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1 MASTER THES SIS Estimating take-off and landing performance from a reduced set of measured flight parameters Ramon Bernat Puigfarregut SUPERVISED BY Dr. Adelinee Villardi de Montlaur Dr. Alastair Kingsbury Cooke Universitat Politècnica de Catalunya Master in Aerospace Science & Technology April 2011

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3 Estimating take-off and landing performance from a reduced set of measured flight parameters BY Ramon Bernat Puigfarregut DIPLOMA THESIS FOR DEGREE Master in Aerospace Science and Technology AT Universitat Politècnica de Catalunya SUPERVISED BY: Dr. Adeline Villardi de Montlaur Escola d'enginyeria de Telecomunicació i Aeroespacial de Castelldefels Dr. Alastair Kingsbury Cooke National Flying Laboratory Centre (Cranfield University)

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5 ABSTRACT This MSc Thesis was undertaken within the National Flying Laboratory Centre in Cranfield University. Two studies were tasked from a set of measured flight parameters. These parameters were recorded by the on-board Inertial Reference System of one of the Centre s airplanes: the British Aerospace Jetstream 31. Three main codes in MATLAB were programmed in order to process the data provided. The conclusions were extracted from the codes outputs. Motivated by a crack appearance at the main landing gear, the first study was aimed to find a way of accurately stating the sink rate for each landing and its vertical acceleration peak at the centre of gravity. Through an iteration as a main operation, this study code deduced an airplane operation fulfilling the manufacturer s specifications. On the other hand, the second study was promoted to consider the low speed performance calculation for teaching purposes. The code, in this case, processed the data provided to find which is the most reliable in order to calculate the Takeoff and Landing distances. After comparing the code outputs obtained with the performance manual parameters, the best source to compute the distances were the body accelerations.

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7 Acknowledgements The Author would like to thank Dr. James Whidborne as a Head of Dynamics Simulation and Control Group for affording the choice to develop the MSc thesis in Cranfield University. The Author would also like to thank Dr. Alastair Cooke and Dr. Jim Gautrey for their supervising and consulting roles, respectively, in the National Flying Laboratory Centre. As well, the Author would like to thank Dr. Adeline Villardi de Montlaur for the thesis topic approval in Cranfield University. Finally the Author would like to thank his family and friends for their support and understanding.

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9 Table of Contents 1. INTRODUCTION Thesis introduction National Flying Laboratory Centre NFLC resources Aims and Objectives Background and History Touchdown Severity study Takeoff and Landing distances study Thesis Overview Considerations for the Takeoff and Landing distances study PREVIOUS CONCEPTS Function irs_earth Accelerations transformation from IRS to CG Accelerations based on the Earth System Function tdlo Function nosteps STUDY OF THE TOUCHDOWN SEVERITY Code explanation Code outputs Conclusions & Proposals STUDY OF THE LANDING & TAKEOFF DISTANCES Codes explanation Format A Format B Codes outputs Landing distances Takeoff distances Conclusions & Proposals BIBLIOGRAPHY... 39

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11 List of Figures Fig. 1.1 British Aerospace Jetstream 31 (Cranfield University)... 2 Fig. 1.2 Scottish Aviation Bulldog Series 120 (Cranfield University)... 3 Fig. 1.3 BAe-j31 Accident cause on February 2009 in Greece... 5 Fig. 1.4 Takeoff and Landing heights (NASA)... 7 Fig. 1.5 BAe Jetstream 31 landing at Cranfield Airport... 7 Fig. 2.1 Function irs_earth flow diagram... 9 Fig. 2.2 Absolute position of IRS and CG on the airplane [m] Fig. 2.3 Relative position of IRS and CG on the airplane [m] Fig. 2.4 Function tdlo flow diagram Fig. 2.5 Function nosteps flow diagram Fig. 3.1 Touchdown Severity code flow diagram Fig. 3.2 Touchdown Severity code outputs comparison Fig. 4.1 Format A - Landing Distances code flow diagram (a) Fig. 4.2 Format A - Landing Distances code flow diagram (b) Fig. 4.3 Format A - Landing Distances code flow diagram (c) Fig. 4.4 One arcminute Earth surface projection value [m] Fig. 4.5 Format A - Landing Distances code flow diagram (d) Fig. 4.6 Format B - Landing Distances code flow diagram Fig. 4.7 Landing distances code outputs comparison Fig. 4.8 Takeoff distances code outputs comparison... 34

