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Calculating LSD converion to GPS Coordinates
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I am working on an app for my Fire Department to help us convert from our Legal Land Description (LSD) system to GPS coordinates. We will use these coordinates to show a point on a Google Maps interface to make responding to Fire Calls a little easier.
Currently there are some free tools such as https://www.lsdfinder.com/map that we use, but they have a limit of 20 lookup per day, and I would like to figure this out for as many people as possible down the line as well.
Some Information
This is a Canadian based system and will only be used to calculate GPS coordinates in our area, but the premise should be editable to other areas. Since our area is quite large, but fully contained within the Third Meridian, we only need to calculate from West of the Third. This sets our starting position at 49.0000°, -106.0000°.
Lets break down what the LSD means.
First lets take a look at an example LSD. It is structured like so: SE 1-15-15 W3. Breaking down what those numbers mean, we get the following (in order)
SE/SW/NE/NW - The QUARTER of the section within the RANGE and TOWNSHIP, split into 4 quadrants. We calculate this last.
1-36 - This is the SECTION inside the RANGE and TOWNSHIP. SECTIONS are 6 x 6 running from bottom left to right, then switching directions as they go up
1-?? = This is the TOWNSHIP, or direction moving NORTH or SOUTH. This is the first calculation and gives your LONGITUDE from the 49° mark.
1-?? = This is the RANGE, or direction moving EAST or WEST. This is the second calculation and gives your LATITUDE from the -106° mark
Here we are going straight up in a line NORTH using our TOWNSHIP from 1 to 17.
SE-1-01-1 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE-1-02-1 W3 = 49.090753° -106.010953° [49° 05' 27" N, 106° 1' 39" W / 13U 426191E 5438037N]
SE-1-03-1 W3 = 49.178087° -106.010949° [49° 11' 41" N, 106° 1' 39" W / 13U 426321E 5447745N]
SE-1-04-1 W3 = 49.265416° -106.010951° [49° 16' 55" N, 106° 1' 39" W / 13U 426451E 5457453N]
SE-1-05-1 W3 = 49.352749° -106.010938° [49° 21' 10" N, 106° 1' 39" W / 13U 426582E 5467162N]
SE-1-06-1 W3 = 49.440101° -106.010959° [49° 26' 24" N, 106° 1' 39" W / 13U 426710E 5476873N]
.... ETC ....
SE 1-14-1 W3 = 50.138980° -106.010563° [NOT CALCULATED / 13U 427786E 5554572N]
SE 1-15-1 W3 = 50.226380° -106.010505° [NOT CALCULATED / 13U 427921E 5564290N]
SE 1-16-1 W3 = 50.313640° -106.010515° [NOT CALCULATED / 13U 428052E 5573992N]
SE 1-17-1 W3 = 50.401041° -106.010490° [NOT CALCULATED / 13U 428186E 5583710N]
As you can see, we have an average increase of LATITUDE by 0.08735 for every additional TOWNSHIP, the third item on the LSD, and that's pretty easy to calculate. But the LONGITUDE is also changing here very slightly. This isn't much, and may be accounted for later, but keep it in mind as it does alter our projections the farther north we move.
Now lets compare the difference in the LATITUDE only first, to see how I got that value
01). 49.003363 - 49 = 0.003363 - 0.003363 = 0.000000 / 0 = 0.0000000000000000
02). 49.090753 - 49 = 0.090753 - 0.003363 = 0.087390 / 1 = 0.0873900000000000
03). 49.178087 - 49 = 0.178087 - 0.003363 = 0.174724 / 2 = 0.0873620000000000 (0.0000280000000000 OR 0.03% less added than 2)
04). 49.265416 - 49 = 0.265416 - 0.003363 = 0.262053 / 3 = 0.0873510000000000 (0.0000390000000000 OR 0.04% less added than 2)
05). 49.352749 - 49 = 0.352749 - 0.003363 = 0.349386 / 4 = 0.0873465000000000 (0.0000435000000000 OR 0.05% less added than 2)
06). 49.440101 - 49 = 0.440101 - 0.003363 = 0.436738 / 5 = 0.0873476000000000 (0.0000424000000000 OR 0.05% less added than 2)
07). 49.527416 - 49 = 0.527416 - 0.003363 = 0.524053 / 6 = 0.0873422666666667 (0.0000477333333333 OR 0.05% less added than 2)
08). 49.614772 - 49 = 0.614772 - 0.003363 = 0.611409 / 7 = 0.0873441428571429 (0.0000458571428571 OR 0.05% less added than 2)
09). 49.702143 - 49 = 0.702143 - 0.003363 = 0.698780 / 8 = 0.0873475000000000 (0.0000425000000000 OR 0.05% less added than 2)
10). 49.789486 - 49 = 0.789486 - 0.003363 = 0.786123 / 9 = 0.0873470000000000 (0.0000430000000000 OR 0.05% less added than 2)
11). 49.876836 - 49 = 0.876836 - 0.003363 = 0.873473 / 10 = 0.0873473000000000 (0.0000427000000000 OR 0.05% less added than 2)
12). 49.964191 - 49 = 0.964191 - 0.003363 = 0.960828 / 11 = 0.0873480000000000 (0.0000420000000000 OR 0.05% less added than 2)
13). 50.051597 - 49 = 1.051597 - 0.003363 = 1.048234 / 12 = 0.0873528333333333 (0.0000371666666667 OR 0.04% less added than 2)
14). 50.138980 - 49 = 1.138980 - 0.003363 = 1.135617 / 13 = 0.0873551538461538 (0.0000348461538462 OR 0.04% less added than 2)
15). 50.226380 - 49 = 1.226380 - 0.003363 = 1.223017 / 14 = 0.0873583571428571 (0.0000316428571429 OR 0.04% less added than 2)
16). 50.313640 - 49 = 1.313640 - 0.003363 = 1.310277 / 15 = 0.0873518000000000 (0.0000382000000000 OR 0.04% less added than 2)
17). 50.401041 - 49 = 1.401041 - 0.003363 = 1.397678 / 16 = 0.0873548750000000 (0.0000351250000000 OR 0.04% less added than 2)
Using our value to calculate LATITUDE (Add (0.08735 * (TOWNSHIP - 1)) + 0.003363 to the 49°) we get the following values, which are within 0.0001°. More than comfortable with this value
SE-1-01-1 W3 = 49.0034°
SE-1-02-1 W3 = 49.0907°
SE-1-03-1 W3 = 49.1781°
.... ETC ....
