Wind may be a major source of guiding errors when
the telescope structure and particularly the
upper part of the telescope tube (see fig. 
)
are exposed to high frequency
fluctuations.
The servo control system of the drives on the two axes of
a modern telescope may have a bandwidth of about 1 to 3 Hz,
effectively compensating quasi-static loads and fluctuating components
up to that frequency.
A possibility to overcome this limitation
will be given in future by servo-controlled tilting secondary mirrors.
Such systems are being developed for the VLT and GEMINI
projects
and should dramatically increase the frequency range
of corrected fluctuations for observations in visible wavelengths.
In the infrared wavelengths however, the requirement for a chopping
secondary mirror may still not be compatible with fast tilt control.
The drives and bearings of a modern telescope are designed to minimize friction and other non-linear effects. Therefore the response of the servo loop to a varying wind loading can be evaluated with good accuracy by a computation in the frequency domain.
Consider the mean aerodynamic torque about one telescope axis y, conventionally defined as:
where 
is the usual expression for dynamic
pressure and 
a torque coefficient determined by wind tunnel tests
or estimated by computation for each orientation of the telescope.
Recalling that the rms
of dynamic pressure 
is
the power spectrum of the aerodynamic torque 
is expressed as:
where is the aerodynamic admittance function for the torque
about axis y,
also determined by wind tunnel tests or computation.
The aerodynamic admittance function represents the low-pass character
of the telescope structure, which averages out the effect of high
frequency turbulence, made of small size vortices.
Then the rms of the guiding error angle 
will be computed as:
where 
is the guiding response function, determined
from the characteristics of the servo loop control systems.
The error 
about the other telescope axis
can be similarly obtained and the total guiding error is then:
The quantities 
and 
will generally depend on the shape of the
telescope and the type of enclosure, and will also be functions of the
orientation angle. They are therefore best evaluated in
wind tunnel tests. Descriptions and data referring to wind tunnel
tests performed for the VLT unit
telescopes are found in [Zago 89b] and [Alexandrou].