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13 List of Tables Table 1.1 Data provided with Format A and B... 4 Table 1.2 Use of the data provided... 6 Table 2.1 Transformation Inputs and Outputs Table 2.2 Earth system based accelerations Inputs and Outputs Table 2.3 Funtion tdlo Inputs and Outputs Table 2.4 Funtion nosteps Inputs and Outputs Table 3.1 Touchdown Severity code Inputs and Outputs Table 3.2 Touchdown Severity code outputs Table 4.1 Format A - Limits of the speed integrations wrt time Table 4.2 Format A - Landing Distances code Inputs and Outputs Table 4.3 Format B - Landing Distances code Inputs and Outputs Table 4.4 Format B - Limits of the speed integrations wrt time Table 4.5 Landing distances code outputs Table 4.6 Takeoff distances code outputs Table 4.7 Performance Manual Tables Inputs and Outputs Table 4.8 Length Errors calculation Table 4.9 Mean Length Error calculation Table 4.10 Possible errors from 1 mg or 1 mrad in constant acceleration model... 37

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15 BarcelonaTech - Escola Politècnica Superior de Castelldefels 1 1. INTRODUCTION 1.1. Thesis introduction National Flying Laboratory Centre The National Flying Laboratory Centre (NFLC) is a department within Cranfield University. The NFLC was established by Cranfield University and the Higher Education Funding Council for England (HEFCE) to provide an airborne facility to support teaching and research needs. In addition, it is required to provide an airborne research platform to support government and industry research and development programmes. Therefore, the activity falls into two broad categories, teaching, and research/development. Teaching, which represents the majority of the activity, involves conducting flight engineering measurements and demonstrations designed to illustrate the practical aspects of the academic material taught on typical aeronautical engineering courses, both undergraduate and post-graduate. In-flight measurements of performance or handling qualities parameters are made which the student records, either manually or electronically. After the flight the student is required to analyse the data to verify the selected engineering principle. Examples include the drag and level flight performance or the static stability of the subject aircraft. In addition, certain aspects of flight are demonstrated and electronically recorded for post flight analysis. Examples include the Dutch roll and short period pitching oscillations. Uniquely, these demonstrations enable the student to connect the engineering mathematics associated with these complex responses to the motion as seen and felt in a real aircraft. The combination of the two activities, measurement and demonstration, is an extremely powerful teaching tool. This teaching facility is utilised by most of the UK universities that offer aeronautical engineering courses and also several UK military training establishments. The teaching activity is characterised by frequent short duration (Iess than 1 hour) flights predominantly operating from/to a base airfield. In both the teaching and the research/development activity, manoeuvres not normally expected or permitted on public transport flights are sometimes necessary to fulfil the purpose of the flight e.g. demonstrations of stall, one engine inoperative flight, and larger than 'normal' roll and pitch attitudes and rates.

16 2 Estimating take-off and landing performance from a reduced set of measured flight parameters NFLC resources The NFLC has two airplanes to develop its activity British Aerospace Jetstream 31 The Jetstream 31 is a small twin turboprop airliner, with a pressurised fuselage, designed to meet the requirements of the United States feederliner and regional airline market. Fig. 1.1 British Aerospace Jetstream 31 (Cranfield University)

