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# GIAA Mailbag

January 1, 2004
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Tips on centering errors for dual-axis compensators and sun effects on tubular vials.

Figure 1. An un-level instrument will cause deviation of the optical plumb line.
Q: I have a total station with a dual-axis compensator. As I understand it, it corrects for errors in the vertical and horizontal angles due to tilt of the vertical axis. But what about centering errors? Does the total station account for the fact that the vertical line through the instrument is not truly vertical, and thus not through the point on which the optical plummet is aimed?

A: You are absolutely correct to be concerned. As long as the magnitude and impact of the error is unknown, you will not be confident that the work you do is of sufficient quality. First, you should evaluate the limits of the compensator's range. This will give you some idea of the maximum tilt you might possibly work under. Second, determine the maximum height of your instrument setup. The distance is determined from the survey point to the center of the horizontal circle of your instrument. Third, perform a simple calculation to determine the maximum centering error (see Figure 1). If the maximum tilt range of the compensator is 10 arc minutes and the maximum height is 4.5 feet, then the maximum error will be:

d = tan 10' (4.5 ft) = 0.013 ft.

Note that this is the centering error. Practically, you must now determine the direction of the tilt and then apply that to the direction of every sighting you make to "reduce the observation back to the surveying point." This is a calculation that is explained in most surveying textbooks, usually in the traversing or geodetic survey operations chapters.

You may have a total station with software that can do all this. However, this will require the software to automatically determine the tilt and its direction, and then apply a correction to the observed horizontal angles. If you don't find a description of the correction for centering due to vertical axis tilt and applying the error, it is very unlikely that you have automatic correction for this condition.

Q: I have observed when the sun strikes the tubular (plate) vial on my instrument that it makes the bubble drift. What's going on?

A: A level bubble, whether tubular or circular, has a circular or spherical surface against which it must rest to work. It then reacts to gravity. If the vial is properly adjusted, then its horizontal axis (tubular vial) or horizontal plane (circular vial) is horizontal when the bubble is centered. Bubble drift can occur for two reasons. One is due to differential heating of the instrument itself, where one side expands or contracts more or less than the other side. Generally, an immediate response to the sun striking the vial is more likely due to differential heating of the tube itself. Neither of these conditions is desirable. The impact on the instrument can be reduced by working where direct sun on the instrument is eliminated-by working at night, in cloudy weather or under a sun umbrella. Heat impact on the tube is reduced the same way, but at a minimum avoid judging whether the instrument is level with the sun striking it. This means shading it (the vial) temporarily with your hand, hat, your body's shadow, or the shadow of the instrument itself. An indication that a bubble is off-center when it is struck directly by the sun should not be treated as conclusive evidence that the instrument is not level; wait until the bubble is shaded and let the temperature across the vial equalize. If the instrument is evenly heated (including the vial), then the level continues to provide accurate information.

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