulations in Flight Gear showed that the value of 15 meters for the internal radius of the runway was not a stopper from an aircraft point of view. Profile of the runway (bank angle) Simulations with a B747-1 (validated on straight runways) in Flight Gear and the subsequent analysis of the flight parameters indicated that the most promising cross-section is the one associated with a linear speed distribution. The Endless Runway

42 Page 42/89 Width of the runway Since the width does not have a strong impact on the take-off distance, it is fixed to 14 meters to limit the size of the Endless Runway. A smaller width is not recommended because of the resulting higher lateral acceleration. Aircraft landing gear During take-off and landing operations performed with the B747-1 model in Flight Gear, the landing gear struts always operated within the defined ranges. Take-off performance From the simulations and the subsequent data analysis, the B747-1 take-off distance on a circular runway is increased of about 1% with respect to its reference value (in a curved abscissa). Landing performance From the simulations and the subsequent data analysis, the B747-1 landing distance on a circular runway is increased of about 13% with respect to its reference value (in a curved abscissa). Lateral acceleration The B747-1 simulations performed in Flight Gear indicated that the lateral accelerations during take-offs are below the accepted limits. For landing, the limit is exceeded for brief periods. The Endless Runway

43 Page 43/89 4. New aircraft tailored for the Endless Runway 4.1 Approach The work presented in this chapter corresponds to the activities performed within Task 3.2 Exploration of new concepts optimized for the Endless Runway. Since the Endless Runway concept offers a real discontinuity with today s airport layout, the project also defines an innovative aircraft that would be tailored to the circular runway and its specific procedures. After the definition of the reference mission for this new airplane called Endless Runway Aircraft Concept (ERAC), the vehicle configuration is the result of both a concept exploration and an analysis of the specific constraints. Subsequently, ERAC is sized according to the classical approach used in conceptual design. The last step consists in performing simulations within the same environment as in T3.1 to assess ERAC from a performance point of view. This process is illustrated in the following figure. Flight Gear Virtual Mission Pilot inputs Flight Dynamics Model : JSBSim Computer Screen Post Flight Analysis Selected shape for the runway Performance analysis ERAC 3D model Telemetry.txt.XML file ERAC conceptual design Mission definition Concept selection Sizing process Aerodynamics Propulsion Figure 39 : Approach to be used in T ERAC Conceptual Design Mission definition In order to compare the performances of ERAC with the ones calculated for the B747-1, the two aircraft should have a similar purpose. However, the B747-1 being designed in the 196 s, its classification as large aircraft is not valid in 213 (see aircraft fleet categories detailed in [18]) nor it will be in 25 for the targeted EIS. The consortium therefore decided to design ERAC according to specifications derived from the B747-1 replacement, the B777-3 [19]: The Endless Runway

44 Page 44/89 The initial cruise altitude is set to 33 ft as for today s airplanes; The seating capacity is fixed to 45 passengers divided into 2 classes; The design range of 8 NM is approaching the one of the B777-3 Extended Range in order to match the value indicated for large aircraft in [18]. It is indeed assumed that future twin-aisle aircraft would have the same range as today s large aircraft. The cruise speed is established to Mach.8 It can be surprising to have the ERAC cruise speed set to M=.8 while the B777-3 currently flies at M=.84. The reason behind this assumption is that several prospective studies presented in [18] recommend a reduction of the cruise speed for environmental purposes. However, since ERAC is a long range aircraft, a severe reduction in the cruise speed would lead to critical increase of the travel time. The next table illustrates this issue showing the impact of the cruise speed on the duration of a Paris to New York flight (58 km). Table 7 : Effect of cruise speed reduction for a Paris to New-York flight Cruise Mach Speed of sound Airspeed Approx. flight duration Difference Number [m/s] [m/s] [km/h] [h] [%] Preliminary requirement analysis Before exploring aircraft configurations, it is important to carry out a preliminary requirement analysis that takes also into account results from the simulations with the B First the numerous manual take-offs and landings stressed the possibility to have a contact between the ground and the aircraft components. Thus, the ground clearance must be reduced at all costs. To achieve this goal, the concept exploration has to consider: a limited wing span; a different wing position; a different engine location. In addition, the previous simulations have shown that the ground handling of the aircraft is critical and ERAC must therefore provide improvements in this area. Finally, because of the complex manoeuver at low speed, ERAC has to be designed in order to have better control in this flight regime ERAC Concepts exploration In the first step of the concept exploration, the idea is to define as many aircraft architectures as possible that match one or more key requirements identified in the previous section. At this stage, the consortium made the assumption that the best control at low speed would be achieved with an increase of the control surfaces. This feature is valid for all proposed architectures. The starting point (or reference configuration) is of course the B747-1 architecture: The Endless Runway

45 Page 45/89 1 Configuration Traditional REFERENCE Fuselage Classic AIRCRAFT number 4 Engine location Wing Wing Tail Landing Gear Low Classic Multi-Bogey Figure 4 : Reference configuration (4 engines) In order to improve the ground clearance, a first option leads to reduce the number of engines (keeping the same overall thrust) and to locate them in the best position along the span, that is to say closer to the fuselage as the external engines were the problematic ones. Particular attention should be given in this case to the critical diameter of the more powerful engines. 2 Configuration Traditional Fuselage Classic Engine number 2 location Wing Wing Low Tail Classic Landing Gear Multi-Bogey Figure 41 : Classical configuration with 2 engines In order to improve the ground stability a common rule recommends to increase the distance between the main landing gears. Moreover, this will increase the ground clearance of aircraft critical elements. The design team has identified four architectures that are based on two smaller fuselages. The idea is to account for the same passenger capacity, but to allow a larger landing gear track. Following this main idea, four options are proposed with variations on the engine number, position and lifting surfaces layout. The Endless Runway

46 Page 46/89 3 Configuration Fuselage Engine Wing Tail Landing Gear Double Fuselage Double Fuselage High Classic Multi-Bogey number 3 location Wing 4 Configuration Fuselage Engine Wing Tail Landing Gear Double Fuselage Double Fuselage High Classic Multi-Bogey number 2 location Wing 5 Configuration Fuselage Engine Wing Tail Landing Gear Double Fuselage Double Fuselage Low T Multi-Bogey number 2 location Tail The Endless Runway

47 Page 47/89 6 Engine Configuration Fuselage Wing Tail Landing Gear Triple Surface Double Fuselage Double Fuselage number 2 location Tail Low Classic Multi-Bogey Figure 42 : Bi-fuselage configurations Still with the idea to increase the landing gear track, a less impressive but also very innovative option is the double-bubble fuselage. This name comes after the shape of the structural cross section of the fuselage. 7 Configuration Fuselage Engine Wing Tail Landing Gear Classic Double Bubble Section Low T Multi-Bogey number 2 location Tail 8 Configuration Fuselage Engine Wing Tail Landing Gear Classic Double Bubble Section High Π Multi-Bogey number 2 location Wing Figure 43 : Large fuselage configuration The Endless Runway