SE-1-06-1 W3 = 49.4401°
SE-1-07-1 W3 = 49.5275°
We will also compare the difference in the LONGITUDE since they have a minor variations like so
01). 106.011008 - 106 = 0.011008 - 0.011008 = -0.000000 Difference
02). 106.010953 - 106 = 0.010953 - 0.011008 = -0.000055 Difference [-0.000055 different than 1]
03). 106.010949 - 106 = 0.010949 - 0.011008 = -0.000059 Difference [-0.000004 different than 2]
04). 106.010951 - 106 = 0.010951 - 0.011008 = -0.000057 Difference [ 0.000002 different than 3]
05). 106.010938 - 106 = 0.010938 - 0.011008 = -0.000070 Difference [-0.000013 different than 4]
.... ETC .....
14). 106.010563 - 106 = 0.010563 - 0.011008 = -0.000445 Difference [-0.000099 different than 13]
15). 106.010505 - 106 = 0.010505 - 0.011008 = -0.000503 Difference [-0.000058 different than 14]
16). 106.010515 - 106 = 0.010515 - 0.011008 = -0.000493 Difference [ 0.000010 different than 15]
17). 106.010490 - 106 = 0.010490 - 0.011008 = -0.000518 Difference [-0.000025 different then 16]
We have a reliable NORTH to SOUTH or TOWNSHIP calculation now. This will give us a fairly accurate LATITUDE reading, and moving west we can average on a correction of 0.0000326 * TOWNSHIP follow the slight curve of the earth.
Now lets move west with LONGITUDES
SE 1-1-01 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE 1-1-02 W3 = 49.003507° -106.146230° [NOT CALCULATED / 13U 416169E 5428479N] 0.000144
SE 1-1-03 W3 = 49.003540° -106.279948° [NOT CALCULATED / 13U 406389E 5428639N] 0.000033
SE 1-1-04 W3 = 49.003654° -106.412969° [NOT CALCULATED / 13U 396661E 5428824N] 0.000114
SE 1-1-05 W3 = 49.003549° -106.546689° [NOT CALCULATED / 13U 386881E 5429003N] -0.000105
SE 1-1-06 W3 = 49.003557° -106.679919° [NOT CALCULATED / 13U 377138E 5429211N] 0.000008
SE 1-1-07 W3 = 49.003586° -106.813429° [NOT CALCULATED / 13U 367374E 5429439N] 0.000029
SE 1-1-08 W3 = 49.003633° -106.947331° [NOT CALCULATED / 13U 357581E 5429687N] 0.000047
SE 1-1-09 W3 = 49.003647° -107.080852° [NOT CALCULATED / 13U 347817E 5429947N] 0.000014
SE 1-1-10 W3 = 49.003733° -107.214384° [NOT CALCULATED / 13U 338052E 5430233N] 0.000086
SE 1-1-11 W3 = 49.003689° -107.347738° [NOT CALCULATED / 13U 328300E 5430522N] -0.000044
If we can compare the difference in the LONGITUDE only first, noticing that the LATITUDE also has a small variation to it, we get the following
01). 106.011008 - 106.011008 = 0.000000 / 0 = 0.0000000000000000
02). 106.146230 - 106.011008 = 0.135222 / 1 = 0.1352220000000000 - 0.011008 = 0.1242140000000000
03). 106.279948 - 106.011008 = 0.268940 / 2 = 0.1344700000000000 - 0.011008 = 0.1234620000000000
04). 106.412969 - 106.011008 = 0.401961 / 3 = 0.1339870000000000 - 0.011008 = 0.1229790000000000
.... ETC .....
10). 107.214384 - 106.011008 = 1.203376 / 9 = 0.1337084444444444 - 0.011008 = 0.1227004444444444
11). 107.347738 - 106.011008 = 1.336730 / 10 = 0.133673000000000 - 0.011008 = 0.1226650000000000
By adding all of the variables up and averaging them our I get the following values for moving west a RANGE (Should be roughly 9.6km)
$longitude_multiplier = 0.1366567395943563;
$longitude_additional = 0.011008;
$longitude = (((($range - 1) * $longitude_multiplier) + 106) + $longitude_additional);
This gets me somewhat CLOSE, but since I cannot accurately find the percent I need to move north while moving west, and west, while moving north, this has been quite troublesome to calculate.
With my system I am getting the following:
Calculated position for SE-1-13-16 W3
50.0521°, -108.0609°
While the real position is:
SE-1-13-16 W3
50.051496° -108.058235°
As you can see, they are CLOSE, but not close enough.
Does anyone have input on this?
coordinate-system gps geolocation license legal-description
edited 2 mins ago
Vince
14.8k32749
asked 1 hour ago
KaboomKaboom
1011
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I am working on an app for my Fire Department to help us convert from our Legal Land Description (LSD) system to GPS coordinates. We will use these coordinates to show a point on a Google Maps interface to make responding to Fire Calls a little easier.
