from message 7888
> whether the most punctilious possible result requires only the
> simple averaging method i proposed yesterday
> or demands the use of a spherical trig instead
> isnt yet clear to me
> but it seems clear that the difference is practically infinitesimal
>
> & i dont know how exacting you or anyone would care to get
> but since this is primarily your try jay
> that is your decision to make
>
> myself i might at least want to find out if spherical trig isnt truer
> or what the resulting coords would be in that case
> but i havent a clue how to get to those answers
>
> yet since there is a certain degree of approximation already
built
> into either computation
> by the positions of the monuments relative to the river
> if not also by the disparity of their coords
> there may actually be no advantage in using the spherical trig
> even if it is technically the truer method
> since our 10 foot circle target area wouldnt displace very far
> in any case
well jay you may be interested to know
i have finally satisfied myself that this analysis is indeed correct
for tho i havent been able to reinvent the necessary spherical trig
i did realize plane trig will be over 99 percent accurate anyway
& likely even 99 point 99 percent
for such relatively short distances as we are dealing with here
wherein the earth appears to be practically flat
so just to get the best possible estimate
of the distance between the 2 different tripoint positions
which could be computed from the monument positions
by common arithmetic on one hand & spherical trig on the other
i simply calculated the plane trig distance
from the center of the sight line or great circle arc between mons
644 & 645a
to the center of the chord subtending that arc
aka the tripoint position as previously computed
by averaging the coords of the monuments
& based on a distance of 4510 feet between the monuments
as measured from the topo
& a global circumference of 24860 miles
i computed this difference or distance to be
3 inches
& 5 eighths
so within the 10 foot bullseye limitation of most gps receivers
& within the also roughly 10 foot bullseye limitation of our data
this difference is practically negligible
however now that we know approximately what this number is
we may as well improve on our monument averaging coords of
nad27 n45d00m38s3775 by w73d20m40s036
by projecting them these 3 & 5 eighths inches due north
to
nad27 n45d00m38s378 by w73d20m40s036
thus producing the truest 10 foot bullseye presently conceivable
tah taah
&or perhaps ever attainable
coincidentally & amusingly
this gives a result identical to simply rounding off the latitude
from ten thousandths of a second to thousandths of a second
which really needed to be done anyway
since such extreme precision was illusionary & pretentious
in these circumstances
& an aside
directed to brian also
since these 3 or 4 inches are the maximum northering
of the great circle arc between 644 & 645a
in relation to the chord of that arc
then at least the usgs position for the tripoint given in bus&ss
is confirmed to be way too far north
in fact only the shortest imaginable segment
or maybe even no part at all
of the great circle arc
proceeding south of west from 644 to 645a
could ever rise north of monument 644
as i immediately intuited but couldnt articulate til now