48 Page 48/89 Introduced by MIT in the NASA N+3 studies [11], this solution, as illustrated in the previous figure, results in a larger (and automatically shorter) fuselage. In this case, the main landing gear can be moved along the span to increase its track. The proposed configurations are based on changes on the wing position as well as the engine position. As described in [18], the flying wing configuration is often cited as a possible architecture for 25 EIS airplanes. Its aerodynamic efficiency makes it indeed an appealing option for long range missions. It is then naturally considered as a possible candidate for ERAC. 9 Configuration Fuselage Engine Wing Tail Landing Gear Flying Wing No Fuselage - - Multi-Bogey number 2 location - Figure 44 : Flying wing configuration The last configuration to be considered for ERAC is derived from the ATR architecture [2]. This aircraft has a high wing that reduces ground clearance problems. Then, the idea is to extend the lower structure of the fuselage connected to the landing gear to achieve a larger track. Such solution requires a tailored fairing on this lower portion of the airframe to minimize the aerodynamic degradation. 1 Configuration Traditional Fuselage Classic Engine number 2 location Wing Wing High Tail T Landing Gear Multi-Bogey Figure 45 : large landing gear fairing configuration The Endless Runway

49 Page 49/89 Regarding configuration N 2, preliminary estimations of the necessary thrust lead to an important size of the engines that will be closer to the ground. Thus, this configuration still has ground clearance issues. For configurations N 3 to N 6, even though the ground stability would be increased, the quadricycle layout is not recommended for unconventional runways [21]. Another drawback of these configurations is that the twofuselage architecture results in a significant increase of the wing span. For the Endless Runway concept, this is a major drawback. Concerning the flying wing option, it has several interesting assets such as the possibility to have a tri-cycle layout for the landing gear with a large track. On the other hand, a known disadvantage is its poor controllability at low speeds. This is a clear stopper when designing an aircraft tailored for the Endless Runway concept. Concerning configuration N 1, preliminary aerodynamics assessments indicated that even if well optimized, the fairing would lead to an important drag penalty. For a long range mission aircraft such as ERAC, the result would be a non-acceptable fuel consumption. The down-selection converges then to configurations N 7 and N 8 as the most promising ERAC architecture, both based on the double-bubble fuselage. However, a closer look to configuration N 8 reveals that the fuselage would require local reinforcements: one in the upper area to fix the wing box and a second one in the lower area to withstand the landing gear loads. In this case, the fuselage weight would be higher than the one obtained for configuration N 7. The consortium decides therefore that configuration N 7 is the most promising option for ERAC. Its main features are synthesized here below: Double bubble fuselage; Low wing; T-Tail empennage; Two engines located in the rear fuselage ERAC sizing Sizing process In order to size ERAC, the design team combines a conventional statistical analysis [22] and the method presented by Jenkinson in [23]. The overall process is illustrated in the next figure: Figure 46 : Sizing process flow diagram The Endless Runway

50 Page 5/89 The statistical analysis requires at first to gather an important database of existing transport aircraft parameters. These data can focus on the overall aircraft (MTOW, cruise speed, etc.) or on certain components (empennages). Subsequently, interpolation rules are defined between the values and various independent variables (among them, the key mission figures: Mach, number of passengers, range) in order to provide a first estimation of ERAC s geometry and MTOW. Table 1 presents the airplanes that have been used to generate the database. It must be nothed that empennage data for the Airbus A35 and Boeing B787 have not been included in the calculation of the interpolation rules. Table 8 : Aircraft database for statistical analysis Manufacturer Model Version Manufacturer Model Version 3 6 R Airbus ER Boeing ER ER DC McDonnel Douglas DC1 3 Ilyushin Il-96 M MD11 ER MD12 HC However, ERAC is an unconventional airplane and such conceptual sizing based on historical data may lead to biased values. For this reason, the sizing process includes an iterative calculation of the necessary mission fuel and the weight estimation of the aircraft components (semi-empirical equations) as recommended in [23]. In order to complete this mission sizing, several assumptions have been made: Since ERAC targets an EIS in 25, the specific fuel consumption (SFC) has to consider evolutions that could be made in the next decades. In [24], a reduction of 15% to 2% for the SFC is indicated. Therefore, during the mission sizing, a value of 15% is taken to keep a conservative approach. Given the long term EIS of ERAC, the mission sizing must also consider the future progress regarding aircraft materials and structures. It is then assumed that composites will be fully mastered and applied on the main wing, control surfaces and empennage leading to a weight reduction of 2% with respect to today s data. For the nacelles, improvements are fixed to a lower value (1%) since composites are already used and the margin for improvement is smaller. ERAC is based on the innovative fuselage called Double Bubble proposed in [11]. The complexity of such structure cannot be captured by the equations proposed in [23]. However, this reference indicates a range for the fuselage with respect to MTOW between 7% and 12%. It is therefore decided to set the fuselage weight to 9% of MTOW to take into account a probable heavier structure because of the Double Bubble concept that is compensated by the use of advanced materials. This value is also corroborated by data obtained according to formulas provided in [22]. The Endless Runway

51 Page 51/89 To calculate the fuel consumption, the efficiency of ERAC must also be estimated. In order to be conservative, the design team made a 5% reduction of the calculated lift-to-drag ratio in [11] for the long range mission. The mission sizing considers then a cruise lift-to-drag of 2. Figure 47 : Double Bubble concept defined by the MIT team for a long range mission [11] To set the payload mass, it is assumed that a passenger weights about 75 kg, to which 2 kg of luggage must be added. For 45 passengers, the resulting payload weight is 4275 kg. Given future s trends regarding on-board systems, it can be foreseen that in 25, ERAC would be an all-electric aircraft (the propulsion system is still based on kerosene). However, it has been decided to design ERAC following today s standing that is a more electrical aircraft. For this reason, the aircraft sizing still considers some hydraulic components Engine selection The engine selection is a critical step in the sizing of a new aircraft concept. In order to determine in an accurate manner the required thrust for ERAC, the design team decided to follow the method proposed by Mattingly in [25]. In this approach, the different phases of the mission are analyzed from a performance point of view and described with an equation that relates the thrust-to-weight ratio (T/W) and the wing loading (W/S) of an airplane. Subsequently, constraints for the different segments are taken into account in the equations. By plotting the evolution of T/W versus W/S (a graph called constraint diagram ), it is then possible to identify the possible combinations that match the requirements. For ERAC sizing, a preliminary The Endless Runway

52 Page 52/89 review of the mission phases indicated that the most critical one regarding the engine sizing is as expected the take-off phase. For this reason, only the relationship between T/W and W/S for take-off has been examined. As a design objective, it is decided that ERAC should take-off in less than 3 meters on an Endless Runway to have an improvement with respect to the B747-1 (31 m). However, the constraint analysis proposed in [25] considers a classical take-off on a straight runway. Since the previous chapter detailing the B747-1 simulation showed an increase of the take-off distance about 9%, the take-off field length constraint has then been fixed to 25 meters. Such value in the early stages of the design process is voluntarily conservative in order to take into account possible performance degradations that are not yet identified. In addition, the design team considered the possibility to operate from an airport located at 3 ft. This latest requirement shifts the feasibility zone in the constraint diagram as illustrated below: Figure 48 : ERAC constraint diagram (take-off phase only) In Figure 47, all feasible T/W and W/S combinations that meet the 25 meters take-off distance on an airport at 3 ft are on or above the red line. As complementary information, values of existing airplanes have been added on the constraint diagram. During the sizing of an airplane designed to take-off and land from a conventional runway, designers have the freedom to choose the most appropriate values for the wing-loading and the T/W ratio. In the case of an airplane tailored to the circular track, the problem is somewhat different: because of ground clearance issues, the span (and thus the wing area) is limited. Thus, the only real variable parameter is the engine thrust. From a practical point of view, with the MTOW and wing area of ERAC converging to their definitive value after a few iterations, it has been possible to fix its wing loading and to identify the required thrust. With this value, the most suitable engine has been selected. The consortium prefers indeed to take an existing engine instead of non-existing one based on the semi-empirical model defined in [14] matching the exact required thrust to The Endless Runway

