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Flight Techniques for Determining Airplane Drag at High Mach Numbers

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Flight Techniques for Determining Airplane Drag at High Mach Numbers A REPORT 84 oo h- a: O Q_ ADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT LIBRARY E^;A9L»SHVFNT REPORT 84 FLIGHT TECHNIQUES FOR DETERMINING AIRPLANE DRAG AT HIGH MACH NUMBERS by DE E. BEELER, DONALD R. BELLMAN and EDWIN J. SALTZMAN AUGUST 1956 NORTH ATLANTIC TREATY ORGANIZATION PALAIS DE CHAILLOT, PARIS 16 REPORT 84 NORTH ATLANTIC TREATY ORGANIZATION ADVISORY GROUP FOR AERONAUTICAL RESEARCH AND DEVELOPMENT FLIGHT TECHNIQUES POR DETERMINING AIRPLANE DRAG AT HIGH MACH NUMBERS by De E, Beeler, Donald R. Bellman and Edwin J. Saltzman This Report was presented at the Plight Test Panel, held from August 27th to 31st, 1956, in Brussels, Belgium. S UMMARY The measurement of total airplane drag in flight is necessary to assess the applicability of wind-tunnel model data. The N.A.C.A. High- Speed Flight Station has investigated and developed techniques for measuring the drag of high-speed research airplanes and current fighter- type airplanes. The accelerometer method for determining drag was found to be the most satisfactory method for research work, because it is the only method permitting a complete coverage of the Mach number and angle- of-attack capabilities of an airplane. Determining drag by the accelerometer method requires the accurate measurement of longitudinal and normal accelerations, angle of attack, and engine thrust. In addition, the static pressure, airspeed, airplane weight, and longitudinal control positions must be measured. The accurate measurement of longitudinal and normal acceleration can be made and recorded by means of specially constructed mechanical accelerometers that have been developed by the N.A.C.A. Fuselage nose booms are used to reduce the flow-field errors in the measurement of static pressure, airspeed, and angle of attack. The errors can be reduced further to an acceptable level by established calibration techniques. Satisfactory methods for determining in flight the thrust of turbojet-afterburner and rocket engines are available. The flight drag data generally can be separated into components consisting of trim, skin-friction, pressure-induced, and wave drags. The comparison of flight and wind-tunnel data must be made on the basis of component drags if a proper interpretation of the results is to be obtained. 533.6.013.12 3c6d2b ii SOMMAIRE II est ne"cessaire de mesurer la resistance aerodynamique totale d'un avion en vol pour etablir dans quelle mesure les rlsultats des experiences effectuees en soufflerie, sur maquettes, peuvent etre appliques aux conditions de vol. Le Centre de Recherches en Vol a grande vitesse du NACA a etabli et mis au point certaines techniques ayant pour but de mesurer la resistance aerodynamique d'avions d'essais a grande vitesse et d'avions de chasse de type courant. II s'est av4re que la methode de determination de cette resistance par l'acc£lerometre est celle qui offre le plus d'avantages dans le domaine de la recherche parcequ'elle seule permet une etude complete des possibilites d'un appareil en ce qui concerne le nombre de Mach et 1'angle d'incidence. La determination de la resistance aerodynamique par la methode de 1'accelerometre exige que soient effectuees des mesures precises des accelerations longitudinales et perpendiculaires, de 1'angle d'incidence et de la poussee de moteur. Des mesures de la pression statique, de la vitesse, du poids, du 1'appareil, et de la position des gouvernes de profondeur sont £galement necessaires. Des mesures precises de 1'accelera­ tion longitudinale et perpendiculaire peuvent etre effectuees et enregis- trees au moyen d'accelerometres mecaniques specialement concus dans ce but et mis au point par le NACA. On a recoursades perches placees a 1'avant du fuselage pour reduire les erreurs dues au champ aerodynamique affectant les mesures de pression statique, de vitesse, et d'angle d' incidence. De plus, on peut raraener 1' influence de ces erreurs a un niveau acceptable en etablissant des techniques d'etalonnage. Il existe, d'autre part, des methodes satisfaisantes pour determiner, en vol, la poussee des dispositifs de post-combustion des turbo-reacteurs, et des moteurs de fusees. La resistance aerodynamique qui se manifeste en vol peut en general se decomposer en: resistances d'equilibrage des moments, de frottement, de forme et d'onde. Les comparaisons entre resultats d'essais en vol et resultats d'experiences en soufflerie doivent £tre etablies sur la base des composantes de la resistance aerodynamique si 1'on veut obtenir une interpretation correcte des resultats. 