GT AE 3310 - Aircraft Performance

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Aircraft PerformanceThe Four Forces of FlightFour Forces in Climbing FlightNow, Bank the AircraftThe Equations of MotionClimbing, Banking FlightFirst Equation of MotionSecond Equation of MotionForces on Horizontal PlaneThird Equation of MotionSummaryAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyAircraft PerformanceAircraft performance is defined as how the aircraft responds (its motion) to the four forces of flight.It is considered to be a branch of the Flight Mechanics discipline.We have already reviewed aerodynamics and propulsion. We use the following information in performance:aerodynamicspropulsiondrag polarthrust or power, SFCAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyThe Four Forces of FlightValways in the direction of the local flight of the aircraft. Shows flow velocity relativeto the airplaneLWperpendicular to by definitionValways acts towards the center of the earthTDparallel to by definitionVεnot necessarily in the flight directionLift, Drag, Weight, ThrustLift and Drag are for complete airplaneSteady, Level FlightAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyFour Forces in Climbing FlightVTDεWLflight pathθθearthlocal climb angleAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyNow, Bank the AircraftφφWcosθT sin εLφBank (roll) angleAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyThe Equations of MotionBased on Newton’s Second Law:F = m anote this is vector formIn scalar form, for arbitrary direction in space, sFs= m asGeneral, Formal DerivationLess Formal, more Physical Derivationrotating spherical earthacceleration of gravity with distance from center of the earthflat, stationary earthAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyClimbing, Banking FlightReplace aircraft with point mass at its center of gravity (because we are only concerned with translational motion).Flight PathW+r1radius of curveL cos φT sin ε cos φsT cos εDcenter of gravity of the airplaneθθVinstananeous flightpath directionAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyFirst Equation of MotionTake components parallel to the flight pathF = T cos ε - D - W sin θThe acceleration isThe force isTherefore, Newton’s Second Lawparallel to the flight path isadVdt=mdVdt=T cos ε - D - W sin θFirst Equation of Motionma = FAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologySecond Equation of MotionTake components perpendicular to the flight pathF = L cos φ + T sin ε cos φ -W cosθThe radial acceleration isThe force isTherefore, Newton’s Second Lawperpendicular to the flight path isaVr1=m=Second Equation of Motion2Vr12L cos φ + T sin ε cos φ -W cosθma = FAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyForces on Horizontal PlaneNow look at flight path from a “top” view+r2projection offlight pathL sin φT cos ε cos θT sin ε sin φD cos θVcos θAE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologyThird Equation of MotionTake components perpendicular to the flight path in the horizontal plane (2)F2= L sin φ + T sin ε sin φThe radial acceleration isThe force isTherefore, Newton’s Second Lawperpendicular to the horizontal flight path isa2(V cos θ)r2=m=Third Equation of Motion2L sin φ + T sin ε sin φma = F(V cos θ)r22AE 3310 PerformanceChapter 4- The Equations of MotionDr. Danielle SobanGeorgia Institute of TechnologySummaryThe three Equations of Motion are simply statements of Newton’s SecondLaw.The three Equations of Motion describe the translational motion of anairplane through three-dimensional space over a flat earth.There are three additional equations of motion that describe the rotationalmotion of the aircraft about its three axes.Final note: the three equations of motion here do not assume a yawcomponent. The free stream velocity vector is assumed always parallelto the symmetry plane of the


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