The trouble with the shallow angle is the return. The error in the measurement results in a greater error in the position than if you used the blessed 90.
It's like a pair of swing ties from two close points. You can measure to the 0.001' (+/- 0.01) and your probable solutions will stretch over a range based on the +/- 0.01' from each arc. (Now apply a more reasonable error estimate and you will see the potential solution increase)
You're right that a distance-distance intersection at a shallow angle (near 0 or 180) is bad and intersecting closer to 90 is good.
But I don't see how that applies to the OP situation.
would arbitrarily changing the baseline azimuth to 90 degrees or 45 degrees improve the integrity??"
I realise my error there - we are talking about angles, not azimuths - regardless of the true or assumed azimuth, the angles and therefore, sine values would be the same.
What I'm still wondering is this:
If I turn an angle of say 1'30" and shoot 200m, but missight the target by 5", I assume the error would be the difference between the sine of 1'30" x 200 and 1'35" x 200 which is about 5mm.
If I turn an angle of 45 degrees 1'30" and shoot 200m, but missight the target by 5", the error would again be the difference between the 2, which is less - about 3mm.
Right? Wrong?
Right? Wrong?
I don't want to say right or wrong because I'm not 100% sure I am following the question or that I am right or wrong.
Here is how I am looking at it -
Currently you are using an almost parallel baseline to the points being measured. Lets assume you are shooting a point as you noted at 0d01m30s at 200m. If you are sighting 5s off lets say you measured 0d01m35s. The angular error would be 0d01m35s minus 0d01m30s or 0d0m05s. Take the sin and multiply by 200 to get about 0.005.
Assume you sight a point about perpendicular to the center of the baseline and offset so you get the angle you mentioned of 45d01m30s. If you were off on sighting the target and measured 45d01m35s instead, the angular error would be 45d01m35s minus 45d01m30s or 0d0m05s. If the distance is the same 200m, then the answer would again be 0.005.
If you set up on the point that is perpendicular to the baseline and offset from the baseline and measured an angle that was supposed to be 67d29m35s but sighted it as 67d29m40s, the angular error would be 67d29m40s minus 67d29m35s or 0d0m05s. In this case, the distance should be about 153.115 so the error would be more along the lines of 0.004. However, the difference in the error would be due to the distance changing. If the distance to point was still 200m, the answer would again be 0.005.
The way I am looking at it is that 5" of sighting error at 200m is going to be the same no matter what you have set your backsight reference bearing as. Either angular error or the distance to the point has to change to make the linear error change.
For 1' 30" and that plus 5" (perfect 200 meter distance)
you are off 4.8 mm sideways (let's assume west) and 0 short
For 45 deg and that plus 5"
you are off 3.4 mm west and 3.4 mm south, for a total 4.8 mm error.
Only the distance and angular error are important to the net error, the angle just rotates the error vector.
Thanks to all for putting up with my confusion - I guess i was only considering the error component perpendicular to the baseline - not the "in/out" error which comes in to play with an increased angle.