53 Page 53/89 have even more reliable reference data on weight, geometric characteristics and consumption to which technological improvements are then applied. This approach results in installing on ERAC an evolution of the GE9-94B (used on today s B777). For a wing loading of about 68 kg/m², T/W equals then to.327, a number that is above the constraint limit. To take into account the evolutions to be made on this engine in the next decades (25 EIS), designers decided to keep the geometry, mass and thrust level constant and to reduce the Thrust Specific Fuel Consumption (TSFC) by 15%. The sizing process considers then an engine with the following characteristics: Maximum thrust at sea level : kn; Maximum diameter : 3.4 m; Total length : 7.3 m; Weight : 755 Kg; TSFC :.458 lb/h/lbf ERAC geometry At the end of the sizing process, the main geometrical parameters of ERAC are defined. The next table details their values: FUSELAGE WING HORIZONTAL TAIL VERTICAL TAIL Table 9 : ERAC main geometrical data Length 66.4 [m] Maximum width 8.7 [m] Span 61 [m] Sweep (1/4 chord) 29 [ ] Area 392 [m²] Taper ratio.2 Span 2.9 [m] Sweep (1/4) chord 31 [ ] Area 81.5 [m²] Taper ratio.3 Span 8.1 [m] Sweep (1/4) chord 3 [ ] Area 6 [m²] Taper ratio ERAC weight breakdown After several iterations between the statistical analysis and the mission sizing according to Jenkinson s method, the process converges to a final value of MTOW and the weight breakdown is completed. The following table details ERAC weight breakdown: The Endless Runway

54 Page 54/89 Table 1 : ERAC Weight Breakdown Weight [kg] % Wing Control surfaces Flaps Empennage Fuselage Landing gear Nacelles Airframe Propulsion system Fixed equipment Empty weight Mission equipment Crew Operative Empty Weight Fuel Payload MTOW It is important to note that using solely the statistical analysis would have led to an MTOW of more than 3 kg (12.6% increase). The coupling of both approaches is then a valuable method that enables designers to decrease uncertainties during the sizing. It is obvious that the assumptions made during the mission sizing have a critical impact on the presented conceptual weight breakdown Final ERAC sketch In the final iterations of the sizing process, AVL [26] and OpenVSP [27] have been used in order to respectively calculate aerodynamics properties and to generate 3D models of ERAC. The acquired additional information allows a refinement of the concept. The following figure illustrates the final ERAC sketch obtained with OpenVSP: The Endless Runway

55 Page 55/89 Figure 49 : ERAC 3D sketch By modeling digital mock-ups, the design team has the possibility to determine the Center of Gravity position in various conditions. Thus, after a few iterations, the design team converges to an optimized position of the various components in order to obtain a satisfactory static margin for ERAC (the neutral point is provided by AVL). With the rear limit of the center of gravity (aft CG position) fixed, the position of the landing has been subsequently set and the shape of the fuselage has been designed in order to obtain the same tip-back angle as the B Since no ground contact issues have been observed in the earlier simulations with Flight Gear, no changes were necessary in this area. In addition, OpenVSP enables wet surface calculations for the aircraft main components. These values are very valuable for more accurate calculations of ERAC aerodynamics properties: Fuselage wet surface: 1175 m² Wing wet surface: 627 m² Horizontal tail wet surface: 163 m²; Vertical tail wet surface: m². The Endless Runway

56 Page 56/ ERAC ground clearance analysis From OpenVSP, it is possible to have an accurate front view of ERAC as illustrated in Figure 49 where it is possible to visualize the chosen landing layout, based on the B747-1 solution. It features a specific large track of the main landing gear to improve the ground handling on the circular runway and increase the ground clearance. d 1 d 2 d 3 Figure 5 : ERAC front view showing reference distances for ground clearance calculations From this drawing, the fixed distance d3 and the distances d1 and d2 for the critical element (only the wingtips in the case of ERAC) are measured and presented in the next table: Table 11 : ERAC key distances for ground clearance calculation Landing gear d3 7,6 [m] d1 5,2 [m] Wingtip d2 3,5 [m] The distance values and their corresponding position of the aircraft are then computed using a program in Python based on the mathematical formulas developed in Appendix B. Results are presented in the following table: Table 12 : ERAC ground clearance calculation for the wingtip Nominal Internal aircraft side External aircraft side distance on flat ground Minimum distance Corresponding abscissa of the center of the landing gear Minimum distance Corresponding abscissa of the center of the landing gear 5,2 [m] 2,48 [m] 122,8 [m] 2,67 [m] 99,2 [m] The Endless Runway

57 Page 57/89 As it will be explained in section 4.5.1, the simulated ERAC lift-off speed is about 174 kts (89,5 m.s -1 ). Therefore, according to Figure 16 (Speed distribution), the aircraft will never roll beyond the 1621 m radius runway circle. Hence the distance to the ground gets in the worst case close to 2,48 m for the downhill wingtip, which is acceptable and is an improvement compared with the B747-1, where the downhill outer engine distance to the runway could get close to 1,18 m. 4.3 ERAC model for Flight Gear Inertial properties Classical performance analyses take into account the weight of the aircraft and the center of gravity. In the case of 6DOF simulations, the inertial properties of the aircraft are also required. These parameters have been then determined with OpenVSP that offers the possibility to make the automatic calculation (see Figure 5). Figure 51 : Inertial properties of ERAC calculated with OpenVSP The next table details all inertial data calculated for three configurations. Because of symmetry of ERAC, products of inertia I XY and I YZ are fixed to. Table 13 : ERAC inertial properties MTOW Cruise Zero Fuel Weight Weight [kg] X CG [m] I XX [Kg.m 3 ] I YY [Kg.m 3 ] I ZZ [Kg.m 3 ] I XZ [Kg.m 3 ] The Endless Runway

58 Page 58/ Refined aerodynamics study Lift-to-drag ratio verification During the sizing process, an important assumption has been made regarding ERAC lift-to-drag ratio for the cruise segment (value fixed to 2). To verify the hypothesis, refined aerodynamics calculations with AVL [26] and an estimation of the zero-lift drag coefficient have been performed. As a first step, the necessary level of lift in cruise must be calculated. Assuming a consumption of half of the fuel and a cruise Mach number equal to.8, the reference lift coefficient for the cruise segment is fixed to Subsequently, AVL is used to find the elevator deflection and the angle of attack associated to the trimmed cruise condition. It is important to detail at this point several features of the AVL model that is used: The main wing is designed using the supercritical airfoil NASA SC(2)-412 with a twist law that avoids stall in the ailerons region; The horizontal tail uses the same airfoil but upside-down; The vertical tail uses a NACA 8 airfoil; In order to match the specific requirement about a better control at low speed, the control surfaces (elevator, rudder, ailerons) are sized using the upper values of the statistical data found in [28]; ERAC fuselage model is based on the D8.1 model that can be found in the AVL package [26] in order to take into account its contribution to the pitching moment. The reference Reynolds number is fixed to The figure here below illustrates the resulting loads on ERAC for the cruise trimmed condition: Figure 52 : Load distribution in the trim condition The associated AVL outputs indicate that the equilibrium is obtained for: α =.375 ; δe = 2.8 The Endless Runway

