ESDU Engineer

Body Aerodynamics

Normal force and pitching moment of non-axisymmetric bodies: square and triangular cross-sections without corner rounding

ESDU 04007 presents a semi-empirical estimation method for normal force and pitching moment of forebody-cylinder combinations whose cross-sections are either a square or an equilateral triangle, without corner rounding. The method is derived from test data for bodies with mostly tangent-ogival and some conical profile forebodies. However, the method can, with care, be applied to other forebody profiles, such as paraboloidal, ellipsoidal and secant-ogival, and some spherically-blunted shapes.

It is assumed that the variation with angle of attack of both normal force and pitching moment may be represented using the classic two-component model. The first component is a linear contribution, which is calculated by applying a theoretical factor to estimated values of normal-force-curve and pitching-moment-curve slopes for an equivalent circular body. The second component is obtained from a correlation of experimentally-derived values of the cross-flow drag coefficient. These are presented for square bodies at zero and 45 degrees of roll angle (‘diamond shape’) and for triangular bodies at zero and 60 degrees of roll angle (‘point up’ and ‘point down’) as a function of cross-flow Mach number. Data for both square and triangular bodies at intermediate roll angles are used to derive a factor to allow predictions to be made for any roll angle. The use of the method of this Item for prediction of normal force generally results in an estimate to within about 15% of the experimental value. Use of the method for prediction of centre of pressure position will generally result in an estimate to within about 0.05 of overall body length of the experimental value for bodies of square cross-section and within about 0.07 for bodies of triangular cross-section.

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Geometrical characteristics of typical bodies.

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Normal force, pitching moment and side force of forebody-cylinder combinations for angles of attack up to 90 degrees and Mach numbers up to 5.

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Normal-force-curve and pitching-moment-curve slopes of forebody-cylinder combinations at zero angle of attack for Mach numbers up to 5.

ESDU 90034
Computer program for the calculation of normal force and pitching moment of forebody-cylinder combinations at angles of attack up to 90 degrees and Mach numbers up to 5, including conical boat-tailing.