# lect21 - Steady flow: velocity is constant at any point •...

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Zoology 440 Biomechanics 2007 Lecture 21. Flapping flight fundamentals. •Recap lift coefficients, gliding and soaring. •Differentiating steady, quasi-steady and unsteady flows. •Circulation takes time to develop. •Methods of analysis. •Wed -- comments on proposals and their return Real wings have drag as well (from two issues: viscosity of finite span). It’s hard to predict it! Two kinds of drag (profile drag and induced drag). Both depend on shape (A R , camber), Re, angle. . C DP = 2 D / ! S U 2 planform area Drag due to lift C di = C L 2 /(e ! A R ) e ~ 0.8 - 0.9 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1.0 Polar plots of wings C L C D NACA airfoil 19.5 22 0 locust 25 30 0 fly 0 25 30 50 maxium lift to drag ratio is good for gliding http://wings.ucdavis.edu/Book/Nature/beginner/index.html#gliding

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Gliding Weight = mg Drag Lift " U At equilibrium L = m g cos( " ) and D = m g sin ( " ) D/L = sin ( " )/ cos( " ) " = tan -1 (D/L) = tan -1 (C D /C L ) = cot -1 (C L /C D ) Soaring slope soaring wave soaring Thermal Soaring
Thrust from lift on a flapping wing for level flight (no accelerations): the mean upward force = mg the mean forward force = " u 2 S body C D, body /2

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Unformatted text preview: Steady flow: velocity is constant at any point • Quasi-steady flow: velocity varies, but forces equilibrate instantly. e.g. F ~ u 2 . • Unsteady flow: velocity varies, and forces depend upon acceleration, time and other factors. C DP = 2 D / ! S U 2 planform area Drag due to lift C di = C L 2 /(e ! A R ) e ~ 0.8 - 0.9 Quasi-steady blade-element approach: calculate the lift and drag forces on each segment of a wing and sum these over the entire wing at each instant in time. L i =C Di u i 2 S i ! /2 Problem: circulation takes time to develop time # # ~ ( \$ t ) 1/2 The reduced frequency parameter is a measure of the unsteady component % = & L/u oscillatory motion/forward motion A trade-off: high frequency motions lead to high relative velocities (and lift). These only happen with flapping, a motion that necessarily requires changes in the direction of circulation. Mechanisms that promote circulation Clap and fling: Wing rotation (pronation and suppination)...
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## This note was uploaded on 06/03/2008 for the course BIOL 427 taught by Professor Daniels during the Spring '08 term at University of Washington.

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lect21 - Steady flow: velocity is constant at any point •...

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