Is it true that:
If one uses BD-FD/FR-BR sets in a traverse, that the zenith angles at point 1 to point 2 plus the zenith angle of the backsight from point 2 to point one, should equal 180 degrees exactly?
If it should be, but it's not, is the "Vertical 0 Datum" calibration of the instrument a factor?
The B/D zenith angles to *each* point should add up to 360. The zenith angles to the backsight are unrelated to the zenith angles to the foresight.
Is your instrument height equal to your target height?
The height of the instrument and reflector play a huge role in what the zenith angle is.
Making an association between set ups is problematic.
Jim Frame, post: 328502, member: 10 wrote: The B/D zenith angles to *each* point should add up to 360. The zenith angles to the backsight are unrelated to the zenith angles to the foresight.
I misread the original question. As has been noted, HI/HR at different setups will almost guarantee that you won't get 180å¡ when adding up the zeniths from those setups.
Jim Frame, post: 328506, member: 10 wrote: I misread the original question. As has been noted, HI/HR at different setups will almost guarantee that you won't get 180å¡ when adding up the zeniths from those setups.
Sorry for not making that clear: Assume HI/HR are identical.
I'd have to say NO (although there are scenarios where they might).
The effects of Earth Curvature, terrestrial refraction, and deflection of the vertical, would make it unlikely (except on VERY short lines).
Loyal
Loyal, post: 328522, member: 228 wrote: I'd have to say NO (although there are scenarios where they might).
The effects of Earth Curvature, terrestrial refraction, and deflection of the vertical, would make it unlikely (except on VERY short lines).
Loyal
Assume very short lines (less than 250').
I guess I should re-phrase the question.
Theoretically, they should add up to 180 degrees. But, as a practical matter, if it's off, is the vertical datum compensation adjustment on the instrument a factor? I thought not, if you're using both faces. I thought that eliminates that as a source of error. Is this adjustment irrelevant if you're shooting both faces?
The compensation adjustment should be done to get the direct and reverse zenith angle readings in ONE setup to ONE target to add up to 360. If it is off a little, that's no big deal when you are averaging direct and reverse in each measurement.
Getting the height of the instrument to match in a second setup is difficult. Calculate it - 5 seconds at 250 ft is 0.006 ft, which is not easy to repeat in a second setup, and the angle gets worse for shorter sights. The other factors Loyal mentions are of course also real, but probably secondary to the setup difficulty. Again, you can calculate them. Find the curvature and refraction equations. See how fast the deflection of the vertical changes in your area (probably negligible in a mile except in mountains).
Bill93, post: 328534, member: 87 wrote:
Getting the height of the instrument to match in a second setup is difficult.
The setups in question are all "zero centering"...on proper instrument tripods with tribrachs. I've made this grasshopper's life easier already by using/making all of my prism heights to the tribrach three pin puck identical to my instrument height, so I don't think that's a significant source of error. I recently started looking at these angles closely, and noticed what I thought might have been blunders (more than a minute at 250')...that's nearly a tenth, and thought it might have to do with the vertical datum adjustment. I'm now thinking not.
rfc, post: 328557, member: 8882 wrote: The setups in question are all "zero centering"...on proper instrument tripods with tribrachs. I've made this grasshopper's life easier already by using/making all of my prism heights to the tribrach three pin puck identical to my instrument height, so I don't think that's a significant source of error. I recently started looking at these angles closely, and noticed what I thought might have been blunders (more than a minute at 250')...that's nearly a tenth, and thought it might have to do with the vertical datum adjustment. I'm now thinking not.
Set up an instrument and prism on tripods say 10m apart.
Input instrument and target heights the same eg zero.
Measure zenith angle or vertical distance between them and then swap them over. Repeat measurement.
The two vertical distance measurements should be the same but opposite sign.
One zenith angle should equal 180 - the other.
If not then your instrument and prisms are not adjusted to the same height above the tribrach.
Over longer distances (> 150m ?) refraction becomes an issue.
Reciprocal measurements will give different vertical distances.
If the measurements a re near simultaneous then (VD1 - VD2)/2 gives the correct vertical distance
You could see if if the two points were a long distance apart. Assuming the earth were a perfect sphere, vertical from the center of the earth out to each point would be like a big "V" from the center of the earth. The Zenith Angles would add up to be Greater than 180 degrees. Another way to put it, is if you were @ the exact same elevation on both "setups" each zenith angle would be slightly greater than 90å¡. For the most part, if were were doing common traverse distances, the difference is insignificant, and you indeed can make that assumption.