Cavern in Feet

[Lev Bishop]

On 10/23/07, David A. Riggs <david.a.riggs at gmail.com> wrote:
> On 10/23/07, Graham Mullan <graham.mullan at wotcc.org.uk> wrote:
> > Ah but which feet do you use, The international foot or the US survey
> > foot? I gather the latter is 610 nm longer than the former.
> >
>
> Being a nation firmly rooted in science, we've standardized on The
> President's foot, a size 10.5 running shoe - it was his idea!  ;-)
>
> Considering that this difference on the longest shot I'd ever consider
> taking underground is three orders of magnitude smaller than the most
> precise measurement I can make with a fiberglass tape (tenth or
> twentieth foot), I'd say that it doesn't matter for a cave survey
> which foot is used.

For most surveys it doesn't matter. But, if you take 60 foot legs, and
measure with a s.d. of 0.0144foot (you'd get that by measuring to the
nearest 1/20 foot), then the systematic error from using "the wrong
foot" will surpass the random error from the tape, at the point where
you have a mere 14400 legs in your survey. (At this point, your survey
will be 163 miles long, and the length error in question will be about
2 feet).

In practice of course there are likely to be other sources of
systematics. For example, a standard class II fibreglass tape is
usually calibrated to 0.0002, and even a class I steel tape is only
calibrated to 0.0001, so you'd need to have spread your surveying over
2500 different tapes for the systematic error from the tapes not to be
dominant over the systematics from using the wrong foot. Of course,
class I is not the limit of accuracy for tape-measured surveys. It's
possible to do a lot better than that. For example, for his
experiments on measuring the speed of light, A A Michelson asked the
US Coast and Geodetic Survey to measure the distance between his
observatory on Mount Wilson and San Antonio peak. This survey was
undertaken, by triangulation, in 1923. For the baseline for the
triangulation, a length of some 40km was measured using 8 measuring
tapes, with a random error of about 3.5mm (one part in 11 million) and
a probable calibration error of one part in 2 million. So, if you
expect to get that kind of accuracy and you decide to work in feet,
then you'll definitely want to be sure of which definition of the foot
you are using, else your systematic error will be some 20 times worse
than your measurement error. There's an interesting description of the
techniques used on the 1923 survey:
http://adsabs.harvard.edu/abs/1927ApJ....65...14B

Graham, since it was you who brought up the need to distinguish the US
survey foot from the international foot, I am curious to hear more
about your survey technique. In particular, where do you buy your
invar tape measures? (And how much did you pay for them?) I have never
seen them listed in any suppliers' catalogue (neither with metres
marking nor with foot markings (US or international)).

Lev