Re: Conversions

Thanks to all who replied. I'll try to get out with the Trimble before the snow starts (I won't be able to find the control points if there is snow on the ground)

Rick

KBH wrote:
do nay of you know know to convert Northing and Eastings to Latitude and Longitude. I manage a large (35 Ac.) soccer complex and the fields are laid out in Northing and Eastings. We have a Trimble DGPS unit and I would like to convert to Lat. and Long. However the 3 control points as well as the corners of all the fields are Northings and Eastings. Any help would be greatly appreciated.



As someone already said, the North and East coordinates would have to be projected from latitude and longitude for them to have a conversion back to latitude and longitude...and UTM or State Plane are projected from latitude and longitude.

However, you want to use the GPS to work with the existing local North and East system ? You have a differential GPS system so that the result will be accurately valid ? Okay, set up on two control points and take latitude and longitude readings. Convert the latitude and longitudes to UTM coordinates and inverse UTM grid direction and distance based on the UTM coordinates. Now calculate local grid direction and distance between the same two points using the local North and East coordinates. Now apply a directional rotation to all of the local coordinates so that they have the directional orientation of UTM. Now note the difference between the UTM North coordinate of a control point with the local rotated North coordinate of the control point and do the same with the East coordinates of the same control point. Now apply these differences (as translation) to each local rotated North coordinate and to each local rotated East coordinate. And you're done. Each local North coordinate has been rotated and translated and each local East coordinate has been rotated and translated. Now when a latitiude and longitude reading is taken it can be converted to UTM North and East coordinates and be spotted relative to the rotated and translated local coordinates (which are now approximately UTM)...or a rotated and translated local coordinate can be converted to latitude and longitude with UTM conversion and reached with the GPS.

Formulas:

E1 is the East coordinate of Point1, E2 is the East coordinate of Point2, N1 is the North coordinate of Point1, and N2 is the North coordinate of Point2.

Grid direction of Point1 to Point2 is InvTan((E2 - E1) / (N2 - N1)) . If (E2 - E1) is positive that is East or if negative that is West. If (N2 - N1) is positive that is North or if negative that is South. And this spots direction calculation in a four quadrant system which can then be converted to a navigation bearing.

Grid distance is the Square Root of ((E2 - E1)^2 + (N2 - N1)^2) .

North coordiante grid forward is Cos(Direction) * distance plus the starting North coordinate where Direction is a navigation bearing as an angle clockwise from North.

East coordiante grid forward is Sin(Direction)* distance plus the starting East coordinate where the Direction is a navigation bearing as an angle clockwise from North.

North coordinate rotation from a N,E of 0,0 is Cos(RotatedDirection) * Distance...where the distance is calculated between the N,E of 0,0 and the point to be rotated and where the RotatedDirection is the calulated direction from 0,0 to the point with rotation angle netted to it...

Then the East coordinate rotation is Sin(RotatedDirection) * Distance...


And here is a user link to 'Geodetic/UTM-Grid Utility' :

http://www.kbhscape.com/gps.htm


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