59 Page 59/89 Figure 53 : ERAC Trefftz Plane AVL enables also the calculation of the induced drag coefficient CD i. As shown in Figure 52, in the cruised trimmed condition, CD i =.147. In order to find the total drag coefficient of ERAC (CD ERAC ), it is necessary to estimate the zero-lift drag coefficient CD. Since CD takes into account the form drag, it is difficult to calculate its accurate value without performing numerical simulations. However, given the exploratory purpose of the Endless Runway project, such time consuming calculations are not viable. It is therefore decided to use the program friction.exe from Mason that can be found in [29]. This program offers the possibility to compute both friction and form drag with an accuracy that is sufficient for conceptual design studies. Using information about ERAC geometry available through the OpenVSP model of ERAC (wetted area and length of components), friction.exe provides the following outputs: CD friction =.944; CD form =.456. It is then possible to calculate the total drag coefficient of ERAC in the cruise trimmed condition: CD ERAC = CD + CD i = CD frictior + CD form + CD i CD ERAC = CD ERAC =.287 Knowing that the corresponding lift coefficient is.6517, the resulting lift-to-drag ratio is This value being superior to the one that has been used in the sizing process, the calculated fuel weight is larger than it could The Endless Runway

60 Page 6/89 be. The value of ERAC MTOW of tons is then higher than it could be. However, since there are some uncertainties related to the assumptions and calculations made during the conceptual study, it is decided that such a conservative approach is preferable and a new sizing process based on this efficiency of 22.7 is not performed Complementary aerodynamics coefficients for Flight Gear As for the B747-1 model, Flight Gear requires values for all aerodynamics coefficients (lift, drag, sideforce, rolling moment, pitching moment, yawing moment). Here below are presented the linear equations used to model these aerodynamic coefficients: For the lift coefficient: C L = C L + C Lα. α + C Lq. q + C Lδe. δ e + C LFlrp For the drag coefficient: 2 C D = C D + k. C L with C D = C DFrictior + C DForm + C DLrrdirgGerr + C DFlrp For the pitching moment coefficient: C m = C m + C mα. α + C mq. q + C mδe. δ e For the side force coefficient: C Y = C Yβ. β + C Yp. p + C Yr. r + C Yδr. δ r For the rolling moment coefficient: C l = C lβ. β + C lp. p + C lr. r + C lδr. δ r For the yawing moment coefficient: C r = C rβ. β + C rp. p + C rr. r + C rδr. δ r AVL is now used to calculate the necessary aerodynamics derivatives at different Mach numbers. The following tables detail the outputs of the aerodynamic assessment: The Endless Runway

61 Page 61/89 Table 14 : Reference database for the lift coefficent Mach C L C Lα C Lq C Lδe [/rad] [/rad/s] [/ ] Table 15 : Reference database for the drag coefficent Mach C di C L C L² k Table 16 : Reference database for the pitching moment coefficent Mach C m C mα C mq C mδe [/rad] [/rad/s] [/ ] Table 17 : Reference database for the side force coefficient Mach C Yβ C Yr C Yδr [/rad] [/rad/s] [/ ] Table 18 : Additional data for sideforce derivative α C Yp [/rad/s] The Endless Runway

62 Page 62/89 Table 19 : Reference database for the rolling moment coefficient Mach C lβ C lp C lδa [/rad] [/rad/s] [/ ] Table 2 : Additional data for rolling moment derivative α C lr [/rad/s] Table 21 : Reference database for the yawing moment coefficient Mach C nβ C np C nr C nδr [/rad] [/rad/s] [/rad/s] [/ ] Table 22 : Additional data for yawing moment derivative α C np [/rad/s] Regarding the Flap effect in Flight Gear, it is assumed in this first study that ERAC has the same high-lift devices as the B747-1 and they cover the same portion of the main wing. The Flap effects can then be extracted from the NASA reference document [12]. Also, since no changes have been made on the landing gear, its effect on the drag coefficient is the same as reported in [12]. The next table summarizes these impacts for ERAC: The Endless Runway

63 Page 63/89 Table 23 : Changes to CL and CD according to the flap position Flap C DLandingGear C DFlap C LFlap Based on the linear equations and the different tables presented earlier, the aerodynamics characteristics are implemented in the Flight Gear.xml file dedicated to ERAC D model To complete the Flight Gear Model, a 3D model of ERAC must be provided in the.ac format. The consortium uses again the program AC3D from Invis [8] to generate the virtual mock-up based on the three views made with OpenVSP. Figure 53 shows the final model with the Endless Runway project logo on the fuselage. It must be noted that in the AC3D model, the control surfaces are not created. Thus, during simulations, the user is not able to see their rotations following pilot s inputs. The aircraft behavior on the other hand takes into account deflections since the flight dynamic model relies on the.xml file. Figure 54 : ERAC 3D model for Flight Gear (.ac format) The Endless Runway

64 Page 64/ ERAC simulations With ERAC flight dynamic model completed and its.ac file validated, it is now possible to make carry out takeoff and landing simulations on the circular runway in Flight Gear (Figure 54) to assess the performance of the aircraft. Figure 55 : Take-off simulation with ERAC on a circular runway For the Flight Gear simulations and the associated performance analysis, two key parameters are the rotation speed and the landing speed that are directly derived from the stall speed. However, since the aerodynamic model used for ERAC is linear, stall cannot be simulated. Given the aerodynamic characteristics presented earlier in the report, it can be assumed that ERAC stall speed is lower than then one of the B It is then possible to use a conservative approach that fixes the key reference speeds to the ones of the B Therefore, ERAC simulations are performed with: a rotation speed set to 16 kts; a landing speed set to 144 kts. With this approach, the take-off performance comparison between the B747-1 and ERAC will mainly be affected by the increased Thrust-to-Weight ratio (there is a small variation in W/S between the two aircraft). The Endless Runway

65 Page 65/ ERAC performance analysis Take-off To analyze the take-off phase of ERAC, the same approach used with the B747-1 simulation is carried out. Again, the first plot to be reviewed is the aircraft trajectory. Illustrated in Figure 55, the flight path shows compliance with the circular take-off on the endless runway concept. Figure 56 : ERAC Take-off flight path In a second step, the recorded data are plotted to identify the rotation speed. Therefore, the consortium observes the evolution of the elevator input over time to fix the time at which the pilot commanded the aircraft rotation. In the second plot of Figure 56, it can be seen that the elevator deflection associated with the rotation occurs at t=4 seconds. At that time, the speed equals 166 kts which corresponds to a difference of 3.8% with reference value. The manual maneuver matches then the ideal ground trajectory detailed in [18]. The Endless Runway

66 Page 66/89 2 Airspeed [Knots] t [s] Elevator Position Norm. [-] t [s] Figure 57 : Evolution of the airspeed and the normalized elevator position over time for ERAC Subsequently, the lift-off speed is verified through the observation of the recorded vertical speed data. From the first plot of Figure 57, it can be seen that ERAC becomes airborne at t=43 seconds. From the second plot of Figure 57, the corresponding lift-off speed is identified (174 knots). With respect to the reference speed provided in [12], the difference is about 3.5%: the manual take-off is then performed accordingly to the reference procedure. 2 Vertical speed [m/s] t [s] 2 Airspeed [Knots] t [s] Figure 58 : Evolution of the vertical speed and airspeed over time for ERAC The Endless Runway

