Wind may be a major source of guiding errors when the the telescope structure and particularly the upper part of the telescope tube (cf. 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 the VLT unit telescopes are found in [Zago 89b] and [Alexandrou].