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Introduction to Aerospace EngineeringLecture slidesChallenge the future1

Introduction Aerospace EngineeringFlight MechanicsDr. ir. Mark Voskuijl15-12-2012DelftUniversity ofTechnologyChallenge the future

3.&4Horizontal flight performanceFlight Mechanics2

Flight mechanicsHours 1Hours 3Hours 5Hours 7Hours 9&&&&&2:4:6:8:10:Introduction, general equations of motionHorizontal flight performanceClimbing and descending flightFlight envelopeExample questions and solutionsFlight Mechanics3

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics4

Equations of motionGeneral equations of motion in symmetric flight (1)Free Body DiagramKinetic DiagrammVLT Xb T D d dtV dVmdtXeWZeZbXbZe XeZbFlight Mechanics 5V

Equations of motionGeneral equations of motion in symmetric flight (2)F madVV : T cos T D W sin mdtd V : L W cos T sin T mVdtFlight Mechanics6

Propulsive forceTypical analytical assumption – JetThrust is assumed to be independent of airspeedFlight Mechanics7

Propulsive forceTypical analytical assumption – PropellerPa is assumed to be constant and independent of airspeedFlight Mechanics8

Propulsive forceAnalytical assumptions - summaryJet: Thrust is (assumed) independent of airspeedPropeller: Power available is (assumed) independent of dFlight Mechanics9

Summary previous lecture You should be able to derive theequations of motion for 2dimensional flight The thrust of a jet aircraft can beassumed independent of airspeed The power available of a propelleraircraft can be assumedindependent of airspeedW dV T cos T D W sin g dtW d F V : g V dt L W cos T sin T F// V:CL2CD CD0 Ae The complete aircraftaerodynamics can be representedby 1 equation; the lift drag polarFlight Mechanics10

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics11

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics12

IntroductionHorizontal flight performance How fast can an aircraft fly? How slow can a given aircraft fly? At what speed should be flown to be able to fly as far as possible?(Interesting for airliners) At what speed should be flown to stay in the air as long aspossible? (Search and rescue, military purposes)Flight Mechanics13

IntroductionWhat to learn?Most important are the lecture sheets!!!Background material:Introduction to Flight (Anderson)Par. 6.1 – 6.2Par. 6.3 – 6.6Par. 6.12 – 6.14Flight Mechanics14

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics15

Equations of motionGeneral equations of motion in symmetric flight (1)Free Body DiagramKinetic DiagrammVLT Xb T D d dtV dVmdtXeWZeZbXbZe XeZbFlight Mechanics 16V

Equations of motionGeneral equations of motion in symmetric flight (2)F madVV : T cos T D W sin mdtd V : L W cos T sin T mVdtFlight Condition:The aircraft is performing a horizontal (straight) and steadyflight.Assumption:The thrust is assumed to be in the direction of flight ( T 0).Flight Mechanics17

Equations of motiondefinitions Straight flight: flight in which the centre of gravity of theaircraft travels along a straight line (d /dt 0) Steady flight: Flight in which the forces and moments acting onthe aircraft do not vary in time, neither in magnitude, nor indirection (dV/dt 0) Horizontal flight: The aircraft remains at a constant altitude( 0) Symmetric flight: flight in which both the angle of sideslip iszero and the plane of symmetry of the aircraft is perpendicular tothe earth ( 0 and the aircraft is not turning)Flight Mechanics18

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http://www.youtube.com/watch?v TCUHQ -l6QgB52 landing in crosswindFlight Mechanics21

Equations of motionHorizontal, steady, symmetric flightF ma 1 0 0dVV : T cos T D W sin m 1 0 dt 0d V : L W cos T sin T mVdtV :T D V : L WNote: Clearly thisis the most simpleform of theequations ofmotionHow do these forces (aerodynamic, propulsive, gravitational) varywith airspeed?Flight Mechanics22

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics23

Performance diagram For a given altitude, configuration and engine control setting, thedrag or power required and thrust or power available are plottedagainst airspeed Also called Pernaud diagram Very useful to determine aircraft performance parametersFlight Mechanics24

Performance diagram Typical shape:Flight Mechanics25

Performance diagramPa T VPr D VFlight Mechanics26

Jet (thrust / power)Propeller (power)Aerodynamics (power / drag)ForcePowerairspeedairspeedFlight Mechanics27

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics28

Horizontal flight performance Minimum airspeed (How slow) Maximum airspeed (How fast) Range (How far) Endurance (How long) Speed stability / instabilityAssumptions: Horizontal steady symmetric flight( L W, T D, Pa Pr ), except for the speed stability sectionFlight Mechanics29

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics30

Minimum airspeedL WC L 12 V 2S WW 2 1V S CLVmin W 2 1S CLmaxFlight Mechanics31

Minimum airspeedFlapsFlight Mechanics32

Minimum airspeedPerformance diagramVminFlight Mechanics33

Minimum airspeedExample calculation Question: An aircraft has a wing loading (W/S) 2400 N/m2 andCLmax 1.4. Find the airspeed at which stall occurs (minimum airspeed)at (i) sea level ( 1.225 kg/m3) and (ii) at 5000m ( 0.737 kg/m3) Answer:L WCL 12 V 2S WVmin W2 1S CL ,max(i)Vmin 240021 51.8 m/s1.225 1.4(ii)Vmin 240021 66.8 m/s0.737 1.4Flight Mechanics34

