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Unformatted text preview: AA311: Atmospheric Flight Mechanics Lecture 14 Dr. Laszlo Techy University of Washington Department of Aeronautics & Astronautics November 04, 2011 Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Aircraft performance Aircraft performance deals with questions like: What is the maximum speed? What is the minimum speed? How fast can the aircraft climb to a given altitude? How far can it fly on a tank of fuel? How long can it stay in the air? What is the minimum takeoff speed? What is the minimum takeoff & landing distance? Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Aircraft performance Refresher: Drag polar: C D = C D + C 2 L π e AR . Straight and level flight: T = D L = W Lift L = 1 2 ρ ∞ V 2 ∞ SC L Drag D = 1 2 ρ ∞ V 2 ∞ SC D Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Thrust required Substituting L = W , we have V ∞ = s 2 W ρ ∞ SC L From this relationship we see that squared speed scales directly with weight, inversely with lift coefficient, inversely with density. Dividing T = D with L = W gives T W = D L = ⇒ T = D L W Hence, to counter the weight of the airplane in level flight the airplane’s engines have to generate T R = W C L / C D Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Thrust required Thrust required T R = W C L / C D To obtain T R as a function of V ∞ : 1 Choose a value of V ∞ . 2 For this value of V ∞ calculate te lift coefficient from C L = W 1 2 ρ ∞ V 2 ∞ S . 3 Calculate C D from C D = C D + C 2 L π e AR . 4 Use T R = W C L / C D to calculate the required thrust. Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Anderson’s CP1 airplane Consider an airplane with parameters b = 35 . 8 ft S = 174 ft 2 W = 2950 lb C D = 0 . 025 e = 0 . 8 Typical general aviation, such as Cessna 182. Will call this CP1. Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Thrust required T R = T R ( V ∞ ) = W C L / C D . Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Thrust required Thrust required: T R = T R ( V ∞ ) = W C L / C D Can we find the minimum drag flight speed? Recall: T R = D That is, minimum drag equals minimum thrust required. Can we find the maximum lifttodrag ratio flight condition? Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Quest for maximum L / D The lifttodrag ratio is a function of angle of attack. Using the drag polar, the lifttodrag ratio becomes C L C D = C L C D + KC 2 L Find the derivative; set it to zero: d dC L C L C D = d dC L C L C D + KC 2 L = C D KC 2 L ( C D + KC 2 L ) 2 = 0 Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Quest for maximum L / D Optimal lift coefficient: C L ( L / D ) max = r C D K Maximum L/D L D max = C L C D max = 1 2 p KC D Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Quest for maximum L / D Optimal lift coefficient: C L ( L / D ) max = r C D K Maximum L/D L D max = C L C D max = 1 2 p KC D Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Angle of attack Different points along the thrustrequired curve...
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 Fall '09

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