I'm trying to average two angle readings with a theodolite by plunging the second reading?

Question

my transit reads continuous from zero to 360...my math isn't turning out so well...and my sources are vague.

Answer 1

Here's a bit of a walkthrough for horizontal angles. If you need to take both horizontal and vertical, it's much the same; only record both your vertical and horizontal readings and take the mean for both sets.

First, you 0-Set on your backsight (The first target), which means your horizontal circle should read 000 00' 00.00" when pointed at the target. Then, turn your angle to the foresight (The second target) and record it. This gives you the first angular value.

Now, without setting your circle to 0 again, you plunge the theodolite so that the sight is now pointing directly away from the foresight. Rotate the horizontal axis in the same direction you turned the previous angle, recording the angular value at both the first and second sight. Determine the angular difference between each set.

Repeat as many times as necessary to achieve your desired level of precision, and determine the mean of all observed values.

As an example, imagine if you had two poles set in the ground, and you wanted to determine the angular value between them from your position. The actual angular value was exactly 90 degrees.

You sight the first pole, and 0-set. When you turn clockwise to the second pole, you read 89 59' 58". You then plunge the instrument, and turn clockwise back to the first pole. There, you read 179 59' 59". Turn clockwise to the second pole, and you record 270 00' 00". When you determine the angular difference between each set, you end up with observed values of 89 59' 58", and 90 00' 01". The mean is then 89 59' 59.5", which is rounded to 90 degrees.

I'd suggest you take more than two observations if your work requires any degree of precision though; I'd feel comfortable with it if you were to give me 6 sets or interiors and exteriors within a few hundredths of each other.