Question

A business jet has a wing area of 88.3 square meters, an aspect ratio of 8.2, an Oswald efficiency factor of .89, a zero-lift drag coefficient of .026, a mass of 19,000 kg, and a maximum static thrust at sea level for each engine of 61,600 N

(A) Calculate the maximum rate of climb at sea level.

(B) Calculate the maximum rate of climb at an altitude of 13 km.

(C) Estimate its absolute ceiling assuming the maximum rate of climb varies linearly with altitude and there are no pressurization/structural issues limiting the aircraft’s ceiling.

Answer 1

wing area, s = 88.3 m^2 AR = 8.2 e = 0.89 c_p/0 = 0.026 M = 19,000kg = 186200 N. T_A = 61,600 N (let it has 2 engines) Total thrust = (2 times 61,600 N) = 123200 N (a) Maximum rate of climb at sea level: Maximum R/C = Maximum excess power/W = P_A-P_R/W P_A = power available P_R = power required \r\n let V_infinity = 50 m/s C_L = 1.38 C_D = C_D middot f C_L^2/ = 0.026 + (1.38)^2/51 times 0.89 times 8.2 = 0.11. Therferore T_R = M/C_L/C_D = 186200 N/(1.38/0.11) = 14842.N P_R = 14892 times 50 = 742100 P_A = 123200 times 50 = 6160000 R/C = 6160000-14842/186200 = 33 m/s (b) At an altitude of 13km, density of air = 0.267 ks/m^3 C_L = 2 times 186200/0.267 times 50 times 50 times 88.3 = 6.32. C_D = C_D middot f + C_L^2/Ohm eAR = 0.026 + (6.32)^2/51 times 0.89 times 8.2 P_R = 186200 times V/(8.32/1.75) = 2607389 (R/C)_max = 6160000-2607389/186200 = 19.08 m/s. (c) Absolute ceilins is that altitude where maximum R/C = 0. At selected max R/C = 33m/s and of 13 km here it is 19.08 m/s, so, 1.08 m/s of loss per km of altitude, so, absolute ceiling for this aircraft will be 17 to 18 km.