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Session Speaker M. SivapragasamSession 01Aircraft Steady and Level Flight 1 M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologySession ObjectivesAt the end of this session, student will be able to: Explain the absolute and functional performance of an aircraftList the crucial aircraft and propulsion parameters influencing the performance characteristics of an aircraftShow the forces acting on an aircraft in steady level flight and derive the equations of motionCalculate the thrust required and available for steady level flight for jet aircraftCalculate the power required and available for steady level flight for propeller-driven aircraftAssess the importance of maximum velocity on aircraft design

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPerformance overviewThere are two types of performance (a) Absolute and (b) FunctionalAbsoluteMaximum speed, Stalling speedBest climbing speed , Best glide speedRate of climb & Ceiling

Typical flight path of a passenger airplaneM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPerformance overviewMaximum range and speed for maximum rangeMaximum endurance and speed for maximum enduranceTake-off distance & Landing distanceThese are specifications oriented, directly connected to aircraft geometry, weight, and the power plant.M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPerformance overviewFunctional : Needed for efficient operation of aircraftWhat is the program of speed and altitude that must be followed in order to go from a given altitude h1 to another altitude h2 in minimum time?During emergency maneuvers or interception of aircraftM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPerformance overviewWhat is the program of airspeed and altitude to follow in order to go from one flight condition (i.e., speed and altitude), to another in minimum time?Similar to above and during missile avoidanceM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyFunctional performanceWhat is the program of altitude and speed such that the aircraft can change from one flight condition (i.e., speed and altitude) to another with minimum expenditure of fuel?What variation in flight conditions will permit the aircraft to cover the greatest distance over the ground?M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyStandard Atmosphere

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyEarth is not a sphereAre the boundaries for the atmospheric regions the same everywhere on the Earth ?No. The Earth is not a perfect sphere.The World Geodetic System (WGS), models the Earth as an oblate spheroidequatorial axis = 6,378,137.000 mpolar axis = 6,356,752.314 mpolar tropopause = 6 kmequatorial tropopause = 17 kmM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyVariation of propertiesAir temperature falls at a constant rate in the troposphere.From the tropopause, the temperature remains constant at -60 C until 20 km above S.L.The lower stratosphere is the limit for atmospheric flight

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyVariation ModelThe International Standard Atmosphere Sea Level : Pressure = Psl = 1.01325 x 105N/m2 Density = sl = 1.225 kg/m3 Temperature = Tsl= 15.0C = 288.15 K Velocity of sound = a0 = 340.3 m/s. (i) 0 to 11 km altitude

T = (288.15 - 6.5*h) K i.e T/Tsl = (1 h /44.331)P / Psl= = (T/Tsl) ^5.256 / sl = = (T/Tsl) ^ 4.256

(2) 11 to 20 kmT=T 11 = 216.65 K, giving the ratio T / Tsl= 0.75187 , P11/Psl = 0.2234 ,11 / sl = 0.2971 . Note T is frozen but not Pressure P and Density P/P11 = 11 / sl = exp[-0.15769(h - 11)].

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMach NumberAir is compressible, a moving aircraft disturbs the surrounding air These disturbances e.g. pressure variations, propagate at the speed of sound through the surrounding airM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMach NumberThe Mach number ( airspeed / speed of sound) measures the importance of this compressibility effect M = V / a , here a = ( RT) 0.5 = 20 (T)*0.5M < 0.8 subsonic incompressible aerodynamics0.8 < M < 1.2 transonic localized compressibility effects1.2 < M < 5 supersonic compressible aerodynamicsM > 5 hypersonic aerodynamic heatingM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyExample

Implications for flight : At higher altitudes density drops drastically, so either V or C L have to make-up for loss in Lift Temperature drops implying acoustic speed drops as well for the same V, Mach number increasesM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyWing Geometry

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyWing Types

(a) Swept back(b) Tapered(c) Elliptic

(e) Swept forward

(d) Rectangular(f) DeltaM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & Technology

