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PREFACE The purpose of this textbook is to present the elements of applied aerodynamics and aeronautical engineering which relate directly to the problems of flying operations. All Naval Aviators possess a natural interest in the basic aerodynamic factors which affect the performance of all aircraft. Due .to the increasing complexity of modern aircraft, this natural interest must be applied to develop a sound understanding of basic engineering principles and an appreciation of some of the more advanced problems of aerodynamics and engineering. The safety and effectiveness of flying operations will depend greatly on the under- standing and appreciation of how and why an airplane flies. The principles of aerodynamics will provide the foundations for developing exacting and precise flying techniques and operational procedures. The content of this textbook has been arranged to provide as com- plete as possible a reference for all phases of flying in Naval Aviation. Hence, the text material is applicable to the problems of flight train- ing, transition training, and general flying operations. The manner of presentation throughout the text has been designed to provide the elements of both theory and application and will allow either directed or unassisted study. As a result, the text material’will be applicable to supplement formal class Iectures and briefings and provide reading material as a background for training and flying operations. Much of the specialized mathematical detail of aerodynamics has been omitted wherever it was considered unnecessary in the field of flying operations. Also, many of the basic assumptions and limita- tions of certain parts of aerodynamic theory have been omitted for the sake of simplicity and clarity of presentation. In order to contend with these specific shortcomings, the Naval Aviator should rely on the assistance of certain specially qualified individuals within Naval Avia- tion. For example, graduate aeronautical engineers, graduates of the Test Pilot Training School at the Naval Air Test Center, graduates of the Naval Aviation Safety Officers Course, and technical representatives of the manufacturers are qualified to assist in interpreting and applying the more difficult parts of aerodynamics and aeronautical engineering. To be sure, the specialized qualifications of these individuals should be utilized wherever possible. iii
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NAVWEPS 00-801-80 PREFACE The majority of aircraft accidents are due to some type of error of the pilot. This fact has been true in the past and, unfortunately, most probably will be true in the future. Each Naval Aviator should strive to arm himself with knowledge, training, and exacting, professional attitudes and techniques. The fundamentals of aerodynamics as pre- sented in this text will provide the knowledge and background for safe and effective flying operations. The flight handbooks for the air- craft will provide the particular techniques, procedures, and operating data which are necessary for each aircraft. Diligent study and continu- ous training are necessary to develop the professional skills and tech- niques for successful flying operations. The author takes this opportunity to express appreciation to those who have assisted in the preparation of the manuscript. In particular, thanks are due to Mr. J. E. Fairchild for his assistance with the por- tions dealing with helicopter aerodynamics and roll coupling phenom- ena. Also, thanks are due to Mr. J. F. Detwiler and Mr. E. Dimitruk for their review of the text material. HUGH HARRISON HURT, Jr. August 1959 University of Southern California Los Angelesj Cnlif. iv
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NAVWEPS OO-801-8O TABLE OF CONTENTS TABLE OF CONTENTS PREFACE.. ,., . iii CHAPTER I: BASIC AERODYNAMICS WING AND AIRFOIL FORCES PROPERTIES OF THE ATMOSPHERE. 1 Static pressure Temperature Density Viscosity Standard atmosphere Pressure altitude Density altitude BERNOULLI’S PRINCIPLE AND SUBSONIC AIRFLOW.. 4 Bernoulli’s equation, Incompressible tlow 6 Variation of static pressure and velocity Kinetic and porcntial energy of flow Static and dynamic prcssurc, 4 Factors affecting dynamic pressure Airspeed measurement.. . . Stagnation prcssurc 9 Measurement of dynamic pressure Pitot and static sources Indicated airspeed DEVELOPMENT OF AERODYNAMIC FORCES.. Streamline pattern and pressure distribution. Generatioaoflift.......................................... Circulation Pressure distribution ....... 14 ....... 14 ....... 16 Airfoil terminology. Aerodynamic force coefficient . . ‘,: Basic lift equation 2 3 Lift coefficient Dynamic prcssurc and surface area ”
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NAVWEPS OO-EOT-80 TABLE OF CONTENTS Interpretation of the lift equation.. . . . . . . . . Lift cocfficicnt versus angle of attack Stall speed and angle of attack Angle of attack versus velocity Primary control of airspeed . . _ . . . _ . mrfou un cnacactectsucs. . . . Section angle of attack and lift coefficient Ty ical section chvactctistics E&t of thickness and cambet Drag characteristics, . . . . . . . :. Drag equation Drag cocficicnt versus angle of attack Lift-drag ratio Power-off glide pctformancc Airfoil drag chanwteristics.. ) . . . Section drag cocfficicnt Ty ical section characteristics E 2 ect of thickness and cunbcr Low drag sections FLIGHT AT HIGH LIFT CONDITIONS. . . . . . . . StaII speeds. . . . . . . . . .,. . . . . . . Maximum lift cc&cicnt Stall angle of attack ..,e * . . ~lrecrorwergnt.................................................... Effect of maneuvering flight,. . Load factor ~ets~s bank angle Stall spad versus load factor Effect of high lift devices., . Effect on stall speed Stall angle of attack and stall recovery. . . . . . HIGH LIFT DEVICES. Types of high lift devices., . Plain flap S S otted flap P lit flap Fowler flap Slots and slats Boundary layer control Operation of high lift devices. Flap retraction and extension Chan Effect o f es in lift, drag, and trim power DEVELOPMENT OF AERODYNAMIC PITCHING MOMENTS Pressure distribution. .~. : . ! . : Center of pressure and aerodynamic center. Pitching moment coefficient. . , Effect of camber Effect of flaps Relationship between center of pressure, aerodynamic centet, and moment coefficient Application to longitudinal stability. . Stability and trim Effect of supersonic flow PW 23 27 29 33 35 3.5 :: 37 39 39 41 43 a: 49 51 vi
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NAVWEPS OO-BOT-BO TABLE OF CONTENTS FRICTION EFFECTS. Viscous Bow.. Boundarglayers.................................................... Laminar flow Transition Turbulent flow ReyooldsNumber.................................................. Definition Skin friction versus Reynolds Number Airflowseparatioa.................................................. Pressure distribution Prcswrc gradient and boundary layer energy Factors affecting separation Scaleeffect......................................................... Effect on aerodynamic characteristics Reynolds Number correlation PLANFORM EFFECTS AND AIRPLANE DRAG EFFECT OF WING PLANFORM.. . . Descr1puon of planform Area, span,, and chord Aspect ratm and taper Sweepback Mean aerodynamic chord Development of lift by a wing.. . vortex system Ti and bound vortices I&cd flow and downwash Scction angle of attack Induced angle of attack INDUCED DRAG. : Induced angle of attack and inclined lift. Induced drag coefficient, Effect of lift coefficient Effect of aspect ratio Effectoflift........................................................ Effea of altitude.. EffectofsPeed...................................................... Effect of aspect ratio. Lift and dra Influcncc of ow aspxt ratio configurations f characteristics EFFECT OF TAPER AND StiEEPtiACK. Spanwise lift distribution localinducedflow................................................. Effect on lift and drag characteristics. .‘, STALL PATI’ERNS. Pnvorablestallpattern.............................................. EffeaofpIanform.................................................. Taper Sweepback Modifications for stall characteristics. vii 52 52 52 54 56 59 61 61 63 66 66 68 68 2; 71 74 74 76 76 77 :: 86
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NAVWEPS 00-801-80 TABLE OF CPNTENTS PARASITE DRAG. Sources of parasite drag. . Parasite drag coefficient.. . . . Parasite and induced drag. Mi.li$z’.?1 p”‘““ite dr2g CxEciczt Airplane efficiency factor Equivalent parasite area Effect of configuration. Effect of altitude., Effectofspeed...................................................... AIRPLANE TOTAL DRAG.. Drag variation with speed Induced and parasite drag Stall speed Minimum drag Specific performance conditions Compressibility drag rise CHAPTER 2. AIRPLANE PERFORMANCE REQUIRED THRUST AND POWER DEFINITIONS. Pan&e 14 ;n&Ced drw _ _.-__._ _._- _- Thrustandpowerrequir~~::::::::::::::::::::::::::::::::::::::::: VARIATION OF THRUST AND POWER REQUIRED Effect of gross weight. Effect of configuratmn. Effect of altitude. AVAILABLE THRUST AND POWER PRINCIPLES OF PROPULSION. Mass flow, velocity change, momentum change.. Newton’s laws, Wastedpower...............................:..................... Power available. Propulsion efficiency. TURBOJET ENGINES Operatingcycle.................................................... Function of the components. Inlet or diffuser Compressor Combustion chamber Turbine Exhaust nozzle Turbojet operating characteristics.. :_ Thrust and power available Effect of velocity Effect of engine speed Specific fuel consumption Effect of altitude Governing apparatus Steady state, acceleration, deceleration Instrumentation viii *am 87 87 91 ;: 92 96 $6 97 99 101 101 104 104 104 104 106 106 107 109 116
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NAVWEPS 00-SOT-80 TABLE OF CONTENTS Pam Turbojet operating limitations 124 Exhaust gas temperature b&pr~$or stall or surge Compressor inlet air temperature Engine speed Time limitations Thrust augmentation. 129 Afterburner Water injection The gas turbine-propeller combination. 132 Equivalent shaft horsepower Governing requirements Operating limitations performance characteristics THE RECIPROCATING ENGINE, 135 Operating chatacterlsucs. . . 135 Operating cycle Brake horsepower Torque, RPM, and BMEP Normal combustion Preignition and detonation Fuel qualities Specific fuel consum tion Effect of altitude an supercharging 8 Effect of humidity Operating limitations. 144 Detonation and preignition Water injection Time limitations Reciprocating loads AIRCRAFT PROPELLERS Operating characteristics, 145 Flow patterns Propulsive cficiency Powerplant matching Governing and feathering Operating limitations.. 148 ITEMS OF AIRPLANE PERFORMANCE STRAIGHT AND LEVEL FLIGHT. 150 Equilibrium conditions Thrust and power required Thrust and powec available Maximum and minimum speed CLIMB PERFORMANCE. 150 Steady and transient climb. 150 Forces acting on the airplane Climb angle and obstacle clcarancc Rate of climb, primary control of altitude Propeller and jet aircraft Climb performance. 156 Effect of weight and altitude Descending flight ix
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NAWEPS 00-801-8~ TABLE OF CONTENTS RANGE PERFORMANCE. :; General range performance. 158 Specific range, v&city, fuel flbw Specific endurance Cruise control and total range Range, propeller driven airplanes. 160 Aerodynamic conditions Effect of weight and altitude Reciprocating and turboprop airplanes Range, turbojet airplanes. :. 164 Aerodynamic conditions Effect of weight and altitude Constant altitude and cruise-climb profiles Effect of wind oh ‘PY~C........,.................................... 168 ENDURANCE PERFORMANCE. 170 General endurance performance.. :. . 170 Spxific cndurancc, velocity, fuel flow Effect of altitude op endurance, : . . . . . . 170 Propcllcr driven airplanes Turbojet aitplaocs OFF-OPTIMUM RANGE AND ENDURANCE. 172 Reciprocating powered airplane.. 172 Turboprop powered airplane, , . . . 173 Turbojet powered airplane... . . I.. . 175 MANEUVERING PERFORMANCE. 176 Relationships of turning flight. . . . . . . 176 Steady turn, bank angle and load factor Induced drag Turning performance.. . . 178 Tom radius and turn rate Effect of bank aaglc and velocity Tactical performance, . 178 Maximum lift FhZZF%3:~2:; pfOt”l~“CC TAKEOFF AND LANDING PERFORMANCE.. .~, 1132 Relationships of accelerated motion. . 182 Acceleration, vclocit distance Uniform and nonum arm acceleration ,J Takeoff performance.. . . . 164 Forces acting on the airplane Accelerated motion Factors of technique Factors affecting takeo# performance. . 187 Effect of gross weight Rffcct of wind Effect of runway slope F’qxt takeoff vcloclty. Effect of altitude and tempcraturc Handbook data Y
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NAVWEPS OO-BOT-BO TABLE OF CONTENTS Landing performance.. . . . . 192 Forces acting on the airplane Accclanted motion Factors of technique Factors affecting landing performance. . . . 196 E&t of gross weight Effect of wind Fg; ~~~~~~~;mpcntwc ro a Impmtance of handbook performance data. . . 200 CHAPTER 3. HIGH SPEED AERODYNAMICS GENERAL CONCEPTS AND SUPERSONIC FLOW PATTERNS NATURE OF COMPRESSIBILITY. ............................... Definition of Mach number. ........................................ Sttbsonic, traasonic, supersonic, and hypersonic flight regimes. ....... Compressible flow conditions ....................................... Comparison of compressible and incompressible flow. ............... TYPICAL SUPERSONIC FLOW PATTERNS., .................. Obliqueshockwave ................................................ Normalshockwave ................................................ Ex nsionwave E t9” .................................................... ect on velocity, Mach number, density, pressure, energy. .. : ........ SECTIONS IN SUPERSONIC FLOW. ............................ nowpatterns ...................................................... Pressure distribution. .............................................. Wavedrag ......................................................... Location of aerodynamic center. .................................... 201 202 204 204 204 207 207 207 211 213 213 213 213 21s 21s CONFIGURATION EFFECTS TRANSONIC AND SUPERSONIC FLIGHT. . 215 Critical Mach ntlm~r 2 15 Shock wave formatton. . . . . . . . . . . . . 218 Shock induced separation.. i.. Porcedivergence................................................... $2: Phenomena of transonic flight.. . 218 Phenomena of supersonic Bight.. . 220 TRANSONIC AND SUPERSONIC CONFIGURATIONS. 220 Airfoil sections.. . 220 Transonic sections Supctsonic sections Wave drag characteristics Effect of Mach number on airfoil characteristics Plaaform effects. ,.......,..... 226 Effect of swcc ack p” Advantages o swcepback Disadvantages of sweepback Effect of nspct ratio and tip shape Control surfaces. . . . . . . . . . 236 Powered controls All movable surfaces
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NAWEPS 00-801-80 TABLE OF CONTENTS Supersonic engine inlets. . 238 Internal and external comprcsrion inlets Inlet performance and powerplant matching Supersonic configurations. 240 AERODYNAMIC HEATING. 242 Ram temperature rise.. _. 242 Effect on structural materials and powerplant performance. 242 CHAPTER 4. STABILITY AND CONTROL DEFINITIONS STATIC STABIL .ITY. ............................................... DYNAMIC STAB1 ‘LITY .................................... TRIM AND CONTROLLABI ,LITY .......................... AIRPLANE REFERENCE AXES. ........................... LONGITUDINAL STABILITY AND CONTROL STATIC LONGITUDINAL STABILITY. ......................... Generalconsiderations:. .. :,_~. ...... . .... . ............... .:..1... ... Contribution of the component surfaces .............................. Wing Fuselage and nacelles Horizontal tail Power-off stability. .................................................. Powereffects ....................................................... Control force stability. ............................................. Maneuveringstability ............................................... Tailoring control forces. ........................................... LONGITUDINAL CONTROL. .................................... Maneuvering control requirement. .................................. Takeoff control requirement. ....................................... Landing control requirement. ....................................... LONGITUDINAL DYNAMIC STABILITY. ..................... Phugoid ........................................................... Short period motions ............................................... MODERN CONTROL SYSTEMS. ................................. Conventional Boosted Power operated DIRECTIONAL STABILITY AND CONTROL DIRECTIONAL STABILITY. ...................................... Defimtuxu ....................................................... ... Contribution of the airplane components ............................ Vertical tail Wing Fuselage and nacelles Power effects .. Crawal conditions. ................................................ DIRECTIONAL CONTROL ....................... >. ............... Directional control requirements. .................. ................ Adverseyaw ....................................................... xii 243 245 247 249 250 -25’0. 253 259 259 264 268 270 275 275 275 277 279 279 281 281 284 284 285 290 290 291 291
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NAVWEPS 00-BOT-80 TABLE OF CONTENTS Spinrecovety..; ................................................... Slipstream rotatmn. ................................................ Cross wind takeoff and landing. ................................... Asymmetrical power. ............................................... LATERAL STABILITY AND CONTROL LATERAL STABILITY, ........................................... Definlttons ........................................................... CONTRIBUTION OF THE AIRPLANE COMPONENTS. Wing.........~.........~ Fuselage and wmg powton, ................................................................................... Sweepback ......................................................... Vertical tail. ........................................................ LATERAL DYNAMIC EFFECTS, ................................ Directional divergence Spiral divergence Dutch roll CONTROL IN ROLL .............................................. . . Rolhsg motmn of an airplane. ...................................... Roliing performance, .............................................. Critical requirements. .............................................. MISCELLANEOUS STABILITY PROBLEMS LANDING GEAR CONFIGURATIONS ......................... Tail wheel type Tricyde type Bicycle type SPINS AND PROBLEMS OF SPIN RECOVERY ................ Principal prospin moments Fundamental principle of recovery Effect of configuration PITCH-UP., ......................................................... Definition Contribution of the airplane components EFFECTS OF HIGH MACH NUMBER.. Longitudinal stability and control Directional stability Dynamic stability and damping PILOT INDUCED OSCILLATIONS.. _. Pilot.control system-airplane coupling High q aed low stick force stability ROLL COUPLING. Inertia and aerodynamic coupling Inertia and wind axes Natural pitch, yaw, and coupled pitch-yaw frequencies Critical roll rates Autorotative rolling Operating limitations HELICOPTER STABILITY AND CONTROL. Rotor gyroscopic effects Cyclic and collective pitch Lon f itudinal, lateral, and directional control Ang e of attack and velocity stability Dynamic stability xiii Pace 291 294 294 294 294 295 295 298 298 298 298 299 300 300 301 305 305 307 313 313 314 315 319
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NAVWEPS OO-BOT-80 TABLE OF CONTENTS CHAPTER 5. OPERAilNG STRENGTH LIMITATIONS GENERAL OEFlNlTlONS AND STRUCTURAL REQUlREMENTS STATIC STRENGTH .._.......... ~.~~~.~ ~..~ Limit load Factor of safety Material properties SERVICE LIFE Pati Loa r e consideration spectrum attd cumulative damage Creep considerations AEROELASTIC EFFECTS. Stiffness and rigidity AIRCRAFT LOADS AND OPERATING LIMITATIONS FLIGHT LOADS-MANEUVERS AND GUSTS. Loadfactor..................................................... Maneuvering load factors.. .I Maximum lift capability Effect of gross weight ^ . ._ ClllStlOadtacfors..............,................................. Gust load increment Effect of gust intensity and lift curve slope Effect of wing loading and altitude Effect of overstrea. THE V-n OR V-g DIAGRAM. Effect of weight, configuration;altihtde, and symmetry of Ior-Ang Limit load factors Ultitnute load facvxs Maximum lift capability Limit airspeed Operating env+pe Maneuver’speed and penetration of turbulence EFFECT OF HIGH SPEED FLIGHT.. Critical gust Aileron reversal Divergence PIutter Compressibility problems LANDING AND GROUND LOADS. Landing load factor Effect of touchdown rate of descent Effect of gross weight Ported landing on unprepared .surfaces EFFECT OF OVERSTRESS ON SERVICE Recognition of overstress’damage Importance of operating limitations LIFE ,... ,.., 328 330 331 331 331 332 ,’ 334 334 339 343 344 xiv
