Cavern in Feet

[Lev Bishop]

On 10/26/07, John B. Halleck <john.halleck at utah.edu> wrote:
> [Lev Biship makes a long winded argument that the difference between the
> types of feet makes no difference in practice.]

I really wasn't intending to make that argument, I just can't resist
figuring out how hard one would have to work in order for the
difference to be relevant. Sorry if it came across differently.
Sometimes it's worth making a very accurate survey, for whatever
reason (I've heard cases where people wanted to use an industrial hole
boring machine to drill into a very small cavern at the end of a long
cave, for example; or maybe you want to measure to a sump from both
ends in order to decide if it might be free-divable -- we have a case
like that in spain, where properly accounting for the (small) magnetic
declination drift over the years of the survey brings the two ends of
the sump much much closer on the survey). It's quite possible that for
large surveys, performed very carefully, even very tiny systematic
errors can really add up. Also, future surveying technology (laser
rangefinders and the like) might reduce the random errors further. We
want survex to be future-proof. So I did a back-of-the-envelope
calculation in my previous email, that came to the conclusion that the
difference between the definitions of the foot was far below what is
likely to matter for standard surveying technique, but it is not
beyond what can be achieved with sufficient care (even if you limit
yourself to 1920's technology).

Being a self-confessed accuracy-nerd, I would very much like to own an
invar tape, so I can see how inaccurate my other measures are :-)
Although I suspect they probably cost some thousands of dollars, so I
doubt I'll be buying one any time soon. If I did have one, I see that
NIST would be happy to calibrate it for me, up to 60m, "at cost",
using their fancy temperature-controlled interferometric setup:
http://ts.nist.gov/MeasurementServices/Calibrations/length.cfm#tapes
The calibration is to 2 parts per million "expanded uncertainty",
corresponding to a standard deviation of less than 1 ppm.

> For example, the Colorado North State Plane Coordinate system has an origin
> OVER TWO MILLION  FEET west of a lot of the region covered in the zone.  In
> 2,000,000 feet the difference between the feet add up...  and the difference
> is large enough to be measured by even a drug store tape measure.
> Maybe you were going for humor with your comments, but the difference
> between 2,000,000 "International" feet and 2,000,000 Survey feet doesn't
> need in invar tape to detect.
>
> It seems to me if someone wants to play by the technical legal rules, they
> should be allowed to without people arguing against it.

I never intended to argue against meeting the legal requirements. But
since you brought it up, I don't actually see how the foot definition
used by survex can be relevant, even in the presence of the offset of
2*10^6 feet which you described. If have I something like:
*units fixedpoint feet ; I forget the exact syntax
*fix entrance1 2000000 2000000 0 ; entrance in N. Colorado SPC, with a
large offset in feet
*fix entrance2 2000100 2000100 0 ; ditto
<survey data with tape distances in feet, metres, furlongs or whatever>

When I process those data in survex, won't everything come out
correctly, regardless of whether survex interprets "feet" as survey
feet or international feet? After all the large offset is just an
offset and everything survex does is with the relative coordinates.
(And survex uses double-precision floating point, so even with that
offset of 2 million feet, it still has nanometre resolution -- if it
used single-precision there would be a problem since it would only
have a few centimetres of resolution in the presence of such a large
offset).

In order for the difference to matter wouldn't you have to be using
fixed points using _both_ kinds of feet in the same survey? And
wouldn't that never happen, because each state/region chooses either
survey feet or international feet for their legal coordinates, not
both? What would be an actual cave-surveying situation where it would
matter?

Lev