Currently there are some free tools such as https://www.lsdfinder.com/map that we use, but they have a limit of 20 lookup per day, and I would like to figure this out for as many people as possible down the line as well.
Some Information
This is a Canadian based system and will only be used to calculate GPS coordinates in our area, but the premise should be editable to other areas. Since our area is quite large, but fully contained within the Third Meridian, we only need to calculate from West of the Third. This sets our starting position at 49.0000°, -106.0000°.
Lets break down what the LSD means.
First lets take a look at an example LSD. It is structured like so: SE 1-15-15 W3. Breaking down what those numbers mean, we get the following (in order)
SE/SW/NE/NW - The QUARTER of the section within the RANGE and TOWNSHIP, split into 4 quadrants. We calculate this last.
1-36 - This is the SECTION inside the RANGE and TOWNSHIP. SECTIONS are 6 x 6 running from bottom left to right, then switching directions as they go up
1-?? = This is the TOWNSHIP, or direction moving NORTH or SOUTH. This is the first calculation and gives your LONGITUDE from the 49° mark.
1-?? = This is the RANGE, or direction moving EAST or WEST. This is the second calculation and gives your LATITUDE from the -106° mark
Here we are going straight up in a line NORTH using our TOWNSHIP from 1 to 17.
SE-1-01-1 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE-1-02-1 W3 = 49.090753° -106.010953° [49° 05' 27" N, 106° 1' 39" W / 13U 426191E 5438037N]
SE-1-03-1 W3 = 49.178087° -106.010949° [49° 11' 41" N, 106° 1' 39" W / 13U 426321E 5447745N]
SE-1-04-1 W3 = 49.265416° -106.010951° [49° 16' 55" N, 106° 1' 39" W / 13U 426451E 5457453N]
SE-1-05-1 W3 = 49.352749° -106.010938° [49° 21' 10" N, 106° 1' 39" W / 13U 426582E 5467162N]
SE-1-06-1 W3 = 49.440101° -106.010959° [49° 26' 24" N, 106° 1' 39" W / 13U 426710E 5476873N]
.... ETC ....
SE 1-14-1 W3 = 50.138980° -106.010563° [NOT CALCULATED / 13U 427786E 5554572N]
SE 1-15-1 W3 = 50.226380° -106.010505° [NOT CALCULATED / 13U 427921E 5564290N]
SE 1-16-1 W3 = 50.313640° -106.010515° [NOT CALCULATED / 13U 428052E 5573992N]
SE 1-17-1 W3 = 50.401041° -106.010490° [NOT CALCULATED / 13U 428186E 5583710N]
As you can see, we have an average increase of LATITUDE by 0.08735 for every additional TOWNSHIP, the third item on the LSD, and that's pretty easy to calculate. But the LONGITUDE is also changing here very slightly. This isn't much, and may be accounted for later, but keep it in mind as it does alter our projections the farther north we move.
Now lets compare the difference in the LATITUDE only first, to see how I got that value
01). 49.003363 - 49 = 0.003363 - 0.003363 = 0.000000 / 0 = 0.0000000000000000
02). 49.090753 - 49 = 0.090753 - 0.003363 = 0.087390 / 1 = 0.0873900000000000
03). 49.178087 - 49 = 0.178087 - 0.003363 = 0.174724 / 2 = 0.0873620000000000 (0.0000280000000000 OR 0.03% less added than 2)
04). 49.265416 - 49 = 0.265416 - 0.003363 = 0.262053 / 3 = 0.0873510000000000 (0.0000390000000000 OR 0.04% less added than 2)
05). 49.352749 - 49 = 0.352749 - 0.003363 = 0.349386 / 4 = 0.0873465000000000 (0.0000435000000000 OR 0.05% less added than 2)
06). 49.440101 - 49 = 0.440101 - 0.003363 = 0.436738 / 5 = 0.0873476000000000 (0.0000424000000000 OR 0.05% less added than 2)
07). 49.527416 - 49 = 0.527416 - 0.003363 = 0.524053 / 6 = 0.0873422666666667 (0.0000477333333333 OR 0.05% less added than 2)
08). 49.614772 - 49 = 0.614772 - 0.003363 = 0.611409 / 7 = 0.0873441428571429 (0.0000458571428571 OR 0.05% less added than 2)
09). 49.702143 - 49 = 0.702143 - 0.003363 = 0.698780 / 8 = 0.0873475000000000 (0.0000425000000000 OR 0.05% less added than 2)
10). 49.789486 - 49 = 0.789486 - 0.003363 = 0.786123 / 9 = 0.0873470000000000 (0.0000430000000000 OR 0.05% less added than 2)
11). 49.876836 - 49 = 0.876836 - 0.003363 = 0.873473 / 10 = 0.0873473000000000 (0.0000427000000000 OR 0.05% less added than 2)
12). 49.964191 - 49 = 0.964191 - 0.003363 = 0.960828 / 11 = 0.0873480000000000 (0.0000420000000000 OR 0.05% less added than 2)
13). 50.051597 - 49 = 1.051597 - 0.003363 = 1.048234 / 12 = 0.0873528333333333 (0.0000371666666667 OR 0.04% less added than 2)
14). 50.138980 - 49 = 1.138980 - 0.003363 = 1.135617 / 13 = 0.0873551538461538 (0.0000348461538462 OR 0.04% less added than 2)
15). 50.226380 - 49 = 1.226380 - 0.003363 = 1.223017 / 14 = 0.0873583571428571 (0.0000316428571429 OR 0.04% less added than 2)
16). 50.313640 - 49 = 1.313640 - 0.003363 = 1.310277 / 15 = 0.0873518000000000 (0.0000382000000000 OR 0.04% less added than 2)
17). 50.401041 - 49 = 1.401041 - 0.003363 = 1.397678 / 16 = 0.0873548750000000 (0.0000351250000000 OR 0.04% less added than 2)
Using our value to calculate LATITUDE (Add (0.08735 * (TOWNSHIP - 1)) + 0.003363 to the 49°) we get the following values, which are within 0.0001°. More than comfortable with this value
SE-1-01-1 W3 = 49.0034°
SE-1-02-1 W3 = 49.0907°
SE-1-03-1 W3 = 49.1781°
.... ETC ....
