f03_fall

# f03_fall - Fluids Lecture 3 Notes 1 2-D Aerodynamic Forces...

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Fluids – Lecture 3 Notes 1. 2-D Aerodynamic Forces and Moments 2. Center of Pressure 3. Nondimensional Coeﬃcients Reading: Anderson 1.5 1.6 Aerodynamics Forces and Moments Surface force distribution The ﬂuid ﬂowing about a body exerts a local force/area (or stress) f vector on each point of the body. Its normal and tangential components are the pressure p and the shear stress τ . ( magnitude greatly exaggerated) V f f τ R M R L D N A α α p local pressure and shear stress components force/area distribution on airfoil τ r ds r resultant force, and moment about ref. point alternative components of resultant force The figure above greatly exaggerates the magnitude of the τ stress component just to make it visible. In typical aerodynamic situations, the pressure p (or even the relative pressure p p ) is typically greater than τ by at least two orders of magnitude, and so f vector is very nearly perpendicular to the surface. But the small τ often significantly contributes to drag, so it cannot be neglected entirely. The stress distribution f vector integrated over the surface produces a resultant force vector R , and also a moment M about some chosen moment-reference point. In 2-D cases, the sign convention for M is positive nose up, as shown in the figure. Force components The resultant force vector R has perpendicular components along any chosen axes. These axes are arbitrary, but two particular choices are most useful in practice. 1

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Freestream Axes: The vector R components are the drag D and the lift L , parallel and perpendic- ular to vector V . Body Axes: The vector R components are the axial force A and normal force N , parallel and perpendicular to the airfoil chord line. If one set of components is computed, the other set can then be obtained by a simple axis transformation using the angle of attack α . Specifically, L and D are obtained from N and A as follows.
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