Jonathan P. How

# Jonathan P. How - 16.333 Handout#1 Prof J P How Due 16.333...

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Unformatted text preview: 16.333 Handout #1 Prof. J. P. How Sept 14, 2004 Due: Sept 28, 2004 16.333 Homework Assignment #1 1. Consider a glider ﬂying in a vertical plane at an angle γ to the horizontal. As we discussed in class, for a glider γ < 0. In a steady glide, the force balance is given by: D + W sin γ = (1) L − W cos γ = (2) The kinematic equations for the system give us that the distance covered along the ground satisfies ˙ x = V cos γ and h ˙ = V sin γ . For small γ we showed that the ﬂight velocity that gives the ﬂattest glide is given by 2 W K V fg = 4 ρS C D where C D = C D + KC 2 L . (a) Show that, for a given height, the distance covered with respect to the ground satisfies dx 1 = = − E R = E Δ h dh γ ⇒ where E = C L /C D and R is the range (assume a constant angle of attack so that E is constant during the glide). What speed does this suggest we should glide at to maximize the range? (b) Now consider the sink rate h ˙ s = − h ˙ . Show that DV h ˙ s ≈ − V γ ≈ = 2 W C D 3 / 2 W ρS C L This suggests that the sink...
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Jonathan P. How - 16.333 Handout#1 Prof J P How Due 16.333...

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