SE-1-06-1 W3 = 49.4401°
SE-1-07-1 W3 = 49.5275°
We will also compare the difference in the LONGITUDE since they have a minor variations like so
01). 106.011008 - 106 = 0.011008 - 0.011008 = -0.000000 Difference
02). 106.010953 - 106 = 0.010953 - 0.011008 = -0.000055 Difference [-0.000055 different than 1]
03). 106.010949 - 106 = 0.010949 - 0.011008 = -0.000059 Difference [-0.000004 different than 2]
04). 106.010951 - 106 = 0.010951 - 0.011008 = -0.000057 Difference [ 0.000002 different than 3]
05). 106.010938 - 106 = 0.010938 - 0.011008 = -0.000070 Difference [-0.000013 different than 4]
.... ETC .....
14). 106.010563 - 106 = 0.010563 - 0.011008 = -0.000445 Difference [-0.000099 different than 13]
15). 106.010505 - 106 = 0.010505 - 0.011008 = -0.000503 Difference [-0.000058 different than 14]
16). 106.010515 - 106 = 0.010515 - 0.011008 = -0.000493 Difference [ 0.000010 different than 15]
17). 106.010490 - 106 = 0.010490 - 0.011008 = -0.000518 Difference [-0.000025 different then 16]
We have a reliable NORTH to SOUTH or TOWNSHIP calculation now. This will give us a fairly accurate LATITUDE reading, and moving west we can average on a correction of 0.0000326 * TOWNSHIP follow the slight curve of the earth.
Now lets move west with LONGITUDES
SE 1-1-01 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE 1-1-02 W3 = 49.003507° -106.146230° [NOT CALCULATED / 13U 416169E 5428479N] 0.000144
SE 1-1-03 W3 = 49.003540° -106.279948° [NOT CALCULATED / 13U 406389E 5428639N] 0.000033
SE 1-1-04 W3 = 49.003654° -106.412969° [NOT CALCULATED / 13U 396661E 5428824N] 0.000114
SE 1-1-05 W3 = 49.003549° -106.546689° [NOT CALCULATED / 13U 386881E 5429003N] -0.000105
SE 1-1-06 W3 = 49.003557° -106.679919° [NOT CALCULATED / 13U 377138E 5429211N] 0.000008
SE 1-1-07 W3 = 49.003586° -106.813429° [NOT CALCULATED / 13U 367374E 5429439N] 0.000029
SE 1-1-08 W3 = 49.003633° -106.947331° [NOT CALCULATED / 13U 357581E 5429687N] 0.000047
SE 1-1-09 W3 = 49.003647° -107.080852° [NOT CALCULATED / 13U 347817E 5429947N] 0.000014
SE 1-1-10 W3 = 49.003733° -107.214384° [NOT CALCULATED / 13U 338052E 5430233N] 0.000086
SE 1-1-11 W3 = 49.003689° -107.347738° [NOT CALCULATED / 13U 328300E 5430522N] -0.000044
If we can compare the difference in the LONGITUDE only first, noticing that the LATITUDE also has a small variation to it, we get the following
01). 106.011008 - 106.011008 = 0.000000 / 0 = 0.0000000000000000
02). 106.146230 - 106.011008 = 0.135222 / 1 = 0.1352220000000000 - 0.011008 = 0.1242140000000000
03). 106.279948 - 106.011008 = 0.268940 / 2 = 0.1344700000000000 - 0.011008 = 0.1234620000000000
04). 106.412969 - 106.011008 = 0.401961 / 3 = 0.1339870000000000 - 0.011008 = 0.1229790000000000
.... ETC .....
10). 107.214384 - 106.011008 = 1.203376 / 9 = 0.1337084444444444 - 0.011008 = 0.1227004444444444
11). 107.347738 - 106.011008 = 1.336730 / 10 = 0.133673000000000 - 0.011008 = 0.1226650000000000
By adding all of the variables up and averaging them our I get the following values for moving west a RANGE (Should be roughly 9.6km)
$longitude_multiplier = 0.1366567395943563;
$longitude_additional = 0.011008;
$longitude = (((($range - 1) * $longitude_multiplier) + 106) + $longitude_additional);
This gets me somewhat CLOSE, but since I cannot accurately find the percent I need to move north while moving west, and west, while moving north, this has been quite troublesome to calculate.
With my system I am getting the following:
Calculated position for SE-1-13-16 W3
50.0521°, -108.0609°
While the real position is:
SE-1-13-16 W3
50.051496° -108.058235°
As you can see, they are CLOSE, but not close enough.
Does anyone have input on this?
coordinate-system gps geolocation license legal-description
edited 2 mins ago
Vince
14.8k32749
asked 1 hour ago
KaboomKaboom
1011
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I am working on an app for my Fire Department to help us convert from our Legal Land Description (LSD) system to GPS coordinates. We will use these coordinates to show a point on a Google Maps interface to make responding to Fire Calls a little easier.