17 BarcelonaTech - Escola Politècnica Superior de Castelldefels Scottish Aviation Bulldog Series 120 The Bulldog is a two-seat side-by-side training aircraft designed by Beagle Aircraft. Cranfield University provides some "hands on" experience for its postgraduate students with this airplane, being usually acrobatic manoeuvres. Fig. 1.2 Scottish Aviation Bulldog Series 120 (Cranfield University) 1.2. Aims and Objectives The present thesis is based on the British Aerospace Jetstream 31, and the purpose is to carry out with two studies from a reduced set of flight parameters measured by the on-board Inertial Reference System (IRS). The two studies are: a) Touchdown Severity. Work out a way of accurately stating the sink rate for each touchdown, and its vertical acceleration peak at the centre of gravity. b) Takeoff and Landing Distances calculation. Analyze how accurate the different parameters available are for determining the Takeoff and Landing Lengths and Runs.

18 4 Estimating take-off and landing performance from a reduced set of measured flight parameters 1.3. Background and History The measured data is provided in two different formats as follows: Table 1.1 Data provided with Format A and B FORMAT A FORMAT B Column Parameter Column Parameter 1 UTC Time 1 Pitch Att 2 Elapsed Time(s) 2 Roll Att 3 Pitch Att 3 Body Pitch Rate 4 Roll Att 4 Body Roll Rate 5 Pitch Rate 5 Body Yaw Rate 6 Roll Rate 6 Body Norm Acc 7 Yaw Rate 7 Body Lat Acc 8 Long Acc 8 Body Long Acc 9 Lat Acc 9 Flt Path Angle 10 Norm Acc 10 Pot Vert Speed 11 IRS True Hdg 11 Vert Accel 12 Press Altitude 12 Earth Vert Speed 13 IAS 13 True Trk 14 TAS 14 True Hdg 15 OAT 15 Flight Path Accel 16 ADC True Trk 16 Track Angle Rate 17 ADC True Hdg 17 Earth Pitch Att Rate 18 GPS Long x Earth Roll Att Rate 19 GPS Lat x Earth Along Trk Horiz Acc 20 GPS Track 20 Earth Cross Trk Horiz Acc 21 GPS GS 21 IRS Status 22 GPS Alt 22 Altitude 23 Fuel 23 IAS 24 Elevator 24 TAS 25 Aileron 25 OAT 26 Rudder 26 Elevator 27 ElevTab 27 Flap 28 Alpha 28 TqL 29 Beta 29 TqR 30 GPS Alt 31 Time

19 BarcelonaTech - Escola Politècnica Superior de Castelldefels Touchdown Severity study The Left Main Landing Gear of the airplane was replaced during a preventive maintenance inspection due to a crack appearance. A figure showing a more developed same problem, which caused an accident on February 2009 in Greece, is attached: Fig. 1.3 BAe-j31 Accident cause on February 2009 in Greece The NFLC is interested into find an accurate way to deduce the airplane touchdown data and compare it with the manufacturer specifications Takeoff and Landing distances study The airplane is used for flight test teaching. No low speed performance study has been performed as a programmed exercise to date. The professor in charge is interested into know how much reliable is the data provided by the IRS for considering the low speed performance analysis in the subject syllabus.

20 6 Estimating take-off and landing performance from a reduced set of measured flight parameters 1.4. Thesis Overview Table 1.2 Use of the data provided Flight case Type Touchdown Severity Runs & Lengths Landing Takeoff A01 TD A02 TD A03 LDG A04 LDG A05 LDG A06 LDG A07 LDG A08 LDG A09 LDG A10 LDG A11 LDG A12 LDG A13 TO A14 TO A15 TO A16 TO B17 LDG B18 LDG B19 LDG B20 LDG B21 LDG B22 LDG B23 LDG B24 LDG B25 LDG B26 LDG B27 LDG B28 LDG B29 LDG B30 LDG B31 TO B32 TO B33 TO B34 TO B35 TO B36 TO B37 TO B38 TO B39 TO