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NAVWEPS 00401-80 TABLE OF CONTENTS CHAPTER 6. APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING mrx PRIMARY CONTROL OF AIRSPEED AND ALTITUDE.. 349 Angle of attack versus airspeed Rate of climb and descent Flying technique REGION OF REVERSED COMMAND. . 353 Regions of normal and reversed command Features of flight in the normal and reversed regions of command THE ANGLE OF ATTACK INDICATOR AND THE MIRROR LANDING SYSTEM. . . 357 The angle of attack indicator The mirror landing system THE APPROACH AND LANDING., 360 The approach The landing flare and touchdown Typical errors THE TAKEOFF.. 365 Takeoff speed and distance Typical errors GUSTS AND WIND SHEAR.. _. t,. 367 Vertical and horizontal gusts POWER-OFF GLIDE PERFORMANCE. . 369 Glide angle and lift-drag ratio Factors affecting glide performance The flameout pattern EFFECTOF ICE AND FROST ON AIRPLANE PERFORMANCE.. 373 Effect of ice Effect of frost ENGINE FAILURE ON THE MULTI-ENGINE AIRPLANE. 376 Effecf of weight and altihtde Control requirements Effeti on performance Etrect of turning flight and configuration GROUND EFFECT., _, 379 Aerodynamic influence of ground effect Ground effect on specific flight conditions INTERFERENCE BETWEEN AIRPLANES IN FLIGHT.. 383 Effect of lateral, vertical, and IongiNdinal separation Collision possibility
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NAVWEPS 00-BOT-BO TABLE OF CONTENTS BRAKING PERFORMANCE. ......................................... Friction cbaracte~istics Braking technique Typical errors of braking technique REFCTSAL SPEEDS , LINE SPEEDS, AND CRITICAL FIELD LENGTH. ............................................................. Refusal speed Line speeds Critical field length, multi-engine operation SONIC BOOMS. ....................................................... Shock waves and audible sound Precautions HELICOPTER PROBLEMS. ........................................... Rotoraerodynamics ..................................................... Retreating blade stall ................................................... Compressjbility effects .................................................. Autorotatton charactertsttcs ............................................. Powersettling ......................................................... THE FLIGHT HANDBOOK. ........................................ SELECTED REFERENCES. ..................................... Iklr\C” ,,“YL)\ ....................................................... Pam 387 391 396 399 400 402 404 405 408 411 413 414 xvi
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NAVWEPS 00-BOT-BO BASIC AERODYNAMICS Chapter 1 BASIC AERODYNAMKS In order to understand the characteristics of his aircraft and develop precision flying tech- niques, the Naval Aviator must be familiar with the fundamentals of aerodynamics. There are certain physical laws which describe the behavior of airflow and define the various aerodynamic forces and moments acting on a surface. These principles of aerodynamics pro- vide the foundations for good, precise flying techniques. WING AND AIRFOIL FORCES PROPERTIES OF THE ATMOSPHERE The aerodynamic forces and moments acting on a surface are due in great part to the prop- erties of the air mass in which the surface is operating.~ The composition, of the earth’s atmosphere by volume is approximately 78 percent. nitrogen, 21 percent oxygen, and 1
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NAVWEe3 OO-BOT-80 BASIC AERODYNAMICS percent water vapor, argon, carbon dioxide, etc. For the majority of all aerodynamic con- siderations air is considered as a uniform mixture of these gases. The usual quantities used to define the properties of an air mass are as follows: STATIC PRESSURE. The absolute static pressure of the air is a property of primary importance. The static pressure of the air at any altitude results from the mass of air supported above that level. At standard sea level conditions the static pressure of the air is 2,116 psf (or 14.7 psi, 29.92 in. Hg, etc.) and at 40,000 feet altitude this static pressure decreases to approximately 19 percent of the sea level value. The shorthand notation for the ambient static pressure is “p” and the standard sea level static pressure is given the subscript “a” for zero altitude, pa. A more usual reference in aerodynamics and perform- ance is the proportion of the ambient sta~tic pressure and the standard sea level static pressure. This static pressure ratio is assigned the shorthand notation of 8 (delta). Altitude pressure ratio Ambient static pressure =Standard sea level static pressure 6 = PIP0 Many items of gas turbine engine perform- ance are directly related to some parameter involving the altitude pressure ratio. TEMPERATURE. The absolute tempera- cure of the air is another important property. The ordinary temperature measurement by the Centigrade scale has a/datum at the freezing point of water but absolute zero temperature is obtained at a temperature of -273“ Centi- grade. Thus, the standard sea level tcmpera- ture of 15” C. is an absolute temperature of 288”. This scale of absolute temperature using the Centigrade increments is the Kelvin scale, e.g., o K. The shorthand notation for the ambient air temperature is “T” and the stand- ard sea level air temperature of 288’ K. is signified by Ta. The more usual reference is, the proportion of the ambient air temperature and the standard sea level air temperature. This temperature ratio is assigned the short- hand notation of 0 (theta). Temperature ratio Ambient air temperature =Standard sea level air temperature @=TITtl ,+273 288 Many items of compressibility effects and jet engine performance involve consideration of the temperature ratio. DENSITY. The density of the air is a prop- erty of greatest importance in the study of aerodynamics. The density of air is simply the mass of air per~cubic foot of volume and is a direct measure of the quantity of matter in each cubic foot of air. Air at standard sea lcvcl conditions weighs 0.0765 pounds per cubic foot and has a density of 0.002378 slugs per cubic foot. At an altitude of 40,000 feet the air density is approximately 25 percent of the sea level value. The shorthand notation used for air density is p (rho) and the standard sea level air density is then pO. In many parts of aerodynamics it is very convenient to consider the proportion of the ambient air density and standard sea level air density. This density ratio is assigned the shorthand notation of c (sigma). density ratio= ambient air density standard sea level air density a = PIP0 A general gas law defines the relationship of pressure temperature, and density when there is no change of state or heat transfer. Simply stated this would be “density varies directly with pressure, inversely with temperature.” Using the properties previously defined, density ratio= Pressure rat’o. temperature rat10 2
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PlAVWEPS 00-8OT-80 BASIC AERODYNAMICS This relationship has great application in aerodynamics and is quite fundamental and necessary in certain parts of airplane perform- ance. VISCOSITY. The viscosity of the air is important in scale and friction effects. The coefficient of absolute viscosity is the propor- tion between the shearing stress and velocity gradient for a fluid flow. The viscosity of gases is unusual in that the viscosity is gen- erally a function of temperature alone and an increase in temperature increases the viscosity. The coefficient of absolute viscosity is assigned the shorthand notation I, (mu). Since many parts of aerodynamics involve consideration of viscosity and density, a more usual form of viscosity measure is the proportion of the co- efficient of absolute viscosity and density. This combination is termed the “kinematic viscosity” and is noted by Y (nu). kinematic viscosity cc coefficient of absolute viscosity density v=PlP The kinematic viscosity of air at standard sea level conditions is 0.0001576 square feet per second. At an altitude of 40,000 feet the kinematic viscosity is increased to 0.0005059 square foot per second. In order to provide a common denominator for comparison of various aircraft, a standard atmosphere has been adopted. The standard atmosphere actually represents the mean or average properties of the atmosphere. Figure 1.1 illustrates the variation of the most im- portant properties of the air throughout the standard atmosphere. Notice that the lapse rate is constant in the troposphere and the stratosphere begins with the isothermal region. Since all aircraft performance is compared and,evaluated in the environment of the stand- ard atmosphere, all of the aircraft instrumenta- tion is calibrated for the standard atmosphere. Thus, certain corrections must apply to the instrumentation as well as the aircraft per- formance if the operating conditions do not fit the standard atmosphere. In order to prop- erly account for the nonstandard atmosphere certain terms must be defined. Pressure .&itudc is the altitude in the standard atmosphere corresponditrg to a particular pressure. The aircraft altimeter is essentially a sensitive barometer calibrated to indicate altitude in the staotlard atmosphere. If the altimeter is set for 29.92 in. Hg the altitude indicated is the pressure altitude-the altitude in the stand- ard atmosphere corresponding to the sensed pressure. Of course, this indicated pressure altitude may not be the actual height above sea level due to variations in remperature, lapse rate; atniospheric pressure, and possible errors in the sensed pressure. The more appropriate term for correlating aerodynamic performance in the nonstandard atmosphere is density &it&-the altitude in the standard atmosphere corresponding to a particular value of air density. The computa- tion of density altitude must certainly involve consideration of pressure (pressure altitude) and temperature. Figure 1.6 illustrates the manner in which pressure altitude and tem- perature combine to produce a certain density altitude. This chart is quite standard in use and is usually included in the performance section of the flight handbook. Many subject areas of aerodynamics and aircraft performance will emphasize density altitude and temperature as the most important factors requiring con- sideration. BERNOULLI’S PRINCIPLE AND SUBSONIC AIRFLOW All of the external aerodynamic forces on a surface are the result of air pressure or air fric- tion. Friction effects are generally confined to a thin layer of air in the immediate vicinity of the surface and friction forces are not the pre- dominating aerodynamic forces. Therefore, 4
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NAVWEPS OO-ROT-80 BASIC AERODYNAMICS ICAO STANDARD ATMOSPHERE *GEOPOTENTIAL OF THE TROPOPAUSE Figure 1.7. Standard Altitude Table
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NAVWEPS 00401-80 BASIC AERODYNAMICS the pressure forces created on an aerodynamic surface can be studied in a simple form which at first neglects the effect of friction and vis- cosity of the airflow. The most appropriate means of visualizing the effect of airflow and the resulting aerodynamic pressures is to study the fluid flow within a closed tube. Suppose a stream of air is flowing through the tube shown in figure 1.2. The airflow at station 1 in the tube has a certain velocity, static pressure, and density. As the airstream approaches the constriction at station 2 certain changes must take place. Since the airflow is enclosed within the tube, the mass flow at any point along the tube must be the same and the velocity, pressure, or density must change to accommodate this continuity of flow. BERNOULLI’S EQUATION. A distin- guishing feature of submnic airflow is that changes in pressure and velocity take place with sniall and negligible changes in density. For this reason the study of subsonic airflow can be simplified by neglecting the variation of density in the flow and assuming the flow to be incomprmiblc. Of course, at high flow speeds whjch approach the speed of sound, the flow must be considered as compressible and “compressibility effects” taken into account. However, if the flow through the tube of figure 1.2 is considered subsonic, the density of the airstream is essentially constant at all sta- tions along the length. If the density of the flow remains constant, static pressure and velocity are the variable quantities. As the flow approaches the con- striction of station 2 the velocity must increase to maintain the same mass flow. As the velocity increases the static pressure will de- crease and the decrease in static pressure which accompanies the increase in velocity can be verified in two ways: (I) Newton’s laws of motion state the requirement of an unbalanced force to pro- duce an acceleration (velocity change). If the airstream experiences an increase in veloc- ity approaching the constriction, there must be an unbalance of force to provide the ac- celeration. Since there is only air within the tube, the unbalance of force is provided by the static pressure at station 1 being greater than the static pressure at the constriction, station 2. (2) The total energy of the air stream in the tube is unchanged. However, the air- .’ stream energy may be in two forms. The airstream may have a potential energy which is related by the static pressure and a kimtic energy by virtue of mass and motion. As the total energy is unchanged, an increase in velocity (kinetic energy) will be accompa- nied by a decrease in static pressure (poten- tial energy). This situation is analagous to a ball rolling along-a smooth surface. As the ball rolls downhill, the potential energy due to position is exchanged for kinetic energy of motion. If .friction- were negli- gibie, the change of potential energy would equal the change in ki,netic energy. This- is also the case for the airflow within the tube. The relationship of static pressure and veloc- ity is maintained throughout the length of the tube. As the flow moves past the constriction toward station 3, the velocity decreases and the static pressure increases. The Bernoulli equation for incompressible flow is most readily explained ,by accounting for the energy of the~airflow within the tube. As the airstream has no energy added or sub- tracted at any point, the sum of the potential +id kinetic energy must be constant. The kinetic energy of an object is found by: “KE. =%MV= where K;E. = kinetic energy, ft.-lbs. M = mass, slugs V’=velocity, ft./set. The kinetic energy of a cubic foot of air is: K&x,, where g= kinetic energy per cu. ft., psf p=air density, slugs per cu. ft. V=ait velocity, ft./set. 6
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NAWEPS DD-BDT-BD BASIC AERODYNAMICS INCREASEOVELOC DECREASE0 HEIG PE + KE = CONSTANT Ftaure 1.2. Airflow Within a Tube
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NAVWEPS 00-ROT-80 BASIC AERODYNAMICS 2500 2000 H=P+q I I 1500 I ci P d 1000 q 500 I 70K P=21 16 PSF P = 2014 PSF P = 2133 PSF q= 34 PSF 9 = 136 PSF q= I7 PSF H- 2150 PSF H = 2150 PSF H = 2150 PSF Figure 1.3. Variation o\ Pressure in Tube
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If the potential energy is represented by the static pressure, p, the sum of the potential and kinetic energy is the total pressure of the air- stream. H=p+% P V’ where H=total pressure, psf (sometimes re- ferred to as “head ’ pressure) p=static pressure, psf. p=density, siugs per cu. ft. V= velocity, ft./set. This equation is the Bernoulli equation for ‘incompressible flow. It is important to ap- preciate that the term >$pV2 has the units of pressure, psf. This term is one of the most important in all aerodynamics and appears so frequently t&it is given the name “dynamic pressure” and the shorthand notation “4”. q= dynamic pressure, psf = jgpv2 With this definition it could be said that the sum of static and dynamic pressure in the flow tube remains constant. Figure 1.3 illustrates the variation of static, dynamic, and total pressure of air flowing through a closed tube. Note that the total pressure is con,stant throughout the length and any change in dynamic pressure produces the same magnitude change in static pressure. The dynamic pressure of a free airstream is the one ‘common denominator of all aero- dynamic forces and moments. Dynamic pres- sure represents the kinetic energy of the free airstream and is a factor relating the capability for producing changes in static pressure on a surface. As defined, the dynamic, pressure varies directly as the density and the square of the velocity. Typical values of dynamic pres- sure, 4, are shown in table l-1 for various true airspeeds in the standard atmosphere. Notice that the dynamic pressure at some fixed veloc- ity varies directly with the density ratio at any altitude. Also, appreciate the fact that at an altitude of 40,oM) feet (where the density ratio, b, is 0.2462) it is necessary to have a true air velocity twice that at sea level in order to product the same dynamic pressure. NAVWEPS 00-801-80 BASIC AERODYNAMICS TABLE l-l. Effect of Speed and Altitvde on Dwzmnic Prerrure True air speed (fr./scc.) m= 169 338 507 616 845 I, 013 - ,I I c _- AIRSPEED MEASUREMENT. If a sym- metrically shaped object were placed in a moving airstream, the flow pattern typical of figure 1.4 would result. The airstream at the very nose of the object would stagnate and the relative flow velocity at this point would be zero. The airflow ahead of the object pos- sesses some certain dynamic pressure and ambient static pressure. At the very nose of the object the local velocity will drop to zero and the airstream dynamic pressure will be converted into an increase in static pressure at the stagnation point. In other words, there will exist a static pressure at the stagnation point which is equal to the airstream total pressure-ambient static pressure plus dynamic pressure. Around the surface of the object the airflow will divide and the local velocity will increase from zero at the stagnation point to some maximum on the sides of the object. If fric- tion and viscosity effects are neglected, the 9
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NAVWEPS OO-EOT-80 BASIC AERODYNAMICS FORWARD STAGNATION AFT STAGNATION POINT POINT AIRSTREAM AHEAD STAGNATION PRESSURE HAS AMBIENT STATIC IS AIRSTREAM TOTAL PRESSURE AND DYNAMIC PRESSURE PRESSURE P+q Ftgure 1.4. Flow Pattern on a Symmetrical Object surface anflow continues to the aft stagnation point where the local velocity is again zero. The important point of this example of aero- dynamic flow is existence of the stagnation point. The change in airflow static pressure which takes place at the stagnation point IS equal to the free stream dynamic pressure, q. The measurement of free stream dynamic pressure is fundamental to the indication of airspeed. In fact, airspeed indicators are sim- ply pressure gauges which measure dynamic pressure related to various airspeeds. Typical airspeed measuring systems are illustrated in figure 1.5. The pitot head has no internal flow velocity and the pressure in the pitot tube is equal to the total pressure of the airstream. The purpose of the static-ports is to sense the true static pressure of the free airstream. The total pressure and static pressure lines are attached to a differential pressure gauge and the net pressure indicated is the dynamic pressure, q. The pressure gauge is then cali- brated to indicate flight speed in the standard sea level air mass. For example, a dynamic pressure of 305 psf would be realized at a sea level flight ,speed of 300 knots. Actually there can be many conditions of flight where the airspeed indicator does not truly reflect the actual velocity through the air mass. The corrections that must be applied are many and lisred in sequence below: (1) The indicated airspeed (IAS) is the actual instrument indication for some given flight condition. Factors such as an altitude other than standard sea level, errors of the instrument and errors due to the installation, compressibility, etc. may create great vari- ance between this instrument indication and the actual flight speed. (2) The calibrated airspeed (CM) is the result of correcting IAS for errors of the 10