Currently there are some free tools such as https://www.lsdfinder.com/map that we use, but they have a limit of 20 lookup per day, and I would like to figure this out for as many people as possible down the line as well.
Some Information
This is a Canadian based system and will only be used to calculate GPS coordinates in our area, but the premise should be editable to other areas. Since our area is quite large, but fully contained within the Third Meridian, we only need to calculate from West of the Third. This sets our starting position at 49.0000°, -106.0000°.
Lets break down what the LSD means.
First lets take a look at an example LSD. It is structured like so: SE 1-15-15 W3. Breaking down what those numbers mean, we get the following (in order)
SE/SW/NE/NW - The QUARTER of the section within the RANGE and TOWNSHIP, split into 4 quadrants. We calculate this last.
1-36 - This is the SECTION inside the RANGE and TOWNSHIP. SECTIONS are 6 x 6 running from bottom left to right, then switching directions as they go up
1-?? = This is the TOWNSHIP, or direction moving NORTH or SOUTH. This is the first calculation and gives your LONGITUDE from the 49° mark.
1-?? = This is the RANGE, or direction moving EAST or WEST. This is the second calculation and gives your LATITUDE from the -106° mark
Here we are going straight up in a line NORTH using our TOWNSHIP from 1 to 17.
SE-1-01-1 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE-1-02-1 W3 = 49.090753° -106.010953° [49° 05' 27" N, 106° 1' 39" W / 13U 426191E 5438037N]
SE-1-03-1 W3 = 49.178087° -106.010949° [49° 11' 41" N, 106° 1' 39" W / 13U 426321E 5447745N]
SE-1-04-1 W3 = 49.265416° -106.010951° [49° 16' 55" N, 106° 1' 39" W / 13U 426451E 5457453N]
SE-1-05-1 W3 = 49.352749° -106.010938° [49° 21' 10" N, 106° 1' 39" W / 13U 426582E 5467162N]
SE-1-06-1 W3 = 49.440101° -106.010959° [49° 26' 24" N, 106° 1' 39" W / 13U 426710E 5476873N]
.... ETC ....
SE 1-14-1 W3 = 50.138980° -106.010563° [NOT CALCULATED / 13U 427786E 5554572N]
SE 1-15-1 W3 = 50.226380° -106.010505° [NOT CALCULATED / 13U 427921E 5564290N]
SE 1-16-1 W3 = 50.313640° -106.010515° [NOT CALCULATED / 13U 428052E 5573992N]
SE 1-17-1 W3 = 50.401041° -106.010490° [NOT CALCULATED / 13U 428186E 5583710N]
As you can see, we have an average increase of LATITUDE by 0.08735 for every additional TOWNSHIP, the third item on the LSD, and that's pretty easy to calculate. But the LONGITUDE is also changing here very slightly. This isn't much, and may be accounted for later, but keep it in mind as it does alter our projections the farther north we move.
Now lets compare the difference in the LATITUDE only first, to see how I got that value
01). 49.003363 - 49 = 0.003363 - 0.003363 = 0.000000 / 0 = 0.0000000000000000
02). 49.090753 - 49 = 0.090753 - 0.003363 = 0.087390 / 1 = 0.0873900000000000
03). 49.178087 - 49 = 0.178087 - 0.003363 = 0.174724 / 2 = 0.0873620000000000 (0.0000280000000000 OR 0.03% less added than 2)
04). 49.265416 - 49 = 0.265416 - 0.003363 = 0.262053 / 3 = 0.0873510000000000 (0.0000390000000000 OR 0.04% less added than 2)
05). 49.352749 - 49 = 0.352749 - 0.003363 = 0.349386 / 4 = 0.0873465000000000 (0.0000435000000000 OR 0.05% less added than 2)
06). 49.440101 - 49 = 0.440101 - 0.003363 = 0.436738 / 5 = 0.0873476000000000 (0.0000424000000000 OR 0.05% less added than 2)
07). 49.527416 - 49 = 0.527416 - 0.003363 = 0.524053 / 6 = 0.0873422666666667 (0.0000477333333333 OR 0.05% less added than 2)
08). 49.614772 - 49 = 0.614772 - 0.003363 = 0.611409 / 7 = 0.0873441428571429 (0.0000458571428571 OR 0.05% less added than 2)
09). 49.702143 - 49 = 0.702143 - 0.003363 = 0.698780 / 8 = 0.0873475000000000 (0.0000425000000000 OR 0.05% less added than 2)
10). 49.789486 - 49 = 0.789486 - 0.003363 = 0.786123 / 9 = 0.0873470000000000 (0.0000430000000000 OR 0.05% less added than 2)
11). 49.876836 - 49 = 0.876836 - 0.003363 = 0.873473 / 10 = 0.0873473000000000 (0.0000427000000000 OR 0.05% less added than 2)
12). 49.964191 - 49 = 0.964191 - 0.003363 = 0.960828 / 11 = 0.0873480000000000 (0.0000420000000000 OR 0.05% less added than 2)
13). 50.051597 - 49 = 1.051597 - 0.003363 = 1.048234 / 12 = 0.0873528333333333 (0.0000371666666667 OR 0.04% less added than 2)
14). 50.138980 - 49 = 1.138980 - 0.003363 = 1.135617 / 13 = 0.0873551538461538 (0.0000348461538462 OR 0.04% less added than 2)
15). 50.226380 - 49 = 1.226380 - 0.003363 = 1.223017 / 14 = 0.0873583571428571 (0.0000316428571429 OR 0.04% less added than 2)
16). 50.313640 - 49 = 1.313640 - 0.003363 = 1.310277 / 15 = 0.0873518000000000 (0.0000382000000000 OR 0.04% less added than 2)
17). 50.401041 - 49 = 1.401041 - 0.003363 = 1.397678 / 16 = 0.0873548750000000 (0.0000351250000000 OR 0.04% less added than 2)
Using our value to calculate LATITUDE (Add (0.08735 * (TOWNSHIP - 1)) + 0.003363 to the 49°) we get the following values, which are within 0.0001°. More than comfortable with this value
SE-1-01-1 W3 = 49.0034°
SE-1-02-1 W3 = 49.0907°
SE-1-03-1 W3 = 49.1781°
.... ETC ....
