Heinz Schwinge (The Accuracy of Cave Survey, NSS Bull., Vol. 24, No. 1, Jan. 1962) showed that, given the accuracies of length and angle measurements, there is an optimum shot length. This occurs when the error due to angle measurement is the same as the error due to length measurement. He considered only horizontal measurements and did not consider station position error. You can look at the situation in several ways. Given some combination of angle error, length error, or shot length, what should you do for the others?
Given the compass and clinometer errors that cannot be improved upon, there is no need for overly precise length measurements. One meter or one foot is not good enough. I use the next smaller tape markings even though they are better than needed. I do not record any finer measurements. It is possible to go the other way with angle measurements that are too accurate.
I have notes from a surface survey with turning angles measured to 0.1 arcseconds and distances measured to 1 meter.
It is possible, under ideal conditions, to get reproducible measurements to 0.1 or 0.2 degrees. I managed this on the DC Grotto compass course. The ultimate limiting factor, even with a perfect compass, is the variation of magnetic north during the day.
From the DC Grotto compass course data I found that the standard deviation between what Suunto compasses consider to be magnetic north is 0.55 degrees. In my paper at the 2000 NSS Convention I compared cave surveys to BCRA Grade 5. No cave survey met the Grade 5 standard. The closest was Hamilton Cave, an easy horizontal maze. I suspect the reason it did not meet the Grade 5 standard is that there was no compass calibration to see their different magnetic norths.
I was notetaker on a surface survey where one person read the same set of instruments for both foresights and backsights. The readings were consistently within a +/-1 degree limit
driggs wrote:I am not qualified to comment on this, but perhaps someone else is... I believe that the
BCRA survey grades actually define standard deviations for instrument slop rather than hard values. Can someone (Bob Thrun?) expand further on this point?
Edit: Despite what I had inferred from the
Survex data format, it appears that this is not the case. See:
http://bcra.org.uk/surveying/
The 1976 BCRA Grades said "Angles accurate to +/-1 degree". This is the wording of the machine shop, not that of statistics. I interpreted the limits as hard limits. Anything out the limits is unacceptable while anything within the limits is equally acceptable. I used a uniform distribution for my paper at the 2000 NSS Convention. Others interpreted the wording to mean 1 or 3 standard deviations Almost nobody tried to establish that their readings were accurate enough. In practice, anyone who used instruments marked in 1-degree increments claimed Grade 5. The grades were revised in 2002 to match actual practice: "Angles measured to +/-1 degree". I wrote an article that touches our present topic in Compass Points 31
http://www.chaos.org.uk/survex/cp/CP31/CP31.pdf The same issue has a letter of mine commenting on differences between compasses and compass readers.
The BCRA Grades and the CRG Grades before them specify station position error. It is difficult to put the target and instruments at exactly the same place. The position error will affect the readings on short shots more than long shots.