21 BarcelonaTech - Escola Politècnica Superior de Castelldefels 7 The data provided is managed according the table before. This allows a flight cases optimization in order to collect as much data as possible. Later on, this data is called from MATLAB codes to be processed and plotted. The conclusions are deduced from the comparison between the codes outputs and the airplane specifications Considerations for the Takeoff and Landing distances study The criterion for determining the final takeoff and initial landing points is stated in the next figure: Fig. 1.4 Takeoff and Landing heights (NASA) Fig. 1.5 BAe Jetstream 31 landing at Cranfield Airport

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23 BarcelonaTech - Escola Politècnica Superiorr de Castelldefels 9 2. PREVIOUS CONCEPTS 2.1. Function irs_earth The body accelerations provided are measured by the Inertial Reference System (IRS) of the airplane. However, the studies have to be based on Earth System accelerations in order to get reliable conclusions. The function irs_earth computes the following two steps before the mean calculations: a) Accelerations transformation from IRS to Centre of Gravity (CG). b) Accelerations based on the Earth System. Fig. 2.1 Function irs_earth flow diagram The function irs_earth is available at the Annex 2.1.

24 10 Estimating take-off and landing performance from a reduced set of measured flight parameters Accelerations transformation from IRS to CG The inputs and outputs are showed in the next table: Table 2.1 Transformation Inputs and Outputs Inputs Outputs Variable Explanation time Time [sec] Q Pitch rate [deg/sec] P Roll rate [deg/sec] R Yaw rate [deg/sec] axi Longitudinal acceleration measured by the IRS [G] ayi Lateral acceleration measured by the IRS [G] azi Normal acceleration measured by the IRS [G] x Longitudinal distance between IRS and CG [m] y Lateral distance between IRS and CG [m] z Normal distance between IRS and CG [m] axc Longitudinal acceleration at the CG [m/sec 2 ] ayc Lateral acceleration at the CG [m/sec 2 ] azc Normal acceleration at the CG [m/sec 2 ] The Q, P and R are differentiated with respect to time to find p equations of motion are used for the accelerations transformation: q, and r. After, the ax ay az c c c ax ay az i i i x( q 2 r x( pq r) y( p x( pq q) y( qr 2 ) y( pq r) z( pr q) 2 r 2 ) z( qr p) p) z( p 2 q 2 ) (2.1)

25 BarcelonaTech - Escola Politècnica Superior de Castelldefels Distances between IRS and CG The distances x, y and z are deduced from the Mass & Balance Manual (Annex 2.2), the System Technical Description (Annex 2.3) and the real airplane (Annex 2.4): Fig. 2.2 Absolute position of IRS and CG on the airplane [m]

26 12 Estimating take-off and landing performance from a reduced set of measured flight parameters Fig. 2.3 Relative position of IRS and CG on the airplane [m] Hence, the distances between the IRS and the CG, in body axes, are: x = 2.96 m y = 0.58 m z = 0.12 m

27 BarcelonaTech - Escola Politècnica Superior de Castelldefels Accelerations based on the Earth System The inputs and outputs are showed in the next table: Table 2.2 Earth system based accelerations Inputs and Outputs Inputs Outputs Variable Explanation axc Longitudinal acceleration at the CG [m/sec 2 ] ayc Lateral acceleration at the CG [m/sec 2 ] azc Normal acceleration at the CG [m/sec 2 ] theta Pitch angle [deg] phi Roll angle [deg] psi Yaw angle [deg] axe Body acceleration on the meridian [m/sec 2 ] aye Body acceleration on the parallel [m/sec 2 ] aze Vertical body acceleration [m/sec 2 ] The accelerations based on the Earth system are calculated through the Direction Cosine Matrix in the following way: ax ay az e e e cos cos sin sin cos cos sin cos sin cos sin sin cos sin sin sin sin cos cos cos sin sin sin cos sin sin cos cos cos 1 ax ay az c c c (2.2)