SE-1-06-1 W3 = 49.4401°
SE-1-07-1 W3 = 49.5275°
We will also compare the difference in the LONGITUDE since they have a minor variations like so
01). 106.011008 - 106 = 0.011008 - 0.011008 = -0.000000 Difference
02). 106.010953 - 106 = 0.010953 - 0.011008 = -0.000055 Difference [-0.000055 different than 1]
03). 106.010949 - 106 = 0.010949 - 0.011008 = -0.000059 Difference [-0.000004 different than 2]
04). 106.010951 - 106 = 0.010951 - 0.011008 = -0.000057 Difference [ 0.000002 different than 3]
05). 106.010938 - 106 = 0.010938 - 0.011008 = -0.000070 Difference [-0.000013 different than 4]
.... ETC .....
14). 106.010563 - 106 = 0.010563 - 0.011008 = -0.000445 Difference [-0.000099 different than 13]
15). 106.010505 - 106 = 0.010505 - 0.011008 = -0.000503 Difference [-0.000058 different than 14]
16). 106.010515 - 106 = 0.010515 - 0.011008 = -0.000493 Difference [ 0.000010 different than 15]
17). 106.010490 - 106 = 0.010490 - 0.011008 = -0.000518 Difference [-0.000025 different then 16]
We have a reliable NORTH to SOUTH or TOWNSHIP calculation now. This will give us a fairly accurate LATITUDE reading, and moving west we can average on a correction of 0.0000326 * TOWNSHIP follow the slight curve of the earth.
Now lets move west with LONGITUDES
SE 1-1-01 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE 1-1-02 W3 = 49.003507° -106.146230° [NOT CALCULATED / 13U 416169E 5428479N] 0.000144
SE 1-1-03 W3 = 49.003540° -106.279948° [NOT CALCULATED / 13U 406389E 5428639N] 0.000033
SE 1-1-04 W3 = 49.003654° -106.412969° [NOT CALCULATED / 13U 396661E 5428824N] 0.000114
SE 1-1-05 W3 = 49.003549° -106.546689° [NOT CALCULATED / 13U 386881E 5429003N] -0.000105
SE 1-1-06 W3 = 49.003557° -106.679919° [NOT CALCULATED / 13U 377138E 5429211N] 0.000008
SE 1-1-07 W3 = 49.003586° -106.813429° [NOT CALCULATED / 13U 367374E 5429439N] 0.000029
SE 1-1-08 W3 = 49.003633° -106.947331° [NOT CALCULATED / 13U 357581E 5429687N] 0.000047
SE 1-1-09 W3 = 49.003647° -107.080852° [NOT CALCULATED / 13U 347817E 5429947N] 0.000014
SE 1-1-10 W3 = 49.003733° -107.214384° [NOT CALCULATED / 13U 338052E 5430233N] 0.000086
SE 1-1-11 W3 = 49.003689° -107.347738° [NOT CALCULATED / 13U 328300E 5430522N] -0.000044
If we can compare the difference in the LONGITUDE only first, noticing that the LATITUDE also has a small variation to it, we get the following
01). 106.011008 - 106.011008 = 0.000000 / 0 = 0.0000000000000000
02). 106.146230 - 106.011008 = 0.135222 / 1 = 0.1352220000000000 - 0.011008 = 0.1242140000000000
03). 106.279948 - 106.011008 = 0.268940 / 2 = 0.1344700000000000 - 0.011008 = 0.1234620000000000
04). 106.412969 - 106.011008 = 0.401961 / 3 = 0.1339870000000000 - 0.011008 = 0.1229790000000000
.... ETC .....
10). 107.214384 - 106.011008 = 1.203376 / 9 = 0.1337084444444444 - 0.011008 = 0.1227004444444444
11). 107.347738 - 106.011008 = 1.336730 / 10 = 0.133673000000000 - 0.011008 = 0.1226650000000000
By adding all of the variables up and averaging them our I get the following values for moving west a RANGE (Should be roughly 9.6km)
$longitude_multiplier = 0.1366567395943563;
$longitude_additional = 0.011008;
$longitude = (((($range - 1) * $longitude_multiplier) + 106) + $longitude_additional);
This gets me somewhat CLOSE, but since I cannot accurately find the percent I need to move north while moving west, and west, while moving north, this has been quite troublesome to calculate.
With my system I am getting the following:
Calculated position for SE-1-13-16 W3
50.0521°, -108.0609°
While the real position is:
SE-1-13-16 W3
50.051496° -108.058235°
As you can see, they are CLOSE, but not close enough.
Does anyone have input on this?
coordinate-system gps geolocation license legal-description
edited 2 mins ago
Vince
14.8k32749
asked 1 hour ago
KaboomKaboom
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I am working on an app for my Fire Department to help us convert from our Legal Land Description (LSD) system to GPS coordinates. We will use these coordinates to show a point on a Google Maps interface to make responding to Fire Calls a little easier.
Currently there are some free tools such as https://www.lsdfinder.com/map that we use, but they have a limit of 20 lookup per day, and I would like to figure this out for as many people as possible down the line as well.