67 Page 67/89 To conclude the take-off distance analysis, the evolution of the altitude is plotted over time. Given the shape of the runway cross-section, at lift-off (t=43 s), ERAC should be at a height of 21 meters. In the first graph of Figure 58, it is shown that at t=43 seconds, an altitude of 2 meters is reached. With such a small difference compared to the ideal trajectory, the manual take-off simulation is accepted. Since the definition of the take-off distance (see ) considers a 35 ft obstacle above the lift-off height, the take-off ground distance in the second graph of Figure 58 must be considered from t= to t=46s, when the aircraft reaches 31 meters. According to the recorded data ERAC takes 245 meters to complete the take-off phase (with all engines operative). 15 Altitude [m] t [s] 3 Ground Distance [m] t [s] Figure 59 : Altitude and ground distance variation over time for ERAC The performance analysis is completed by reviewing the steering inputs and lateral accelerations during takeoff. The first plot in Figure 59 demonstrates that it is possible to control ERAC during the take-off run with discontinuous inputs (with increasing values) that are never close to the physical limit (7 degrees). The average value is notably low as it reaches 1.6 degrees. The second plot in Figure 59 focuses on the other hand on the lateral accelerations that are sustained by the passengers during the take-off phase. The limit of 1.2 m/s² is never exceeded and the average value is low (.2133 m/s²). The Endless Runway

68 Page 68/89 2 Steering [deg] t [s] Acceleration along Y [m/s²] t [s] Figure 6 : Steering and lateral acceleration variation over time for ERAC Landing In order to analyze the landing segment carried out with ERAC, the same telemetries as in section are reviewed. In order to have an overview of the landing phase, the trajectory is plotted in 3 dimensions (Figure 61). Flight Path 3 2 z [m] y [m] x [m] Figure 61 : Landing Flight Path with ERAC The Endless Runway

69 Page 69/89 On the previous figure, it is possible to see the trajectory of the air segment that is tangent to the circular runway. In addition, the circular ground run on the runway is visible. By looking at the recorded value of the landing gear compression ratio, it can be said that touchdown happens at t=4 seconds. At this time, the airspeed is about 136 kts, which is extremely close to the landing speed during simulations with the B L.G.2 c ompression Airspeed [Knots] t [s] t [s] Figure 62 : Evolution of the landing gear compression and the airspeed over time with ERAC Given the runway cross-section and its associated speed distribution, such speed is attained when the runway is about 1 meters above the ground (simulation indicates 1.5 meters which shows that the simulated procedure matches the objective). Given the definition of the performance criteria in , it can be said that the landing distance starts when the aircraft has an altitude of 26 meters (t=.5s). The plots presented in Figure 63 indicate then a landing distance of about 193 meters. The Endless Runway

70 Page 7/89 3 Altitude (m] t [s] 2 Ground Distance [m] t [s] Figure 63 : Altitude and ground distance evolution over time with ERAC Since the B747-1 and ERAC have approximately the same W/S and the landing speed is the same, this result is not surprising. As for the passenger comfort, the recorded lateral accelerations show that the limit of 1.2 m/s² is never exceeded and the average value is about.47 m/s². Acceleration along Y [m/s²] t [s] Figure 64 : Lateral acceleration evolution over time with ERAC The Endless Runway

71 Page 71/ Requirements review In [16], a list of requirements for ERAC has been defined. The following table recalls these requirements and details how ERAC complies with them. REQ AIRCRAFT Number Definition The endured acceleration during the curved ground roll at take-off and landing shall not exceed sustainable values for passengers safety and comfort. The take-off and landing speeds shall be within the maximum speed allowed by the runway. The aircraft shall land at a precise point at a given speed and a given bank angle. The aircraft shall take-off at a precise point at a given speed and a given bank angle. Take-off and landing vertical slopes shall be high enough to avoid any contact between the extended landing gears and the higher part of the runway when the aircraft is airborne and overflying the runway. The landing gear shall be able to withstand the loads generated during landing. The landing gear layout shall provide satisfactory stability during ground run (take-off and landing). Engines forces should consider a ground run on a circular and therefore non-symmetrical runway. The tip-back angle of aircraft should be tailored to the runway transversal profile to avoid ground contact during take-off rotation. Comments During take-off ERAC is not subject to lateral accelerations above the limit of 1.2 m/s². For landing, ERAC sustains really short lateral accelerations above 1.2 m/s². The average value over the complete manoeuver is however well below the limit. The rotation speed and the landing speed of ERAC are the same as the B747-1 and therefore, they are within the maximum speed allowed by the runway. Within Flight Gear, it has been possible to manually land ERAC at a precise point at a given speed and a given bank angle. Within Flight Gear, it has been possible to manually takeoff with ERAC at a precise point at a given speed and a given bank angle. Take-off and landing simulations of ERAC with Flight Gear have been performed without contact between the extended landing gear and the runway. During landing, the landing strut never reaches its physical limit. ERAC has an increased landing gear track. It is thus more stable during ground rolls. The engines located on the rear part of the fuselage are close to the symmetry plane. In the OEI case, the required compensation would be less than on a classical aircraft with engines under the wing. The ground run on a nonsymmetrical runway is then less risky. The rear part of ERAC s fuselage has been designed to have the same tip-back angle as the B There haven t been indeed any ground contacts during simulations with the B The Endless Runway

72 Page 72/ The aircraft configuration shall ensure clearance between aircraft components (e.g., wingtips and engines) and the banked runway. The flight crew shall receive the landing or take-off point in negotiation with ATC. The flight crew shall be able to follow the take-off and landing sequence thanks to appropriate on-board navigation systems. The engines located on the rear part of the fuselage allow a larger ground clearance for ERAC. This specific requirement that has not been considered in the early stages of ERAC design and simulations. This specific requirement that has not been considered in the early stages of ERAC design and simulations. 4.7 Conclusion on exchange parameters The simulations performed in Flight Gear on ERAC enabled the consortium to define the exchange parameters associated to T3.2: Size of the circle (radius) Simulations in Flight Gear showed that the value of 15 meters for the internal radius of the runway was not a stopper when performing take-offs and landings with ERAC. Profile of the runway (bank angle) The profile of the runway has been selected following simulations with the B747-1 solely as indicated in [3]. Width of the runway The width of the runway has been selected following simulations with the B747-1 solely as indicated in [3]. Aircraft landing gear During take-off and landing operations performed with ERAC model in Flight Gear, the landing gear struts (based on B747-1 parameters) always operated within the defined ranges. Aircraft engine design ERAC sizing according to specific constraints leads to a higher thrust-to-weight ratio than today s airplanes. This increase is required given the limitation on decreasing the wing loading (aircraft span is limited because of the ground clearance). Take-off performance From the simulations and the subsequent data analysis, ERAC decreases the take-off distance on a circular runway of about 21% with respect to the Boeing as expected because of the higher Thrust-to-Weight ratio. Landing performance From the simulations and the subsequent data analysis, ERAC needs as expected the same landing distance as the Boeing (similar W/S). However, it must be noted that the landing speed at which the simulation have been performed is a conservative choice. The landing distance could then be smaller. The Endless Runway

73 Page 73/89 Lateral acceleration ERAC simulations performed in Flight Gear indicated that the lateral accelerations during take-offs and landings are below the accepted limits. The Endless Runway

