AE 1350 Lecture Notes #10

TOPICS 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 Theory Ground Roll 80% of total takeoff distance, from experience. Transition and climb 20% of total takeoff distance, from experience We attempt to compute the ground roll as accurately as possible. Add an extra 20% distance to account for transition and climb. Rotate to take-off

Ground Roll Let v be the aircraft speed. dv/dt = a where a= acceleration of the vehicle a= (All horizontal forces acting on the aircraft) / (Mass of aircraft) Assume “a” to be a constant. Integrate: v = at Velocity at lift-off v LO = a t LO Integrate again: d = 1/2 a t 2 d LO = 1/2 a t 2 LO = v 2 LO /(2a)

Ground Roll (Continued) From the previous slide, the total roll distance is d LO = 1/2 a t 2 LO = v 2 LO /(2a) a = Acceleration of the aircraft due to horizontal forces on it. These forces are: Thrust, Drag, Ground Friction Thrust far exceeds the other two factors during takeoff. Thus, a = T/(Aircraft Mass) = T g/ (W) Then, total roll distance is d LO = v 2 LO /(2a) = v 2 LO. W/(2Tg)

Ground Roll (Continued) Total roll distance d LO = v 2 LO. W/(2Tg) The pilot usually lifts off at 1.2 times stall velocity. Stall velocity V Stall is defined from: 1/2  V 2 Stall C Lmax S= W V 2 Stall = W/(1/2  C Lmax S) v 2 LO =(1.2 V Stall ) 2 = 1.44 W/(1/2  C Lmax S) Then, d LO = v 2 LO. W/(2Tg)= 1.44 (W) 2 / (Tg  S C Lmax ) Include factors of safety for transition and climb: Take-off Distance, in feet = 37.5 (W) 2 / (T  S C Lmax ) = 37.5 (W/S) /[(T/W)  C lmax ] where  = Density Ratio =  Sea-Level,, W in lbs, S in square feet

Landing Performance There is considerable scatter in landing distances due to use of spoiler, brakes, reverse thrust, human factors ground conditions : wet runway, dry runway

FAR-25 Regulations Landing Performance 50ft V approach =V A =1.3 V stall for civilian aircraft V approach =V A =1.2 V stall for military aircraft V approach =V A =1.1 V stall for carrier based aircraft Total Landing Distance, in feet = 0.3 (V approach in knots ) 2 Ground Roll These results are empirical, because of variations in pilot technique.

Lift Coefficients for your Design For fighter design, use the following C lmax –With flaps up, –With flaps down, during take-off: –With flaps down, during landing: 1.6 to 2.6 For transport design, use the following C lmax –With flaps up, –With flaps down, during take-off: –With flaps down, during landing: 1.8 to 2.8