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NAVWEPS 00-807-80 BASIC AERODYNAMICS PITOT-STATIC SYSTEM w / :% . I. q PITOT WITH SEPARATE STATIC SOURCE PRESSURE INDICATED BY GAUGE IS DIFFERENCE BETWEEN TOTAL AND STATIC PRESSURE, H-p= q Figure. 1.5. Airspeed Measurement instrument and errors due to position or lo- cation of the installation. The instrument error must be small by design of the equip- ment and is usually negligible in equjpment which is properly maintained and cared for. The position error of the installation must be small in the range of airspeeds involving critical performance conditions. Position errors are most usually confine,d to the static source in that the actual static pressure sensed at the static port may be different from the free airstream static pressure. When the .,aircraft is operated through a large range’ of angles of attack, the static pressure distribution varies ‘quite greatly and it becomes quite difficult to’minimize the static source error. In most instances a compensating group of static sources may be combined to reduce the position error. In order to appreciate the magnitude of this problem, at flight speed near 100 knots a 11 0.05 psi position error is an airspeed error of 10 knots. A typical variation of air- speed system position error is illustrated in figure 1.6. (3) The equivalent airspeed (PAS) is the result of correcting the (CAS) for compressi- bility effects. At high flight speeds the stagnation pressure recovered in the pitot tube is not representative of the airstream dynamic pressure due to a magnification by compressibility. Compressibility of the airflow produces a stagnation pressure in the pitot which is greater than if the flow were incompressible. As a result, the air- speed indication is given an erroneous mag- nihcation. The standard airspeed indicator is calibrated to read correct when at standard sea level conditions and thus has a com- pressibility correction appropriate for these conditions. However, when the aircraft is operating above standard sea level altitude, Revised January 1965
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NAVWEPS 00-801-80 BASIC AERODYNAMICS TYPICAL POSITION ERROR CORRECTION INDICATED AIRSPEED, KNOTS COMPRESSIBILITY CORREt 300 CALIBRATED AIRSPEED, KNOTS Figure 1.6. Airspeed Corrections (sheet 1 of 2) 12
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NAVWEPS 00-801-80 BASIC AERODYNAMICS DENSITY ALTITUDE CHART +g& ‘Id -30fl1111v AlISNxl Figure 1.6. Airspeed Corrections (sheet 2 of 2)
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NAVWEPS 00-SOT-80 BASIC AERODYNAMICS the inherent compensation is inadequate and additional correction must be applied. The subtractive corrections that must be applied to CA$ depend on pressure altitude and CAS and are shown on figure 1.6 for the subsonic flight range. The equivalent airspeed (EAS) is the flight speed in the standard sea level air mass which would produce the same free stream dynamic pressure as the actual flight condition. (4) The true airspeed (TAS) results when the &4X is corrected for density altitude. Since the airspeed indicator is calibrated for the dynamic pressures corresponding to airspeeds at standard sea level conditions, variations in air density must be accounted for. To relate EAS and TAX requires con- sideration that the EAS coupled with stand- .ard sea level density produces the same dy- namic pressure as the TAX Soupled with the ^^_._^ 1 .:.. 2---:... ,.f *L., bl:A.* rnrJ;r;m.. dCLUd, ‘all UcIIJIcy “I L11L “‘6°C C”IIUACI”L‘. From this reasoning, it can be shown that: (TAS)2p=(EAS)2 po d - or, TAS=EAS 62 P TAS= EAS 2 4 where TAX= true airspeed EAS=equivalent airspeed p=actual air density PO= standard sea level air density n=altitude density ratio, p/pa The result shows that the TAX is a function of EAS and density altitude. Figure 1.6 shows a chart of density altitude as a function of pressure altitude and temperature. Each par- ticular density altitude fixes the proportion between TAX and EAS. The use of a naviga- tion computer requires setting appropriate values of pressure altitude and temperature on the scales which then fixes rhe proportion be- tween the scales of TAS and EAS (or TAS and CAS when compressibiliry corrections are applicable). Revlted Jmuoy 1965 14 Thus, the airspeed indicator system measures dynamic pressure and will relate true flight velocity when instrument, position, compress- ibility, and density corrections are applied. These corrections are quite necessary for ac- curate determination of true airspeed and accurate navigation. Bernoulli’s principle and the concepts of static, dynamic, and total pressure are the basis of aerodynamic fundamentals. The pressure distribution caused by the variation of local stack and dynamic pressures on a surface is the source of the major aerodynamic forces and moment. DEVELOPMENT OF AERODYNAMIC FORCES The typical airflow patterns exemplify the relationship of static pressure and velocity defined by Bernoulli. Any object placed in an airstream will have the a& to impact or stag- nate at some point near the leading edge. The pressure at this point of stagnation will be an absolute static pressure equal to the total pres- sure of the airstream. In other words, the static pressure at the stagnation point will be greater than the atmospheric pressure by the amount of the dynamic pressure of the air- stream. As the flow divides and proceeds around. the object, the increases in local ve- locity produce decreases in static pressure. This procedure of flow is best illustrated by the flow patterns and pressure distributions of figure 1.7. STREAMLINE PATTERN AND PRES- SURE DISTRIBUTION. The flow pattern of the cylinder of figure 1.7 is characterized by the streamlines which denote the local flow direction. Velocity distribution is noted by the streamline pattern since the streamlines effect a boundary of flow, and the airflow between the streamlines is similar to flow in a closed tube. When the streamlines contract and are close together, high local velocities exist; when the streamlines expand and are far apart, low local velocities exist. At the
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NAVWEPS 00-8OT-80 BASIC AERODYNAMICS PEAK SUCTION PRESSURE PRESSURE DISTRIBUTION ON A 5v’ )ER STAGNATION NEGLECTING FRICTION (PERFECT FLUID) CONSIDERING FRICTION EFFECTS (VISCOUS FLOW) PRESSURE DISTRIBUTION ON A SYMMETRICAL AIRFOIL AT ZERO LIFT -PEAK SUCTION S AFT STAGNATION POINT NEGLECTING FRICTION VISCOUS FLOW Figure 1.7. Streamline Pattern and Pressure Distribution 15
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NAVWEPS OO-BOT-80 BASIC AERODYNAMICS forward stagnation point the local velocity is zero and the maximum positive pressure re- sults. As the flow proceeds from the forward stagnation point the velocity increases as shown by the change in streamlines. The local velocities reach a maximum at the upper and lower extremities and a peak suction pres- sure is produced at these points on the cylinder. (NOTE: Positive pressures are pressures above atmospheric and negative or .ruction pressures are less than atmospheric.) As the flow continues aft from the peak suction pressure, the diverging streamlines indicate decreasing local velocities and increasing local pressures. If friction and compressibility effects are not considered, the velocity would decrease to zero at the aft stagnation point and the full stagna- tion pressure would be recovered. The pressure distribution for the cylinder in perfect fluid flow would be symmetrical and no net force (lift or dragj wvuid rcsuit. Of course, thr relationship between static pressure and ~eloc- ity along the surface is defined by Bernoulli’s equation. The flow pattern for the cylinder in an actual fluid demonstrates the effect of friction or viscosity. The viscosity of air produces a thin layer of retarded flow immediately adjacent to the surface. The energy expended in this “boundary layer” can alter the pressure dis- tribution and destroy the symmetry of the pattern. The force unbalance caused by the change in pressure distribution creates a drag force which is in addition to the drag due to skin friction. The streamline pattern for the symmetrical airfoil of figure 1.7 again provides the basis for the velocity and pressure distribution. At the leading edge the streamlines are widely diverged in the vicinity of the positive pres- sures. The maximum local velocities and suction (or negative) pressures exist where the streamlines are the closest together, One notable difference between the flow on the cylinder and the airfoil is that the maximum velocity and minimum pressure points on the airfoil do not ,necessarily occtir at the point of maximum thickness. However, a similarity does exist in that the minimum pressure points correspond to the points where the streamlines are closest together and this condition exists when the streamlines are forced to the great- est curvature. GENERATION OF LIFT. An important phenomenon associated with the production of lift by an airfoil is the “circulation” im- parted to the airstream. The best practical illustration of this phenomenon is shown in figure 1.8 by the streamlines and pressure dis- tributions existing on cylinders in an airstream. The cylinder without circulation has a sym- metrical streamline pattern and a pressure dis- tribution which creates n-0 n_et lift. If the cylinder is given a clockwise rotation and induces a rotational or circulatory flow, a dis- tinct change takes place in the streamline pat- tern and p’ess.~re &str~‘“u~~oii, The vriocitirs due to the vortex of circulatory flow cause increased 104 velocity on the upper surface of the cylinder and decreased local velocity on the lower surface of the cylinder. Also, the circulatory flow produces an upwash immedi- ately ahead and downwash immediately be- hind the cylinder and both fore and aft stagna- tion points are lowered. The effect of the addition of circulatory flow is appreciated by the change in the pressure distribution on the cylinder. The increased local velocity on the upper surface causes an increase in upper surface suction while the decreased local velocity on the lower surface causes a decrease in lower surface suction. As a result, the cylinder with circulation will produce a net lift. This mechanically induced circulation-called Magnus effect-illustrates the relationship between circulation and lift and is important to golfers, baseball and tennis players as well as pilots and aerodynamicists. The curvature of the flight path of a golf ball or baseball rcluites an unbalance df force which is created by rotation of the ball. The pitcher that can accurately control a .powerful 16
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NAVWEPS 00-8OT-80 BASIC AERODYNAMICS CYLINDER WITHOUT CIRCULATION INCREASED LOCAL VELOCITY UPWASH mSWNWASH ---- \ LDECREASED LOCAL VELOCITY CYLINDER WITH CIRCULATION MAGNUS EFFECT BY ROTATING CYLINDER AIRFOIL LIFT -ZERO LIFT I UPWASH 7 INCREASED LOCAL I ,-VELOCITY POSITIVE LIFT DECREASED LOCAL VELOCITY Figure 1.8. Generation of Lift (sheet 1 of 2) 17
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NAVWEPS 00-SOT-80 BASIC AERODYNAMICS Figure 7.8. Generation of Lift (sheet 2 of 2) 18
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NAVWEPS GO-BOT-BO BASIC AERODYNAMlCS BASIC AIRFOIL SHAPE AND ANGLE OF ATTACK ORIGINAL ANGLE OF ATTACK AND DYNAMIC/PRESSURE, 9 ORIGINAL ANGLE OF ATTACK BUT INCREASED DYNAMIC PRESSURE ORIGINAL ANGLE OF ATTACK AND DYNAMIC PRESSURE BUT ONE-HALF ORIGINAL SIZE AIRFOIL SHAPE AND ANGLE OF ATTACK DEFINE RELATIVE PRESSURE DISTRIBUTION Figure 1.9. Airfoil Pressure Distribution 19
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NAVWEPS 00-801-80 BASIC AERODYNAMICS rotation will be quite a “curve ball artist” the golfer that cannot control the lateral mo- tion of the club face striking the golf ball will impart an uncontrollable spin and have trouble with a “hook” or “slice.” While a rotating cylinder can produce a net lift from the circulatory flow, the method is relatively inefficient and only serves to point out the relationship between lift and circula-, tion. An airfoil is capable of producing lift with relatively high efficiency and the process is illustrated in figure 1.8. If a symmetrical airfoil is placed at zero angle of attack to the airstream, the streamline pattern and pressure distribution give evidence of zero lift. HOW- ever, if the airfoil is given a positive angle of attack, changes occur in the streamline pattern and pressure distribution similar to changes caused by the addition of circulation to the cylinder. The positive angle of attack causes increased velocity on the upper surface with an increase in upper surface suction while the decreased velocity on the lower surface causes a decrease in lower surface suction. Also, upwash is generated ahead of the airfoil, the forward stagnation point moves under the leading edge, and a downwash is evident aft of the airfoil. The pressure distribution 0” the airfoil now provides a net force perpendicu- lar to the airstream-lift. The generation of lift by an airfoil is depend- ent upon the airfoil being able to create circu- lation in the airstream and develop the lifting, pressure distribution on the surface. In all cases, the generated lift will be the net force caused by the distribution of pressure over the upper and lower surfaces of the airfoil. At low angles of attack, suction pressures usually will exist on both upper and lower surfaces. but the upper surface suction must be greater for positive lift. At high angles of attack near that for maximum lift, a positive pressure will exist on the lower surface but this will account for approximately one-third the net lift. The effect of free stream density and velocity is a necessary consideration when studying the development of the various aerodynamic forces. Suppose that a particular shape of airfoil is fixed at a particular angle to the airstream. The relative velocity and pressure distribution will be determined by the shape of the airfoil and the angle to the airstream. The effect of varying the airfoil size, air density and air- speed is shown in figure 1.9. If the same air- foil shape is placed at the same angle to an airstream with twice as great a dynamic pres- sure the magnitude of the pressure distribution will be twice as great but the r&rive shape of the pressure distribution will be the same. With twice as great a pressure existing over the surface, all aerodynamic forces and mo- ments will ~double. If a half-size airfoil ib placed at the same angle to the original air- stream, the magnitude of the pressure distri- bution is the same as the origina! airfoi! and again the relative shape of the pressure dis- tribution is identical. The same pressure act- ing on the half-size surface would reduce all aerodynamic forces to one-half that of the original. This similarity of flow patterns means that the stagnation point occurs at the same place, the peak suction pressure occurs at the same place, and the actual magnitude of the aerodynamic forces and moments depends upon the airstream dynamic pressure and the surface area. This concept is extremely im- portant when attempting to separate and ana- lyze the most important factors affecting the development of aerodynamic forces. AIRFOIL TERMINOLOGY. Since the shape of an airfoil and the inclination to the airstream are so important in determining the pressure distribution, it is necessary to properly define the airfoil terminology. Figure 1.10 shows a typical airfoil and illustrates the various items of airfoil terminology (1) The chord line is a straight line connect- ing the leading and trailing edges of the airfoil. 20
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NAVWEPS 00-8DT-80 BASIC AERODYN,AMlCS LOCAT,ON DF THICKNESS MAX. THICKNESS UPPER SURFACE MEAN CAMBER t CA CH6RD -I t- v LOCATION OF MAXIMUM CAMBER RE;L:r; 0 7 LIFT & 0 G DRAG a Figure 1.10. Airfoil ~erminoh \ 21
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NAVWEPS oOgOT-8O BASIC AERODYNAMICS (2) The chord is the characteristic dimen- sion of the airfoil. (3) The mean-camber line is a line drawn halfway between the upper and lower sur- faces. Actually, the chord line connects the ends of the mean-camber line. (4) The shape of the mean-camber line is very important in determining the aerody- namic characteristics of an airfoil section. The maximum camber (displacement of the mean line from the chord line) and the Ioca- tion of the maximum camber help to define the shape of the mean-camber line. These quantities are expressed as fractions or per- cent of the basic chord dimension. A typi- cal iow speed airfoil may have a maximum camber of 4 percent located 40 percent aft of the leading edge. (5) The thickness and thickness distribu- tion of the profile are important properties of a section. The maximum tbicknus and location of maximum thickness define thick- ness and distribution of thickness and are expressed as fractions or percent of the chord. A typical low speed airfoil may have a. maximum thickness of 12 percent located 30 percent aft of the leading edge. (6) The leading edge radius of the airfoil is the radius of curvature given the leading edge shape. It is the radius of the circle centered on a line tangent to the leading edge camber and connecting tangency pcints of upper and lower surfaces with the leading edge. Typi- cal leading edge radii are zero (knife edge) to 1 or 2 percent. (7) The Iift produced by an airfoil is the net force produced perpendicular to the n&a- tive wind. (8) The drag incurred by an airfoil is the net force produced parallel to the relative wind. (9) The angle of attack is the angle between the chord line and the relative wind. Angle of attack is given the shorthand notation a (alpha). Of course, it is important to dif- i ferentiate between pitch attitude angle and 22 angle of attack. Regardless of the condi- tion of flight, the instantaneous flight path of the surface determines the direction of the oncoming relative wind and the angle of attack is the angle between the instantaneous relative wind and the chord line. To respect the definition of angle of attack, visualize the flight path of the aircraft during a loop and appreciate that the relative wind is defined by the flight path at any point dur- ing the maneuver. Notice that the description of an airfoil profile is by dimensions which are fractions or percent of the basic chord dimension. Thus, when an airfoil. profile is specified a relative shape is described. (NOTB: A numerical sys- tem of designating airfoil profiles originated by the National ~Advisory Committee for Aero- nautics [NACA] is used to describe the main geometric features and certain aerodynamic properties. NACA Report Nol 824 wi!! pro- vide the detail of this system.) AERODYNAMIC FORCE COEFFICIENT. The aerodynamic forces of lift and drag depend on the combined effect of many different vari- ables. The important single variables could IX: (1) Airstream velocity (2) Air density (3) Shape or profile of the surface (4) Angle of attack (5) Surface area (6) Compressibility effects (7) Viscosity effects If the effects of viscosity and compressibility are not of immediate importance, the remain- ing items can be combined for consideration. Since the major aerodynamic forces are the result of various pressures distributed on a surface, the surface area will be a major factor. Dynamic prcssurc of the airstream is another common denominator of aerodynamic forces and is a major factor since the magnitude of a pressure distribution depends on the source energy of the free stream. The remaining major factor is the relative peJJ#re dittribution