533.6.013,12 3c6d2b ill CONTENTS Page SUMMARY LIST OF FIGURES NOTATION vi INTRODUCTION 2. METHODS 1 2.1 General 1 2.2 Stabilized Flight Method 1 2.3 Energy Method 2 2.4 Accelerometer Method 2 MEASUREMENTS 3 3. 1 General 3 3.2 Acceleration 3 3.3 Angle of Attack 4 3.4 Thrust 5 3.5 Static Pressure 8 3.6 Airplane Weight 8 3.7 Control-Surface Position 9 4. TREATMENT OF FLIGHT DATA 9 5. COMPARISON OF FLIGHT AND WIND-TUNNEL DATA 10 6. CONCLUDING REMARKS 10 REFERENCES 11 FIGURES 13 APPENDIX I Derivation of Drag Equations A-iii APPENDIX II Derivation of Thrust Equations B-iii DISTRIBUTION iv LIST OF FIGURES Page Fig.1 Comparison of drag coefficients determined by energy and accelerometer methods for a typical push-down, pull-up maneuver 13 Pig.2 Schematic diagram of N.A.C.A. magnetically-damped accelerometer 14 Fig.3 Typical fuselage nose-boom installation showing Pitot-static head and angle-of-attack and angle-of-sideslip vanes 15 Fig.4 Theoretical effects on angle-of-attack measurements of upwash from the nose boom and fuselage at low speeds 16 Fig.5 The variation of angle-of-attack error due to upwash with Mach number and lift coefficient 17 Fig.6 Air-cooled, fixed Pitot probe for the measurement of jet thrust of turbojet engine-afterburner combination 18 Fig. 7 Swinging Pitot probe for the measurement of total-pressure profiles across the exit of a turbojet engine-afterburner combination 19 Fig.8 Typical nozzle calibration for a turbojet engine 20 Fig. 9 Effect of ratio of boom length to fuselage diameter on Mach number error 21 Fig.10 Variation of Mach number error with Mach number 22 2 Fig. 11 Variation of Cn with C, showing deviation of data from theo­ retical parabolic relationship for 60° sweptback wing 23 Pig.12 Effect of Reynolds number on the theoretical skin-friction drag and on the comparison of flight and wind-tunnel zero-lift drag data 24 NOTATION A cross-sectional area of exhaust jet stream (ft2) AJ cross-sectional area of inlet duct (ft2) A rocket-nozzle exit area (ft2) AL measured airplane longitudinal acceleration (g units) A^ rocket-nozzle throat area (ft2) Ax true airplane longitudinal acceleration (g units) Az true airplane normal acceleration (g units) a^ velocity of sound in inlet duct (ft/sec) ag velocity of sound under ambient conditions (ft/sec) Cn drag coefficient, = D/qS Cn friction drag coefficient uf Cn parasite drag coefficient Cf jet-nozzle coefficient CL lift coefficient, = L/qS CN normal-force coefficient, = nW/qS Cx axial-force coefficient, - Dx/qS c.c' constants D drag force along airplane flight path (lb) Dx drag force along airplane axis (lb) DnmQuV maximum equivalent fuselage diameter (ft) EA total airplane energy (ft lb) F; engine jet thrust (lb) Pn engine net thrust (lb) F ram drag of inlet air (lb) vi g acceleration of gravity (ft/sec2) h altitude (ft) L airplane lift normal to flight path (lb) L^ airplane lift normal to airplane axis (lb) M airplane Mach number Mj Mach number within inlet duct N engine speed (r.p.m.) n normal-load factor (g units) P total pressure (lb/ft2) P static pressure (lb/ft2) 2 Pc rocket combustion-chamber pressure (lb/ft ) Pj static pressure in inlet duct (lb/ft2) 2 Pe rocket-nozzle exit static pressure (lb/ft ) 2 P0 ambient pressure (lb/ft ) q dynamic pressure (lb/ft2) R gas constant (ft/°R) Re Reynolds number r. radius of nose boom r distance from nose boom center line to center of flow-indicating vane S wing area (ft2) T static temperature (°R) Td static temperature in inlet duct (°R) Tt total temperature (°R) TQ ambient temperature (°R) t time (sec) V velocity (ft/sec) vii Vd air velocity in inlet duct (ft/sec) VQ airplane velocity (ft/sec) W airplane weight (lb) w mass-flow rate (lb sec/ft) w„ air mass-flow rate (lb sec/ft) wf fuel mass-flow rate (lb sec/ft) X distance from static-pressure orifices to fuselage nose (ft) X' distance from flow-direction vane to fuselage nose (ft) a airplane angle of attack (angle between airplane axis and flight path) (deg) a^ indicated angle of attack (deg) afc true angle of attack (deg) y flight-path angle (angle between flight path and the horizontal) (deg) y ratio of specific heats of gases Aa error in angle of attack (deg) AM error in Mach number At time increment (sec) 8 altitude normalizing factor, = P/2116 6 temperature normalizing factor, = Tt/518.4 p gas density (lb/ft3) p. density of air in inlet duct (lb/ft3) PQ atmospheric density (lb/ft3). viii FLIGHT TECHNIQUES FOR DETERMINING AIRPLANE DRAG AT HIGH MACH NUMBERS De E. Beeler, Donald R. Bellman, and Edwin J. Saltzman* 1. INTRODUCTION Considerable research effort has been directed in recent years toward improving the performance of aircraft to achieve efficient supersonic flight. The verification and evaluation of the latest thinking, for the most part, is a result of model testing. However, questions on the adequacy of the model tests are raised when effects of scale and power are considered.
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