ME 425: Aerodynamics
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1 ME 425: erodynamics r..b.m. oufique Hasan Professor epartment of Mechanical Engineering Bangladesh University of Engineering & echnology (BUE), haka ecture-25 26/0/209 irplane pa Performance toufiquehasan.buet.ac.bd Consider an airplane in steady, unaccelerated, climbing flight as shown in figure. he velocity along the flight path is, and flight path inclined to the horizontal at angle θ. heforce balance results: + : ( i) + : cos ( ii) *ift is smaller than weight!!! *hrust will accommodate the rest of the weight. Eq. (i) and (ii) are the equations of motion for steady climbing flight. 2
2 Now multiply Eq. (i) by ate of Climb(/C) vertical velocity component /C 3 he power required to overcome the aerodynamic drag is known as power-required for steady, level flight. So, P Not only to overcome the drag, the airplane power plant has to produce more power for climb in take off condition. his can ne available from the power plant and known as power available, P (P = ). he difference is known as excess power; P P excess power excess power excess power /C /C /C excess power 4 2
3 Maximum climb angle, θ he equations of motion for steady climbing flight cos cos Now replace in the drag term of Eq. (iii) ( iii) ( iv) cos cos For θ <20 ; cos θ.0 (Nominal stall angle for airfoil < 20 ) han 5 Maximum climb angle, θ For the case of jet-propelled airplane (turbo-jet), the thrust is essentially constant with velocity. hus for imum climb angle, θ (in case of turbo-jet engine): sin for turbo-jet engine 6 3
4 jet-powered executive aircraft, Cessna Citation 3 has the following characteristics: ing span = 6.25 m ing area = m 2 gross weight = N Fuel capacity = 9 gal Power plant = 2 x turbofan engine N at seal level Parasite drag coefficient, C,0 = 0.02 Oswald efficiency factor, e = 0.8 θ raw the rate of climb curve (/C curve) of Cessna Citation jet for steady-flight at sea-level where ρ =.225 kg/m 3 7 /C excess power P P, 0 0 C = C (m/s) =/(q S) C,0+C 2 /πe = C /C /(C /C ) (kn) P,0 = * P = * /C (k) (k) (m/min) Sea-level condition (0) () ? Maximum /C does not occur at (/) lso check the behavior of climb angle, θ with flight velocity 8 4
5 Sea-level Maximum /C /C (m/min) /C (m/s) flight Maximum /C does not occur at imum flight velocity nor at (/) and θ 9 Gliding Flight Consider an airplane in steady, equilibrium power off (=0) gliding flight as shown in figure. he velocity along the flight path is, and flight path inclined at θ below horizontal: + : ( i) + : cos ( ii) Power off glide (=0) hen tan cos For minimum θ (i.e. smallest equilibrium glide) min tan 0 5
ME 425: Aerodynamics
ME 45: Aerodynamics r. A.B.M. oufique Hasan Professor epartment of Mechanical Engineering Bangladesh University of Engineering & echnology (BUE), haka Lecture-4 //9 Airplane pa Performance toufiquehasan.buet.ac.bd
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