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existing on the surface. Of course, the ve- locity distribution, and resulting pressure dis- tribution, is determmed by the.shape or pro- file of the surface and the angle of a’track. Thus, any aerodynamic force can be repre- sented as the product df three major factors: the surface area of the objects the dynamic pressure of the airstream the coefficient or index of force determined by the relative pressure distribution This relationship is expressed by the following equation : F= C,qS where F = aerodynamic force, lbs. C,=coeflicient of aerodynamic force ,iay;mic pressure, psf S=surface area, sq. ft. In order to fully appreciate the importance of the aerodynamic force coe&cient, C,, the , above equation is rearranged to alternate forms : In this form, the aerodynamic force coefficient Js appreciared as the aerodynamic force per surface area and dynamic pressure. In other words, the force coefficient is a dimensionless ratio between the average aerodynamic pres- sure (aerodynamic force.per ‘area) and the air- stream dynamic pressure. All the aerodynamic forces of lift and drag are studied on this basis- the common denominator in each case being surface area and dynamic pressure. By such a definition, a “lift coefficient” would .be the ratio between lift pressure and dynamic pres- sure; a “drag coefficient” would be the ratio between drag pressure and.:d.ynamic pressure. The use of the coefficient form of an aero- dynamic force is necessary since the force coellicient is: (1) An index 04 the aerodynamic force independent of area, density, and velocity. NAVWEPS m-60T-30 BASIC AERODYNAMICS It is derived from the relative pressure and velocity distribution. (2) Influenced only by the shape of the surface and angle of attack since these factors determine the pressure distribution. (3) An index which allows evaluation of the effects of compressibility and viscosity. Since the effects of area, density, and velocity are obviated by the coefficient form, com- pressibility and viscosity effects can be separated for study. THE BASIC LIFT EQUATION. Lift has been dehned as the net force developed per- pendicular to the relative wind. The aero- dynamic force of lift on an airplane results from the generation of a pressure distribution on the wing. This lift force is described by the following equation: L=C& where L=lift, lbs. C, = lift coefficient. q= dy;:mic pressure, psf +p S= wing surface area, sq. ft. The lift coefhcient used in this equation is the ratio of the lift pressure and dynamic pressure and is a function of the shape of the wing and angle of attack. If the lift coefficient of a conventional airplane wing planfoi-m were plotted versus angle of attack, the result would be typical of the graph of figure 1.11. Since the effects of speed, density, area, weight, alti- tude, etc., are eliminated by the coefficient form, an indication of the true lift capability is ob- tained. Each angle of attack produces a par- ticular lift coefficient since the angle of attack is the controlling factor in the pressure dis- tribution. Lift coeflicient increases with angle of attack up to the maximum lift coefficient, c L,,,~., and, as angle of attack is increased be- yond the maximum lift angle, the airflow is unable to adhere to the upper surface. The airflow then separates from the upper surface and stall occurs. JNTERPRETATION OF THE LIFT EQUA- TION. Several important relationships are 23
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H P LIFT COEFFICIENT CL LIFT PRESSURE DYNAMIC PRESSURE L qs 600 ANGLE OF ATTACK, DEGREES a Figure 7.7 1. Typical lib Characteristics
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NAVWEPS 00.401-80 BASIC AERODYNAMICS Thus, a sea level airspeed (or EAS) of 100 knots would provide the dynamic pressure necessary at maximum lift to produce 14,250 Ibs. of lift. If the airplane were operated at a higher weight, a higher dynamic pressure would be required to furnish the greater lift and a higher stall speed would result. If the airplane were placed in a steep turn, the greater lift required in the turn would increase the stall speed. If the airplane were flown at a higher density altitude the TAX at stall would increase. However, one factor common to each of these conditions is that the angle of attack at C,,,, is the same. It is important to realize that stall warning devices must sense angle of attack (a) or pressure distribution (related to CL). Another important fact related by the basic lift equation and lift curve is variation of angle of attack and lift coefficient with airspeed. Suppose that the example airplane is flown in steady, wing 1eveJ flight at various airspeeds with lift equal to the weight. It is obvious that an increase in airspeed above the stall speed will require a corresponding decrease in lift coeflicient and angle of attack to maintain steady, lift-equal-weight flight. The exact relationship of lift coefficient and airspeed is evolved from the basic lift equation assuming constant lift (equal to weight) and equivaIent airspeeds. derived from study of the basic lift equation and the typical wing lift curve. One impor- tant fact to be appreciated is that the airplane shown in figure 1.11 stalls at the same angle of attack regardless of weight, dynamic pres- sure, bank angle, etc. Of course, the stall speed of the aircraft will be affected by weight, bank angle, and other factors since the product of dynamic pressure, wing area, and lift co- efficient must produce the required lift. A rearrangement of the basic lift equation de- fines this relationship. L = c&Y using q =$ (I’ in knots, TAX) solving for V, - V=17.2 & J L,J Since the stall speed is the minimum flying speed necessary to sustain flight, the lift co- efficient must be the maximum (CL,,,,). Suppose that the airplane shown in’ figure 1.11 has the following properties: Weight = 14,250 lbs Wing area=280 sq. ft. C &=1.5 If the airplane is flown in steady, level flight at sea level with lift equal to weight the stall speed would be: ,- V.= 17.24&$ where V.= stall speed, knots TAS W= weight, lbs. (lift = weight) va= 17.2 J (I.&4E;280) = 100 knots C‘ v, p -= - C %n.* 0 V The example airplane was specified to have: Weight = 14,250 lbs. C L,,,=lS V,= 100 knots EAS The following table depicts the lift coefficients and angles of attack at various airspeeds in steady flight. 25
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loo. ................. l.lm 1.30 20.00 110 .................. ,826 1.24 15.P 17.0 .................. ,694 1.04 12.7’ lY) .................. .444 .61 8.20 200 .................. 230 .38 4.6’ MO. ................. ,111 .I7 2.10 4&l. ................. .c453 .o!J 1.10 30.7. ................. ,040 .06 .T= 600 .................. .028 .04 .5O Note that for the conditions of steady flight, each airspeed requites a specific angle of attack and lift coefficient. This fact provides a fun- damental concept of flying technique: Angle of attack is tbs primary Control of airspeed in steady flight. Of course, the control stick or wheel allows the pilot to control the angle of attack and, thus, control the airspeed in steady flight. In the same sense, the throttle controls the output of the powerplant and allows the pilot to control rate of climb and descent at various airspeeds. The teal believers of these concepts ate pro- fessional instrument pilots, LSO’s, and glider pilots.. The glider pilot (or flameout enthusi- ast) has no recourse but to control airspeed by angle of attack and accept whatever rate of descent is incurred at the various airspeeds. The LSO must become quite proficient at judg- ing the flight path and angle of attack of the airplane in the pattern. The more complete visual reference field available to the LSO allows him to judge the angle of attack of the airplane mote accurately than the pilot. When the airplane approaches the LSO, the precise judgment of airspeed is by the angle of attack rather than the rate of closure. If the LSO sees the airplane on the desired flight path but with too low an angle of attack, the airspeed is too high; if the angle of attack is too high, the airspeed is too low and the ait- plane is approaching the stall. The mirror landing system coupled with an angle of attack indicator is an obvious refinement. The mit- tot indicates the desired flight path and the NAVWEPS WOT-BO BASIC AERODYNAMICS angle of attack indicator allows precision con- trol of the airspeed. The accomplished insttu- ment pilot is the devotee of “attitude” flying technique-his creed being “attitude plus power equals performance.” During a GCA approach, the professional instrument pilot controls airspeed with stick (angle of attack) and rate of descent with power adjustment. Maneuvering flight and certain transient conditions of flight tend to complicate the relationship of angle of attack and airspeed. However, the majority of flight and, certainly, the most critical regime of flight (takeoff, ap- proach, and landing), is conducted in essen- tially steady flight condition. AIRFOIL LIFT CHARACTERISTICS. Air- foil section properties differ from wing or airplane properties because of the effect of the planform. Actually, the wing may have vati- ous airfoil sections from root to tip with taper, twist, sweepback and local flow components in a spanwise direction. The resulting aeto- dynamic properties of the wing are determined by the action of each section along the span and the three-dimensional flow. Airfoil sec- tion properties are derived from the basic shape or profile in two-dimensional flow and the force coefficients are given a notation of lower case letters. For example, a wing or airplane lift coefficient is C, while an airfoil section lift coefficient is termed cr. Also, wing angle of attack is Q while section angle of attack is differentiated by the use of 01~. The study of section properties allows an objective consider- ation of the effects of camber, thickness, etc. The lift characteristics of five illustrative airfoil sections are shown in figure 1.12. The section lift coe&icient, c,, is plotted versus section angle of attack, olO, for five standard NACA airfoil profiles. One characteristic fea- ture of all airfoil sections is that the slope of the various lift curves is essentially the same. At low lift coefhcients, the section lift coeffi- cient increases approximately 0.1 for each degree increase in angle of attack. For each of the airfoils shown, a S’ change in angle of 27
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NAVWEPS OD-8OT-80 BASIC AERODYNAMICS (DATA FROM NACA REPORT NO. 824) SECTION ANGLE OF ATTACK mo, DEGREES Figure 1.12. Lift Characteristics of lypicol Airfoil Sections 28
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attack would produce an approximate 0.5 change in lift coefficient. Evidently, lift,~curve slope is not a factor important in the selection of an airfoil. An important lift property affected by the airfoil shape is the section maximum lift co- efficient, ci-. The effect of airfoil shape on ci- can be appreciated by comparison of the lift curves for the five airfoils of figure 1.12. The NACA airfoils 63X06,63-009, and 63i-012 ate symmetrical sections of a basic thickness distribution but maximum thicknesses of 6, 9, and 12 percent respectively. The effect of thickness on ~1% is obvious from an inspec- tion of these curves : NACA 63-005 .~. :. Cl.82 9.0° NACA 6Mo9. 1.10 10.5~ NACA 63‘-01?,. 1.40 13.80 The 12-percent section has a cr- approxi- mately 70 percent greater than the 6-percent thick section. In addition, the thicker airfoils have greater benefit from the use of various high lift devices. The effect of camber is illustrated by the lift curves of the NACA 4412 and 631-412 sections. The NACA 4412 section is a 12 percent thick airfoil which has 4 percent maximum camber located at 40 percent of the chord. The NACA 63i-412 airfoil has the same thickness and thickness distribution as the 631-012 but camber added to give a “design”’ lift coefficient (c, for minimum section drag) of 0.4. The lift curves for these two airfoils show that camber has a beneficial e&t on cl-. ScCdO” %.I a0 for “&* NACA 6h-312 (symmctricd) :. 1.40 13.e NACA 631-412 Whmd). 1.73 IS. z” An additional effect of camber is the change in zero lift angle. While the symmetrical NAVWEPS OO-BOT-BO BASIC AE,RODYMAMlCS sections have zero lift at zero angle of attack, the sections with positive camber have nega- tive angles for zero lift. The importance of maximum lift coefficient is obvious. If the maximum lift coefficient is high, the stall speed will be low. However, the high thickness and camber necessary for high section maximum lift coefficients may produce low critical Mach numbers and large twisting moments at high speed. In other words, a high maximum lift coefficient is just one of the many features desired of an airfoil section. DRAG CHARACTERISTICS. Drag is the net aerodynamic force parallel to the relative wind and its source is the pressure distribution and skin friction on the surface. Large, thick bluff bodies in an airstream show a predomi- nance of form drag due to the unbalanced pres- sure distribution. However, streamlined bodies with smooth contours show a ptedomi- nance of drag due to skin friction. In a fashion similar to other aerodynamic forces, drag forces may be considered in the form of a coefficient which is independent of dynamic pressure and surface area. The basic drag equation is as follows: D=GqS where D=drag, lbs. C,= drag coefficient q= dynamic pressure, psf UP =z (V in knots, TAS) S= wing surface area, sq. ft. The force of drag is shown as the product of dynamic pressure, surface area, and drag co- efficient, C,. The drag coefficient in this equation is similar to any other aerodynamic force coefficient-it is the ratio of drag pres- sure to dynamic pressure. If the drag co- efficient of a conventional airplane were plotted versus angle of attack, the result would be typical of the graph shown in figure 1.13. At low angles of attack the drag coefficient is low and small changes in angle of attack create only slight changes in drag coefficient. At 29
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NAVWEPS 00-BOT-80 BASIC AERODYNAMICS I ANGLEOFATTACK,DEGREES a Figure 7.73. Drag Characteristics (sheet 1 of 21 30
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CD ANGLE OF ATTACK, DEGREES a Figure 7.13. Brag Characferistics (sheet 2 of 2)
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NAVWEPS Oe8OT-80 BASIC AERODYNAMICS higher angles of attack the drag coefficient is much greater and small changes in angle of attack cause significant changes in drag. As stall occurs, a large increase in drag takes place. A factor more important in airplane per- formance considerations is the lift-drag ratio, L/D. With the lift and drag data available for the airplane, the proportions of CL and CD can be calculated for each specific angle of attack. The resulting plot of lift-drag ratio with angle of attack shows that L/D increases to some maximum then decreases at the higher lift coefficients and angles of attack. Note that the maximum lift-drag ratio, (L/D),,,, occurs at one specific angle of attack and lift coefIi- cient. If the airplane is operated in steady flight at (L/D),,,, the total drag is at a mini: mum. Any angle of attack lower or higher than that for (L/D),,, reduces the lift-drag ratio and consequently increases -the total drag for a given airpiane iift. The airplane depicted by the curves of Figure 1.13 has a maximum lift-drag ratio of 12.5 at an angle of attack of 6”. Suppose this airplane is operated in steady flight at a gross weight of 12,500 lbs. If flown at the airspeed and angle of attack corresponding to (L/D),.., the drag would be 1,000 lbs. Any higher or lower airspeed would produce a drag greater than 1,000 lbs. Of course, this same airplane could be operated at higher or lower gross weights and the same maximum lift-drag ratio of 12.5 could be obtained at the same angle of attack of 6”. However, a change’ in gross weight would require a change in airspeed to support the new weight at the same lift co- efficient and angle of attack. Type airplane: (L/D) emz High performance sailplane. 25-40 Typical patrol or transport.. 12-20 High Performance bomber. 2~25 Propeller powered trainer.. 1~15 J et trainer.. 14-16 Transonic fighter or attack.. lo-13 Supersonic fighter or attack. 4-9 (subsonic) 32 Revised Januay 1965 The configuration of an airplane has a great effect on the lift-drag ratio. Typical values of (L/D),.. are listed for various types of airplanes. While the high performance sail- plane may have. extremely high lift-drag ratios, such an aircraft has no real economic or tactical purpose. The supersonic fighter may have seemingly low lift-drag ratios in subsonic flight but the airplane configurations required for supersonic flight (and high [L/D]‘* at high Mach numbers) precipitate this situa- tion. Many important items of airplane perform- ance are obtained in flight at (L/D),... Typi- cal performance conditions which occur at (L/D),., are: maximum endurance of jet powered air- planes maximum range of propeller driven air- planes maximum climb angle for jet powered air- planes maximum power-off glide range, jet or Prop The most immediately interesting of these items is the power-off glide range of an air- plane. By examining the forces acting on an airplane during a glide, it can be shown that the glide ratio is numerically equal to the lift-drag ratio. For example, if the airplane in a glide has an (L/D) of 15, each mile of alti- tude is traded for 15 miles of horizontal dis- tance. Such a fact implies that the airplane should be flown at (L/D)- to obtain the greatest glide distance. An unbelievable feature of gliding perform- ance is the effect of airplane gross weight. Since the maximum lift-drag ratio of a given airplane is an intrinsic property of the aero- dynamic configuration, gross weight will not affect the gliding performance. If a typical jet trainer has an (L/@- of 15, the aircraft 1 can obtain a maximum of 15 miles horizontal distance for each mile of altitude. This would be true of this particular airplane at any gross
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weight if the airplane is flown at the angle of attack for (L/D),. Of course, the gross weight would affect the glide airspeed neces- sary for this particular angle of attack but the glide ratio would be unaffected. AIRFOIL DRAG CHARACTERISTICS. The total drag of an airplane is composed of the drags of the individual components and the forces caused by interference between these components. The drag of an airplane con- figuration must include the various drags due to lift, form, friction, interference, leakage, etc. To appreciate the factors which affect the drag of an airplane configuration, it is most logical to consider the factors which affect the drag of airfoil sections. In order to allow an objective consideration of the effects of thickness, camber, etc., the properties of two-dimensional sections must be studied. Airfoil section properties are derived from the basic profile in two-dimensional. flow and are provided the lower case shorthand notation to distinguish them from wing or airplane properties, e.g., wing or airplane drag coe5- cient is C, while airfoil section drag coefficient is c,. The drag characteristics of three illustrative airfoil sections are shown in figure 1.14. The section drag coe&cient, c,, is plotted versus the section lift coefficient, cr. The drag on the airfoil section is composed of pressure drag and skin friction. When the airfoil is at low lift coe&cients, the drag due to skin friction predominates. The drag curve for a conven- tional airfoil tends to be quite shallow in this region since there is very little variation of skin friction with angle of attack. When the airfoil is at high lift coefficients, form or pressure drag predominates and the drag co- efficient varies rapidly with lift coefficient. The NACA 0006 is a thin symmetrical profile which has a maximum thickness of 6 percent located at 30 percent of the chord. This section shows a typical variation of cd and cr. The NACA 4412 section is a 12 percent thick airfoil with 4 percent maximum camber at NAVWEPS OO-EOT-RO BASIC AERODYNAMICS 40 percent chord. When this section is com- pared with the NACA 0006 section the effect of camber can be appreciated. At low lift coefficients the thtn, symmetrical section has much lower drag. However, at lift coeffi- cients above 03 the thicker, cambered section has the lower drag. Thus, proper camber and thickness can improve the lift-drag ratio of the section. The NACA 63,412 is a cambered 12 percent thick airfoil of the ‘“laminar flow” type. This airfoil is shaped to produce a design lift coe5cient of 0.4. Notice that the drag curve of this airfoil has distinct aberrations with very low drag coefficients near the lift coeffi- cient of 0.4. This airfoil profile has its camber and thickness distributed to produce very low uniform velocity on the forward surface (mini- mum pressure point well aft) at this lift coeffi- cient. The resulting pressure and velocity distribution enhance extensive laminar flow in the boundary layer and greatly reduce the skin friction drag. The benefit of the laminar flow is appreciated by comparing the minimum drag of this airfoil with an airfoil which has one-half the maximum thickness-the NACA ooo6. The choice of an airfoil section will depend on the consideration oftmany different factors. While the cI, of the section is an important quality, a more appropriate factor for con- sideration is the maximum lift coefficient of the section when various high lift devices are applied. Trailing edge flaps and leading edge high lift devices are applied to increase the cr,, for low speed performance. Thus, an appropriate factor for comparison is the ratio of section drag coe5cient to section maximum lift coefficient with flaps-cd/crm,. When this quantity is corrected for compressibility, a preliminary selection of an airfoil section is possible. The airfoil having the lowest value of c&~, at the design flight condition (en- durance, range, high speed, etc.) will create the least section drag for a given .design stall speed.
