ESDU 86021:2015

ESDU 86021 is a comprehensive introduction to the concept and
use of derivatives in determining aircraft stability. After
explaining a systematic method for expressing aerodynamic forces,
moments and derivatives in dimensionless form, the equations of
motion for an aircraft treated as a rigid body are developed and
the linearised small-perturbation form introduced. The conditions
are outlined for the separation of the equations into a lateral and
a longitudinal set, and a detailed study is made of the behaviour
of an aircraft disturbed with controls fixed from straight
symmetric level flight. A comprehensive practical worked example
illustrates the use of the techniques. A comparison is made between
the ISO notation for derivatives used by ESDU and the most widely
used notation in the USA, equations are given for deriving the
longitudinal derivatives from the force and moment coefficients,
and reference is included to all the ESDU validated data for
lateral derivatives. Also included is the traditional treatment of
static stability and manoeuvre margins, and the relation between
static and dynamic stability is discussed. A description is given
in simple terms of commonly occurring lateral modes of an aircraft
following a disturbance.

Conversion factors are summarised for aerodynamic derivatives,
for dynamic-normalised concise derivatives, and for obtaining
dynamic-normalised quantities.

A computer program to obtain the roots of the characteristic
equations for the controls-fixed longitudinal and lateral stability
of an aircraft is provided as ESDUpac A8621.