AE 1350 Lecture Notes #10TOPICS TO BE STUDIEDTakeoff Performance TheoryGround RollGround Roll (Continued)Slide 6Landing PerformanceFAR-25 Regulations Landing PerformanceLift Coefficients for your DesignAE 1350 Lecture Notes #10TOPICS TO BE STUDIED•Take-off and Landing Performance•There is considerable variations due to–pilot technique–ground conditions•FAR 25 regulations cover how take-off and landing distances must be computed.•In your design, estimate wing area S to meet specified take-off and landing distances.Takeoff Performance TheoryGround Roll80% of total takeoffdistance, from experience.Transition and climb20% of total takeoffdistance, from experienceWe attempt to compute the ground roll asaccurately as possible.Add an extra 20% distance to account for transition and climb.Rotate totake-offGround RollLet v be the aircraft speed.dv/dt = awhere a= acceleration of the vehiclea= (All horizontal forces acting on the aircraft) / (Mass of aircraft)Assume “a” to be a constant.Integrate: v = at Velocity at lift-off vLO = a tLOIntegrate again: d = 1/2 a t2 dLO = 1/2 a t2LO = v2LO/(2a)Ground Roll (Continued)From the previous slide, the total roll distance isdLO = 1/2 a t2LO = v2LO/(2a)a = Acceleration of the aircraft due to horizontal forces on it.These forces are: Thrust, Drag, Ground FrictionThrust far exceeds the other two factors during takeoff.Thus, a = T/(Aircraft Mass) = T g/ (W)Then, total roll distance is dLO = v2LO/(2a) = v2LO. W/(2Tg)Ground Roll (Continued)Total roll distance dLO = v2LO. W/(2Tg)The pilot usually lifts off at 1.2 times stall velocity.Stall velocity VStall is defined from: 1/2 V2Stall CLmax S= WV2Stall= W/(1/2  CLmax S)v2LO =(1.2 VStall)2 = 1.44 W/(1/2  CLmax S)Then, dLO = v2LO. W/(2Tg)= 1.44 (W)2 / (Tg S CLmax)Include factors of safety for transition and climb: Take-off Distance, in feet = 37.5 (W)2 / (TS CLmax)= 37.5 (W/S) /[(T/W) Clmax]where  = Density Ratio = Sea-Level,, W in lbs, S in square feetLanding PerformanceThere is considerable scatter in landing distances due touse of spoiler, brakes, reverse thrust, human factorsground conditions : wet runway , dry runwayFAR-25 RegulationsLanding Performance50ftVapproach=VA=1.3 Vstall for civilian aircraftVapproach=VA=1.2 Vstall for military aircraftVapproach=VA=1.1 Vstall for carrier based aircraftTotal Landing Distance, in feet = 0.3 (Vapproach in knots)2Ground RollThese results are empirical, because of variations in pilot technique.Lift Coefficients for your Design•For fighter design, use the following Clmax–With flaps up, 1.2 - 1.8–With flaps down, during take-off: 1.4 - 2.0–With flaps down, during landing: 1.6 to 2.6•For transport design, use the following Clmax–With flaps up, 1.2 - 1.8–With flaps down, during take-off: 1.6 - 2.2–With flaps down, during landing: 1.8 to