28 14 Estimating take-off and landing performance from a reduced set of measured flight parameters 2.2. Function tdlo The function tdlo finds the touchdown/liftoff position based on the maximum vertical body accelerations. Fig. 2.4 Function tdlo flow diagram The inputs and outputs are showed in the next table: Table 2.3 Funtion tdlo Inputs and Outputs Inputs Outputs Variable aze theta altg time w time3 Explanatio on Vertical body acceleration [m/sec 2 ] Pitch angle [deg] Altitude from the GPS [ft] Time [sec] Touchdown / Liftoff position Touchdown / Liftoff time [sec] First, the functionn creates a matrix with the maximum vertical accelerations and their position in the array aze. After, it rejects the maximums located at an altitude higher than 400 ft and the positions where the airplane has a negative pitch. At the end, the functionn keeps with the highest maximum vertical acceleration remaining. The function tdlo is available at the Annex 2.5..

29 BarcelonaTech - Escola Politècnica Superiorr de Castelldefels Function nosteps There are some data which have a relatively long measurement time. Data as barometric altitude or True Air Speed (TAS) are provided with stepped series. The functionn nosteps finds a more accurate series of data. Fig. 2.5 Function nosteps flow diagram The inputs and outputs are showed in the next table: Table 2.4 Funtion nosteps Inputs and Outputs Inputs Outpu Variable Explanatio on dataa Data series time Time [sec] data2 Improved data series The function starts filtering the right data: it keeps the first values of each step. Later, the slopes between the right data are calculated. Finally, the wrong data is replaced by the slopes. The function nosteps is available at the Annex 2.6.

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31 BarcelonaTech - Escola Politècnica Superior de Castelldefels STUDY OF THE TOUCHDOWN SEVERITY 3.1. Code explanation The inputs and outputs are showed in the next table: Table 3.1 Touchdown Severity code Inputs and Outputs Inputs Outputs Variable Explanation time Time [sec] Q Pitch rate [deg/sec] P Roll rate [deg/sec] R Yaw rate [deg/sec] axi Longitudinal acceleration measured by the IRS [G] ayi Lateral acceleration measured by the IRS [G] azi Normal acceleration measured by the IRS [G] theta Pitch angle [deg] phi Roll angle [deg] psi Yaw angle [deg] altg Altitude from the GPS [ft] altp Barometric altitude [ft] aze(td) Displays vertical acceleration at touchdown [G] theta(td) Displays pitch angle at touchdown [deg] Format B - tql(td) Displays left engine torque at touchdown [x10] vs(td) Displays vertical speed at touchdown [ft/sec] Plots vs. time [sec] Vertical acceleration [G] Vertical speed [ft/min] Altitudes [ft]: altp, altg, Earth, Final Pitch angle [deg] The code has three main branches. First, it finds the touchdown position through the functions irs_earth and tdlo. Later, based on the vertical acceleration computed with the function irs_earth, it begins the main code line: the iteration. The GPS altitude is taken as initial value for the vertical acceleration double integration wrt time. However, the initial vertical speed for the acceleration integration wrt time is unknown. The iteration begins with an initial vertical speed of 1000 ft/min, and keeps adding 1 ft/min to this initial value until the altitude (double integration) at the touchdown is equal to the GPS altitude at touchdown. Finally the code arranges the corrected barometric altitude with the altitude computed by the double integration. The Touchdown Severity study code is available at the Annex 3.1.

32 18 Estimating take-off and landing performance from a reduced set of measured flight parameters Fig. 3.1 Touchdown Severity code flow diagram

33 BarcelonaTech - Escola Politècnica Superior de Castelldefels Code outputs The code outputs are exposed in the next table: Table 3.2 Touchdown Severity code outputs Flight Case Earth Vert Acc [G] Earth Vert Speed [ft/sec] Pitch [deg] Left engine torque [x10] A A A A A A A A A A A A B B B B B B B B B B B The code has been run with 23 touchdown cases. Their outputs from the Command Window are assembled and compared in the table before and the next figure. The code also plots four graphs for checking the intermediate steps. For space matters, just one touchdown case outputs are available at the Annex 3.2.

