The study of the static longitudinal stability of an airplane is very
important. Longitudinal stability, as we shall see, is intimately
related to the e.g. travel and the loading configuration of an airplane.
In addition the handling characteristics of an airplane in longitudinal
flight are also determined by the static margin.
The well known condition for a longitudinally stable airplane is -
α is the angle of attack and CM
is the moment coefficient about c.g. The condition for neutral stability
is then -
the pitching moment is independent of the angle of attack. In what
follows, it may be shown, that the longitudinal stability creation
for a conventional airplane is closely linked to the c.g. position,
and that the neutral stability condition Eq. (5.A.2) dictates the
almost c.g. location.
pitching moment has contributions from the fuselage, nacelle, wing
and tail. Summed together they appear as may also be calibrated in
a similar manner. The positions of both ailerons are measured and
differential angular positions noted. The rudder position is measured
with the help of a protractor by attaching a pointer to the rudder.
stick force strain gages are calibrated directly by fixing the control
arm and subjecting it to various loads applied through static weights.
calibration curves are given in Fig. 4.5 - 4.10 However, it is necessary
to do your own calibration.
Test Procedure :
condition of stick-fixed neutral stability requires determination
of the c.g. position for which dSe / dCL is
zero. A simple method of doing this in flight is to fly the airplane
for a given c.g. location at various speeds or CL and measure the
corresponding elevator angle to trim. The procedure is repeated for
different c.g. locations. The slope of the Se - CL curves are plotted
against xc.g. and the intersection of this curve with the xc.g. axis
gives the stick fixed neutral point.
free neutral stability the c.g. position is obtained from d(Fs / q)
/ dcL = 0. In flight this is measured by flying the airplane with
a given c.g. location at different speeds (i.e. CL
and q values) and measuring the stick force at each speed. The procedure
is repeated for different c.g. locations. The slope of the (FS
/q) - CL curve is plotted against x c.g axis
gives the stick free neutral point.
alternative method consists of measuring the tab angle required to
trim the airplane at each speed.
points are determined by measuring the elevator deflection angle Se
, airspeed V, stick force FS, or tab angle te.
airspeed may be obtained from the ASI and correcting the readings
using a calibration chart. The elevator angle is measured installing
a potentiometer in the elevator torque tube system so that the elevator
deflection may be transformed to an electrical signal. The potentiometer
is calibrated on the ground by physically measuring the elevator angle
with an inclinometer and plotting it against the potentiometer reading.
stick force may be measured by placing four strain gauges in a bridge
circuit on the stick and sealing it off against moisture and dust.
The signals are amplified before feeding it to an indicator. Calibration
is done by applying known loads to the stick and plotting it against
the flight procedure suggested will enable collection of both the
stick fixed and stick free neutral points together.
turbulence free procedure and a stable prescribed altitude is
chosen and the airplane trimmed at a suitable speed so that
the stick forces, in the entire range of investigation, are
within the pilot's control. This speed may be determined by
trimming the airplane at some speed and checking for the stick
forces by flying at the extreme ends of the range of investigation.
Two or three trials should be sufficient to determine a comfortable
trim speed. This, however, need not be done if the tab is used
to trim the airplane at each speed.
airplane is flown at various speed (and trimmed if t is to be
measured) from rear stall t the maximum attainable speed at
a chosen altitude. When the speed stablizes the readings from
the ASI, elevator potentiometer and the stick forse potentiometer
or the trim tab are taken.
procedure is repeated for different power settings, flap deflections
and various external configurations to obtain a complete picture
of the longitudinal stability of the airplane.
In general both CM and CL
are principally functions of , M, TC and ½
pV2. Therefore, the neutral point is not index of stability with respect
to Se alone but relates to the entire family of trim curves.
curves of Se - CL , Fs/q - CL
may not always turn out to be linear so that the neutral points may
become a function of CL also.
to improve the stick force gradients and the longitudinal stability,
a down spring or a bob weight is attached to the elevator system.
This usually produces a uniform pull force on the stick independent
of speed which is helpful when the airplane is flying with rearward
c.g. positions. However, they are not very satisfactory in ground
operations where the heavy pull force required to keep the stick neutral
may be objectionable.