Aircraft Flight Definitions

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & Technology

Aircraft Flight DefinitionsM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyAirplane powerplantsTwo types of engines common in aviation todayReciprocating piston engine with propellerAverage light-weight, general aviation aircraftRated in terms of POWER (kW)Jet (Turbojet, turbofan) engineLarge commercial transports and military aircraftRated in terms of THRUST (N)

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust vs. PowerJets Engines (turbojets, turbofans for military and commercial applications) are usually rate in ThrustThrust is a Force with units (N = kg m/s2)For example, the PW4000-112 is rated at 450 kN of thrustGE 404-F2j3 Powering Tejas is rated at 49 kN thrust (dry) and 80 kN (after burner)M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust Vs PowerPiston Engines are usually rated in terms of PowerPower is a precise term and can be expressed as:Energy / time with units (kg m2/s2) / s = kg m2/s3 = WattsNote that Energy is expressed in Joules = kg m2/s2Force * Velocity with units (kg m/s2) * (m/s) = kg m2/s3 = WattsUsually rated in terms of horsepower (1 hp = 550 ft lb/s = 746 W)M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust Vs PowerExample:Airplane in a level, un-accelerated flight at a given altitude with speed VPower Required, PR=TR*V [W] = [N] * [m/s]M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower and Thrust

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyDependence of Thrust on Altitude and Velocity

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust And Thrust Coefficient

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust dependence on Velocity

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower Dependence on Velocity

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPropeller Efficiency

Where,V = airspeed, m/sn = rotation rate, revolution/sD = propeller diameterM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust of Propeller Aircraft

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust of a Jet engine Aircraft

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyWing LoadingWing loading is the loaded weight of the aircraft divided by the area of the wing Usually defined as W/S (N/m 2) or M/S (kg/m2)A measure of wings carrying capacityAs velocity increases, more lift is produced by each unit area of wingSo smaller the wing loading, higher should be the operating speed.With increased W/S landing and take-off speeds will be higher.maneuverability decreasesM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyTypical Wing LoadingsAircraftWing Loading, (kg/m2)RoleYearBuzz Z33.9paraglider2010Fun 1606.3hang glider2007ASK 2133glider1979Ikarus C4238microlight1997Cessna 15251trainer1978Vans RV-467sports1980Eurofighter311fighter1998F-104514fighter-bomber1958A380663airliner2007B747740airliner1970MD-11F844airliner1990M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust LoadingThis is the ratio between thrust (or power) generated by the engine to the weight of the aircraftThis is not a unique number nor is it a constantThrust of a turbojet or turbofan can be boosted by an afterburner for military applicationsAt a huge cost of specific fuel consumptionM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust LoadingThrust and power depend on density of air and hence altitude.Thrust is max at sea level, unfortunately so is drag, hence (T/D)max is at altitude M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyTypical Thrust LoadingsVehicleT / WScenarioConcorde0.4Max Takeoff Weight, Full ReheatEnglish Electric Lightning0.6maximum takeoff weight, No ReheatF-22 Raptor0.85maximum takeoff weight, Dry ThrustMikoyan MiG-291.1F-15 Eagle1nominally loadedF-16 Fighting Falcon1.1Hawker Siddeley Harrier1.1Eurofighter Typhoon1.25English Electric Lightning1.2light weight, full reheatSpace Shuttle1.5Take-off F-15 Eagle1.6light weight, full afterburnerF-22 Raptor1.6light weight, full afterburnerDassault Rafale1.7light weight, full afterburnerM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust and Wing Loading Trade-off

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPart 1 Introduction SummaryIn this session the following topics were dealt with :Standard Atmosphere, Aircraft & Wing Drag, Drag polar Aircraft Propulsion : Thrust, Power and SFC variation with flight conditionsCrucial parameters for design : T/W, W/S, Drag polar, L/W , CL,max, Cd0 and their dependenciesM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPerformance Road Map

