• Introduction
• Example: The Bassett Creek Tract, Georgia, U.S.A.

Property Surveying

by Jim Herod

Introduction

This Maple application computes the perimeter of a tract of land based on the latitude and longitude measurements marking its corners. The distance formula used comes from http://jan.ucc.nau.edu/~cvm/latlongdist.html  This formula is not a Great Circle Distance Formula. However, the Great Circle Distance for points as close together as those in a tract of farm land will not differ appreciably from the straight line formula. There is probably more error due to the topography of the terrain.

Example: The Bassett Creek Tract, Georgia, U.S.A.

Along the Old Line Road at North 31 degrees, 40.203 minutes, West 87 degrees, 39.639 minutes take a dirt road on the west side. At 0.1 miles into this dirt road, there is a fork in the road. Either fork leads into the property. The left fork enters the property on the south side, the right fork enters the property on the east side.

If you proceed on the right fork, at 0.5 miles from Old Line Road, there is a side road to the right. Continue straight ahead. At 0.8 miles from Old Line Road, there is a side road to the left. Continue straight ahead. You enter the property at 1.1 miles from Old Line Road.

If you proceed on the left fork, at 0.4 miles you exit what in 2003 was F. E. Glen's property. At 0.5 miles there is a side road to the left, at 0.9 miles take the left fork, at 1.2 miles take the right fork, and at 1.3 miles take the right fork. You enter the property at 1.6 miles from Old Line Road

We found stakes in the ground at

         North 31 degrees 40.506 minutes, West 87 degrees 41.035 minutes,

         North 31 degrees 40.619 minutes, West 41 degrees 41.010 minutes,

         North 31 degrees 40.725 minutes, West 87 degrees 40.524 minutes.

The South East corner of this property coincides with a Section Corner. We found a small sign attached to a tree stating that this is a Section Corner. The sign was marked T 8, R 4, Sec 9. The location of the corner is

        North 31 degrees 40.287 minutes, West 87 degrees 40.520 minutes.

What follows is a map of the property. Also distances are computed along the property lines starting from the southwest corner, moving northward, and indicating distances for each straight line.

>	restart;with(plots):

Warning, the name changecoords has been redefined

>	data:= [[31,40.296,87,41.041],[31,40.506,87,41.035],         [31,40.507,87,41.013],[31,40.619,87,41.010],         [31,40.616,87,40.777],[31,40.681,87,40.775],         [31,40.725,87,40.524],[31,40.287,87,40.520],         [31,40.296,87,41.041]]:

>	pts:=[seq([-data[i][4],data[i][2]],i=1..9)]:

>	Map:=plot(pts,scaling=constrained): roads:=textplot({[-40.749,40.290,`R`],[-40.522,40.591,`R`]}):

>	display([Map,roads]);

>	Digits:=20:

>

for n from 1 to 8 do LatA:=data[n][1]+data[n][2]/60: LonA:=-data[n][3]-data[n][4]/60: LatB:=data[n+1][1]+data[n+1][2]/60: LonB:=-data[n+1][3]-data[n+1][4]/60: LatAR:=LatA*Pi/180: LonAR:=LonA*Pi/180: LatBR:=LatB*Pi/180: LonBR:=LonB*Pi/180: evalf(cos(LatAR)*cos(LonAR)*cos(LatBR)*cos(LonBR)+   cos(LatAR)*sin(LonAR)*cos(LatBR)*sin(LonBR)+   sin(LatAR)*sin(LatBR)): angle:=arccos(%): distance[n]:=evalf(angle*3963.1,5)*miles: Or[n]:=evalf(distance[n]*5280*feet/miles,5): od: n:='n':

>	for n from 1 to 8 do print(distance[n]=Or[n]); od;

>	sum(distance[p],p=1..8); sum(Or[p],p=1..8);