Newtonian Aerodynamic Forces from Poisson's Equation.
by J. Pike.
AIAA Journal, Vol 11, No. 4, pp. 499-504, April. 1973.

The aerodynamic forces on convex bodies in Newtonian flow, at any angle of incidence and yaw, are found as analytic solutions to Poisson;s equation. These solutions can be obtained for bodies of any of a wide range of geometries for which the particular integral of the equation can be derived. In the case of bodies for which the extent of the windward surface does not change with incidence or yaw, a simple general analytic expression is found containing four constants of integration. These constants can be obtained either from Newtonian forces calculated at a convenient orientation or from experimental values. Thus the method can be used not only to obtain Newtonian force estimates but also to provide a "near Newtonian" fit to experimental data. In either case, the derivatives of the forces and the maximum value of lift-to-drag ratio can be determined analytically by differentiating. As an example, the maximum lift-to-drag ratio of symmetrical noses is considered.

This paper demonstates the way in which Newton's Impact theory implies universal relations which allow the aerodynamic forces to be derived.

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Last amended: Dec 2013.