ESDU 91004:2014

$89.05

Pitching moment derivative due to rate of pitch for projectiles at supersonic speeds

Published By	Publication Date	Number of Pages
ESDU	2014-12-01	28

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Category: ESDU

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Description

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.