34 20 Estimating take-off and landing performance from a reduced set of measured flight parameters Fig. 3.2 Touchdown Severity code outputs comparison

35 BarcelonaTech - Escola Politècnica Superior de Castelldefels Conclusions & Proposals According the analyzed flight cases, there is no vertical acceleration higher than 1.5 G and pitch higher than 6 deg at touchdown. The manufacturer specifications regarding the sink rate limit at touchdown are 6 ft/sec at Maximum Take-off Mass (7059 kg), and 10 ft/sec at Maximum Landing Mass (6759 kg). Just one of the flight cases (A11) exceeds the value of 10 ft/sec and the others don t reach the 6 ft/sec. Hence the aircraft is, essentially, operated according to the specifications. The pilot, based on his own experience, states the touchdown vertical acceleration increases with pitch. One reason may be the shock-absorber is not working axially with high pitch values, but the torque also has to be considered in this relation for properly conclusions because it decreases the sink rate. These three parameters are compared with the format B flight cases in the bar diagram. However, after checking the diagram, no clear rule can be extracted about the effects of the pitch and torque on the vertical acceleration. As a proposal for future studies, in order to check the results obtained, several touchdowns may be performed with the next features: a) Flat touchdown to allow the shock-absorber works axially. b) Torque setting in order to avoid a possible sink rate increase due to the lack of lift as a result of the low pitch attitude.

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37 BarcelonaTech - Escola Politècnica Superior de Castelldefels STUDY OF THE LANDING & TAKEOFF DISTANCES 4.1. Codes explanation Two very similar codes have been designed for the Landing & Takeoff distances study purposes. Only the Landing distances code is explained in order to avoid redundancy. However, punctual considerations about the Takeoff distances code are provided when necessary. The two codes are available at the Annexes 4.1 and Format A The inputs and outputs are stated at the table 4.2. As showed in fig. 4.1, the code finds the touchdown position through the functions irs_earth and tdlo. Also, the function irs_earth outputs the Earth accelerations on the meridian and the parallel, which are integrated wrt time to find the Ground Speed. This Ground speed, in turn, is integrated wrt time to find the distances deduced from the accelerations. The limits of the speed integrations wrt time in order to compute the distances are specified in the next table: Table 4.1 Format A - Limits of the speed integrations wrt time Landing Takeoff MATLAB variables u (initial) w v (final) Length Run Format A 50 ft AGL Touchdown Last turn on rwy GPS GS < 20 kts Length Run Format A Last GPS GS min Liftoff 35 ft AGL The barometric altitude, True Air Speed and GPS Ground Speed are improved with the function nosteps. Previously, the barometric altitude is corrected by the GPS altitude at touchdown. The initial Landing position is deduced from the improved barometric altitude and the touchdown position. On the other hand, the initial Takeoff position is found from the last GPS GS minimum. The wind is computed and displayed from the Landing initial position, TAS and GPS GS.

38 24 Estimating take-off and landing performance from a reduced set of measured flight parameters Table 4.2 Format A - Landing Distances code Inputs and Outputs. Inputs Outputs Variable time Q P R axi ayi azi theta phi psi altg altp gs tas trk Ldg time. lat long wind from axe/aye from position from tas from gs aze [G] trk;hdg [deg] altp;altg;final [ft] tas;gs(gps); gs(acc) [kts] lat vs. long Explanation Time [sec] Pitch rate [deg/sec] Roll rate [deg/sec] Yaw rate [deg/sec] Longitudinal acceleration measured by the Lateral IRS [G] acceleration measured by the IRS [G] Normal acceleration measured by the IRS [G] Pitch angle [deg] Roll angle [deg] Yaw angle [deg] Altitude from GPS [ft] Barometric altitude [ft] Ground speed from GPS [kts] True Air Speed [kts] Track [deg] Landing time estimation [sec] Latitude [deg] Longitude [deg] Displays landing wind [kts] Displays Landing Runs & Lengths [m] Plots vs. time [sec] Plots position [deg]