74 Page 74/89 5. Conclusion 5.1 Aircraft aspects for the Endless Runway The study of the aircraft aspects of the Endless Runway had to answer to five decisive requirements in order to contribute to an overall assessment of the innovative system that includes airport assessment and ATM integration: To indicate whether it is possible for a 21 civil transport aircraft to take-off and land on a circular runway; To investigate the required changes on an aircraft to use the Endless Runway concept; To calculate the take-off and landing performance of the aircraft; To identify the best suited new configuration for taking-off and landing from a circular runway; To compare the take-off and landing performances of this unconventional aircraft to the ones of a standard aircraft. Given the requested level of details, a new design and simulation environment more advanced than the usual conceptual design process used in prospective studies has been set-up by the consortium. Since the analysis of the aircraft behavior on a banked circular runway necessitates a complete 6 DOF dynamic model, this new environment is based on the use of Flight Gear, a free and open-source simulator. Then, a suite of tools (OpenVSP, AVL, friction.exe, AC3D) has been added to the classical sizing methods in order to provide all mandatory inputs for the take-off and landing simulations. From a practical point of view, this innovative process allows to simulate a mission with any aircraft of which characteristics are indicated by designers (existing reference data or results of a multi-disciplinary design). During the mission, key aircraft parameters (speed, altitude, etc.) are recorded. Subsequently a post-flight analysis as the one completed during flight tests is completed in order to determine the aircraft performances. In a first step, this environment has been used to model a current aircraft (Boeing 747-1) based on reliable data, to assess its feasibility to take-off and land on a circular runway and to determine its performances in the standard all-engines-operative case. The first result from the Flight Gear simulations is that a Boeing B747-1 with no specific modifications can take-off and land from the banked runway with average lateral accelerations that are within the acceptable limits. However, the maneuvers are riskier than on a classical track because of the smaller ground clearance. In addition, the telemetry analysis indicated that in the case of the Endless Runway, the take-off and landing distances increase respectively of about 8.4% and 12.8%. Regarding take-off, this increase is due to the nonlinear trajectory as well as the positive slope that the aircraft has to counter during the ground roll. This difference is then used by the consortium as a key exchange parameter for the evaluation of the ATM aspects. Still related to B747-1, additional parametric studies have been made in order to select the most appropriate runway cross section as well as its reference width. Initial simulations indicated that a cross section generating a square speed distribution is not suited for take-off because of the smaller ground clearance. Then, the consortium decided to select the shape associated with a linear speed evolution since it limits the runway height (associated to cost) and there is no difference regarding the level of performances when compared with the cross section offering a square root speed distribution. Regarding the reference width, the value of 14 meters has been selected as a good trade-off between 15 m and 13 m in order to once again limit the overall size while reducing the lateral acceleration sustained by the passengers. These conclusions have been also used by the consortium as a key exchange parameter required for the airport design. In a second phase, the design and simulation process has been used to define an airplane tailored to the circular runway, which is called Endless Runway Aircraft (ERAC). From a mission point of view, ERAC is capable to transport 45 passengers at Mach.8 over a distance of 8 Nm. Taking into account the ground clearance The Endless Runway

75 Page 75/89 issue that may appear on classical aircraft architecture, the necessity for an improved ground handling and the need to improve the take-off and landing performances, ERAC features: A double bubble fuselage (as the D8 series proposed by MIT) enabling a larger landing gear track and providing a certain lift; A T-tail empennage; 2 engines providing a thrust-to-weight ratio of.32 located in the rear part of the fuselage decreasing thus the risk of contact with the runway; Larger control surfaces to increase its maneuverability during low-speed phases. The conservative sizing resulted in a large aircraft of about tons of which higher ground clearance reduce in an important manner the risk of ground contact during take-offs and landings with respect to a B In addition, the take-off distance in the nominal case (all engines operative) on the Endless Runway is reduced of about 21% without generating critical accelerations for the passengers. For landing, since there are no significant changes on W/S between ERAC and the B747-1, the landing distance is the same. Improvements on the sustained accelerations must be however noted. The tailored ERAC airplane offers then a level of takeoff performance on a circular runway that is better than the B747-1 on a classical runway. Such an improvement is a key element in achieving the calculation of the airport capacity 1. Overall, this complete work focused on the aircraft aspects of the Endless Runway allowed the development of an innovative design and simulation environment, the assessment of an existing aircraft through 6DOF simulations, the evaluation of different runway shapes and the design of a tailored new concept. These efforts provided by the consortium to achieve these goals are valuable and the associated development of competences will be used in future European projects. Moreover, this project demonstrated that a true revolutionary solution for the future of air transport is viable only if benefits are observed considering at the same time the aircraft, the airport and the air traffic management. 5.2 Perspective Looking at future studies related to the aircraft aspects of the Endless Runway, it must noticed that ERAC design relied primarily on low-fidelity tools. There are thus several tasks that should be completed in order to improve the definition of the new airplane: Definition of key performances indicators for operations on an Endless Runway The definition for the take-off and landing distance (see ) has a strong impact on the performance level of the aircraft. Before initiating further technical studies regarding the aircraft aspect, it is then mandatory to discuss and define with the support of regulatory texts the safest performance indicators. Double bubble fuselage weight estimation ERAC features the innovative fuselage concept proposed by MIT. However, the weight estimation relied on statistical data and the results are thus uncertain. A detail structural analysis of the double bubble fuselage would then add a notable accuracy in the sizing process. Automated mission Even if the manual flights performed in Flight Gear resulted in reliable outputs, a fully automated mission would lead to quicker results and would help in the extension of the parametric studies. Such 1 The ATM simulations leading to the Endless Runway airport capacity estimations were done in parallel, and therefore are based on current aircraft performances ([34]). The Endless Runway

76 Page 76/89 automation would allow also to assess the impact of various trajectories with an accurate control of the vertical speed for example. High-fidelity aerodynamics assessment part 1 The use of AVL and friction.exe allowed a rapid first estimation of the lift-to-drag ratio of ERAC. However, given the unconventional shape of the fuselage, CFD calculations would be required in order to reduce uncertainties, especially regarding drag. High-fidelity aerodynamics assessment part 2 CFD calculations would be required to assess with accuracy the ground effect on a circular runway, especially with changes on the wing tip ground clearance associated to the local bank angle, or with the wing tip located outside the reference width. High-fidelity aerodynamics assessment part 3 All simulations have been performed without considering side-wind. However, before running such tests, a model of the wind profile on the circular runway must be generated. A CFD assessment would then be necessary to capture the physics behind the complex phenomena that consists of two asymmetric cases: for a given cross section, the wind can come from the external side and the internal side. Design of an all-electric aircraft In the present study, the sizing of ERAC considers hydraulic components. Given its EIS, it is highly probable that the airplane would be all-electric regarding the systems. It would then be necessary to perform a complete resizing of ERAC focusing on the evolution of the on-board systems between today and 25. Such a study would also include specific analyses of the required equipment to be installed both on the aircraft and on the ground to perform fully automated take-offs and landings. Refined 3D Model of ERAC The current ERAC model generated with AC3D only features the external shell, the landing gear and a basic cockpit. For futures studies, even if it is not mandatory for research purposes, it would be better for dissemination purposes to enhance this model by adding the movable control surfaces as well as the high lift devices. In addition, following a more accurate study of the on-board system, the cockpit could be completely redesigned to match the specific constraints related to automated take-offs and landing on circular runways. Smaller AC design The selected configuration for ERAC is directly related to its long range mission. It would be interesting to perform the same architecture exploration for a medium range aircraft. In this case, the solution proposed by Bombardier with its Q4 looks tailored for an Endless Runway. The Endless Runway

