--- In
BoundaryPoint@yahoogroups.com, "Ron McConnell"
<rcmcc@e...> wrote:
>
> SUBJECT WAS:
> "Decimal digits for Latitude and Longitude: 0.001" Lat/Long"
>
> "aletheiak" asks,
> "could you show more details of your computations?"
>
> Be careful what you ask for. :)
bravo
this is just what i wanted
thanx
& please look for my comments inserted below
>
> ======================================
>
> *** Dave Patton's post to comp.info.gis and
sci.geo.cartography
> with light editing + some info ***
> A)
> Official NAD27 coordinates for two Canada/USA border
monuments:
> M02300 MONUMENT 194 48 59 56.85 117 04 17.79
> M02310 MONUMENT 195 48 59 57.42 117 01 39.71
>
>
<
http://www.internationalboundarycommission.org/coordinates/
M49thp.txt>
>
> B)
> The Canada/USA border is defined as being straight lines
> between border monuments.
> C)
> The NAD83/91 coordinates shown on this plaque
>
> Land Surveyor's Associaton of Washington (LSAW)
> Historical Society Monument #5
>
> STATE PLANE COORDINATES: DEMEYER [?]
the name of the surveyors
& i am with you loud & clear on everything else so far too
as well as on everything from here down to my next insert
> NORTHING: 751827.675 EASTING: 2552579.905
> LATITUDE: N 48º 59' 57.110"
> LONGITUDE: W 117º 01' 56.715"
> ELEVATION: 5932.34 FEET, 1808.182 METERS
> DATUM: NAD 83/91
>
> <http://www.confluence.org/photo.php?visitid=8945&pic=5>
>
> [Lat/Long represent what? No obvious "center" mark.
see the text running down the right column in daves report
roughly midway down the page
http://tinyurl.com/6zgwc
http://www.confluence.org/confluence.php?lat=49&lon=-117&visi
t=4
this postulates
as does the text of the plaque itself
that the coords given on the plaque refer not to any point on the
plaque itself but to the marked center point of the 1909 usgs disk
at the apex of this admittedly peculiar monumental ensemble
& the surveyor himself has confirmed this interpretation to dave
see also his pics 2 & 3
so we are indeed working with 3 known monumented points
no fuzziness at all here
we really do know & have spoken up
more below
> Isn't there usually an inscribed reference point?
> Assume center of plaque until someone
> who really knows speaks up. RCMcC]
>
> What is the 'best' way for a 'recreational user' to
> accurately calculate the distance(north or south)
> between the plaque coordinates and the boundary line?
>
> The distance involved is small, so using typical
> 'recreation-grade' mapping software will not be
> sufficiently accurate.
>
> I'm more interested in learning how to do this myself,
> rather than just having someone who has the facilities
> tell me the answer
>
> Dave Patton
>
>
==================================================
===================
>
> Dave notes that the border is defined
> by the line of sight between monuments.
> There are 3 candidates for the "line of sight":
> (1) great circle (shortest spherical distance,
> constantly varying azimuth along the path),
> (2) rhumb line (constant azimuth along the path,
> greater distance than great circle),
> and (3) WGS-84 ellipsoidal geodesic path
> (more accurate version of great circle
> for earth's non-spherical shape),
> (4) Other?
> For the short distances here,
> there is little practical difference among them.
right & i surmise that the difference is not merely negligible but
would actually be imperceptible within the degree of exactitude of
the coords we are actually working with
namely degminsecs plus only 2 entirely reliable decimal places
for even if the plaque expresses 3 full decimal places rather than
only the 2 & a half i believe it represents
the somewhat coarser ibc coords will limit our overall degree of
certainty to 2 decimal places
isnt that so
which means
tho we can see the precise meridian of idwa as a hairline on the
1909 disk
unless we can actually see the sight line of the ibc markers
we can only hope to find roughly the correct foot
& not really even the correct half foot let alone the correct inch
of the true bcidwa point on the visible meridian
or do you not agree with this preliminary assessment
the submillimetric exactitude of your solution here below seems
to indicate that you dont agree
but based on my computations in messages 14910 & 14912
& even assuming a corrected starting point on the disk rather
than on the plaque as you supposed
i suspect your degree of exactitude may be spurious in at least a
couple of decimal places
if not in all 4 of your significant digits
yikes
tho i cant put my finger on where our analyses diverge
> My GCB program calculates all three.
