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Unformatted text preview: AOE 3104 Homework #4 Solutions Problem 1. A sailplane of mass 500 kg has an aspect ratio AR = 22 and a wingspan b = 15 m. The drag parameter values are C D = 0 . 01 and K = 0 . 015. The glider is released at 3,000 m on a standard day. Estimate the best range and best endurance in still air. State your assumptions clearly. Solution. The range in gliding flight is R = Δ h parenleftbigg C L C D parenrightbigg so maximum range occurs when L/D is maximum, i.e., for C L = C L md = radicalbigg C D K = 0 . 8165 and C D = C D md = 2 C D = 0 . 0200 Substituting values, we find R = 122 . 5 km. Assuming that L = W cos γ ≈ W and approximating the density the constant value ρ = ρ (1500 m) = 1 . 0581 kg / ft 3 , we have E ≈ Δ h radicalbigg ρS 2 W C (3 / 2) L C D Endurance in gliding flight is maximum for constant power flight conditions, i.e., for C L = C L mp = radicalbigg 3 C D K = 1 . 4142 and C D = C D mp = 4 C D = 0 . 0400 Substituting values, we find E = 1 . 16 hours. To test our assumptions, first notice that γ = arctan( C D mp /C L mp ) = 1 . 62 ◦ so it is quite reasonable to assume cos γ ≈ 1. We may check the assumption of constant density by breaking the descent into to phases of 1500 meters each, and using some average density over the respective segments. Doing so, and using densities at 2200 and 800 meters, respectively, we still find that E = 1 . 16 hours, so the assumption of constant density is reasonable for this problem. Problem 2. A business jet has the following parameter values b = 50 ft , S = 325 ft 2 , C D = 0 . 015 , e = 0 . 85 . The maximum weight is 20,000 lb, which includes the full fuel capacity of 1000 gallons (at a fuel density of 6.67 lb/gal). Each of the twin engines can produce a maximum 3500 lb of thrust at sea level. The weight specific fuel consumption is γ t = 0 . 55 (lb fuel / hr) / lb thrust . Find the maximum range and the maximum endurance at sea level (constant altitude) for filght at a constant angle of attack....
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This document was uploaded on 02/05/2012.
 Fall '09

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