Managing Systematic and Accidental Angle Measurement Errors

Errors in Observations

Any observation can be affected by two types of errors. One of them is accidental, while the other, systematic, may or may not exist depending on the state of the instrument. Accidental errors, caused by a lack of appreciation of the instrument and the observer, are random; we will never know their exact value, so we are reduced to knowing the maximum value in one or more measurements. Systematic errors may result from poor adjustment of the instrument; they are spread by known laws and are therefore measurable and detectable. They are the most dangerous for the execution of an observation since they are not random.

Checking the Instrument: Angle Meter

Before using an angle meter, we must ensure that:

• The axis of collimation is perpendicular to the axis of trunnions (horizontal collimation error).
• The secondary axis is perpendicular to the main axis (trunnion error).
• The line 100-300 of the blade is horizontal.
• The vertical axis is the horizontal collimation line of the vertical circle 100-300 (vertical collimation error).

Horizontal Collimation Error

This error occurs when there is a lack of perpendicularity between the axis of collimation and the secondary axis (trunnions). To detect it, a point is observed in the telescope positions Circle Direct (CD) and Circle Inverted (CI). The point should have a visual that is virtually horizontal. The average of the observed readings for CD and CI (± 200g) is free from the influence of this error. In this case, the overhead reading done for visual topography can be considered free from error.

Trunnion Error

This error is due to a lack of perpendicularity between the main shaft and the trunnion shaft of the instrument. For detection, observations are used via CD and CI. In this case, the horizontal visual vanishes, so the visual has to be as steep as possible. Similarly to the previous case, the average of CD and CI readings is free from the influence of this error. In this error, as in horizontal collimation, the topographic visual zenith angle can be considered free of error.

Total Azimuthal Effect

The combination of these two errors gives us the potential impact on the horizontal reading. The average between CD and CI is free from error. The observation would first involve the horizontal collimation error, calculating its value, and then showing the trunnion error. By adding to or deducting the value of the horizontal collimation error, we show the deviation of the reading for this error, calculating the tilt of the trunnion axis.

Vertical Collimation Error

For an instrument to be correct, the sum of the overhead readings in CD and CI must be 400g. Otherwise, it may be due to two causes:

1. An eclimeter error or mismatch with the vertical 0g position (lack of a horizontal 100g-300g line).
2. Vertical displacement of the reticle.

In both cases, the sum of CD + CI will not be 400g. The difference in the reading shall be twice the observed error.