77 Page 77/89 6. References [1] Flightpath 25 Europe s Vision for Aviation, Report of the High Level Group on Aviation Research, 211 [2] Aeronautics and Air Transport: Beyond Vision 22 (Towards 25), Background Document for ACARE (Advisory Council for Aeronautics Research in Europe, 21 [3] Anderson J. D., Aircraft performance and design, McGraw-Hill, [4] Cook M. V., Flight Dynamics Principles, Butterworth-Heinemann, 28. [5] Website: [6] Website: [7] Website: [8] Website: [9] Website: [1] Raymer D. P., Advanced Technology Subsonic Transport Study N+3 Technologies and Design Concepts, 211. [11] The MIT, Aurora Flight Sciences, and Pratt&Whitney Team, Greitzer E. M., Slater H. N., Volume 1: N+3 Aircraft Concept Designs and Trade Studies, 21. [12] Hanke C. R., The simulation of a Jumbo Jet Transport Aircraft Volume II : Modeling data, D6-3643, 197. [13] Website: [14] Roux E., Pour une approche analytique de la dynamique du vol, PhD thesis, 25 [15] Roux E., Réacteurs simple et double flux, 27 [16] Hesselink H. et.al., D1.3 The Endless Runway Concept Description, The Endless Runway Concept, High-level overview, Deliverable of the Endless Runway Project, version 2., December 212 [17] The Circular Runway, AD , 1965 [18] Loth S., Dupeyrat M. et.al., D1.2 - The Endless Runway State of the Art, runway and airport design, ATM procedures and aircraft, Deliverable of the Endless Runway Project, version 2., November 211 [19] Website: [2] Website: [21] Raymer D. P, Aircraft Design A Conceptual approach, AIAA Education Series), 1999 [22] Roskam J., Airplane Design: Part I Preliminary Sizing of Airplanes, Darcorporation, 1985 [23] Jenkinson L. R., Simpkin P., Rhodes D., Civil Jet Aircraft Design, 1999 [24] Seitz A., Schmitt D., Donnerhack S., Emission Comparison of Turbofan and Open Rotor Engines under Special Consideration of Aircraft and Mission Design Aspects [25] Mattingly J. D., Heiser W. H., Pratt D. T., Aircraft Engine Design, AIAA, 22 [26] Website : [27] Website : [28] Roskam J., Airplane Design: Part II Preliminary Configuration Design and Integration of the Propulsion System, Darcorporation, 22 [29] Website : [3] Schmollgruber P., D3.1 Work Plan WP3 Aircraft Configuration, Deliverable of the Endless Runway Project, version 1., January 213 [31] Traction éléctrique, Jean-March Allenbach and all, deuxième edition entièrement revue et augmentée, Presses Polytechniques et Universitaires Normandes [32] Avions civils a réaction : Plans 3 vues et données caractéristiques, éditions Elodie Roux, 27 [33] Center of mass tutorial: [34] Loth S., Dupeyrat M., Hesselink H., D4.3 The Endless Runway Simulation: Modelling and Analyses, Deliverable of the Endless Runway Project, version 1., September 213 The Endless Runway

78 Page 78/89 Appendix A Key parameters of the Endless Runway project The following table presents the key parameters of the Endless Runway project produced and exchanged between the following work packages of the project: WP2 - Airport, WP3 - Aircraft and WP4 - ATM. Parameter WP2 WP3 WP4 Size of the circle (radius) contribute contribute yes Profile of the runway (bank angle) yes Width of the runway yes contribute Outer area of the runway (connection to outside) yes contribute High speed exits and entries contribute yes Taxiway lay out (incl. inner and outer circles) yes contribute Apron lay out yes contribute De-icing areas location yes TMA lay out Terminal building location & organisation (incl. pax movements) yes yes contribute Other buildings locations, incl. tower yes contribute Gate and stand distribution yes contribute Airport curb side and APM yes Aircraft landing gear Aircraft engine design yes yes Other coordination issue WP2 WP3 WP4 High-level scenarios yes Simulation scenarios Runway operational procedures (landing) Runway operational procedures (take-off) yes yes yes Take-off performance Landing performance yes yes Runway allocation (segments) Taxiway operational procedures TMA operational procedures yes yes yes Key Performance Indicators for the simulations evaluation contribute contribute yes The Endless Runway

79 Page 79/89 Appendix B Appendix B.1 Detail of the calculations Calculation of the various runway profiles equations x V 2 y = 1 g R 1 + x dx R Three runway profiles are studied, where the speed V varies as a function of the aircraft position on the runway, represented by its abscissa x: 1. Linear V = K x 2. Square V = K x 2 3. Square Root V = K x 1. Linear relation V = K x y = K2 gr X x x dx R Let s transform the polynomial form in a form that can easily be integrated: x 2 x 2 x x + 1 x x = R 2 R 1 + x 2 R = R 1 + x 2 R = R R 1 + x = R 2 1 R R R R x x 1 R R Then : y = K2 X 1 R 2 gr x x 1 dx = K2 R R g 1 x 2 x + R 2R ln 1 + x X = K2 2 R R g 1 X R X + ln 1 + X R R R To conclude: y = K2 2 R g 1 X R X + ln 1 + X, with K = R R V mrx W rrrrrr The Endless Runway

80 Page 8/89 2. Square relation V = K x 2 y = K2 gr X x x dx R Let s transform the polynomial form in a form that can easily be integrated: x 4 x 4 x x x x = R 4 R 1 + x 4 R = R 1 + x 4 R = R R R R R Then: X y = K2 R 4 1 gr x + x x R R dx R To conclude: = K2 R 3 g x4 1 + x R = R 4 3 4R x3 2 3R + x2 x + R 2R ln 1 + x R = K2 3 R X4 g 3 4R X3 2 3R + X2 X + R 2R ln 1 + X R 1 + x2 R 2 x R + 1 x R X 1 + x R y = K2 3 R X4 g 3 4R X3 2 3R + X2 X + R 2R ln 1 + X, with K = V mrx 2 R W rrrrrr The Endless Runway

81 Page 81/89 3. Square Root relation V = K x y = K2 gr X x 1 + x dx R Let s transform the polynomial form in a form that can easily be integrated: x 1 + x R Then : x x R = R R 1 + x = R 1 + x = R x R R R X y = K2 R gr x dx = K2 g x R ln 1 + x X = K2 R g X R ln 1 + X R R To conclude: y = K2 g X R ln 1 + X R, with K = V mrx W rrrrrr Appendix B.2 runway profile Calculation of the runway volume for the linear speed evolution The aim is to calculate a primitive of V = 2πK2 2 R To get a primitive of a polynomial form in (x-r ), we proceed as follows: g R x 1 (x R ) 2 2 R 2 x R + ln 1 + x R dx. R R R V = 2πK2 2 R ((x R g ) + R ) 1 (x R ) 2 2 x R + ln 1 + x R dx 2 R R R R R V = 2πK2 2 R 1 2 g 2R ((x R ) 3 + R (x R ) 2 ) 1 (x R R ) 2 + R (x R ) + xln x dx R R R V = 2πK2 2 R (x R ) (x R g 2R 2R ) 2 + (x R ) + xln x dx R R A primitive of the function x xln x can be calculated by integration by parts: R We state that: R u(x) = ln x R v (x) = x u (x) = 1 x v(x) = x2 2 xln x dx = [v(x)u(x)] u (x)v(x)dx = x2 R 2 ln x x x2 dx = R 2 2 ln x x2 R 4 Therefore: The Endless Runway