Some Information
This is a Canadian based system and will only be used to calculate GPS coordinates in our area, but the premise should be editable to other areas. Since our area is quite large, but fully contained within the Third Meridian, we only need to calculate from West of the Third. This sets our starting position at 49.0000°, -106.0000°.
Lets break down what the LSD means.
First lets take a look at an example LSD. It is structured like so: SE 1-15-15 W3. Breaking down what those numbers mean, we get the following (in order)
SE/SW/NE/NW - The QUARTER of the section within the RANGE and TOWNSHIP, split into 4 quadrants. We calculate this last.
1-36 - This is the SECTION inside the RANGE and TOWNSHIP. SECTIONS are 6 x 6 running from bottom left to right, then switching directions as they go up
1-?? = This is the TOWNSHIP, or direction moving NORTH or SOUTH. This is the first calculation and gives your LONGITUDE from the 49° mark.
1-?? = This is the RANGE, or direction moving EAST or WEST. This is the second calculation and gives your LATITUDE from the -106° mark
Here we are going straight up in a line NORTH using our TOWNSHIP from 1 to 17.
SE-1-01-1 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE-1-02-1 W3 = 49.090753° -106.010953° [49° 05' 27" N, 106° 1' 39" W / 13U 426191E 5438037N]
SE-1-03-1 W3 = 49.178087° -106.010949° [49° 11' 41" N, 106° 1' 39" W / 13U 426321E 5447745N]
SE-1-04-1 W3 = 49.265416° -106.010951° [49° 16' 55" N, 106° 1' 39" W / 13U 426451E 5457453N]
SE-1-05-1 W3 = 49.352749° -106.010938° [49° 21' 10" N, 106° 1' 39" W / 13U 426582E 5467162N]
SE-1-06-1 W3 = 49.440101° -106.010959° [49° 26' 24" N, 106° 1' 39" W / 13U 426710E 5476873N]
.... ETC ....
SE 1-14-1 W3 = 50.138980° -106.010563° [NOT CALCULATED / 13U 427786E 5554572N]
SE 1-15-1 W3 = 50.226380° -106.010505° [NOT CALCULATED / 13U 427921E 5564290N]
SE 1-16-1 W3 = 50.313640° -106.010515° [NOT CALCULATED / 13U 428052E 5573992N]
SE 1-17-1 W3 = 50.401041° -106.010490° [NOT CALCULATED / 13U 428186E 5583710N]
As you can see, we have an average increase of LATITUDE by 0.08735 for every additional TOWNSHIP, the third item on the LSD, and that's pretty easy to calculate. But the LONGITUDE is also changing here very slightly. This isn't much, and may be accounted for later, but keep it in mind as it does alter our projections the farther north we move.
Now lets compare the difference in the LATITUDE only first, to see how I got that value
01). 49.003363 - 49 = 0.003363 - 0.003363 = 0.000000 / 0 = 0.0000000000000000
02). 49.090753 - 49 = 0.090753 - 0.003363 = 0.087390 / 1 = 0.0873900000000000
03). 49.178087 - 49 = 0.178087 - 0.003363 = 0.174724 / 2 = 0.0873620000000000 (0.0000280000000000 OR 0.03% less added than 2)
04). 49.265416 - 49 = 0.265416 - 0.003363 = 0.262053 / 3 = 0.0873510000000000 (0.0000390000000000 OR 0.04% less added than 2)
05). 49.352749 - 49 = 0.352749 - 0.003363 = 0.349386 / 4 = 0.0873465000000000 (0.0000435000000000 OR 0.05% less added than 2)
06). 49.440101 - 49 = 0.440101 - 0.003363 = 0.436738 / 5 = 0.0873476000000000 (0.0000424000000000 OR 0.05% less added than 2)
07). 49.527416 - 49 = 0.527416 - 0.003363 = 0.524053 / 6 = 0.0873422666666667 (0.0000477333333333 OR 0.05% less added than 2)
08). 49.614772 - 49 = 0.614772 - 0.003363 = 0.611409 / 7 = 0.0873441428571429 (0.0000458571428571 OR 0.05% less added than 2)
09). 49.702143 - 49 = 0.702143 - 0.003363 = 0.698780 / 8 = 0.0873475000000000 (0.0000425000000000 OR 0.05% less added than 2)
10). 49.789486 - 49 = 0.789486 - 0.003363 = 0.786123 / 9 = 0.0873470000000000 (0.0000430000000000 OR 0.05% less added than 2)
11). 49.876836 - 49 = 0.876836 - 0.003363 = 0.873473 / 10 = 0.0873473000000000 (0.0000427000000000 OR 0.05% less added than 2)
12). 49.964191 - 49 = 0.964191 - 0.003363 = 0.960828 / 11 = 0.0873480000000000 (0.0000420000000000 OR 0.05% less added than 2)
13). 50.051597 - 49 = 1.051597 - 0.003363 = 1.048234 / 12 = 0.0873528333333333 (0.0000371666666667 OR 0.04% less added than 2)
14). 50.138980 - 49 = 1.138980 - 0.003363 = 1.135617 / 13 = 0.0873551538461538 (0.0000348461538462 OR 0.04% less added than 2)
15). 50.226380 - 49 = 1.226380 - 0.003363 = 1.223017 / 14 = 0.0873583571428571 (0.0000316428571429 OR 0.04% less added than 2)
16). 50.313640 - 49 = 1.313640 - 0.003363 = 1.310277 / 15 = 0.0873518000000000 (0.0000382000000000 OR 0.04% less added than 2)
17). 50.401041 - 49 = 1.401041 - 0.003363 = 1.397678 / 16 = 0.0873548750000000 (0.0000351250000000 OR 0.04% less added than 2)
Using our value to calculate LATITUDE (Add (0.08735 * (TOWNSHIP - 1)) + 0.003363 to the 49°) we get the following values, which are within 0.0001°. More than comfortable with this value
SE-1-01-1 W3 = 49.0034°
SE-1-02-1 W3 = 49.0907°
SE-1-03-1 W3 = 49.1781°
.... ETC ....
