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Exercise 9: Consider our aircraft is flying, W = 160000N, Wing area is 42 m2,
power available of engine is 2 MW and the parabolic drag polar is CD= 0,014 + 0,05C 2 L
a) Find angle of climb and rate of climb. If aircraft’s velocity at mean sea level is 120 m/s (Assume L =W)
b) Find the max angle of climb and the climb rate under that condition
c) Find the max rate of cimb and the angle of climb under that condition Answer L=W = 160000 N S = 42 m2 PAvai = 2 MW = 2.106 W C 2
D = 0,014 + 0,05C L a) V = 120 m/s γ and RC =? 1 L = ρ V 2 S C 2 L 1
160000 = .1,225 .1202 .42 .C 2 L CL= 0,432 C 2
D = 0,014 + 0,05C L
CD= 0,014 + 0,05.0,4322 = 0,023 P C sin γ= Avai − D = 2.106
− 0,023 γ=¿ 0,05 rad = 2.86 degree W . V C 160000.120 0,432 L
RC = V. sinγ = 120.0,05 = 6 m/s b) γmax and RC =? P 2. 106
A = Avai .√ 1.ρ.S =
. √ 1.1,225.42 = 0,158 W 3/2 2 1600003/ 2 2 A k. 3/ 2 C 2 - . C - C L 2 L d = 0 0,158 0,05. C 2 - . C 3/2 C =0,3817 L - 0,014 = 0 C 2 L L = 2,712 D . ρ . S . C P
√12 L C γ =0,12rad=6,9degree max sin γ = Avai . − D W W CL P P P C
RC = Avai− Req = Avai − D . cosγ . √2mgcosγ = 5,8 m/s W W W C ρ . C . S L L
c) RCmax and γ=¿ ?
C =4 C =4.0,014=0,056 D d mp
C =√3Cd=√3.0,014=0,91 Lmp k 0,05 V =
.( k )1/4=√2.160000 .( 0,05 )1/4=82,37 EAS √2mg mp ρ , S 3 C 1,225.42 0 d 3.0,014 P C sin γ= Avai − D =¿ 2. 106
−0,056 γ=0,09rad =5,16 degree W . V CL 160000.82,37 0,91
RC = V. sinγ = 82,37.0,09 = 7,413 m/s = 1456 ft/min