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyForces on an airplaneModel airplane as rigid body with four natural forces acting on itLift, LPerpendicular to flight path (to relative wind)Drag, DParallel to flight path direction (to incoming relative wind)Propulsive Thrust, TFor most airplanes propulsive thrust acts in flight path directionMay be inclined with respect to flight path angle, aT, usually small angleM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyForces on an airplane4. Weight, WAlways acts vertically toward center of earthInclined at angle, q, with respect to lift direction

Apply Newtons Second Law (F=ma) to curvilinear flight pathForce balance in direction parallel to flight pathForce balance in direction perpendicular to flight pathM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyOverall airplane dragNo longer concerned with aerodynamic detailsDrag for complete airplane, not just wing

Wing or airfoilEntire AirplaneLanding GearEngine NacellesTail SurfacesM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyDrag polarCD,0 is parasite drag coefficient at zero lift (aL=0)CD,i drag coefficient due to lift (induced drag)Oswald efficiency factor, e, includes all effects from airplane

CD,0 and e are known aerodynamics quantities of airplane

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyCD min typical fighter planes (Nikolai)

Ref : NicolaiM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyCD min typical fighter planes

Ref : NicolaiM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyEffect of Sweepback

Sweep back reduces the effective Mach number on the wing This in turn shifts the drag rise M to a higher valueM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyEffect of M on Drag PolarTwo important effects are seen with increasing M C D0 and induced drag both increase

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyDrag polar Examples

Ref : NicolaiM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyGeneral equations of motion

Apply Newtons 2nd Parallel to flight path:Apply Newtons 2nd Perpendicular to flight path:Free Body DiagramM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyLevel, unaccelerated flightAircraft is flying at constant speed (no accelerations)Sum of forces = 0 in two perpendicular directionsWeight of airplane is perfectly balanced by lift (L = W)Engines produce enough thrust to balance total drag at this airspeed (T = D)

TDLWM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPerformance Parameters of InterestThese above 4 parameters and a couple of others (less important), determine the performance of the aircraft under consideration.Lift-to-Drag Ratio

Load Factor

Thrust-to-weight Ratio

Wind LoadingM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyTrimmed Flight

Trimmed lift coefficient, CL Proportional to weight Decrease with V2 At constant airspeed, increases with altitudeTrimmed angle of attack, Constant if dynamic pressure and weight are constant If dynamic pressure decreases, angle of attack must increaseM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyThrust for Steady Level Flight

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyVelocity for Minimum Thrust Flight

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMustang P51 Example

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower Required for Trimmed Flight

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyVelocity for Min Power Level Flight

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyLimit velocities for given engine

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyLimit Speeds for a Jet Engine

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyLimit Speeds for a Propeller

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyL/D Maximum condition

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyVelocity, CD and L/D at Max conditionMax L/D depends only C D0 and

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMustang Example

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower available

Jet EnginePropeller Drive EngineM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & Technology

Power required PR vs. V qualitatively

(Resembles TR vs. V)

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower required

PR varies inversely as CL3/2/CD

Recall: TR varies inversely as CL/CDM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower required

Zero-Lift PRLift-Induced PRZero-Lift PR ~ V3Lift-Induced PR ~ 1/VM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower required

At point of minimum PR, dPR/dV=0M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & Technology

Power requiredV for minimum PR is less than V for minimum TR

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower requiredWe will show that for a piston-engine propeller combinationTo fly longest distance (maximum range) we fly airplane at speed corresponding to maximum L/DTo stay aloft longest (maximum endurance) we fly the airplane at minimum PR or fly at a velocity where CL3/2/CD is a maximumPower will also provide information on maximum rate of climb and altitudeM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & Technology

Power available and maximum velocityPropeller DriveEngine1 hp = 550 ft lb/s = 746 WPRPA

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyPower available and maximum velocity

