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In recent years there has been extensive research on three-dimensional flow separation. There are two different approaches: the phenomenological approach and a mathematical approach using topology. These two approaches are reviewed briefly and the shortcomings of some of the past works are discussed. A comprehensive approach applicable to incompressible and compressible steady-state flows as well as incompressible unsteady flow is then presented. The approach is similar to earlier topological approaches to separation but is more complete and in some cases adds more emphasis to certain points than in the past. To assist in the classification of various types of flow, nomenclature is introduced to describe the skin-friction portraits on the surface. This method of classification is then demonstrated on several categories of flow to illustrate particular points as well as the diversity of flow separation. The categories include attached, two-dimensional separation and three different types of simple, three-dimensional primary separation, secondary separation, and compound separation. Hypothetical experiments are utilized to illustrate the topological terminology and its role in characterizing these flows. These hypothetical experiments use colored oil injected onto the surface at singular points in the skin-friction portrait. Actual flow-visualization information, if available, is used to corroborate the hypothetical examples.

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Methods now used to obtain aerodynamic coefficients from free-flight data introduce assumptions and limitations into the equations of motion (e.g., linear aerodynamics, small amplitudes of oscillation, constant roll rate, etc.) so that closed-form solutions can be obtained. Experimental free-flight data are then "fit" by adjusting coefficients and initial conditions in these expressions. A method described herein eliminates the need for closed-form solutions by employing numerical solutions to the equations of motion. This makes possible a far more general treatment. A least-squares technique employing differential corrections must be used; for this, partial derivatives of each dependent variable with respect to each unknown coefficient, including all initial conditions, must be known accurately at every data station. Application of the method of parametric differentiation yields the required accuracy in these partial derivatives and rapid convergence of the solution is usually obtained. Four cases are presented to illustrate specific points: 1) linear aerodynamics, duplication of existing methods; 2) nonlinear aerodynamics, simultaneous analysis of four ballistic-range flights of models of the Gemini capsule; 3) varying freestream density along a trajectory; and 4) large amplitude (to 40° resultant angle of attack) rolling motion of a trimmed Apollo Command Capsule model.

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