> Hand calculations for the plane geometry triangle
> agree well with the fancy computer spherical
> triangle stuff for these distances.
>
> But, how to find the north-south distance from
> a 3rd point to an intermediate point on the line
> isn't obvious.
ok
but i still think it is obvious
at least within the above stated parameters of exactitude
it seems entirely reducible to a simple ratio computation as
detailed in the mentioned message 14912
while i admit i dont follow all your maths & notes here below
Fortunately, someone has figured out
> a formula that can be applied.
>
> ==========================
>
> RCMcC
> Angles and Distance greatly distorted.
what do you mean specifically by the above comment
>
> [194] -- 3212 m -- I -- [195]
> \ | /
> 2946 m 267.048 m
> \ /
> [LSAW 5]
>
> ^ North (up) South (down) V
> <- West East ->
>
> ==========================================
>
> PROPOSED RCMcC SOLUTION
>
> Given (all NAD-27 converted to NAD-83 with CORPSCON )
>
> Monument #194 = Point 1 = Lat1/Long1 = N 48.999056º W
117.072683º
> Monument #195 = Point 2 = Lat2/Long2 = N 48.999215º W
117.028771º
> LSAW#5 plaque = Point 3 = Lat3/Long3 = N 48.999197º W
117.032421º
i would agree that 5 decimal digits of whole degrees do seem to
be fully warranted in being roughly equivalent to degminsec plus
2 decimal digits
so this much is probably not garbage
but i think your 6th digit may be questionable for points 1 & 2
still even if i am right
that only confutes 1 or your 4 significant digits
& you are still looking good at about 3 inches due north of the
1909 disk center anyway
i suppose
but it is still magic to me unless you can walk me thru it some
more
>
> TBD
> Where: Great Circle between Points 1 & 2 (GC1-2)
>
> Find intermediate Point I on GC1-2 = LatI/LongI
> that is due north or south of Point 3
> where LongI = Long3 = W 117.032421º
> LatI = TBD from formula from
>
> Ed Williams' Aviation Formulary
>
> <http://williams.best.vwh.net/avform.html>
>
> "Latitude of point on GC"
>
> [edited]
>
> latI = atan(
> ( sin( lat1 ) * cos( lat2 ) * sin( lonI - lon2 )
> - sin( lat2 ) * cos( lat1 ) * sin( lonI - lon1 ) )
> / ( cos( lat1 ) * cos( lat2 ) * sin( lon1 - lon2 ) )
> )
>
> Result:
> Point I = LatI/LongI = N 48.999202º W 117.032421º
> = 0.024 sec lat or 7.473 cm = 2.942 in. due north
> of Point 3 on LSAW #5 plaque {center?]
>
> ============================
>
> I have a draft fortran 77 program
> with all the excruciating details
> which works this problem for these three points.
not sure i want all that
as i am already way over my head
but maybe you can at least show me how i am going wrong in
not expecting or crediting such exactitude as you are delivering
many thanx ron
it is wonderful to even be able to talk to someone who
understands all this
> If this is something BP folks do occasionally,
> it could be generalized to allow variable input
> and worldwide distances, and to take care
> of the special cases where the formula fails.
> I can email the source code and executable file
> to interested parties. Someone can do
> a modern fancy GUI translation.
>
> This approach is all subject to correction,
> of course.
>
> Cheers, 73,
>
> Ron McC.
> w2iol@a...
>
> Ronald C. McConnell, PhD
>
> WGS-84: N 40º 46' 57.6" +/-0.1"
> W 74º 41' 22.1" +/-0.1"
> FN20ps.77GU31 +/-
> V +5058.3438 H +1504.2531
>
> http://home.earthlink.net/~rcmcc
>
> "The first day or so,
> we all pointed to our countries.
> The third or fourth day,
> we were pointing to our continents.
> By the fifth day,
> we were only aware of one Earth."
>
> -Prince Sultan Bin Salmon Al-Saud,
> Saudi Arabian astronaut