Jet EnginePA = TAVPR

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyAltitude effects on power required and available

Recall PR = f(r)Subscript 0 denotes seal-level conditionsM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyAltitude effects on power required and available

Vmax,ALT < Vmax,sea-levelM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyHow fast can you fly?Maximum flight speed occurs when thrust available, TA=TRReduced throttle settings, TR < TACannot physically achieve more thrust than TA which engine can provide

Intersection of TRcurve and maximumTA defined maximumflight speed of airplaneM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyFurther implications for design: VmaxMaximum velocity at a given altitude is important specification for new airplaneTo design airplane for given Vmax, what are most important design parameters?Similarly maximum altitude at which an aircraft can fly is called Ceiling A/C limited to slightly lower altitude called service ceiling from safety considerations

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyFurther implications for design: Vmax

Steady, level flight: T = D

Steady, level flight: L = W

Substitute into drag equation

Turn this equation into a quadraticequation (by multiplying by q)and rearranging

Solve quadratic equation and set thrust, T, to maximum available thrust, TA,maxM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyFurther implications for design: Vmax

TA,max does not appear alone, but only in ratio (TA/W)maxS does not appear alone, but only in ratio (W/S)M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyVmax does not depend on thrust alone or weight alone, but rather on ratios(TA/W)max: maximum thrust-to-weight ratioW/S: wing loadingVmax also depends on density (altitude), CD,0, ARIncrease Vmax byIncrease maximum thrust-to-weight ratio, (TA/W)maxIncreasing wing loading, (W/S)Decreasing zero-lift drag coefficient, CD0Further implications for design: VmaxM. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMinimum Thrust - ExampleAircraft is P51 MustangWing Span = 9.83 mWing Area = 21.83 m2Max mass = 3465 kgWing Loading W /S = 1555.7 N /m2Assume C d0 = 0.0163, = 0.0576 V min T = [ 2/ *(W/S) ( / C D0 ) 0.5 ] 0.5 = [ 2/ *(1557.7) ( / C D0 ) 0.5 ] 0.5

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMaximum SpeedsTwo equilibrium airspeeds for a given thrust or power settingLow speed, high CL, high !High speed, low CL, low !Achievable airspeeds between minimum and maximum values with maximum thrust or powerM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMaximum Speeds

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyMustang - Example

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyExample: Beechcraft Queen AirThe results we have developed so far for lift and drag for a finite wing may also be applied to a complete airplane. In such relations:CD is drag coefficient for complete airplaneCD,0 is parasitic drag coefficient, which contains not only profile drag of wing (cd) but also friction and pressure drag of tail surfaces, fuselage, engine nacelles, landing gear and any other components of airplane exposed to air flowCL is total lift coefficient, including small contributions from horizontal tail and fuselageSpan efficiency for finite wing replaced with Oswald efficiency factor for entire airplane

M. S. Ramaiah University of Applied Sciences#M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyExample: Beechcraft Queen AirExample: To see how this works, assume the aerodynamicists have provided all the information needed about the complete airplane shown in fig

Beechcraft Queen Air Aircraft Data

W = 38,220 NS = 27.3 m2, AR = 7.5 , e (complete airplane) = 0.9CD,0 (complete airplane) = 0.03

What thrust and power levels are required of engines to cruise at 300 kmph at sea-level?How would these results change at 11,000 m M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologyManoeuvre Limits

M. S. Ramaiah University of Applied Sciences#Faculty of Engineering & TechnologySummaryIn this session following topics were discussed:Absolute and functional performance of an aircraftCrucial aircraft and propulsion parameters influencing the performance characteristics of an aircraftForces acting on an aircraft in steady level flight and derivation of the equations of motionThrust required and available for steady level flight for jet aircraftPower required and available for steady level flight for propeller-driven aircraftImportance of maximum velocity on aircraft designM. S. Ramaiah University of Applied Sciences#Faculty of Engineering & Technology