39 BarcelonaTech - Escola Politècnica Superior de Castelldefels 25 Fig. 4.1 Format A - Landing Distances code flow diagram (a)

40 26 Estimating take-off and landing performance from a reduced set of measured flight parameters Fig. 4.2 Format A - Landing Distances code flow diagram (b) The runway track is found through track data and a Landing length estimation in time. In conjunction with the heading, this serves for deducing the last turn performed by the airplane on the runway. The final Landing position is either the previous one or the one where the GSP GS is lower than 20 kts, whatever comes first. On the other hand, the final Takeoff position is deduced from the improved barometric altitude and the touchdown position. Fig. 4.3 Format A - Landing Distances code flow diagram (c) A nautical mile is the average distance of one arcminute projection in an arc of maximum circumference, that is to say a meridian or the equator. The latitude data is always following a meridian, but this is not the case for the longitude data. Hence, this has to be corrected according to the next table for accurate distances calculations. The hypotenuse can be now extracted through the Pythagoras method in order to find the distances deduced from position.

41 BarcelonaTech - Escola Politècnica Superior de Castelldefels 27 Fig. 4.4 One arcminute Earth surface projection value [m] Fig. 4.5 Format A - Landing Distances code flow diagram (d) Finally, the code integrates the improved GPS GS and TAS wrt time to find the distances with and without wind respectively.

42 28 Estimating take-off and landing performance from a reduced set of measured flight parameters Format B The inputs and outputs are showed in the next table: Table 4.3 Format B - Landing Distances code Inputs and Outputs. Inputs Outputs Variable Explanation time Time [sec] Q Pitch rate [deg/sec] P Roll rate [deg/sec] R Yaw rate [deg/sec] axi Longitudinal acceleration measured by the ayi Lateral IRS [G] acceleration measured by the IRS [G] azi Normal acceleration measured by the IRS [G] theta Pitch angle [deg] phi Roll angle [deg] psi Yaw angle [deg] altg Altitude from GPS [ft] altp Barometric altitude [ft] tas True Air Speed [kts] trk Track [deg] Ldg time. Landing time estimation [sec] tqr Right engine torque [%] tql Left engine torque [%] from tas Displays Landing Run & Distance [m] aze [G] trk;hdg [deg] altp;altg;final [ft] Plots vs. time [sec] tas [kts] tqr;tql [%] The code finds the touchdown position through the functions irs_earth and tdlo. The barometric altitude and True Air Speed are improved with the function nosteps. Previously, the barometric altitude is corrected by the GPS altitude at touchdown.

43 BarcelonaTech - Escola Politècnica Superior de Castelldefels 29 Fig. 4.6 Format B - Landing Distances code flow diagram

44 30 Estimating take-off and landing performance from a reduced set of measured flight parameters The limits of the speed integrations wrt time in order to compute the distances are specified in the next table: Table 4.4 Format B - Limits of the speed integrations wrt time Landing Takeoff MATLAB variables u (initial) w v (final) Length Run Format B 50 ft AGL Touchdown Last turn on rwy Torque < 16 % Length Run Format B Torque > 100 % Liftoff 35 ft AGL The initial Landing position is deduced from the improved barometric altitude and the touchdown position. On the other hand, the initial Takeoff position is fixed when the torque of one of the engines.exceeds 100%. The final Landing position determination differs with respect to the format A one in just one point: the torque of one of the engines lower than 16% instead of the GPS GS below 20 kts. On the other hand, the final Takeoff position is deduced from the improved barometric altitude and the touchdown position. The improved TAS is integrated wrt time to find the distances without wind. Neither the wind nor the distances with wind can be computed with format B because no relation with GS or position data from GPS is provided.