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NAVWEPS DD-BOT-BD BASK AERODYNAMICS (DATA FROM NACA REPORT ~0.824) SMOOTH SURFAC e-L-- -.2 Cl .2 .4 .6 .8 LO’---I.2 1.4 1.6 1.8 SECTION LIFT COEFFICIENT Cl Figure 1.14. Drag Characteristics of Typical Airfoil Sections 34
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PLIGHT AT HIGH LIFT CONDITIONS It is frequently stated that the career Naval Aviator spends more than half his life “below a thousand feet and a hundred knots.” Re- gardless of the implications of such a state- ment, the thought does cunnute the relation- ship of minimum flying speeds and carrier aviation. Only in Naval Aviation is there such importance assigned to precision control of the aircraft at high lift conditions. Safe operation in carrier aviation demands precision control of the airplane at high lift conditions. The aerodynamic lift characteristics of an airplane are portrayed by the curve of lift coefficient versus angle of attack. Such a curve is illustrated in figure 1.15 for a specific airplane in the clean and flap down configura- tions. A given aerodynamic configuration ex- periences increases in lift coefficient with in- creases in angle of attack until the maximum lift coefficient is obtained. A further increase in angIe of attack produces stall and the lift coefficient then decreases. Since the maximum lift coefficient corresponds to the minimum speed available in flight, it is an important point of reference. The stall speed of the air- craft in level flight is related by the equation: V7.=17.2 J-- c w .ln2s where V.-stall speed, knots TAS W=gross weight, lbs. c Lnoz= airplane maximum lift coefficient csaltitude density ratio S= wing area, sq. ft. This equation illustrates the effect on stall speed of weight and wing area (or wing load- ing, W/S), maximum lift coefficient, and alti- tude. If the stall speed is desired in EAS, the density ratio will be that for sea level (u= 1.000). EFFECT OF WEIGHT. Modern configu- rations of airplanes are characterized by a large percent. of the maximum gross weight being NAVWEPS 00-BOT-RO BASIC AERODYNAMICS fuel. Hence, the gross weight and stall speed of the airplane can vary considerably through- out the flight. The effect of only weight on stall speed can be expressed by a modified form of the stall speed equation where density ratio, c r,,,.,, and wing area are held constant. V _i_z- K J v.,- K where V*,=stall speed corresponding to some gross weight, WI V@a= stall speed corresponding to a dif- ferent gross weight, WP As an illustration of this equation, assume that a particular airplane has a stall speed of 100 knots at a gross weight of 10,000 lbs. The stall speeds of this Sam: airplane at other gross weights would be: ll,W 100x 4, ‘&~=lO, 12,ooO 110 14,4al 120 9mJ 95 8,100 90 Figure 1.15 illustrates the effect of weight on stall speed on a percentage basis and will be valid for any airplane. Many specific condi- tions of flight are accomplished at certain fixed angles of attack and lift coefficients. The effect of weight on a percentage basis on the speeds for any specific lift coefficient and angle of attack is identical. Note that at small variations of weight, a rule of thumb may express the effect of weight on stall speed- “a 2 percent change in weight causes a I per- cent change in stall speed.” EFFECT OF MANEUVERING FLIGHT. Turning flight and maneuvers produce an effect on stall speed which is similar to the effect of weight. Inspection of the chart on figure 1.16 shows the forces acting on an airplane in a steady turn. Any steady turn requires that the vertical component of Iift be equal to 35
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NAVWEPS OD-SOT-80 BASIC AERODYNAMICS EFFECT OF FLAPS CL LIFT COEFFICIENT I 5 IO I5 20 25 ANGLE OtATTACK EFFECT OF WEIGHT ON STALL SPEED Figure 1.15. Flight at High Lift Conditions 34
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NAVWEPS 00-8OT-80 BASIC AERODYNAMICS EFFECT OF HIGH LIET DEVICES. The primary purpose of high lift devices (flaps, slots, slats, etc.) is to increase the CLn, of the airplane and reduce the stall speed. The take- off and landing speeds are consequently re- duced. The effect of a typical high lift device is shown by the airplane lift curves of figure 1.15 and is summarized here: weight of the airplane and the horizontal com- ponent of lift be equal to the centrifugal force. Thus, the aircraft in a steady turn develops a lift greater than weight and experiences in- creased stall speeds. Trigonometric ‘relationships allow deter- mination of the effect of bank angle on stall speed and load factor. The load factor, B, is the proportion between lift and weight and is determined by: L fizz-- W 1 n=- cos I$ where n=load factor (or “G”) cos 6 = cosine of the bank angle, + (phi) Typical values of load factor determined by this relationship are: .+.- 00 130 300 450 600 759 n-l.00 1.035 1.154 1.414 z.ooo 4.ooo The stall speed in a turn can be determined by: where v,+= stall speed at some bank angle + V,= stall speed for wing level, lift-equal- weight flight n=load factor corresponding to the bank angle The percent increase in stall speed in a turn is shown on figure l.i6. Since this chart is predi- cated on a steady turn and constant CL,, the figures a!e valid for any airplane. The chart shows that no appreciable change in load fac- tor or stall speed occurs at bank angles less than 30“. Above 4S” of bank the increase in load factor and stall speed is quite rapid. This fact emphasizes the need for avoiding steep turns at low airspeeds-a flight condition common to stall-spin accidents. 37 c.mip~tion L. (II far C‘, clun(tla~Up) . . . . . . . . . . . . . 1.5 200 Php down. 2.0 IS.9 The principal effect of the extension of flaps is to increase the C,, and reduce the angle of attack for any given lift coefficient. The in- crease in CL,, afforded by flap deflection re- duces the stall speed in a certain proportion, the effect described by the equation: - v,=v, z% J Ch, where V,,= stall speed with flaps down v,=stall speed without flaps C,= maximum lift coefficient of the clean configuration C&,= maximum lift coefficient with flaps down For example, assume the airplane described by the lift curves of figure 1.15 has a stall speed of 100 knots at the landing weight in the clean configuration. If the flaps are lowered the reduced stall speed is reduced to: =86.5 knots
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NAVWWS 00-8OT-80 BASIC AERODYNAMICS .#a, GANK~ANGLE, DEGREES EFFECT OF c LMAX ONSTALL SPEED 250 200 ANT 150 % 100 50 IO 20 30 40 50 PERCENTDECREASE IN STALL SPEED Figure 7.76. Flight at High Liff Conditions 38 Revised Jarwary 1965
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Thus, wirh rhe higher lift coefficienr available, less dynamic pressure is required to provide the necessary lift. Because of the stated variation of stall speed with C-, large changes in CL- are necessary to produce significant changes in stall speed. This effect is illustrated by the graph in figure 1.16 and certain typical values are shown below: Percent increase in CL. .~. 2 10 so loo 300 Percent reduction in stall speed 1 5 18 29 50 The contribution of the high lift devices must be considerable to cause large reduction in stall speed. The most elaborate combination of flaps, slots, slats, and boundary layer con- trol throughout the span of the wing would be required to increase C,- by 300 percent. A common case is that of a typical propeller driven transport which experiences a 70 per- cent increase in CzIM1 by full flap deflection. A typical single engine jet fighter with a thin swept wing obtains a 20 percent increase in CL- by full flap deflection. Thin airfoil sec- tions with sweepback impose distinct limita- tions on the effectiveness of flaps and the 20 percent increase in CL- by flaps is a typical- if not high-value for such a configuration. One factor common to maximum lift condi- tion is the angle of attack and pressure distri- bution. The maximum lift coefficient of a particular wing configuration is obtained at one angle of attack and one pressure distribu- tion. Weight, bank angle, load factor, density altitude, and airspeed have no direct effect on the stall angle of attack. This fact is sufficient justification for the use of angle of attack indi- cators and stall warning devices which sense pressure distribution on the wing. During flight maneuvers, landing approach, takeoff, turns, etc. the airplani will stall if the critical angle of attack is cxcccdcd. The airspeed ar which stall occurs will be determined by weight, load factor, and altitude but the stall NAVWEPS OO-EOT-RO BASIC AERODYNAMICS angle of attack is unaffected. At any parricu- lar altitude, the indicated stall speed is a func- tion of weight and load factor. An increase in altitude will produce a decrease in density and increase the true airspeed at stall. Also, an increase in altitude will alter compressibility and viscosity effects and, generally speaking, cause the in,&ztcd stall speed to increase. This parti&lar consideration is usually sig- nificant only above altitudes of 20,000 ft. Recovery from stall involves a very simple concept. Since stall is precipitated by an excessive angle of attack, the angle of attack must be dccmmd. This is a fundamental princi- ple which is common to any airplane. An airplane may be designed to be “stall- proof” simply by reducing the effectiveness of the elevators. If the elevators are not power- ful enough to hold the airplane to high angles of attack, the airplane cannot be stalled in any condition of flight. Such a requirement for a tactical military airplane would seriously re- duce performance. High lift coefficients near the maximum are required for high maneuver- ability and low landing and takeoff speeds. Hence, the Naval Aviator must appreciate the effect of the many variables affecting the stall speed and regard “attitude flying,” angle of attack indicators, and stall warning devices as techniques which allow more precise control of the airplane at high lift conditions. HIGH LIFT DEVICES There are many different types of high lift devices used to increase the maximum lift co- efficient for low speed flight. The high lift devices applied to the trailing edge of a section consist of a flap which is usually 15 to 25 per- cent of the chord. The deflection of a flap produces the effect of a large amount of camber added well aft on the chord. The principal types of flaps are shown applied to a basic sec- tion of airfoil. The effect of a 30’ deflection of a 25 percent chord flap is shown on the lift and drag curves of figure 1.17. 39
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NAVWEPS 00-BOT-80 BASIC AERODYNAMICS BASIC SECTION PLAIN FLAP SPLIT FLAP SLOTTED FLAP FOWLER FLAP EFFECT ON SECTION-LIFT AND DRAG CHARACTERISTICS OF A 25% CHORD FLAP DEFLECTED 30° I SLOTTED 3.0 - 2.5 - 2.0 - 1.5 - I.O- .5 - 0 -I- O FOW&ER SECTION ANGLE OF ATTACK SECTION DRAG COEFFICIENT o,,, DEGREES cd Figure 1.17. Flap Configurations 40 Revised January 1965
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The plainjap shown in figure 1.17 is a simple hinged portion of the trailing edge. The effect of the camber added well aft on the chord causes a significant increase in cbr. In addi- tion, the zero lift angle changes to a more negative value and the drag increases greatly. The split flap shown in figure 1.17 consist of plate deflected from the lower surface of the section and produces a slightly greater change in c ImoT than the plain flap. However, a much larger change in drag results from the great turbulent wake produced by this type flap. The greater drag’may not be such a disadvan- rage when ir is realized that it may be advan- tageous to accomplish steeper landing ap- proaches over obstacles or require higher power from the engine during approach (to minimize engine acceleration time for waveoR). The slottedPap is similar to the plain flap but the gap between the main section and flap leading edge is given specific contours. High energy air from the lower surface is ducted to the flap upper surface. The high energy air from the slot accelerates the upper surface boundary layer and delays airflow separation to some higher lift coefficient. The slotted flap can cause much greater increases in c,,, than the plain or split flap and section drags are much lower. The Fowkr&zp arrangement is similar to the slotted flap. The difference is that the de- flected flap segment is moved aft along a set of tracks which increases the chord and effects an increase in wing area. The Fowler flap is characterized by large increases in c,,, with minimum changes in drag. ,. One additional factor requiring consider- ation in a comparison of flap types is the aero- dynamic twisting moments caused by the flap. Positive camber produces a nose down twisting moment-especially great when large camber is used well aft on the chord (an obvious implication is that flaps are not prac- tical on a flying wing or tailless airplane). The deflection of a flap causes large nose down moments which create important twisting NAVWEPS OO-BOT-BO BASIC AERODYNAMICS loads on the structure and pitching moments that must be controlled with the horizontal tail. Unfortunately, the flap types producing the greatest increases in c,,- usually cause the greatest twisting moments. The Fowler flap causes the greatest change in twisting moment while the split flap causes the least. This factor-along with mechanical complexity of the installation-may complicate the choice of a flap configuration. The effectiveness of flaps on a wing con- figuration depend on many different factors. One important factor is the amount of the wing area affected by the flaps. Since a certain amount of the span is reserved for ailerons, the actual wing maximum lift prop- erties will be less than that of the flapped two-dimensional section. If the basic wing has a low thickness, any type of flap will be less effective than on a wing of greater thick- ness. Sweepback of the wing can cause an additional significant reduction in the effec- tiveness of flaps. High lift devices applied to the leading edge of a section consist of slots, slats, and small amounts of local camber. The fixed slot in a wing conducts flow of high energy air into the boundary layer on the upper surface and delays airflow separation to some higher angle of attack and lift coefficient. Since the slot alone effects no change in camber, the higher maximum lift coefficient will be obtained at a higher angle of attack, i.e., the slot simply delays stall to a higher angle of attack. An automatic slot arrangement consists of a leading edge segment (slat) which is free to move on tracks. At low angles of attack the slat is held flush against the leading edge by the high positive local pressures. When the section is at high angles of attack, the high local suction pressures at the leading edge create a chordwise force forward to actuate the slat. The slot formed then allows the section to continue to a higher angle of attack and produce a clno. greater than that of the 41
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NAVWEPS CO-BOT-BO BASIC AERODYNAMICS AUTOMATIC SLOT BOUNDARYLAYERCONTROL BY UPPER SURFACE SUCTION BOUNDARY LAYER CONTROL BY FLAP AUGMENTATION 0 2.4 FIXED SLOT\ I LOW SUCTION ,BASIC SECTION NO SUCTION 0-l 0~ : -5 0 5 IO I5 20 0 5 IO I5 20 25 SECTION ANGLE OF ATTACK SECTION ANGLE OF ATTACK 00, DEGREES 00, DEGREES Figure 7.18. Ekt of Slots and Boundary Layer Control 42
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basic section. The effect of a fixed slot on the lift characteristics is shown in figure 1.18. .UO~J ana’ &Z~J can produce significant in- creases in cl, but the increased angle of attack for maximum lift can be a disadvantage. If slots were the only high lift device on the wing, the high take off and landing angles of attack may complicate the design of the landing gear. For this reason slots or slats are usually used in conjunction with flaps since the flaps provide reduction in the maxi- mum lift angle of attack. The use of a slot has two important advantages: there is only a negligible change in the pitching moment due to the slot and no significant change in section drag at low angles of attack. In fact, the slotted section will have less drag than the basic section near the maximum lift angle for the basic section. The slot-slat device finds great application in modern airplane configurations. The tail- less airplane configuration can utilize only the high lift devices which have negligible effect on the pitching moments. The slot and slat are often used to increase the cl- in high speed flight when compressibility effects are con- siderable. The small change in twisting mo- ment is a favorable feature for any high lift device to be used at high speed. Leading edge high lift devices are more effective on the highiy swept wing than trailing edge flaps since slats are quite powerful in controlling the flow pattern. Small amounts of local camber added to the leading edge as a high lift device is most effective on wings of very low thick- ness and sharp leading edges. Most usually the slope of the leading edge high lift device is used to control the spanwise lift distribution on the wing. ‘Boundary larcr control devices are additional means of increasing the maximum lift coe&- cient of a section. The thin layer of airflow adjacent to the surface of an airfoil shows re- duced local velocities from the effect of skin friction. When at high angles of attack this boundary layer on the upper surface tends to NAVWEPS OO-BOT-RO BASIC AERODYNAMICS stagnate and come to a stop. If this happens the airflow will separate from the surface and stall occurs. Boundary layer control for high lift applications features various devices to maintain high velocity in the boundary layer to allay separation of the airflow. This con- trol of the boundary layer kinetic energy can be accomplished in two ways. One method is the application of a suction through ports to draw off low energy boundary layer and replace it with high velocity air from outside the boundary layer. The effect of surface suction boundary layer control on lift characteristics is typified by figure 1.18. Increasing surface suction produces greater maximum lift coe5- cients which occur at higher angles of attack. The effect is similar to that of a slot because the slot is essentially a boundary layer control device ducting high energy air to the upper surface. Another method of boundary layer control is accomplished by injecting a high speed jet of air into the boundary layer. This method produces essentially the same results as the suction method and is the more practical in- stallation. The suction type BLC requires the installation of a separate pump while the “blown” BLC system can utilize the high pres- sure source of a jet engine compressor. The typical installation of a high pressure BU system would be the augmentation of a de- flected flap. Since any boundary layer control tends to increase the angle of attack for maxi- mum lift, it is important to combine the bound- ary layer control with flaps since the flap de- flection tends to reduce the angIe of attack for maximum lift OPERATION OF HIGH LIFT DEVICES. The management of the high lift devices on an airplane is an important factor in flying opera- tions. The devices which are actuated auto- matically-such as automatic slats and slots- are usually of little concern and cause little complication since relatively small changes in drag and pitching moments take place. How- ever, the flaps must be properly managed by the pilot to take advantage of the capability
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of such a device. To illustrate a few principles of flap management, figure 1.19 presents the lift and drag curves of a typical airplane in the clean and flap down configurations. In order to appreciate some of the factors involved in flap management, assume that the airpIane has just taken off and the flaps are extended. The pilot should not completely retract the flaps until the airplane has sufficient speed. If the flaps are retracted prematurely at insufhcient airspeed, maximum lift coefi- cient of the clean configuration may not be able to support the airplane and the airplane will sink or stall. Of course, this same factor must be considered for intermediate flap posi- tions between fully retracted and fully ex- tended. Assume that the airplane is allowed to gain speed and reduce the flight lift coefii- cient to the point of flap retraction indicated on figure 1.19. As the configuration is altered from the “cluttered” to the clean configura- tion, three important changes take place: (1) The reduction in camber by flap re- traction changes the wing pitching moment and-for the majority of airplanes-requires retrimming to balance the nose up moment change. Some airplanes feature an automat- ic retrimming which is programmed with flap deflection. (2) The retraction of flaps shown on figure 1.19 causes a reduction of drag coeffi- cient at that lift coefficient. This drag reduction improves the acceleration of the airplane. (3) The retraction of flaps requires an increase in angle of attack to maintain the same lift coefficient. Thus, if airplane accel- eration is low through the flap retraction speed range, angle of attack must be in- creased to prevent the airplane from sinking. This situation is typical after takeoff when gross weight, density altitude, and tempera- ture are high. However, some aircraft have such high acceleration through the flap re- traction speed that the rapid gain in air- speed requtres much less noticeable attitude change. NAVWEPS OO-EOT-SO BASIC AERODYNAMICS When the flaps are lowered for landing essen- tially the same items must be considered. Ex- tending the flaps will cause these. changes to take place: (1) Lowering the flaps requires retrim- ming to balance the nose down moment change. (2) The increase in drag requires a higher power setting to maintain airspeed and altitude. (3) The angle of attack required to pro- duce the same lift coefficient is less, e.g., flap extension tends to cause the airplane to “balloon.” An additional factor which must be consid- ered when rapidly accelerating after takeoff, or when lowering the flaps for landing, is the limit airspeed for flap extension. Excessive airspeeds in the flap down configuration may cause structural damage. In many aircraft the effect of intermediate flap deflection is of primary importance in certain critical operating conditions. Small initial deflections of the flap cause noticeable changes in C’s,, without large changes in drag coefficient. This feature is especially true of the airplane equipped with slotted or Fowler flaps (refer to fig. 1.17). Large flap deflections past 30’ to 33’ do not create the same rate of change of Cs- but do cause greater changes in CD. A fact true of most airplanes is that the first 50 percent of flap deflection causes mwc than half of the total change in Cr.- and the last 50 percent of flap deflection causes mo~c than half of the total change in Cs. The effect of power on the stall speed of an airplane is determined by many factors. The most important factors affecting this relation- ship are powerplant type (prop or jet), thrust- to-weight ratio, and inclination of the thrust vector at maximum lift. The effect of the propeller is illustrated in figure 1.20. The slisstream velocity behind the propeller is different from the free stream velocity depend- ing on the thrust developed. Thus, when the propeller driven airplane is at low air+ceds 45
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NAVWEPS OO-BOT-80 BASIC AERODYNAMICS n INDUCED FLOW r SLIPSTREAM FROM PROPELLER n c; figure 1.20. Power Effects 46
