ESDU 91004 gives a semi-empirical method for estimating the derivative for an axisymmetric forebody-cylinder combination with or without boat-tailing and fins. Slender body theory provides an equation for the sum of the pitching moment derivatives due to pitch rate and due to acceleration in heave that is modified empirically to correlate tunnel and range data extracted from the literature. It involves the normal-force-curve slope which is obtained from ESDU 89008 with correction from ESDU 87033 for the effect of boat-tailing. To obtain the pitch rate derivative@ the slender body prediction for the derivative due to acceleration in heave is subtracted from the predicted sum; that requires the pitching-moment-curve slope also obtained from ESDU 89008 and 87033. For the body alone@ predictions are within 20 per cent of the experimental values. It is noted that higher values of the acceleration in heave derivative can arise when transition occurs at the base@ but values for the sum of the derivatives predicted by ESDU 91004 are conservative and apply when transition is near the pitching axis; this effect does not influence the pitch rate derivative. Range data had a greater scatter than tunnel data and it is suggested that incorrect Magnus effect corrections could cause that. A method is suggested for including the effect of fins@ which is empirical and based on limited data. It involves modifying the body alone prediction and using ESDU 70012 to obtain the normal-force-curve slope@ ESDU 91007 for body interference@ and ESDU 70012 for the aerodynamic centre of the surfaces. Worked examples illustrate the use of the method and sketches show typical correlations achieved.
ESDU 91004 A-2014 history
2014ESDU 91004 A-2014 Pitching moment derivative due to rate of pitch for projectiles at supersonic speeds