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Damping Factor



Flight simulators are intended to fairly represent the handling
qualities of the airplane they set out to mimic.
One measure of simulators as of airplanes is dynamic response
to change - of control inputs, or of gusts. Some examples that provide
a reasonable survey of behavior are short and long period
pitching response, yaw damping and spiral behavior.

The measures are familiar to teachers as the damped behavior of
a driven oscillation. To establish the parameters of a system like
y = exp(time/tau)*cos(frequency*time + phi) a particularly simple
calculation involves locating successive peaks of the damped oscillation
and calculating the exponential decay constant ln(A(n+1) - A(n))
from successive peak amplitudes A(n) etc.
dividing this number by a suitable divisor provides an approximation
to the Damping Factor.
This number is often in the range of lightly damped oscillations - as it
might be 0.03

tau the exponential time constant is familiar to electrical engineers.
The time to half amplitude (or half-life), a related number, is familiar
to physicists and chemists.
When evaluating such behavior, the benchmark value is compared
with an allowable range.
Damping, for example might be evaluated in two ways:
half-life (time) +/- 10%
or
Damping Factor +/- 0.02

I am interested that these measures represent different allowable behaviors.
In an aircraft response characterized with a damping factor of say 0.02
an allowable band of +/- 0.025 would I think, allow divergent oscillation,
which is
easily recognizable as different in kind from light damping.
By contrast an allowable time variation in time to half amplitude, seems to
provide
an increasingly stringent requirement on decay envelope slope at increasing
half-lives.
Any thoughts?

Brian Whatcott Altus OK