45 BarcelonaTech - Escola Politècnica Superior de Castelldefels Codes outputs Landing distances The code outputs are exposed in the next table: Table 4.5 Landing distances code outputs Landing Lengths [m] Landing Runs [m] Flight Wind Case GS GS GS GS Position TAS Position TAS [kts] acc GPS acc GPS A A A A A A A A A A B B B B B B B B B B B B B B The code has been run with 24 landing cases. Their outputs from the Command Window are assembled and compared in the last table and the next figure. The code also plots five graphs for checking the intermediate steps. For space matters, just two landing cases outputs (one each format) are available at the Annexes 4.3 and 4.4.

46 32 Estimating take-off and landing performance from a reduced set of measured flight parameters Fig. 4.7 Landing distances code outputs comparison

47 BarcelonaTech - Escola Politècnica Superior de Castelldefels Takeoff distances The code outputs are exposed in the next table: Table 4.6 Takeoff distances code outputs Takeoff Lengths [m] Takeoff Runs [m] Flight Wind Case GS GS GS GS Position TAS Position TAS [kts] acc GPS acc GPS A A A A B B B B B B B B B The code has been run with 13 takeoff cases. Their outputs from the Command Window are assembled and compared in the last table and the next figure. The code also plots five graphs for checking the intermediate steps. For space matters, just two takeoff cases outputs (one each format) are available at the Annexes 4.5 and 4.6.

48 34 Estimating take-off and landing performance from a reduced set of measured flight parameters Fig. 4.8 Takeoff distances code outputs comparison

49 BarcelonaTech - Escola Politècnica Superior de Castelldefels Conclusions & Proposals Data extracted from the Performance manual of the airplane has been used in order to compare the results obtained (Annex 4.7). The manual tables just consider Takeoff and Landing lengths. As well, the Takeoff table does not consider wind. Hence, just the length will be contrasted for the both cases and, especially, just the length without wind for the Takeoff case. The tables Inputs selected and Outputs obtained are: Table 4.7 Performance Manual Tables Inputs and Outputs Ambient Temperature Airfield Altitude Weight Wind Inputs ISA at SL = 15 Cdeg 400 ft 6500 kg as applicable Runway slope 0 % Outputs Takeoff length (no wind) Landing length (no wind) 1220 m 1100 m A Length Errors calculation has been performed for comparison purposes. It is showed at the next table.

50 36 Estimating take-off and landing performance from a reduced set of measured flight parameters Table 4.8 Length Errors calculation Flight case GS Acc GS GPS Position TAS Wind Takeoff Lengths [%] [kts] Manual Lengths with wind [m] A A A A B B B B B B B B B Landing Lengths [%] A A A A A A A A A A B B B B B B B B B B B B B B

51 BarcelonaTech - Escola Politècnica Superior de Castelldefels 37 The mean error for each source and manoeuvre has been computed from the table before: Table 4.9 Mean Length Error calculation Mean Error [%] Landing Takeoff GS Acc GS GPS Position TAS A bad measurement of 1 mg or 1 mrad extracted from the IRS can imply the next errors (assuming constant acceleration model): Table 4.10 Possible errors from 1 mg or 1 mrad in constant acceleration model Time [sec] t Velocity [m/sec] at Displacem. [m] ½at Angle [deg] t Taking into account the possible errors stated at the table before, the most accurate parameter provided by IRS to determine Takeoff and Landing Lengths are (from best to worst): 1. Body accelerations 2. GPS Position 3. GPS Ground Speed 4. True Air Speed (considering TAS just for no wind calculations)

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53 BarcelonaTech - Escola Politècnica Superior de Castelldefels 39 Bibliography [1] Cook, M.V., Flight Dynamics Principles, Elsevier Ltd., Oxford (2007) [2] Stengel, R.F., Flight Dynamics, Princeton University Press, Princeton (2004) [3] AAIASB, Accident of the a/c SX-SKY of Sky Express at the Heraklion Airport N. Kazantzakis on 12th February 2009, p. 3-4,17 (2009) [4] Simpkins, A.D., The development of a low cost flight test instrumentation facility, p (2006) [5] NASA, Quest for Performance: The Evolution of Modern Aircraft,