I thought about this a while and then did some math. At 15° a 1" change causes a Sine change that is 4 times the value at 45°. But that is pretty inconsequential at the typical traverse distances.
What I do recall is that in typical precise transit work one typically turned and added 3D & 3R on the plate. At 15° one would only cover 1/4 of a full circle so angular errors may be due to the imprecision of the circle. To minimize circle errors one would have to turn 12D & 12R. That many observations introduces other sources of errors.
What say you?
Paul in PA
You could turn 3D & 3R and rotate the lower plate about 120 degrees
between D & R combos to reduce the plate error. It would reduce random errors
from turning so many angles. Or you could just hire Ted...
For a traverse, there is nothing special about 15° or any other angle.
"Weak angles" near 0 and 180 were a concern in triangulation networks, however, because skinny triangles reduce the precision with which distances can be computed throughout the triangulation from the baseline distance(s). This is obviously not an issue in a traverse, though, where the lengths of all lines are directly measured.
Also, when computing points from bearing-bearing intersections and distance-distance intersections, an intersection angle near 0 or 180 provides a big uncertainty (along the semimajor axis) for the computed intersection point. Again, this is not relevant to traverses, since no traverse points are being established by b-b or d-d intersections.
- Doug
Glass Circles for Theodolites and Total Stations
> What say you?
I'd say you ought to consider buying a total station that was manufactured after 1980. Concerns about errors in circle graduation date from quite a bit earlier, back when circles were mechanically divided. There possibly are a few posters whose surveying careers predate etched glass circles engraved using master masks, but wait a few years and count again.
They aren't weak for a traverse with a total station. As I stated the other day and as stated above, they relate to the triangulation and resections. For a total station traverse, make the geometry as acute or obtuse as you please.
Another pervasive myth, right up there with don't erase in a field book (not even on a sketch drawing) and the R/W always gets that perfect number width.
Stephen
If you take an extreem case...
If you have a very small acute angle and 2 long distances, then the distance between the ends of the legs will not be as accurate as if you had an obtuse angle and 2 shorter distances.
Wouldn't the ideal, most accurate simple traverse be a regular polygon?
Hello, Did I Not Say With A Transit ?
I brought this up because I was considering the original source of why 15° was a weak angle. That is specifically because of the way a transit circle was manufactured. I fully understand that because of that the considerations for a modern theodolite are different.
As far as geodetic work the same applies to the early mechanically machined theodolite circles. A typical 16 D&R set (480°) would not even cover two full circles, so the errors are similar.
Next the plans in geodetic surveying were to measure a single precise baseline and use geometry to determine other distances many traverse points away. At that stage the Sine Cosine changes are a concern. Since with modern EDMs and/or GPS we get a precise distance for every observed line, again the geometry is less important.
Please comment on the old methods and technologies.
Paul in PA
15° now and then
> Please comment on the old methods and technologies.
15° wouldn't have been considered a "weak" bearing angle with a surveying compass. If you are using a groma to survey, 15° angles may present a bit more of a problem, however.
>
> Another pervasive myth, right up there with don't erase in a field book (not even on a sketch drawing) and the R/W always gets that perfect number width.
>
Love it, Stephen. There are a lot of those "pervasive myths" running rampant among our profession. We've been too focused on mentoring our field crews on "what" to do and haven't passed down the truer knowledge of "why" we do it.
JBS
Hello, Did I Not Say With A Transit ?
> I brought this up because I was considering the original source of why 15° was a weak angle. That is specifically because of the way a transit circle was manufactured.
Paul,
That is an idea that I have never seen before. Can you provide a citation with some more detail? Or did you decide this yourself?
- Doug
16 D&R
A set of 16 D&R is measured by dividing the half circle into 16 parts and then advancing the plate 11°15'± between each set.
The whole circle is used when reading the reverse.
16 D&R
Dave,
Are you agreeing with Paul that transits measure small angles less precisely than larger angles?
- Doug
A and B verniers on American-style transits
> > I brought this up because I was considering the original source of why 15° was a weak angle. That is specifically because of the way a transit circle was manufactured.
>
> Paul,
>
> That is an idea that I have never seen before. Can you provide a citation with some more detail? Or did you decide this yourself?
Doug, I suspect that Paul is failing to recall that transits were typically fitted with an A and B vernier reading nominally 180° opposite points on the circle. This was done to cancel circle eccentricity errors. The idea that by the early 20th century American transits with machine-divided circles had some large errors in their divisions isn't all that plausible.