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics35

SolutionTmax DMaximum airspeedL WJet aircraftL CDTmax D WL CLCD CD0 k CL2 Pilot applies maximum throttle(max. thrust or Power available)ForceC D0Tmax k CL CLWTkCL2 max CL CD0 0Wax 2 bx c 0Maximum thrust CL .DragVmaxVL W V Flight MechanicsW2 1S CL36

Maximum airspeedExampleThe following data is known of the Cessna Citation II (subsonic jet)Aircraft Weight : W 60 kN,Wing area : S 30 m2,(Parabolic) Lift-Drag polar : CD CDo kCL2; CDo 0.022, k 0.047, CLmax 1.35,Maximum Thrust at 0 m ISA :T0 12 kN.The aircraft is flying at an altitude of H 0 m in the International StandardAtmosphere ( 0 1.225 kg/m3)Thrust is assumed to be independent of the airspeedCalculate (1) the maximum airspeed of this aircraft when flying at H 0 mand (2) the corresponding Mach numberFlight Mechanics37

Maximum airspeedSolutionSteady symmetric horizontal flight:Maximum Mach number?L W, T DWithMmax L CL 12 V 2S, D CD 12 V 2SThrust must be at maximum to achieve VmaxCombining the above yields:CL W 60000C 5 CD LCDT 120005Vmaxaa RT 1.4 287.05 288.15 340.3 m/sMmax 172.1 0.5340.3Lift drag polar:CD CD0 k CL2C L C D0 05kkCL0.022CL2 05 0.047 0.047CL2 CL 0.11Vmax W2 1 S CL60000 21 172.1 m/s30 1.225 0.11Flight Mechanics38

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal steady symmetric flightPerformance diagramAircraft performance in horizontal flight1.2.3.4.5.Minimum airspeedMaximum airspeedRangeEnduranceSpeed instability / stability6. Summary7. Example exam questionFlight Mechanics39

Range How can we fly as far as possible for a given amount of fuel? How can we fly a given distance with the minimum amount of fuel?Specific range is defined as the ratio V/F, where F equals thefuel flowDimensional analysis: V V m s F F N / s m N Or, put in words, specific range is the distance that can beflown for 1 Newton of fuel. Clearly, this variable must bemaximisedFlight Mechanics40

RangeMaximum range propeller aircraftFc P Pbr F c PPa jPa Pr (steady horizontal flight)F cPPrDV cP j jV j 1 F cP D j and cP can be assumed to be constant as a function of airspeed(over the range of cruising speeds) for propeller aircraft C V Rmax Dmin L F max C D maxFlight Mechanics41

RangeMaximum range propeller aircraftFlight Mechanics42

Problem!Result:Prop: maximum range at maximum CL / CDDear pilot, could you please fly at CL / CD max?We must give an airspeed to the pilotFlight Mechanics43

SolutionCD CD0C L2 AeResult:Prop: maximum range at maximum CL / CDCD f CL d CL dCL CD 0 dCCD 1 CL DdCL 0CD2 y f ( x)d g ( x) hg ' gh ' dx h( x) h2dCD CD dCL CLCL2CD0 2CL Ae AeCLCL CD0 AeL WW 2 1V S CLFlight Mechanics44

RangeExample: Spirit of St. Louis Charles Lindbergh (1927) First solo, non stop flight across theAtlantic oceanFlight Mechanics45

Performance diagramSpirit of St Louis(ref: NASA)Note:The Pr curve shiftsdown when weightdecreases. This meansthat Charles had todecrease airspeedduring the flightFlight Mechanics46

Contents1.2.3.4.5.Summary previous lectureIntroductionEquations of motion horizontal symmetric flightPerformance diagramAircraft performance in horizontal flight1. Minimum airspeed2. Maximum airspeed3. Range1. Propeller2. Jet4. Endurance5. Speed instability / stability6. Summary7. Example exam questionFlight Mechanics47

RangeJet aircraftSo, at what speed should the pilot fly to maximise specific range?FcTTTypically, cT can be considered to be constantT DF cTT cT DVV F cT D VF max V D max D V minFlight Mechanics48

RangeJet aircraftPerformance diagram (jet) D D 1 V L LV max maxL W CD1 D W V max C L V maxC L 12 V 2S W V D CD WVCL1W 2 1S CL W 2 1S CLWW 2 CLS C D2 CL D V C 2 min D maxFlight Mechanics49

Problem!Result:Jet: maximum range at maximum CL / CD2Dear pilot, could you please fly at CL / CD2 max?We must give an airspeed to the pilotFlight Mechanics50

SolutionCD CD0C L2 AeResult:Jet: maximum range at maximum CL / CD2CD f CL d CL dCL CD2 0 CD2 1 CL 2CDCdCDdCL4DdCD 1 CD 2dCLCLCL2C 2CL 1 D0 Ae Ae 2CLCL 13CD0 Ae y f ( x) d g ( x) hg ' gh ' dx h( x) h2 0L WW 2 1V S CLFlight Mechanics51

How environmentally (un)friendly areaircraft? Example: Boeing 747: W 3000 kNS 510 m2b 60 mhcr 11000 mMcr 0.85 Estimated: CD0 0.02; e 0.85; tot 0.40Flight Mechanics52

How environmentally (un)friendly areaircraft really W/S 5882 N/m2; A 7.06 a 295 m/s; V 250 m/s ( 900 km/hr)W 2 1 0.517S V 2C L2CD CD 0.0342 AeCL 15.1CDCD D W 198.4 kNCLPa Pr DV 49591 kJ/sCL 0Flight Mechanics53