• All conversions from millivolts to arcseconds are : 20"/mV.
• There is no evidence for a temperature dependence in the scales.
• The time constants are sufficiently short that full accuracy is achieved after a small number (2) of seconds.

Inclinometer scales

Our inclinometers are 701-series products of Applied Geomechanics Inc. The manufacturer's dossier I have is for the meter with serial number 354. They measure tilts in 2 orthogonal directions, and they are operated at the JCMT in differential mode, as opposed to single-ended mode. The latter used the ground as a reference voltage; the former is almost entirely protected against spurious voltage noise, but loses a factor of 2 in the scale factor. They are also operated in low gain , giving a range of approximately 0.5 degrees from the horizontal, and a scale of approximately 0.05 microradians per millivolt, or 20mV = 1". This is an average of the X- and Y- scales for this meter; X is actually 19.6, and Y is 20.4.

These scales are confirmed to this accuracy (+-2%) by calibration experiments - see particularly the figures , but we note that the manufacturer's calibrations were done at 20 deg C, whilst our own confirmatory experiments were undoubtedly taken under cooler conditions.

Zero-points and Temperature effects
The scale factor of tilt with temperature is K_s = 0.05% per degree C, typical, and the zero-points are expected to be stable to within K_Z = 0.3" per deg C, typical.

The third output channel from the inclinometers is intended to supply a voltage proportional to the temperature. The scale is quoted by the manufacturer as 0.1 degrees C per mV (10mV/degree). Prior to June 1997 there were a limited number (8) of data ports betweeen the antenna leg temperature monitoring system and the VAXes. The temperature from the inclinometer located on the TMU platform was not recorded before that date. Earlier analyses provided (quadratic) relationships between the inclinometer temperatures and the antenna leg temperatures, but are really only somewhat related (see also a more recent comparison ). In any case we really want to correct the inclinometry data for the temperature of the inclinometers. Additionally, different thermal response times of the legs and the inclinometers make using such relationships positively dangerous if sub-arcsecond accuracy is desired.

It remains, perhaps, to be demonstrated that inclinometry taken under different thermal conditions can be reconciled by appropriate corrections using the temperature data.

Expected errors if no thermal correction is applied
The inclinometers are rather roughly levelled when relocated; this means output readings of +-300mV or so. They subsequently experience tilts of +- 20" or so; +- 400mV. The zero-points often settle, or perhaps wander with temperature, but a reading of + or - 1000mV would signal a need for a re-levelling in any case. From one inclinometry run to the next, however, and making comparisons for one azimuth at a time, the expected drift in any inclinometer reading will probably not exceed 200mV. If such measures are taken at the same temperature, no systematic difference occurs. However, if the temperature difference is, say, T degrees C the corresponding difference in tilt will be no more than

              (0.0005 per degree) * (200mV) * T degrees / (10 (mv/"))     = 0.01*T"        .

Time constants
The maufacturer's specifications also say ;
"After an instantaneous change in tilt, the output signal settles to 90% of its final value after 3 time constants, and to 98% of this value after 4 time constants."
The time constant is quoted as 0.5 seconds. Our standard operating procedures allows the elapse of 4 seconds (= 8 time constants) between the end of a telescope slew and the output signal sampling.