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# Coords in Northing and Easting, In Feet--Help!

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I think I need surveyor help on this one...

I thought it would be fun to hunt down all the boundary monuments for my town, and went down to the Town Engineer's Office.

They had a map, but it did not give coords. in Lat/Long or UTM. Instead, it marks each monument with numbers of feet (N) and (W), to 2 decimal places, and the apparent "origin" (0/0 point) appears to be abount .75 mi. (S) and 1.5 mi. (E) of our town.

Apparently these are "surveyor's coordinates" and apparently they can be used to grid our town completely.

I haven't encountered this before. Can someone please tell me where I can go look for an explanation of this type of coordinates? And is there a way I can convert these coordinates into Lat/Long or UTM?

[My town, Winchester, MA, was set off from Woburn in 1852. I stopped by the Woburn City Engineer's Office and received a roughly 16x20" print of a CAD drawing of their city, complete with Lat/Long on each marker and photos of each mark, both from 1899 and from 2002! Wow! They also had a 1899 document, also of folio size, that had the results of the original survey of the city's boundary marks, complete with triangulation diagrams, coords, azimuths, and bearings for each. Wow again!]

Thanks!

-Paul

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Sounds like you can go from your town's coordinate system to UTM is two steps

1) Find the UTM coordinates of the town's origin. You can do this with various on-line aids (used to be Topozone was easy for this, but no more)

2) Convert feet to meters. Remember UTM uses northing and easting, so you'll have to invert the west coordinates.

Add the distance from the origin to the result of step one and you should have your answer for the UTM coordinates of your point.

For something the size of your town, you can ignore spherical corrections. i.e. consider your town a plane surface.

Take a sample point to check your method.

Edited by Papa-Bear-NYC

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Note about previous post: UTM north and the local town north will be different. So if you do get a listing of a few points in the town system that you can also get UTM on, then you will need to do a transformation which will be a scale, translation and rotation. There are a lot of programs around to do that, or it can be done by hand. Then you can take any number of town coordinates and convert them into UTM.

Did the 1899 map show town coordinates? If so you should be able to use it to compute a conversion.

Coordinates like that are very very common as surveyors set up a simple rectangular grid all the time to do their work and computations. It has primarily only been in the last 15 years with GPS that more surveyors are using State Plane coordinate systems with greater regularity.

So what you need is at least 2 points for which you have coordinates in the local system, and you also have geodetic or UTM coordinates. Then a fairly good transformation can be computed. If the map makes it clear what the orientation of the system is relative to true north, then only one point might be able to be used.

We have a similar system in the D.C. area called WSSC coordinates and is based upon 0,0 being the center of the U.S. Capitol Dome. True north is Grid North at the origin. It has been used for a lot of mapping and infrastructure surveys even out into surrounding counties.

- jlw

I think I need surveyor help on this one...

I thought it would be fun to hunt down all the boundary monuments for my town, and went down to the Town Engineer's Office.

They had a map, but it did not give coords. in Lat/Long or UTM. Instead, it marks each monument with numbers of feet (N) and (W), to 2 decimal places, and the apparent "origin" (0/0 point) appears to be abount .75 mi. (S) and 1.5 mi. (E) of our town.

Apparently these are "surveyor's coordinates" and apparently they can be used to grid our town completely.

I haven't encountered this before. Can someone please tell me where I can go look for an explanation of this type of coordinates? And is there a way I can convert these coordinates into Lat/Long or UTM?

[My town, Winchester, MA, was set off from Woburn in 1852. I stopped by the Woburn City Engineer's Office and received a roughly 16x20" print of a CAD drawing of their city, complete with Lat/Long on each marker and photos of each mark, both from 1899 and from 2002! Wow! They also had a 1899 document, also of folio size, that had the results of the original survey of the city's boundary marks, complete with triangulation diagrams, coords, azimuths, and bearings for each. Wow again!]

Thanks!

-Paul

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The program CORPSCON, which you can find a link for on the NGS web site or by web search, may make it easy to do the conversions.

It will do UTM to/from lat-lon and can express the UTM in feet for you if you want. Or use State Plane Coordinates in the same way you would use UTM. It doesn't matter what datum or units you use as long as you are consistent so the correct offset is determined between that system and the local system.

The issue that isn't as clear in my mind is whether you need to deal with the definition of North. In UTM or SPC the direction has to get distorted a little in the operation of flattening out the earth. The grid north in these systems varies with respect to true north as you move around in the grid zone. I would guess the local system was made with the grid north matching true north (line of constant longitude).

Also the scale factor varies slightly, but that is probably of less concern than if the UTM or SPC grid is twisted from true in your neighborhood. Perhaps if I get some time I'll poke around with some examples in your area to see how significant these effects are.

... Now I see jwahl has beat me to the punch as I was pondering and typing. Good for him; he's far more authoritative than me.

Edited by Bill93

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Thanks again you all!

JWahl, yes, the City of Woburn's CAD drawing gives me Lat/Long for 8 points (boundary markers) that are along the common Winchester-Woburn town line.

If I understand Bill93, I can use CORPSCON to convert the Lat/Long for these points to UTM, expressed in feet, and then get from there to a conversion formula for my town N/E coordinate system. I'm not sure how the last step works, however.

I have a feeling that this would be very good experience for me...I would finally understand UTM better .

And Papa-Bear, I don't know where Winchester's origin point is (and so far, they can't enlighten me). I can just tell that it's way outside our boundaries.

-Paul

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I ran an example for two points near Woburn a little over a couple miles apart along a north-south line, all computations at sea level.

N42 28 00 W071 09 00 (NAD83)

N42 30 00 W071 09 00

The INVERSE program says this is 3702.7559 meters = 12,147.479 ft

and the azimuth is exact 0 or 180 degrees.

CORPSCON converts these to UTM zone 19 (72W to 66 W longitude) NAD83 US survey ft

E 1,060,513.876 N 15,432,486.884

E 1,060,821.789 N 15,444,630.915

differences

E 307.913 N 12,144.031 hypotenuse 12,147.934 ft

This distance is 0.45 ft different between geodetic INVERSE and CORPSCON UTM at sea level.

The 308 feet of eastward distance is due to the direction of UTM grid north, which is 1 deg 27' 09" averaged along this line.

Repeating in State Plane Coordinates, zone 2001 Massachusetts Mainland,

E 750,602.629 N2,995,279.334 ft

E 750 552.782 N3,007,427.074

differences

49.847 12,147.740 hypotenuse 12,147.842 ft

convergence angle 0 deg 14' 06.4 sec

This is very slightly closer to matching, but grid versus true north is still off 50 ft in 2.3 miles (opposite direction from UTM). The distance is closer at 0.363 ft difference, as expected also for SPC fit to a smaller zone than UTM.

The answer is YES you do have to apply the angle correction, but not a scale correction for use in a handheld GPS. I would set up a spreadsheet with columns for the given local W and N coordinates, the coordinates rotated around the local origin using sin and cos of the 14' 06.4" angle, the rotated values minus conversion constants (to be found) to get SPC feet. Convert a few of the given lat-lon to SPC for comparison. Try different values for the offset conversion constants until you get a decent match to the known values. Convert the rest to lat-lon using CORPSCON.

The conversion constants will be the local origin location expressed in SPC, with signs depending on whether you took care of the signs in the equations or in the constant values. The origin is customarily outside the area of interest so that users do not have to deal with sign changes around the mapped area.

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