Kent
> Didn't you post something along those lines a few year back?
That may have been a thread in which the topic of discussion was "weak" geometry for two-point resections (free stationing). Same song, different verse.
Peter
It would be better to have two 20-foot traverse lines and two 1,000-foot lines in one traverse loop, than it would be to have 12 20-foot traverse lines to go the same loop distance.
I agree that strength-of-figure is a much lesser play in an angle-and-edm-distance traverse. A super-short leg may not be the greatest idea in the world, but remember, too, you can sight much more precisely on your short leg. (say to a tack right smack in the middle of the monument vs. a pole that is not as wide as even your cross-hair.
The question was: what is the definition of the term "weak angle" as it applies to land surveying. I have been in land surveying for 37 years and have heard it often and it has nothing to do with the geometry of the angles. It has everything to do with traverse legs in a traverse that vary widly making the theory of a compass adjustment, where you balance the error of the traverse angles evenly, not work very well.
Merlin
Apologies Moe...
Upon further thought I do agree that the relatively small uncertainty in the distance measurement of a traverse point is quite effective at reducing error ellipse size.
Sorry for any misinformation I may have contributed.
Others are correct in pointing out the difference between a traverse and triangulation position.
Strength of figure is something I can only find reference to in triangulation. I can find no reference in my texts regarding strength of figure and trilateration.
As I stated above, sorry for any misinformation I may have contributed.
Strength of figure is a concern in triangulation not traversing.
to kevin samuel and jeff wright
i am currently working on some mockup LSA data files to demonstrate my assertions.
allow me to recommend the text i often refer to: adjustment computations spatial data analysis by charles ghilani and paul wolf. the text does include a student version of LSA. said version is not as easy to create data files as, say, star net. but the book and LSA are only about $60.
http://surveying.wb.psu.edu/psu-surv/free.htm
will post data files soon
I recently learned that Star*Net has a demo mode for free, limit 10 points but otherwise full functionality. Many thanks to whoever mentioned that!
I used it to run an example with two simple open traverse runs to the same area. Each has two legs from a known fixed point, and all values have the same standard errors of measurement and centering. One has two 65 degree angles. The other has a 179 or 181 degree angle and a 3 degree angle.
There isn't much difference in the 95% confidence ellipses, but the one with extreme angles is actually a trifle better. Something doesn't smell right-how can it be better? I expected them to be nearer the same error. I also tried closing 4-6 with perfect values and huge std errors so it wouldn't really affect the result but would let the least squares have more redundancy to crank on. Same result.
Interesting Bill, thanks for posting this.
>
I didn't notice your experiment the first time around, Kent, and it's been a long time since i studied or used LS analysis, but i'd have to agree with you:
I'd have thought the sizes of the ellipses at 3 and 5 would be identical (but oriented perpendicular to the BS line), and the sizes of the ellipses at 4 and 6 would be (larger than the 1st pair but) also identical.
Strange.
The missing ingredient is how direction was determined. That may influence the error propagation. Can you post the Star*Net data file, or otherwise describe all the constraints?
I think the key to understanding the differences, where you first expect things to be the same, is in the centering error. Whether the targets and instrument are in a straight line or at some other angle affects how the centering errors are leveraged into position uncertainties. Then when those are combined with angle and distance uncertainties, you get various combinations.
# 2D Network
# set origin and orientation
# Coords are North, East
B 1-2 90-0-0 !
C 1 0 0 ! !
C 2 0 200 ! !
# Distances
D 2-3 200
D 3-4 200
D 1-5 200
D 5-6 200
# Angles at-from-to
A 2-1-3 65-00-00
A 3-2-4 65-00-00
A 1-5-2 179-00-00
A 5-6-1 3-00-00
I don't have time to collect the pictures and post them right now. But if you run the example using perfect centering and the given measurement std errors, and then repeat with perfect measurements and given centering, you'll see that the centering is what makes the uncertainty unequal between 3 and 5, and then 4 and 6.
Here are the pictures I referred to showing that it is centering error that gives the unexpected results.
Info from the help section in Star*Net explains their formulas that account for effects of centering, using I and T as the centering std errors of Instrument and Targets.
--------------------
Horizontal Turned Angles: The standard error contribution for an angle due to the horizontal centering error of the instrument is equal to:
Inst StdErr = d3/(d1*d2) * I
Where:
d1 and d2 are the horizontal distances to the targets
d3 is the horizontal distance between the two targets
The standard error contribution for an angle due to the horizontal centering error of both targets is equal to the following:
Target StdErr (Both) = Sqrt(d12+d22) / (d1*d2) * T
Combining the entered standard error for an angle with the standard error contributions from the instrument and target centering, we get the total standard error for an angle:
Total Angle Std Err = Sqrt( AngStdErr^2 + InstStdErr^2 + TargetStdErr^2 )
------------------------
There are some assumptions here. Obviously the results in the real world of setting up a tribrach and leaving it in place while exchanging target and instrument would be different from setting up the tribrachs afresh every time you made a measurement. There seems to be no way to tell the program this, nor to have different centering errors for different stations.
> There seems to be no way to tell the program this, nor to have different centering errors for different stations.
This would be accomplished with the .INST inline option using an instrument you've previously defined in your instrument library as having the desired centering errors.