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Aero Engineering 315 Lesson 15 3-D (Finite) Wings Part I

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Airfoil Lab Review Due Thursday (lesson 17) Use spreadsheet template (posted on k: drive) Closely follow lab handout directions Review Excel tutorial if needed Compare to published data for NACA 0012 provided in supplemental hand out Re = 3.0 x 10 6 Key Formula: P x = P ref – [ oil x 32.2 x (h x –h ref )/12] Airfoil Lab Spreadsheet

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Lessons 15 and 16 Objectives Define and calculate aspect ratio Explain wing tip effects on lift and drag Describe design techniques to reduce induced drag State which planform shape minimizes induced drag Describe span efficiency factor Calculate the 3-D lift curve slope and lift coefficient Calculate induced and total drag coefficients

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3-D Wing Geometry Aspect Ratio (AR): High ARLow ARTypical Values Fighters:2-5 Transports:6-10 Gliders:10-15

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Wing Twist Wing twist is applied to create a delay in stall for outboard portions of wings Two types of twist: 1. Geometric twist – wing is physically twisted to change the angle-of-attack at the tip 2. Aerodynamic twist – not a physical twist, but a different airfoil at the tip (usually one with a higher stall – i.e. thinner or less camber at tip) Root Angle of Twist Tip

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Remember the A-10? at wing root NACA 6713 at wingtip

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So what’s up with a “real wing”?

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Wingtip Vortices

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upper surface flow (inboard) lower surface flow (outboard) The pressure imbalance at the wingtip sets up a spanwise component of flow, strongest at the tips, weakest in the center. Front View Top View

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A Cessna Citation was flown above a cloud bank at approximately 165 knots. The trailing vortices descended over the fog layer due to downwash, and were made visible by the distortion at the interface.

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Tip effects and lift curve Notice the slope is decreased for the wing, but the zero lift angle of attack is unchanged—these 3-D effects are directly a result of lift (i.e. pressure differential) being created on the wing Airfoil clcl clcl and C L Wing CLCL Caused by: Pressure loss at tip Pressure simply “leaks” to top of the wing Downwash Local flow is diverted down by vortices

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Downwash Spanwise flow comes off each wingtip and creates a trailing vortex. These vortices, in turn, deflect the local flow over the wing downward. This deflection is called “downwash.” One result is reduced lift! V Downwash Effective flow direction over wing eff is the downwash angle

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Induced drag — big picture Wingtip vortex is an unavoidable consequence of wingtips and results in reduced lift & increased drag Induced drag is greatest when the pressure difference between upper and lower surfaces is greatest High angles of attack Takeoff and landing Induced drag will be zero when there is no pressure difference (i.e. at zero lift)

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Next Lesson (16)… Prior to class Complete reading (4.1 – 4.2) In Class Calculate 3-D lift and drag Span efficiency factor Design strategies to minimize induced drag

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