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and high power, the dynamic pressure in the shaded area can be much greater than the free stream and this causes considerably greater lift than at zero thrust. At high power con- ditions the induced flow also causes an effect similar to boundary layer control and increases the maximum lift angle of attack. The typical four-engine propeller driven airplane may have 60 to 80 percent of the wing area affected by the induced flow and power effects on stall speeds may be considerable. Also, the lift of the airplane at a given angle of attack and air- speed will be greatly affected. Suppose the airplane shown is in the process of landing flare from a power-on approach. If there is a sharp, sudden reduction of power, the air- plane may drop suddenly because of the reduced lift. The typical jet aircraft does not experience the induced flow velocities encountered in propeller driven airplanes, thus the only sig- nificant factor is the vertical component of thrust. Since this vertical component con- tributes to supporting the airplane, less aero- dynamic lift is required to hold the airplane in flight. If the thrust is small and the thrust inclination is slight at maximum lift angle, only negligible changes in stall speed will re- sult. On the other hand, if the thrust is very great and is given a large inclination at maxi- mum lift angle, the effect on stall speed can be very large. One important relationship remains-since there is very little induced flow from the jet, the angle of attack at stall is essentially the same power-on or power-off. DEVELOPMENT OF AERODYNAMIC PITCHING MOMENTS The distribution of pressure over a surface is the ,source of the aerodynamic moments as well as the aerodynamic forces. A typical example of this fact is the pressure distribution acting on the cambered airfoil of figure 1.21. The upper surface has pressures distributed which produce the upper surface lift; the lower surface has pressures distributed which pro- duce the lower surface lift. Of course, the NAVWEPS 00-801~0 BASIC AERODYNAMICS net lift produced by the airfoil is difference between the lifts on the upper and lower sur- faces. The point along the chord where the distributed lift is effectively concentrated is termed the “center of pressure, c.p.“ The center of pressure is essentially the “center of gravity” of the distributed lift pressure and the location of the c.p. is a function of camber and section lift coe&cient Another aerodynamic reference point is the “aerodynamic center, d.e.” The aerodynamic center is defmed as the point along the chord where all changes in lift effectively take place. To visualize the existence of such a point, notice the change in pressure distribution with angle of attack for the symmetrical airfoil of figure 1.21. When at zero lift, the upper and lower surface lifts are equal and located at the same point. With an increase in angle of attack, the upper surface lift increases while the lower surface lift decreases. The change ,of lift has taken place with no change in the center of pressure-a characteristic of sym- metrical airfoils. Next, consider the cambered airfoil of figure 1.21 at zero lift. To produce zero lift, the upper and lower surface lifts must be equal. One difference noted from the symmetrical air- foil is that the upper and lower surface lifts are not opposite one another. While no net lift exists on the airfoil, the couple produced by the upper and lower surface lifts creates a nose down moment. As the angle of attack is in- creased, the upper surface lift increases while the lower surface lift decreases. While a change in lift has taken place, no change in moment takes place about the point where the lift change occurs. Since the moment about the aerodynamic center is the product of a force (lift at the c.P.) and a lever arm (distance from c.9. to a.~.), an increase in lift moves the center of pressure toward the aero- dynamic center. It should be noted that the symmetrical air- foil at zero lift has no pitching moment about the aerodynamic center because the upper and 47
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NAVWEPS DD-BOT-80 BASIC AERODYNAMICS CAMBERED AIRFOIL UPPER DEVELOPING POSITIVE LIFT NET LIFT LOWER SURFACE LIFT SYMMETRICAL AIRFOIL AT ZERO LIFT CAMBERED AIRFOIL AT ZERO LIFT UPPER SURFACE LOWER SURFACE LIFT SYMMETRICAL AIRFOIL AT POSITIVE LIFT UPPER SURFACE LIFT LOWER SURFACE LIFT t CHANGE IN LIFT + O.C. A- UPPER SURFACE FLOWER SURFACE LIFT CAMBERED AIRFOIL AT POSITIVE LIFT A- UPPER SURFACE LIFT LOWER SURFACE LIFT k- CHANGE IN LIFT c + PITCHING MOMENT 0.e. Figure 1.27. Development of Pitching Moments 48
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lower surface lifts act along the same vertical line. An increase in.lift on the symmetrical airfoil produces no change in this situation and the center of pressure remains fixed at the aero- dynamic center. The location of the aerodynamic center of an airfoil is not affected by camber, thickness, and angle of attack. In fact, two-dimensional in- compressible airfoil theory will predict the aerodynamic center at the 25 percent chord point for any airfoil regardless of camber, thickness, and angle of attack. Actual airfoils, which are subject to real fluid flow, may not have the lift due to angle of .attack concentrated at the exact 25 percent chord point. However, the actual location of the aerodynamic center for various sections is rarely forward of 23 percent or aft of 27 percent chord point. The moment about the aerodynamic center has its source in the relative pressure distribu- tion and requires application of the coefficient form of expression for proper evaluation. The moment about the aerodynamic center is ex- pressed by the following equation : where A&, = moment about the aerodynamic center, a.c., ft.-lbs. CMa.c,=coefbcient of moment about the a.c. q= dynamic pressure, psf S=wing area, sq ft. c=chord, ft. The moment coefficient used in this equation is the dimensionless ratio of the moment pressure to dynamic pressure moment and is a function c ML3.C. %.c. = p- of. the shape of the airfoil mean camber line. Figure 1.22 shows the moment coefficient, NAVWEPS O&601-80 BASIC AERODYNAMICS C%C. versus lift coefficient for several repre-. sentative sections. The sign convention ap- plied to moment coefficients is that the nose-up moment is positive. The NACA Ooog airfoil is a symmettical sec- tion of 9 percent maximum thickness. Since the mean line of this airfoil has no camber, the coefhcient of moment about the aerody- namic center is zero, i.e., the c.p. is at the ac. The departure from zero cno.+ occurs only as the airfoil approaches maximum lift and the stall produces a moment change in the negative (nose-down) direction. The NACA 4412 and 63,-412 sections have noticeable positive cam- ber which cause relatively large moments about the aerodynamic center. Notice that for each sectionshowninfrgure 1.22, the c,,,.... isconstant for all lift coefficients less than cl,-. The NACA 23012 airfoil is a very efficient conventional section which has been used on many airplanes. One of the features of the ~section is a relatively high c& with only a small c,,,,,,; The pitching moment coefficients 1 for this section are shown on figure 1.22 along with the effect of various type flaps added to the basic section. Large amounts of camber applied well aft on the chord cause large nega- tive moment coefficients. This fact is illus- trated by the large negative moment coefli- cients produced by the 30” deflection of a 25 percent chord flap. me kc. is a quantity determined by the shape of the mean-camber line. Symmetrical airfoils have zero c,,,,. and the c.p. remains at the a.~. in unstalled flight. The airfoil with positive camber will have a negative c,,,~,~, which means the c.p. is behind the a.~. Since the c5.c. is constant in unstalled flight a certain relationship between lift coefficient and center of pressure can be evolved. An example of this relationship is shown in figure 1.22 for the NACA 63i-412 airfoil by a plot of c.p. versus c,. Note that at low lift coefficients the center of pressure is well aft-even past the trailing edge-and an increase in C~ moves the c.p, for- ward toward the a.~. The c.9. approaches the 49 Revised Jmuoy 1965
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NAVWEPS 00-801-80 BASIC AERODYNAMICS 5 1 I 25k I I g -0.2 NACA 23012 WITH SPLIT FLAP AT 3D” I \ z I ” I I 1 1 I F I 25% -0.3 - NACA 23012 WITH PLAIN FLAP AT 30’ 1 I --T--rT~, I I I . \ NACA 23012 WITH SLOTTED FLAP &T 30” -0.4 7 Revised January 1965 CP POSITION PERCENT CHORD AFT OF LEADING EDGE Figure 1.22. Section Moment Characteristics 50
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CHANGE IN LIFT DUE TO UPGUST NAVWEPS D&801-80 BASIC AERODYNAMICS CHANGE IN LIFT DUE TO UPGUST C:G. 1 O.C. t (UNSTABLE) C:G. t LIFT 1 WEIGHT Figure 1.23. Application to Stability AC. as a limit but as stall occurs, the drop in suction near the leading’ edge cause the c.p. to move aft. Of course, if the airfoil has negative camber, or a strongly reflexed trailing edge, the moment about the aerodynamic center will be positive. In this case, the location of the aerodynamic center will be unchanged and will remain at the quarter-chord position. The aerodynamic center is the point on the chord where the coefficients of moment are constant-the point where all changes in lift take place. The aerodynamic center is an cx- tremely important aerodynamic reference point and the most direct application is to the longi- tudinal stability of an airplane. To simplify the problem assume that the airplane is a tailless or flying wing type. In order for this type airplane to have longitudinal stability, the center of gravity must be ahead of the aerodynamic center. This very necessary fea- ture can be visualized from the illustrations of figure 1.23. If the two symmetrical airfoils are subject to an upgust, an increase in lift will take place at the 4.c. If the c.g. is ahead of the ax., the change in lift creates a nose down moment about the c.g. which tends to return the air- foil to the. equilibrium angle of attack. This stable, “weathercocking” tendency to return to equilibrium is a very necessary feature in any airplane. If the c.g. is aft of the a.~., the change in lift due to the upgust takes place at the AC. and creates a nose up moment about the c.g. This nose up moment tends to displace the airplane farther from the equilibrium and is unstable-the airplane is similar to a ball balanced on a peak. Hence, to have a stable airplane, the c.g. must be located ahead of the airplane rl.c. 51
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NAVWEPS OO-SOT-SO BASIC AERODYNAMICS An additional requirement of stability is that the airplane must stabilize and be trimmed for flight at positive lift. When the c.g. is located ahead of d.c., the weight acting at the c.g. is supported by the lift developed by the section. Negative camber is required to pro- duce the positive moment about the aerody- namic center which brings about equilibrium ot balance at positive lift. Supersonic flow produces important changes in the aerodynamic characteristics of sections. The aerodynamic center of airfoils in subsonic flow is located at the 25 percent chord point. As the airfoil is subject to supersonic flow, the aerodynamic center changes to the 50 percent chord point. Thus, the airplane in transonic flight can experience large changes in longitu- dinal stability because of the large changes in the position of the aerodynamic center. FRICTION EFFXTS &--v~se the +ir hAas .~~.v-~c~~v air -7ill --- , .“I”., L, , I. 11 -11 counter resistance to flow over a surface. The viscous nature of airflow reduces the local velocities on a surface and accounts for the drag of skin friction. The retardation of air particles due to viscosity is greatest immedi- ately adjacent to the surface. At the very sur- face of an object, the air particles are slowed to a relative velocity of near zero. Above this area other particles experience successively smaller retardation until finally, at some dis- tance above surface, the local velocity reaches the full value of the airstream above the sur- face. This layer of air over the surface which shows local retardation of airflow from vis- cosity is termed the “boundary layer.” The characteristics of this boundary layer are illus- trated in figure 1.24 with the flow of air over a smooth flat plate. The beginning flow on a smooth surface gives evidence of a very thin boundary layer with the flow occurring in smooth laminations, The boundary layer flow near the leading edge is similar to layers or laminations of air slid- ing smoothly over one another and the obvi- ous term for this type of flow is the “laminar” 52 boundary layer. This smooth laminar flow exists without the air particles moving from a given elevation. As the flow continues back from the leading edge, friction forces in the boundary layer continue to dissipate energy of the airstream and the laminar boundary layer increases in thickness with distance from the leading edge. After some distance back from the leading edge, the laminar boundary layer begins an oscillatory disturbance which is unstable. A waviness occurs in the laminar boundary layer which ultimately grows larger and more severe and destroys the smooth laminar flow. Thus, a transition takes place in which the laminar boundary layer decays into a “turbu- lent” boundary layer. The same sort of transition can be noticed inthe smoke from a cigarette in still air. At, first, the smoke ribbon is smooth and laminar, then develops a definite waviness, and decays into a random turbulent smoke pattern. As soon as the transition to. the turbulent boundary layer takes place, the boundary layer thickens and grows at a more rapid rate. (The small scale, turbulent flow within the boundary layer should not be confused with the large scale turbulence associated with airflow separation.) The flow in the turbu- lent boundary layer allows the air particles to travel from one layer to another producing an energy exchange. However, some small lami- nar flow continues to exist in the very lower levels of the turbulent boundary layer and is referred to as the “laminar sub-layer.” The turbulence which exists in the turbulent bound- ary layer allows determination of the point of transition by several means. Since the turbu- lent boundary layer transfers heat more easily than the laminar layer, frost, water, and oil films will be removed more rapidly from the area aft of the transition point. Also, a-small probe may be attached to a stethoscope and positioned at various points along a surface. When the probe is in the laminar area, a low “hiss” will be heard; when the probe is in
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DEVELOPMENT OF BOUNDARY L~AYER ON A SMOOTH FLAT PLATE TURBULENT BOUNDARY LLAMINAR SUB-LAYER COMPARISON OF VELOCITY PROFILES FOR LAMINAR AND TURBULENT BOUNDARY LAYERS TURBULENT I PROFILE I LAMINAR PROFILE - LOW THICKNESS - GREATER THICKNESS - LOW VELOCITIES NEXT TO SURFACE - HIGHER VELOCITIES NEXT TO SURFACE - GRADUAL VELOCITY CHANGE - SHARP VELOCITY CHANGE - LOW SKIN FRICTION - HIGHER SKIN FRICTION figure 7.24. Boundary Layer Charactorisfics
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NAVWEPS CO-SOT-80 BASIC AE,RODYNAMlCS the turbulent area, a sharp “crackling” will be audible. In order to compare the characteristics of the laminar and turbulent boundary layers, the velocity profiles (the variation of boundary layer velocity with height above the surface) should be compared under conditions which could produce either laminar or turbulent flow. The typical laminar and turbulent pro- files are shown in figure 1.24. The velocity profile of the turbulent boundary layer shows a much sharper initial change of velocity but a greater height (or boundary layer thickness) required to reach the free stream velocity. As a result of these differences, a comparison will show: (1) The turbulent boundary layer has a fuller velocity profile and has higher local velocities immediately adjacent to the sur- face. The turbulent boundary layer has higher kinetic energy in the airflow next to the surface. (2) At the surface, the laminar boundary layer has the less rapid change of velocity with distance above the plate. Since the shearing stress is proportional to the velocity gradient, the lower velocity gradient of the laminar boundary layer is evidence of a lower friction drag on the surface. If the conditions of flow were such that either a turbulent or a laminar boundary layer could exist, the laminar skin friction would be about one-third that for turbulent flow. The low friction drag of the laminar bound- ary layer makes it quite desirable. However, the transition tends to take place in a natural fashion and limit the extensive development of the laminar boundary layer. REYNOLDS NUMBER. Whether a lam- inar or turbulent boundary layer exists depends on the combined effects of velocity, viscosity, distance from the leading edge, density, etc. The effect of the most important factors is combined in a dimensionless parameter called “Reynolds Number, RN.” The Reynolds Number is a dimensionless ratio which por- trays the relative magnitude of dynamic and viscous forces in the flow. where RiV=Reynolds Number, dimensionless V= velocity, ft. per sec. x= distance from leading edge, ft. Y= kinematic viscosity, sq. ft. per sec. While the actual magnitude of the Reynolds Number has no physical significance, the quantity is used as an index to predict and correlate various phenomena of viscous fluid, flow. When the RN is low, viscous or fric- tion forces predominate; when the RN is high, dynamic or inertia forces predominate. The effect of the variables in the equation for Reynolds Number should be understood. The RN varies directly with velocity and distance back from the leading edge and inversely with kinematic viscosity. High RN’s are obtained with large chord surfaces, high velocities, and low altitude; low RN’sresult from small chord surfaces, low velocities, and high altitudes- high altitudes producing high values for kine- matic viscosity. The most direct use of Reynolds Number is the indexing or correlating the skin friction drag of a surface. Figure 1.25 illustrates the variation of the friction drag of a smooth, flat plate with a Reynolds Number which is based on the length or chord of the plate. The graph shows separate lines of drag coeffi- cient if the flow should be entirely laminar or entirely turbulent. The two curves for lam- inar and turbulent friction drag illustrate the relative magnitude of friction drag coefficient if either type of boundary layer could exist. The drag coefficients for either laminar or tur- bulent flow decrease with increasing RN since the velocity gradient decreases as the boundary layer thickens.
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NAWWEPS OD-EOT-SO BASIC AERODYfflAMICS FRICTION DRAG OF A SMOOTH FLAT PLATE c ,020 - E D ,010 - iii .008 - yu’ .%2 - O” 0 :% - :: ,002 - ‘\ 2i ‘1 .OOl * 1 I 1 1 1 0.1 0.5 1.0 5.0 10.0 50 100 REYNOLDS NUMBER RN(MILLIONS) CONVENTIONAL AfdD LAMINAR FLOW SECTIONS TRANSITION NACA / L NACA 0009 P DRAG BUCKET” I I -1.0 -3 0 .5 I.0 I.§ SECTION LIFT COEFFICIENT, cl Figure 7.25. Skin Friction Drag 55 Weaised January 1965
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NAVWEPS 00-SOT-80 BASIC AERODYNAMICS If the surface of the plate is smooth and the original airstream has no turbulence, the plate at low Reynolds Numbers will exist with pure laminar flow. When the RN is increased to approximately 530,000, transition occurs on the plate and the flow is partly turbulent. Once transition takes place, the drag coefficient of the plate increases from the laminar curve to the turbulent curve. As the RN approaches very high values (20 to 50 million) the drag curve of the plate approaches and nearly equals the values for the turbulent curve. At such high RN the boundary layer is predominantly turbulent with very little laminar flow-the transition point is very close to the leading edge. While the smooth, flat plate is not ex- actly representative of the typical airfoil, basic fluid friction phenomena are illustrated. At RN less than a half million the boundary layer will be entirely laminar unless there is extreme surface roughness or turbulence induced in the airstream. Reynolds Numbers between one and five million produce boundary layer flow which is partly laminar and partly turbulent. At RN above ten million the boundary layer characteristics are predominantly turbulent. In order to obtain low drag sections, the transition from laminar to turbulent must be delayed so that a greater portion of the sur- face will be influenced by the laminar bound- ary layer. The conventional, low speed air- foil shapes are characterized, by minimum pressure points very close to the leading edge. Since high local velocities enhance early transition, very little surface is covered by the laminar boundary layer, A comparison of two 9 percent thick symmetrical airfoils is presented in figure 1.25. One section is the “conventional” NACA C!UO~ section which has a minimum pressure point at approxi- mately 10 percent chord at zero lift. The other section is the NACA 66039 which has a minimum pressure point at approximately 60 percent chord at zero lift. The lower local velocities at the leading edge and the favor- able pressure gradient of the NACA 66-009 delay the transition to some point farther aft on the chord. The subsequent reduction in friction drag at the low angles of attack ac- counts for the “drag bucket” shown on the graphs of cd and cI for these sections. Of course, the advantages of the laminar flow airfoil are apparent only for the smooth airfoil since surface roughness or waviness may pre- clude extensive development of a laminar boundary layer. AIRFLOW SEPARATION. The character of the boundary layer on an aerodynamic surface is greatly influenced by the pressure gradient. In order to study this effect, the pressure distribution of a cylinder in a perfect fluid is repeated in figure 1.26. The airflows depict a local velocity of !zero at the forward stagnation point and a maximum local velocity at the extreme surface. The airflow moves from the high positive pressure to the minimum pressure point-a favorable pressure gradient (high to low). As the air moves from the extreme surface aft, the local velocity decreases to zero at the aft stagnation point. The static pressure increases from the minimum (or max- imum suction) to the high positive pressure at the aft stagnation point-an adverse pres- sure gradient (low to high). The action of the pressure gradient is such that the favorable pressure gradient assists the boundary layer while the adverse pressure gradient impedes the flow of the boundary layer. The effect of an adverse pressure gradi- ent is illustrated by the segment X-Y of figure 1.26. A corollary of the skin friction drag is the continual reduction of boundary layer energy as flow continues aft on a surface. * The velocity profiles of the boundary layer are shown on segment X-Y of figure 1.26. In the area of adverse pressure gradient the bound- ary layer flow is impeded and tends to show a reduction in velocity next to the surface. If the boundary layer does not have sufhcient kinetic energy in the presence of the adverse pressure gradient, the lower levels of the boundary layer may stagnate prematurely. 56
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NO SEPARATION NAWWEPS 00-8OT-80 BASIC AERODYNAMICS SEPARATION 1 BOUNDARY LAYER SEPAF --‘-.’ iAT ION /------- SEPARATION AT STALL REVERSE FLOW b SHOCK WAVE SHOCK WAVE INDUCED FLOW SEPARATION Figure 1.26. Airflow Separation (sheet 7 of 2) 57
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Figure 7.26. Airflow Separation (sheet 2 of 2)
