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. :)
======================================
*** 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 [?]
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.
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.
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. Fortunately, someone has figured out
a formula that can be applied.
==========================
RCMcC
Angles and Distance greatly distorted.
[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
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.
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@...
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