82 Page 82/89 V = 2πK2 2 R (x R ) 4 2 (x R ) 3 (x R ) 2 + x2 g 8R 6R 2 2 ln x x2 R R 4 R Appendix B.3 Runway Ground clearance of aircraft critical elements with the Endless Let s pose: R : inner radius of the circular runway W: runway width in its inner part S: runway stop point where the external part of the runway meets the ground The function f, continuous and differentiable, representing the transversal profile of the runway is defined on the [ R, S] interval as: if R x x f(x) = f 1 (x) if x W (with f 1 () = ) f 2 (x) if W x S (with f 2 (W) = f 1 (W)) For differentiability reasons, we will also make sure that: f 1 (+) = f 1 (W ) = f 2 (W +) The aircraft is located on the inner part of the runway of which the transversal profile is defined as above by the function f. The relevant aircraft elements are modelled geometrically in a simplified way. The absorption of the landing gears is not taken into account. On the following transversal view, the aircraft is considered to move tangentially to the runway, whereas in reality it will head slightly towards the outwards or the inwards of the runway (steering always lower than 6 ). The following figures present the various points that are considered for the calculation. z f 2 O f 1 I I C d J θ x J G d d F E E W S x The Endless Runway

83 Page 83/89 x E d 2 45 I W R Figure 65 - Transversal and top views of the aircraft on the runway C: center of the line passing through the considered symmetrical aircraft elements J: point of contact between the ground and the left landing gear outer wheel F: point of contact between the ground and the right landing gear outer wheel G: center of segment [JF] (middle of the landing gear) E: external aircraft element E : shortest distance between E and the graph of f I: internal aircraft element I : shortest distance between I and the graph of f θ: angle between (JF) and z= (as the absorption of the landing gears is not taken into account, it will be the same angle than between (IE) and z=). d 1 : distance between the center of the line passing through the considered symmetrical aircraft elements and the ground d 2 : distance between the center of the line passing through the considered symmetrical aircraft elements and the element d 3 : half width of the main landing gears span (half the distance between J and F) d 1, d 2 and d 3 are known aircraft geometrical properties. We suppose that d 3 < d 2. O The distance between aircraft elements (wingtips, engines) and the ground is reduced on the circular runway compared to a flat runway due to its curved profile. For example, if we consider an element placed at point E (e.g. wingtip, bottom of the engine or of the propellers), its clearance to the ground is equal to the distance between E and E. The same reasoning applies between for the inboard element I for which the clearance to the ground is equal to the distance between I and I. The Endless Runway

84 Page 84/89 Let s find an analytical expression of these distances. As J can move along the runway profile, the coordinates of F, G, C and E are determined based on the abscissa of J, x J. We will concentrate on the runway part where the aircraft operates, that is to say between and W where f is defined by f1 ( x J < x F W). The coordinates of the reference point J are: Let s first find θ, F and G. By construction: JF = 2d 3 J x J z J = f 1 (x J ) Trigonometric considerations give the following system: These two equations can combine and be expressed as: x F x J = 2d 3 cos θ f 1 (x F ) f 1 (x J ) = 2d 3 sin θ f 1 (x J + 2d 3 cos θ) f 1 x J 2d 3 sin θ = (1) Solving this equation will give us the value of θ for each position of the aircraft on the profile. Knowing θ, we can now compute the coordinates of F: F x F = x J + 2d 3 cos θ z F = f 1 (x F ) = f 1 x J + 2d 3 sin θ As G is at the middle of the segment [JF], we find the coordinates of G: Which is equivalent to: x G = x J + x F G 2 z G = z J + z F 2 G x G = x J + d 3 cos θ z G = f 1 x J + d 3 sinθ Then, geometrical considerations allow determining the coordinates of C: Which can be expressed as: C x C = x G d 1 sin θ z C = z G + d 1 cos θ C x C = x J + d 3 cos θ d 1 sin θ z C = f 1 x J + d 1 cos θ + d 3 sin θ A. Distance between an external element of the aircraft and the runway The coordinates of E can be obtained from the Chasles relation: OE = OC + CE Knowing C coordinates, geometrical considerations give: The Endless Runway

85 Page 85/89 Or better: E(x G d 1 sin θ + d 2 cos θ ; z G + d 1 cos θ + d 2 sin θ) E x E = x J d 1 sin θ + (d 2 + d 3 )cos θ z E = f 1 x J + d 1 cos θ + (d 2 +d 3 )sin θ Let s now compute the shortest distance between E and the runway. 1. The aircraft is completely on the flat part inwards of the circular runway E is also above the flat section. The distance between E and the ground is equal to d The departing aircraft arrives on the runway from the high-speed 45 taxiway and finishes its turn on the runway to line up tangentially to a circle of the circular runway, or the arriving aircraft leaves the runway towards the high-speed exit taxiway The distance between E and the runway is minored by the distance when the aircraft is tangent to the runway circle. This corresponds to case 3 described below. 3. The aircraft rolls on the inner part of circular runway In this configuration, J and F are above the inner runway profile defined by f 1. When F reaches the limit with f 2, it means that is abscissa is equal to W, as shown on Figure 61. z d 2 F mrx f 2 J mrx d 1 d 3 G mrx O f 1 θ mrx x Jmax W S x Figure 66 - Aircraft position when the landing gear reaches the limit between f1 and f2 This limit translates mathematically into the following coordinates of F max : F mrx x F max = W z Fmax = f 1 (W) Using the previous expression of the coordinates of F: W = x J max + 2d 3 cos θ mrx f 1 (W) = f 1 x Jmax + 2d 3 sin θ mrx x J max = W 2d 3 cos θ mrx f 1 x Jmax = f 1 (W) 2d 3 sin θ mrx Solving the following equation allows to find θ max : Knowing θ max, let s find the coordinates of J max : f 1 (W 2d 3 cos θ mrx ) f 1 (W) + 2d 3 sin θ mrx = The Endless Runway

86 Page 86/89 J mrx x J max = W 2d 3 cos θ mrx z Jmax = f 1 (x Jmax ) In the next paragraphs, we will therefore consider that x J x Jmax. The purpose is to minimize the distance between E(x E, y E ) and a point M x (x, f(x)) of the runway profile defined by f 1, e.g. d(x) = (x x E ) 2 + (f 1 (x) z E ) 2. To reach this minimum, we can compute the derivative of d. d (x) = 1 2 2x 2x E + 2f 1 (x)f 1 (x) 2y E f 1 (x) d(x) = (x x E) + f 1 (x)(f 1 (x) z E ) d(x) Of course, we assume that the distance between E and the runway profile is never null, e.g. d(x), as no aircraft element should be in contact with the ground. Let s take a look at the numerator of d (x), N(x) = (x x E ) + f 1 (x)(f 1 (x) z E ). It can be seen as the scalar product of EM x (x x E, f 1 (x) z E ) and V 1, x f 1 (x), which is a direction vector of the tangent to the profile at the point M x. We can rewrite: N(x) =. EM x V x We are at an extremum of d when its derivative gets null and its sign changes. The derivative is null means that N(x) =. EM x V x =, in other words, (EM x ) and the tangent to f 1 at point M are perpendicular. Due to the complexity of the f 1 function, it is not possible to prove analytically that the sign changes only once in order to prove the uniqueness of M x. However, drawing the function N (equivalent to d in terms of the sign variations and annulation) with a Python program has shown that it gets null only once on the considered interval. This means that the distance is minimized for only one point of the runway profile, where the tangent to f 1 is perpendicular to the line passing through this point and E. This unique point is named E. Figure 67 - Distance between an aircraft external element E and the runway profile points for various positions of J As we have seen before, its abscissa x E is solution of the following equation: Its ordinate is obviously equal to z E = f 1 (x E ). d (x) = (x x E ) + f 1 (x)(f 1 (x) z E ) = From a programming point of view, looking for E is more efficient than computing the distances between E and the points of the profile and then finding the minimum, this for all positions of J. The Endless Runway