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Premature stagnation of the boundary layer means that all subsequent airflow will overrun this point and the boundary layer will separate from the surface. Surface flow which is aft of the separation point will indicate a local flow direction forward toward theseparation point- a flow reversal. If separation occurs the posi- tive pressures are not recovered and form drag results. The points of separation on any aero- dynamic surface may be noted by the reverse flow area. Tufts of cloth or string tacked to the surface will lie streamlined in an area of unseparated flow but will lie forward in an area behind the separation point. The basic feature of airflow separation is stagnation of the lower levels of the boundary layer. Airjh ~cparation muh when the lower lcvcls of the boundary layer do not have sujicicnt kinetic cncrgy in the prwncc of an advcm ps.wrc gradient. The most outstanding cases of air- flow separation are shown in figure 1.26. An airfoil at some high angle of attack creates a pressure gradient on the upper surface too severe to allow the boundary layer to adhere to the surface. When the airflow does not adhere to the surface near the leading edge the high suction pressures are lost and stall occurs. When the shock wave forms on the upper surface of a wing at high subsonic speeds, the increase of static pressure through the shock’ wave creates a very strong obstacle for the boundary layer. If the shock wave is sufhciently strong, separation will follow and “compressibility buffet” will result from the turbulent wake or separated flow. In order to prevent separation of a boundary layer in the presence of an adverse pressure gradient, the boundary layer must have the highest possible kinetic energy. If a choice is available, the turbulent boundary layer would be preferable to the laminar boundary layer because the turbulent velocity profile shows higher local velocities next to the surface. The most effective high lift devices (slots, slotted flaps, BLC) utilize various techniques NAVWEPS OO-SOT-80 BASIC AERODYNAMICS to increase the kinetic energy of the upper sur- face boundary layer to withstand the more severe pressure gradients common to the higher lift coefficients. Extreme surface roughness on full scale aircraft (due to surface damage, heavy frost, etc.) causes higher skin friction and greater energy loss in the boundary layer. The lower energy boundary layer may cause a noticeable change in C,-” and stall speed. In the same sense, vortex generators applied to the surfaces of a high speed airplane may allay compressibility buffet to some degree. The function of the vortex generators is to create a strong vortex which introduces high velocity, high energy air next to the surface to reduce or delay the shock induced separation. These examples serve as a reminder that separation is the result of premature stagnation of the boundary layer-insufficient kinetic energy in the presence of an adverse pressure gradient. SCALE EFFECT. Since the boundary layer friction and kinetic energy are dependent on the characteristics of the boundary layer, Reynolds Number is important in correlating aerodynamic characteristics. The variation of the aerodynamic characteristics with Reynolds Number is termed “scale effect” and is ex- tremely important in correlating wind tunnel test data of scale models with the actual flight characteristics of the full size aircraft. The two most important section characteristics affected by scale effects are drag and maximum lift-the effect on pitching moments usually being negligible. From the known variation of boundary layer characteristics with Rey- nolds Number, certain general effects may be anticipated. With increasing Reynolds Num- ber, it may be expected that the section maxi- mum lift coefficient will increase (from the higher energy turbulent boundary layer) and that the section drag coefficient will decrease (similar to that of the smooth plate). These effects are illustrated by the graphs of figure 1.27. The characteristics depicted in figure 1.27 are for the NACA 4412 airfoil (4 percent 59
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RN MILLION -6.0 11 s 4 8 12 16 20 SECTION ANGLE OF ATTACK =o 1 DEGREES -I- RN - 1.5 MILLION I I I 1- -.5 0 .5 I.0 1.5 SECTION LIFT COEFFICIENT c.l figure 1.27. Effect of Reymafds Number on Section Ckacteristics of NACA 4412
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camber at 40 percent chord, 12 percent thick- ness at 30 percent chord)--a fairly typical “conventionaal” airfoil section. The lift curve show a steady increase in cl with increasing RN. However, note that a>maller change in cr occurs between Reynolds Numbers of 6.0 ad 9.0 million than occurs between 0.1 and 3.0 million. In other words, greater changes in CI occur in the range of Reynolds Num- bers zhere the laminar (low energy) boundary layer predominates. The drag curves for the section show essentially the same feature-the greatest variations occur at very low Reynolds Numbers. Typical full scale Reynolds Num- bers for aircraft in flight may be 3 to 5@O million where the boundary layer is predominately turbulent. Scale model tests may involve Reynolds Numbers of 0.1 to 5 million where the boundary layer be predominately laminar. Hence, the “scale” corrections are very neces- sary to correlate the principal aerodynamic characteristics. The very large changes in aerodynamic characteristics at low Reynolds Numbers are due in great part to the low energy laminar boundary layer typical of low Reynolds Num- bers. Low Reynolds Numbers are the result of some combination of low velocity, small size, and high kinematic viscosity RN= ( 3 Thus, small surfaces, low flight speeds, or very high altitudes can provide the regime of low Reynolds Numbers. One interesting phenom- enon associated with low BN is the high form drag due to separation of the low energy boundary layer. The ordinary golf ball oper- ates at low RN and would have very high form drag without dimpling. The surface roughness from dimpling disturbs the laminar boundary layer forcing a premature transition to turbulent. The forced turbulence in the boundary layer reduces the form drag by pro- viding a higher energy boundary layer to allay separation. Essentially the same effect can be produced on a model airplane wing by roughening the leading edge-the turbulent NAVWEPS DD-RDT-80 BASIC AERODYNAMICS boundary layer obtained may reduce the form drag due to separation. In each instance, the forced transition will be beneficial if the reduc- tion in form drag is greater than the increase in skin friction. Of course, this possibility exists only at low Reynolds Numbers. 1,n a similar sense, “trip” wires or small surface protuberances on a wind tunnel model may be used to force transition of the boundary layer and simulate the effect of higher Reynolds Numbers. PLANFORM EFFECTS AND AIRPLANE DRAG EFFECT OF WING PLANFORM The previous discussion of aerodynamic forces concerned the properties of airfoil sec- tions in two-dimensional flow with no consid- eration given to the influence of the planform. When the effects of wing planform are intro- duced, attention must be directed to the ex- istence of flow components in the spanwise direction. In other words, airfoil section properties deal with flow in two dimensions I while plonform properties consider flow in three dimensions. In order to fully describe the planform of a wing, several terms are required. The terms having the greatest influence on the aerody- namic characteristics are illustrated in figure 1.28. (1) The wing r?rc11, S, is simply the plan surface area of the wing. Although a por- tion of the area may be covered by fuselage or nacelles, the pressure carryover on these surfaces allows legitimate consideration of the entire plan area. (2) The wing ~ptia, 6, is measured tip to tip. (3) The avcragc chord, c, is the geometric average. The product of the span and the average chord is the wing area (6X6=$). (4) The aspect ratio, AR, is the proportion of the span and the average chord. AR=b/c
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NAVWEPS 00-SOT-80 BASIC AERODYNAMICS p-----y S= WING AREA, SO. FT. b= SPAN, FT c = AVERAGE CHORD, FT AR = ASPECT RATIO AR = b/c AR= b:s I b ----_I CR = ROOT CHORO, FT Ct = TIP CHORD, FT x = TAPER RATIO A= SWEEP ANGLE, DEGREES MAC : MEAN AERODYNAMIC CHORD, FT. Figure 1.28. Description of Wing Planform 61
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If the planform has curvature and the aver- age chord is not easily determined, an alternate expression is: AR = b2/.S The aspect ratio is a fineness ratio of the wing and this quantity is very powerful in determing the aerodynamic characteristics and structural weight. Typical aspect ratios vary from 33 for a high performance sail- plane to 3.5 for a jet fighter to 1.28 for a flying saucer. (5) The raat chord, c,, is the chord at the wing centerline and the rip chord, c,, is measured at the tip. (6) Considering the wing planform to have straight lines for the leading and trail- ing edges, the taper ratio, A (lambda), is the ratio of the tip chord to the root chord. A=& The taper ratio affects the lift distribution and the structural weight of the wing. A rectangular wing has a taper ratio of 1.0 while the pointed tip delta wing has a taper ratio of 0.0. (7) The sweep angle, A (cap lambda), is usually measured as the angle between the line of 25 percent chords and a perpendicular to the root chord. The sweep of a wing causes definite changes in compressibility, maximum lift, and stall characteristics. (8) The mean aerodynamic chord, MAC, is the chord drawn through the centroid (geographical center) of plan area. A rec- tangular wing of this chord and the same span would have identical pitching moment characteristics. The MAC is located on the reference axis of the airplane and is a primary reference for longitudinal stability considera- tions. Note that the MAC is not the average chord but is the chord through the centroid of area. As an example, the pointed-tip delta wing with a taper ratio of zero would have an average chord equal to one-half the NAVWEPS OO-BOT-BO BASIC AERODYNAMICS root chord but an MAC equal to two-thirds ~‘of the root chord. The aspect ratio, taper ratio, and sweepback of a planform are the principal factors which determine the aerodynamic characteristics of a .wing. These same quantities also have a defi- nite influence on the structural weight and stiff- ness of a wing. DEVELOPMENT OF LIFT BY A WING. In order to appreciate the effect of the planform on the aerodynamic characteristics, it is neces- sary to study the manner in which a wing produces lift.’ Figure 1.29 illustrates the three- dimensional flow pattern which results when the rectangular wing creates lift. J.f a wing is producing lift, a pressure differ- ential will exist between the upper and lower surfaces, i.e., for positive lift, the static pres- sure on the upper surface will be less than on the lower surface. At the tips of the wing, the existence of this pressure differential creates the spanwise flow components shown in figure 1.29: For the rectangular wing, the lateral flow developed at the tip is quite strong and a strong vortex is created at the tip. The lateral ‘flow-and consequent vortex strength-reduces inboard from the tip until it is zero at the centerline. The existence of the tip vortex is described by the drawings of figure 1.29. The rotational pressure flow combines with the local airstream flow to produce the resultant flow of the trailing vortex. Also, the downwash flow field behind a delta wing is illustrated by the photographs of figure 1.29. A tuft-grid is mounted aft of the wing to visualize the local flow direction by deflection of th,e tuft ele- ments. This tuft-grid illustrates the existence of the tip vortices and the deflected airstream aft of the wing. Note that an increase in angle of attack increases lift and increases the flow deflection and strength of the tip vortices. Figure 1.30 illustrates the principal effect of the wing vortex system. The wing pro- ducing lift can be represented by a series of
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NAWWEPS 00-8OT-80 BASIC AERODYNAMICS WING UPPER SURFACE TIP VORTEX WING LOWER SURFACE VORTICES ALONG TRAILING EDGE TRAILING EDGE I/ I I I UPPER SURFACE LEADING EDGE FLOW FLOW LOW PRESSURE- ,- HIGH PRESSURE) Figure 1.29. Wing Three Dimensional Flow (sheet 1 of 2) Revised January 1965
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NAVWEPS OO-BOT-RD BASIC AERODYNAMICS DOWNWASH FLOW FIELD BEHIND A DELTA WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS AT VARIOUS ANGLES OF ATTACK --A-- 30” OF FLOW ANGULARITY II “T (DEG) 0 16 32 I) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE. TRAILING EDGE. FROM NACA TN 2674 Figure 1.19. Wing Three Dimensional Flow (sheet 2 of 2) 65
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NAVWEPS 00-8OT-80 BASIC AERODYNAMICS vortex filaments which consist of the tip or trailing vortices coupled with the bound or line vortex. The tip vortices are coupled with the bound vortex when circulation is induced with lift. The effect of this vortex system is to create certain vertical velocity components in the vicinity of the wing. The illustration of these vertical velocities shows that ahead of the wing the bound vortex induces an up- wash. Behind the wing, the coupled action of the bound vortex and the tip vortices in- duces a downwash. With the action of tip and bound vortices coupled, a final vertical velocity (220) is imparted to the airstream by the wing producing lift. This result is an inevitable consequence of a finite wing pro- ducing lift. The wing Producing lift applies the equal and opposite force to the airstream and deflects it downward. One of the impor- tant factors in this system is that a downward velocity is created at the aerodynamic center (w) which is one half the final downward velocity imparted to the airstream (2~). The effect of the vertical velocities in the vicinity of the wing is best appreciated when they are added vectorially to the airstream velocity. The remote free stream well ahead of the wing is unaffected and its direction is opposite the flight path of the airplane. ‘Aft of the wing, the vertical velocity (2~) adds to the airstream velocity to produce the down- wash angle e (epsilon). At the aerodynamic center of the wing, the vertical,velocity (w) adds to the airstream velocity to produce a downward deflection of the airstream one-half that of the downwash angle. In other words, the wing producing lift by the deflection of an airstream incurs a downward slant co the wind in the immediate vicinity of the wing. Hence, the JeCtionJ of the wing operate in an average rela- tive wind which is inclined downward one-half the final dowraw& angle. This is one important feature which distinguishes the aerodynamic properties of a wing from the aerodynamic properties of an airfoil section. The induced velocities existing at the aero- dynamic center of a finite wing create an aver- age relative wind which is different from the remote free stream wind. Since the aerody- namic forces created by the airfoil sections of a wing depend upon the immediate airstream in which they operate, consideration must be given to the effect of the inclined average rela- tive wind. To create a certain lift coefficient with the airfoil section, a certain angle must exist be- tween the airfoil chord line and the avcragc relative wind. This angle of attack is a,,, the section angle of attack. However, as this lift is developed on the wing, downwash is in- curred and the average relative wind is in- clined. Thus, the wing must be given some angle attack greater than the required section angle of attack to account for the inclination of the average relative wind. Since the wing must be given this additional angle of attack because of the induced flow, the angle between the average reiative wind arid tlie remote fiCC stream is termed the induced angle of attack, ai. From this influence, the wing angle of attack is the sum of the section and induced angles of attack. a=ul)+a; where a= wing angle of attack OLD= section angle of attack OI;= induced angle of attack INDUCED DRAG Another important influence of the induced flow is the orientation of the actual lift on a wing. Figure 1.30 illustrates the fact that the lift produced by the wing sections is perpen- dicular to the average relative wind. Since the average relative wind is inclined down- ward, the section lift is inclined aft, by the same amount-the induced angle of attack, ai. The lift and drag of a wing must continue to be referred perpendicular and parallel to the remote free stream ahead of the wing. In this respect, the lift on the wing has a component of force parallel to the remote free stream. This component of lift in the drag direction is the undesirable-but unavoidable-conse- 66
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NAVWEPS DD-ROT-80 BASIC AERODYNAMICS BOUND OR :INE VORTEX , OR TIP VORTEX DEFLECTED AIRSTREAM (UPW BOUND VORTEX ONLY VERTICAL VELOCITIES IN THE VICINITY OF THE WING COUPLED BOUND AND AVERAGE RELATIVE WIND TIP VORTICES V t REMOTE FREE STREAM AT WING A.C. DOWNWASH ANGLE D it INDUCED DRAG EFFECTIVE LIFT- REMOTE FREE STREAM Figure 1.30. Wing Vortex System and Induced Flow 67
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NAVWEPS OO-SOT-~O BASIC AERODYNAMICS quence of developing lift with a finite wing and is termed INDUCED DRAG, D+ In- duced drag is separate from the drag due to form and friction and is due simply to the de- velopment of lift. By inspection of the force diagram of figure 1.30, a relationship between induced drag, lift, and induced angle of attack is apparent. The induced drag coeficient, CDi, will vary directly with the wing lift coefficient, C,, and the in- duced angle of attack, as. The effective lift is the vertical component of the actual lift and, if the induced angle of attack is small, will be essentially the same as the actual lift. The J horizontal and vertical component of drag is insignificant under the same conditions. By a detailed study of the factors involved, the fol- lowing relationships can be derived for a wing with an elliptical lift distribution: (1) The induced drag equation follows the same form as applied to any other aerody- namic force. Di=CDigS where Di=induced drag, lbs. 4= :Vymic pressures; psf =295 Cni= induced drag coefficient S=wing area, sq. ft. (2) The induced drag coefficient can be derived as : or CD,-C, sin ai CD& c,P =0.318 -Jjj ( ) where C,= lift coefficient sin ai=natural sine of the induced angle of attack, Eli, degrees r=3.1416, constant AR= wing aspect ratio (3) The induced angle of attack can be derived as: a~= 18.24 & (degrees) ( ) (NOTE: the derivation of these relationships may be found in any of the standard engi- neering aerodynamics textbooks.) These relationships facilitate an understanding and appreciation of induced drag. The induced angle of attack Eli= 18.~4$~ ( > depends on the lift coefficient and aspect ratio. Flight at high lift conditions such as low speed or maneuvering flight will create high induced angles of attack while high speed, low lift flight will create very small induced angles .of attack. The inference is that high lift coefli- cients require large downwash and result in large ,induced angles of attack. The effect of aspect ratio is significant since a very high aspect ratio would produce a negligible induced angle of attack. If the aspect ratio were in- finite, the induced angle of attack would be zero and the aerodynamic characteristics of the wing would be identical with the airfoil sec- tion properties. On the other hand, if the wing aspect ratio is low, the induced angle of attack will be large and the low aspect ratio airplane must operate at high angles of attack at maximum lift. Essentially, the low aspect ratio wing affects a relatively small mass of air and consequently must provide a large de- flection (downwash) to produce lift. EFFECT OF LIFT. The induced drag co- e&cient ( C&l CDi=0.31E - shows somewhat sim- ,I AR ilar effects of lift coefficient and aspect ratio. Because of the power of variation of induced drag coefficient with lift coefficient, high lift coefli- cients provide very high induced drag and low lift coefficients very low induced drag. The di- rect effect of C, can be best appreciated by assum- ing an airplane is flying at a givenweight, alti- tude, and airspeed. If the airplane is maneuvered from steady level flight to a load factor of two, hWd Jonua~ 1965 68
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the lift coefficient is doubled and the induced drag is four times 0.1 grsat. If the flight load factor is changed from one to five, the induced drag is twenty-five times as great. If all other factors are held constant to single out this effect, it could be stated that “induced drag varies as the square of the lift” Di, ’ 0 L! Di,= L1 where Di,= induced drag corresponding to some original lift, L1 Di,= induced drag corresponding to some new lift, Lp (and q (or EAS), S, AR are constant) This expression defines the effect of gross weight, maneuvers, and steep turns on the induced drag, e.g., 10 percent higher gross weight increases induced drag 21 percent, 4G maneuvers cause 16 times as much induced drag, a turn with 4s0 bank requires a load factor of 1.41 and this doubles the induced drag. EFFECT OF ALTITUDE. The effect of altitude on induced drag can be appreciated by holding all other factors constant. The gen- eral effect of altitude is expressed by: where Dil= induced drag corresponding to some orig- inal altitude density ratio, 0, D&= induced drag corresponding to some new altitude density ratio, q (and L, S, AR, V are constant) This relationship implies that induced drag would increase with altitude, e.g., a given airplane flying in level flight at a given TAS at 40,000 ft. (u=O.25) would have four times as much induced drag than when at sea level (u= 1.00). This effect results when the lower NAVWEPS 0040240 BASIC AERODYNAMICS air density requires a greater deflection of the airstream to produce the same lift. However, if the airplane is flown at the same EAS, the dynamic pressure will be the same and induced drag will not vary. In this case, the TAS would be higher at altitude to provide the same EAS. EFFECT OF SPEED. The general effect of speed on induced drag is unusual since low air- speeds are’associated with high lift coefficients and high lift coefficients create high induced drag coefficients. The immediate implication is that induced drag inmaw with decreasing air J@. If all other factors are held constant to single out the effect of airspeed, a rearrange- ment of the previous equations would predict that “induced drag varies inversely as ,the square of the airspeed.” where Dil= induced drag corresponding to some orig- inal speed, Vi Di,= induced drag corresponding to some new speed, Vs (and L, S, AR, ,J are constant) Such an effect would imply that a given air- plane in steady flight would incur one-fourth as great an induced drag at twice as great a speed or four times as great an induced drag at half the original speed. This variation may be illustrated by assuming that an airplane in steady level flight is slowed from 300 to 150 knots. The dynamic pressure at 1% knots is one-fourth the dynamic pressure at 300 knots and the wing must deflect the airstream four times as greatly to create the same lift. The same lift force is then slanted aft four times as greatly and the induced drag is four times as great. The expressed variation of induced drag with speed points out that induced drag will be of
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greatest importance at low speeds and prac- tically insignificant in flight at high dynamic pressures. For example, a typical single en- gine jet airplane at low altitude and maximum level flight airspeed has an induced drag which is less than 1 pcrccont of the total drag. How- ever, this same airplane in steady flight just above the stall speed could have an induced drag which is approximately 75 pnrcnt of the total drag. EFFECT OF ASPECT RATIO. The effect of aspect ratio on the induced drag is the principal effect of the wing planform. The relationship for induced drag coefIicient emphasizes the need of a high aspect ratio for the airplane which is continually operated at high lift coefficients. In other words, airplane configurations designed to operate at high lift coefficients during the major portion of their flight (sailplanes, cargo, transport; patrol, and antisubmarine types) demand a high aspect ratio wing to minimize the induced drag. While the high aspect ratio wing will minimize induced drag, long, thin wings increase structural weight and have relatively poor stiffness characteristics. This fact will temper the preference for a very high aspect ratio. Airplane configurations which are developed for very high speed flight (es- specially supersonic flight) operate at relatively low lift coefficients and demand great aero- dynamic cleanness. These configurations of airplanes do not have the same preference for high aspect ratio as the airplanes which op- erate continually at high lift coefficients. This usually results in the development of low aspect ratio planforms for these airplane con- figurations. The effect of aspect ratio on the lift and drag characteristics is shown in figure 1.31 for wings of a basic 9 percent symmetrical section. The basic airfoil section properties are shown on these curves and these properties would be NAVWEPS OD-SOT-BO BASIC AERODYNAMICS typical only of a wing planform of extremely high (infinite) aspect ratio. When a wing of some finite aspect ratio is constructed of this basic section, the principal differences will be in the lift and drag characteristics-the mo- ment characteristics remain essentially the same. The effect of decreasing aspect ratio on the lift curve is to increase the wing angle of attack necessary to produce a given lift co- efficient. The difference between the wing angle of attack and the section angle of attack is the induced angle of attack, orit18.24 L AR’ which increases with decreasing aspect ratio. The wing with the lower aspect ratio is less sensitive to changes in angle of attack and re- quires higher angles of attack for maximum lift. When the aspect ratio is very low (below 3 or 6) the induced angles of attack are not accurately predicted by the elementary equa- tion for 01~ and the graph of C, versus 01 develops distinct curvature. This effect is especially true at high lift coefhcients where the lift curve for the very low aspect ratio wing is very shallow and CL- and stall angle of attack are less sharply defined. The effect of aspect ratio on wing drag char-. acteristics may be appreciated from inspection of figure 1.31. The basic section properties are shown as the drag characteristics of an infinite aspect ratio wing. When a planform of some finite aspect ratio is constructed, the wing drag coefficient is the rtlm of the induced drag coe&- c,” cient, C,,=O.318 AR, and the section drag co- efhcient. Decreasing aspect ratio increases the wing drag coefficient at any lift coefficient since the induced drag coefficient varies inversely with aspect ratio. When the aspect ratio is very low, the induced drag varies greatly with lift and at high lift coefficients, the induced drag is very high and increases very rapidly with lift coefficient. While the effect of aspect ratio on lift curve slope and drag due to lift is an important re- lationship, it must be realized that design for 71