SE-1-06-1 W3 = 49.4401°
SE-1-07-1 W3 = 49.5275°
We will also compare the difference in the LONGITUDE since they have a minor variations like so
01). 106.011008 - 106 = 0.011008 - 0.011008 = -0.000000 Difference
02). 106.010953 - 106 = 0.010953 - 0.011008 = -0.000055 Difference [-0.000055 different than 1]
03). 106.010949 - 106 = 0.010949 - 0.011008 = -0.000059 Difference [-0.000004 different than 2]
04). 106.010951 - 106 = 0.010951 - 0.011008 = -0.000057 Difference [ 0.000002 different than 3]
05). 106.010938 - 106 = 0.010938 - 0.011008 = -0.000070 Difference [-0.000013 different than 4]
.... ETC .....
14). 106.010563 - 106 = 0.010563 - 0.011008 = -0.000445 Difference [-0.000099 different than 13]
15). 106.010505 - 106 = 0.010505 - 0.011008 = -0.000503 Difference [-0.000058 different than 14]
16). 106.010515 - 106 = 0.010515 - 0.011008 = -0.000493 Difference [ 0.000010 different than 15]
17). 106.010490 - 106 = 0.010490 - 0.011008 = -0.000518 Difference [-0.000025 different then 16]
We have a reliable NORTH to SOUTH or TOWNSHIP calculation now. This will give us a fairly accurate LATITUDE reading, and moving west we can average on a correction of 0.0000326 * TOWNSHIP follow the slight curve of the earth.
Now lets move west with LONGITUDES
SE 1-1-01 W3 = 49.003363° -106.011008° [49° 00' 12" N, 106° 1' 40" W / 13U 426058E 5428322N]
SE 1-1-02 W3 = 49.003507° -106.146230° [NOT CALCULATED / 13U 416169E 5428479N] 0.000144
SE 1-1-03 W3 = 49.003540° -106.279948° [NOT CALCULATED / 13U 406389E 5428639N] 0.000033
SE 1-1-04 W3 = 49.003654° -106.412969° [NOT CALCULATED / 13U 396661E 5428824N] 0.000114
SE 1-1-05 W3 = 49.003549° -106.546689° [NOT CALCULATED / 13U 386881E 5429003N] -0.000105
SE 1-1-06 W3 = 49.003557° -106.679919° [NOT CALCULATED / 13U 377138E 5429211N] 0.000008
SE 1-1-07 W3 = 49.003586° -106.813429° [NOT CALCULATED / 13U 367374E 5429439N] 0.000029
SE 1-1-08 W3 = 49.003633° -106.947331° [NOT CALCULATED / 13U 357581E 5429687N] 0.000047
SE 1-1-09 W3 = 49.003647° -107.080852° [NOT CALCULATED / 13U 347817E 5429947N] 0.000014
SE 1-1-10 W3 = 49.003733° -107.214384° [NOT CALCULATED / 13U 338052E 5430233N] 0.000086
SE 1-1-11 W3 = 49.003689° -107.347738° [NOT CALCULATED / 13U 328300E 5430522N] -0.000044
If we can compare the difference in the LONGITUDE only first, noticing that the LATITUDE also has a small variation to it, we get the following
01). 106.011008 - 106.011008 = 0.000000 / 0 = 0.0000000000000000
02). 106.146230 - 106.011008 = 0.135222 / 1 = 0.1352220000000000 - 0.011008 = 0.1242140000000000
03). 106.279948 - 106.011008 = 0.268940 / 2 = 0.1344700000000000 - 0.011008 = 0.1234620000000000
04). 106.412969 - 106.011008 = 0.401961 / 3 = 0.1339870000000000 - 0.011008 = 0.1229790000000000
.... ETC .....
10). 107.214384 - 106.011008 = 1.203376 / 9 = 0.1337084444444444 - 0.011008 = 0.1227004444444444
11). 107.347738 - 106.011008 = 1.336730 / 10 = 0.133673000000000 - 0.011008 = 0.1226650000000000
By adding all of the variables up and averaging them our I get the following values for moving west a RANGE (Should be roughly 9.6km)
$longitude_multiplier = 0.1366567395943563;
$longitude_additional = 0.011008;
$longitude = (((($range - 1) * $longitude_multiplier) + 106) + $longitude_additional);
This gets me somewhat CLOSE, but since I cannot accurately find the percent I need to move north while moving west, and west, while moving north, this has been quite troublesome to calculate.
With my system I am getting the following:
Calculated position for SE-1-13-16 W3
50.0521°, -108.0609°
While the real position is:
SE-1-13-16 W3
50.051496° -108.058235°
As you can see, they are CLOSE, but not close enough.
Does anyone have input on this?
coordinate-system gps geolocation license legal-description
coordinate-system gps geolocation license legal-description
edited 2 mins ago
Vince
14.8k32749
asked 1 hour ago
KaboomKaboom
1011
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 mins ago
Vince
14.8k32749
asked 1 hour ago
KaboomKaboom
1011
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 mins ago
Vince
14.8k32749
edited 2 mins ago
Vince
14.8k32749
edited 2 mins ago
Vince
14.8k32749
14.8k32749
asked 1 hour ago
KaboomKaboom
1011
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
KaboomKaboom
1011
asked 1 hour ago
KaboomKaboom
1011
1011
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Kaboom is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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