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NAVWEPS 00-8OT-80 BASIC AERODYNAMICS 0’ I-- E E :: i t (NO SWEEPBACK) i (3 5 3 I .4 BASIC SECTION 1 \A”=‘NFl~;~lB WING ANGLE OF ATTACK a DEGREES AR,=5 AR = 2.5 I I I (LOW MACH NUMBER) I .I0 .I5 .20 .25 I WING DRAG COEFFICIENT, CD Figure 1.31. Effect of Aspect Ratio on Wing Characteristics 72
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NAWEPS OO-BOT-BO BASIC AERODYNAMICS takeoff distance may occur. Also, the initial climb performance may be marginal at an excessively low airspeed. There are modern configurations of airplanes of very low aspect ratio (plus sweepback) which-if over- rotated during a high altitude, high gross weight takeoff-cannot fly out of ground effect. With the more conventional airplane configuration, an excess angle of attack pro- duces a well defined stall. However, the modern airplane configuration at an excessive angle of attack has no sharply defined stall but developes an excessive amount of induced drag. To be sure that it will not go unsaid, an excessively low angle of attack on takeoff creates its own problems-excess takeoff speed and distance and critical tire loads. (2) During appra& where the pilot must exercise proper technique to control the flight path. “Attitude plus power equals performance.” The modern high speed con- figuration at low speeds will have low lift- drag ratios due to the high induced drag 1 and can require relatively high power set- tings during the power approach. If the pilot interprets that his airplane is below the desired glide path, his first reaction rnu~t trot be to just ease the nose up. An increase in angle of attack without an increase in power will lower the airspeed and greatly increase the induced drag. Such a reaction could create a high rate of descent and lead to very undesirable consequences. The an- gle of attack indicator coupled with the mirror landing system provides reference to the pilot and emphasizes that during the steady approach “angle of attack is the primary control of airspeed and power is the primary control of rate of climb or descent.” Steep turns during approach at low airspeed are always undesirable in any type of air- plane because of the increased stall speed and induced drag. Steep turns at low airspeeds in a low aspect ratio airplane can create extremely high induced drag and can incur dangerous sink rates. very high speed flight does not favor the use of high aspect ratio planforms. Low aspect ratio planforms have structural advantages and allow the use of thin, low drag sections for high speed flight. The aerodynamics of transonic and supersonic flight also favor short span, low aspect ratio surfaces. Thus, the modern con- figuration of airplane designed for high speed flight will have a low aspect ratio planform with characteristic aspect ratios of two to four. The most important impression that should result is that the typical modern configuration will have high angles of attack for maximum lift and very prodigious drag due to lift at low flight speeds. This fact is of importance to theNaval Aviator because the majority of pilot- caused accidents occur during this regime of flight-during takeoff, approach, and landing. Induced drag predominates in these regimes of flight. The modern configuration of high speed air- plane usually has a low aspect ratio planform with high wing loading. When wing sweep- back is coupled with low aspect ratio, the wing lift curve has distinct curvature and is very flat at high angles of attack, i.e., at high CL, C, in- creases very slowly with an increase in 01. In addition, the drag curve shows extremely rapid rise at high lift coefficients since the drag due to lift is so very large. These effects produce flying qualities which are distinctly different from a more “conventional” high aspect ratio airplane configuration. Some of the most important ramifications of the modern high speed configuration are: (1) During takeoff where the airplane must not be over-rotated to an excessive angle of attack. Any given airplane will have some fixed angle of attack (and CJ which produces the best takeoff performance and this angle of attack will not vary with weight, density altitude, or temperature. An excessive angle of attack produces additional induced drag and may have an undesirable effect on takeoff performance. Takeoff acceleration may be seriously reduced and a large increase in 73 Revised January 1965
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NAVWEPS 004OT-80 BASIC AERODYNAMICS (3) During the landing phase where an excessive angle of attack (or excessively low airspeed) would create high induced drag and a high power setting to control rate of descent. A common error in the technique of landing modern conbgurations is a steep, low power approach to landing. The steep flight path requires considerable maneuver to flare the airplane for touchdown and necessitates a definite increase in angle of attack. Since the maneuver of the flare is a transient condition, the variation of both lift and drag with angle of attack must be considered. The lift and drag curves for a high aspect ratio wing (fig. 1.31) show con- tinued strong increase in C, with 01 up to stall and large changes in Co only at the point of stall. These characteristics imply that the high aspect ratio airplane is usually capable of flare without unusual results. The in- __^_“^ :- ---I.. -c _&-__ 1. .-* n.-. -..- : 1 C,LaLDC 111 a,l5~~ VI ~LL~CL do *we p~ovmes the increase in lift to change the flight path direction without large changes in drag to decelerate the airplane. The lift and drag curves for a low aspect ratio wing (fig. 1.31) show that at high angles of attack the lift curve is shallow, i.e., small changes in C, with increased a. This implies a large rotation needed to provide the lift to flare the airplane from a steep approach. The drag curve for the low aspect ratio wing shows large, powerful increases in C, with Cr. well below the stall. These lift and drag charac- teristics of the low aspect ratio wing create a distinct change in the flare characteristics. If a flare is attempted from a steep approach at low airspeed, the increased angle of attack may provide such increased induced drag and rapid loss of airspeed that the airplane does not actually flare. A possible result is that an even higher sink rate may be incurred. This is one factor favoring the use of the “no-flare” or “minimum flare” type landing technique for certain modern configurations. These same aerodynamic properties set the best glide speeds of low aspect ratio airplanes above the speed for (L/D)-. The additional speed pro- vides a more favorable margin of flare capabil- ity for flameout landing from a steep glide path (low aspect ratio, low (L/D)-, low glide ratio). The landing technique must emphasize proper control of angle of attack and rate of descent to prevent high sink rates and hard landings. As before, to be sure that it will not go unsaid, excessive airspeed at landing creates its own problems-excessive wear and tear on tires and brakes, excessive landing distance, etc. The effect of the low aspect ratio planform of modern airplanes emphasizes the need for proper flying techniques at low airspeeds. Excessive angles of attack create enormous induced drag which can hinder takeoff per- formance and incur high sink rates at landing. Since such aircraft have intrinsic high mini- mum flying speeds, an excessively low angle of attack at takeoff or landing creates its own problems. These facts underscore the im- portance of a “thread-the-needle,” professional flying technique. EFFECT OF TAPER AND SWEEPBACK The aspect ratio of a wing is the primary factor in determining the three-dimensional characteristics of the ordinary wing and its drag due to lift. However, certain local effects take place throughout the span of the wing and these effects are due to the distribution of area throughout the span. The distribution of lift along the span of a wing cannot have sharp discontinuities. (Nature just doesn’t arrange natural forces with sharp discontinuities.) The typical lift distribution is arranged in some elliptical fashion. A representative dis- tribution of the lift per foot of span along the scan of a wing is shown in figure 1.32. The natural distribution of lift along the span of a wing provides a basis for appreciating the effect of area distribution and taper along the span. If the elliptical lift distribution is 74
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NAVWEPS OfJ-RDT-8D BASIC AERODYNAMICS A I I TYPlChL L&i. PER kT. OF ‘SPAN ’ LIFT DISTRIBUTION Figure 4.32. Sponwise Lift Distribution
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NAVWEPS OD-8OT-80 BASIC AERODYNAMICS matched with a planformwhose chord is dis- tributed in an elliptical fashion (the elliptical wing), each square foot of area along the span produces exactly the same lift pressure. The elliptical wing planform then has each section of the wing working at exactly the same local lift coefhcient and the induced downflow at the wing is uniform throughout the span. In the aerodynamic sense, the elliptical. wing is the most efficient planform because the uni- formity of lift coefficient and downwash incurs rbt iea$t induced drag for a given aspect ratio. The merit of any wing @anform is then meas- ured by the closeness with which the distribu- tion of lift coefficient and downwash approach that of the elliptical planform. The effect of the elliptical planform is illus- trated in figure 1.32 by the plot of local lift coefficient to wing lift coefficient, f! G’ versus scm:spnn L.“CY.ICG. ,4;..t,or, Tbac e!liptical wing p* duces a constant value of$=J.O throughout the span from root to tip.‘ Thus, the local section angle of attack, LYE, and local induced angle of attack, CY,, are constant throughout the span. If the planform area distribution is anything other than elliptical, it may be ex- pected that the local section and induced angles of attack will not be constant along the span. A planform previously considered is the simple rectangular wing which has a taper ratio of 1.0. A characteristic of the rectangular wing is a strong vortex at the tip with local downwash behind the wing which is high at the tip and low at the root. This large non- uniformity in downwash causes similar varia- tion in the local induced angles of attack along the span. At the tip, where high downwash exists, the local induced angle of attack is greater than the average for the wing. Since the wing angle of attack is composed of the sum of at and aor a large local (x, reduces the local a0 creating low local lift coefficients at the tip. ‘Ihe reverse is true at the root of the rectangular wing where low local downwash exists. This situation creates an induced angle of attack at the root which is less than the average for the wing and a local section angle of attack higher than the average for the wing. The result is shown by the graph of figure 1.32 which depicts a local lift coefficient at the root almost 20 percent greater than the wing lift coefficient. The effect of the rectangular planform may be appreciated by matching a near elliptical lift distribution with a planform with a constant chord. The chords near ‘the tip develop less lift pressure than the root and consequently have lower section lift coe&- cients. The great nonuniformity of local lift coefficient along the span implies that some sections carry .more than their share of the load while others carry less than their share of the load. Hence, for a given aspect ratio, the rectangular planform will be less efficient -t-- -L. -11:. -!-~I LlLill UK C‘lqJLlCal wing. For exampie, a rectangular wing of AR=6 would have 16 percent higher induced angle of attack for the wing and 5 percent higher induced drag than an elliptical wing of the same aspect ratio. At the other extreme of taper is the pointed wing which has a taper ratio of zero. The extremely small parcel of area at the pointed tip is not capable of holding the main tip vortex at the tip and a drastic change in down- wash distribution results. The pointed wing has greatest downwash at the root and this downwash decreases toward the tip. In the immediate vicinity of the pointed tip, an upwash is encountered which indicates that negative induced angles of attack exist in this area. The resulting variation of local lift coefficient shows low cr at the root and very high c, at the tip. This effect may be appre- ciated by realizing that the wide chords at the root produce low lift pressures while the very narrow chords toward the tip are sub- ject to very high lift pressures.. The varia- tion of 2 throughout the span of the wing of L taper ratio==0 is shown on the graph of figure 76
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1.32. As with the rectangular wing, the non- uniformity of downwash and lift distribution result in inefficiency of rhis planform. For example, a pointed wing of AR=6 would have 17 percent higher induced angle of attack for the wing and 13 percent higher induced drag than an elliptical wing of thesame aspect ratio. Between the two extremes of taper will exist planforms of more tolerable efficiency. The variations of 2 for a wing of taper ratio =0.5 closely approxtmates the lift distribution of the elliptical wing and the drag due to lift characteristics are nearly identical. A wing of AR=6 and taper ratio=0.5 has only 3 percent higher ai and 1 percent greater CD: than an elliptical wing of the same aspect ratio. ,A separate effect on the spanwise lift dis- tribution is contributed by wing sweepback. Sweepback of the planform tends to alter the lift distribution similar to decreasing the taper ratio. Also, large sweepback tends to increase induced drag. The elliptical wing is the ideal of the sub- sonic aerodynamic planform since it provides a minimum of induced drag for a given aspect ratio. However, the major objection to the elliptical planform is the extreme difficulty of mechanical layout and construction. A highly tapered planform is desirable from the stand- point of structural weight and stiffness and the usual wing planform may have a taper ratio from 0.45 to 0.20. Since structural con- siderations are quite important in the develop- ment of an airplane configuration, the tapered planform is a necessity for an efficient configu- ration. In order to preserve the aerodynamic efficiency, the resulting planform is tailored by wing twist and section variation to obtain as near as possible the elliptic lift distribution. STALL PATTERNS An additional effect of the planfotm area distribution is on stall pattern of wing. The desirable stall pattern of any wing is a stall which begins on the root sections first. The NAVWEPS OD-ROT-RO RASIC AERODYNAM!CS advantages of root stall first are that ailerons remain effective at high angles of attack, favorable stall warning results from the buffet on the empennage and aft portion of the fuse- lage, and the loss of downwash behind the root usually ptovides a stable nose down moment to the airplane. Such a stall pattern is favored but may be difficult to obtain with certain wing configurations. The types of stall patterns in- herent with various planforms are illustrated in figure 1.33. The various planform effects are separated as follows : (A) The elliptical planform has constant local lift coefficients throughout the span from root to tip. Such a lift distribution means that all sections will reach stall at essentially the same wing angle of attack and stall will begin and progress uniformly throughout the span. While the elliptical wing would reach high lift coefficients before incipient stall, there would be little advance warning of complete stall. Also, the ailerons may lack effectiveness when the wing operates near the stall and lat- eral control may be difficult. (B) The lift distribution of the rectangular wing exhibits low local lift coefficients at the tip and high local lift coe5cients at the root. Since the wing will initiate stall in the area of highest local lift coefficients, the rectangular wing is characterized by a strong root stall tendency. Of course, this stall pattern is fav- orable since there is adequate stall warning buffet, adequate aileron effectiveness, and usu- ally strong stable moment changes on the ait- plane. Because of the great aerodynamic and structural ine&ciency of this planform, the rectangular wing finds limited application only to low cost, low speed light planes. The sim- plicity of construction and favorable stall characteristics are predominating requirements of such an airplane. The stall sequence fot a rectangular wing is shown by the tuft-grid pictures. The progressive flow separation il- lustrates the strong root stall tendency. (C) The wing of moderate taper (taper ratio=0.5) has a lift distribution which closely
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NAVWEPS 00-SOT-80 BASIC AERODYNAMICS .5- SPANWISE LIFT DISTRIBUTION ROOT I TIP ELLIPTICAL RECTANGULAR, X=1.0 n ~PROGRE,,,s= MODERATE TAPER, A= 0.5 HIGH TAPER, A=O.25 Revised January 1965 Figure 1.33. Stall Patterns (sheet I of 8) 78
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NAVWEPS OeBOT-80 BASIC AERODYNAMICS DOWNWASH FLOW FIELD BEHIND A RECTANGULAR WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS AR=2.31, k=l.O -II- 30° OF FLOW ANGULARITY OT (DEG) 0 ‘8 - 16 STALL 18 (a) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE TRAILING EDGE FROM NACA TN 2674 F;gure 1.33. Stall Patterns (sheet 2 of 8) 79
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NAWEPS oD-80~~0 BASIC AERODYNAMICS SURFACE TUFT PHOTOGRAPHS FOR RECTANGULAR WING AR=2.31, k-l.0 8 STALL 18 FROM NACA TN 2674 Figuse 1.33. Stall Patterns (sheet 3 of 8) 80
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NAVWEPS Oo-8OT-80 BASIC AERODYNAMICS DOWNWASH FLOW FIELD 8EHlNO A SWEPT TAPERED WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS 45’ DELTA, AR=4.0,X=O -It- 30° OF FLOW ANGULARITY 94 (DEG) 0 8 STALL 16 STALL (a) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE TRALLING EDGE FROM NACA TN 2674 Figure 1.33. Staff Patterns (sheet 4 of 81 81
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NAVWEPS 00-BOT-BO BASIC AERODYMAAlllCS SURFACE TUFT PHOTOGRAPHS FOR A SWEPT, TAPERED WING 45O DELTA, AR=4.0. x=0 i =0 DEGREES a = 12 DEGREES a = 8 DEGREES B = 16 DEGREES a = 20 DEGREES FROM NACA TN 2674 Figure 1.33. Stall Patterns (sheet 5 of 8’)
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NAVWEPS OO-SOT-80 S )YE STREAMERS OhI F!ilJ MOnFl Ftgure 7.33. Staff Patterns (sheet 6 of 8)
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NAVWEPS 00-8OT-80 BASIC AERODYNAMICS DOWNWASH FLOW FIELD BEHIND A SWEPT,TAPERED WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS 60° DELTA, AR=2.31, X = 0 --+-- 30” OF FLOW ANGULARITY QT (DEG) 0 8 I6 STALL 24 STALL 32 (a) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE TRAILING EDGE FROM NACA TN 2674 Figure 1.33. Stall Patterns (sheet 7 of 8) 84
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NAVWEPS OD-801-80 BASIC AERODYNAMICS SURFACE TUFT PHOTOGRAHS FOR A SWEPT, TAPERED WlNG 60° DELTA, AR=2.31, A=0 a = 0 DEGEES /STALL . d a =32 DEGREES FROM NACA TN 2674 Figure 1.33. Std Patterns (sheet 8 018)
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NAVWEPS 00-801-80 BASIC AERODYNAMICS approximates that of the elliptical wing. Hence, the stall pattern is much the same as the elliptical wing. (D) The highly tapered wing of taper ratio=0.25 shows the stall tendency inherent with high taper. The lift distribution of such a wing has distinct peaks just inboard from the tip. Since the wing stall is started in the vicinity of the highest local lift coefficient, this planform has a strong “tip stall” tendency. The initial stall is not started at the exact tip but at the station inboard from the tip where highest local lift c,oefficients prevail. If an actual wing were allowed to stall in this fashion the occurrence of stall would be typi- fied by aileron buffet and wing drop. There would be no buffet of the empennage or aft fuselage, no strong nose down moment, and very little-if any-aileron effectiveness. In order to prevent such undesirable happenings, the wing must be tailored to favor the stall pattern. The wing may be given a geometric. twist or “washout” to decrease the local angles of attack at the tip. In addition, the airfoil section may be varied throughout the span such that sections with greater thickness and camber are located in the areas of highest local lift coefhcients. The higher ct- of such sections can then develop the higher local C~S and be less likely to stall. The addition of leading edge slots or slats toward the tip increase the local c t- and stall angle of attack and are useful in allaying tip stall and loss of aileron effectiveness. Another device for im- proving the stall pattern would be the forcing of stall in the desired location by decrctising the section ctmar in this vicinity. The use of sharp leading edges or “stall strips” is a powerful device to control the stall pattern. .(E) The pointed tip wing of taper ratio equal to zero develops extremely high local lift coefficients at the tip. For all practical purposes, the pointed tip will be stalled at any condition of lift unless extensive tailoring is applied to the wing. Such a planform has no practical application to an airplane which is definitely subsonic in performance. (F) Sweepback applied to a wing planform alters the lift distribution similar to decreasing taper ratio. Also, a predominating influence of the swept planform is the tendency for a strong crossflow of the boundary layer at high lift coefficients. Since the outboard sections of the wing trail the inboard sections, the out- board suction pressures tend to draw the boundary layer toward the tip. The result is a thickened low energy boundary layer at the tips which is easily separated. The develop ment of the spanwise flow in the boundary layer is illustrated by the photographs of figure 1.33. Note that the dye streamers on the upper surface of the~swept wing develop a strong spanwise crossflow at high angles of attack. Slots, slats, and flow fences help to allay the strong tendency for spanwise flow. When sweepback and taper are combined in a planform, the inherent tip stall tendency is considerable. If tip stall of any significance is allowed to occur on the swept wing, an addi- tional complication results: the forward shift in the wing center of pressure creates an un- stable nose up pitching moment. The stall sequence of a swept, tapered wing is indicated by the tuft-grid photographs of figure 1.33. An additional effect on sweepback is the re- duction in the slope of the lift curve and maxi- mum lift coeflicient. When the sweepback is large and combined with low aspect ratio the lift curve is very shallow and maximum lift coefficient can occur at tremendous angles.of attack. The lift curve of one typical low aspect ratio, highly tapered, swept wing air- plane depicts a maximum lift coefficient at approximately 43’ angle of attack. Such dras- tic angles of attack are impractical in many respects. If the airplane is operated at such high angles of attack an extreme landing gear configuration is required, induced drag is ex- tremely high, and the stability of the airplane may seriously deteriorate. Thus, the modern conhguration of airplane may have “minimum
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