CEE 316
Surveying Engineering
Homework 7
Coordinate Systems and Transformations
1- Compute the Geodetic Azimuth of the line AB. The Longitude and latitude values are:
A = (47 32' 00"N, 122 09' 00"W)
B = (47 46' 00"N, 122 11' 00"W)
Both points are in the north zone of WA state plane coordinate system where the central
meridian is 120 50' 00". Use WOLFPACK to compute the SPCS in NAD83 and SI feet.
Answer:
Using WolfPack:
Ya = N = 60,145.2367 ft,
Xa = E = 400,865.880 ft,
Mapping Angle at A = 0°58'49.0263"
Yb =N = 86,163.4539 ft
Xb = E = 396,750.4437 ft
Mapping Angle = -1°01'32.0763"
Grid Azimuth = tan-1 (X / Y) = - 8 59’ 18”, 4th quad, azimuth = 351 0’ 41”
The line AB is west of the central meridian, subtract the mapping angle at A get
Geodetic azimuth at A = 351 0 41 – 0 58 49 = 350 1’ 52”
2-Points A and B are in the overlap area between the north and the south zones of
Washington State Plane Coordinate System. Point C is in the south zone and is outside of
the overlap area. In a survey that extended from the north zone to the south zone, the
coordinates of points A and B in the north zone are:
XA = 774,301.12 m, YA = 96.555.61 m
XB = 471,606.54 m, YB = 46,714.46 m
Coordinates of point C in the south zone are:
XC = 499,606.54m, YC = 55,606.3 m
Compute the grid azimuth of the line BC in the south zone, and the length of the line AC.
Note that all units are in meters. Use WOLFPACK when needed, in the input choose the
units to be meters and the system to be SPCS84.
Answer:
Transform the coordinates of A and B to south zone using WolfPack, first transform
A and B to geodetic coordinates, then to south zone:
Point A :
Latitude A = 47°48'34.9505"
Longitude A = 117°10'10.3033"
In the south zone:
E = Xa = 749,418.2648 m, N = Ya = 280,545.9623 m
Point B:
Latitude B = 47°25'10.3278"
Longitude B= 121°12'34.5867"
In the south zone:
E = Xb = 446,444.8615 m, N = Yb = 232,124.7149 m
Bearing of AB in the south zone = 80 55 10, negative departure and latitude, the
line is in the third quad.
Azimuth of AB = 260 55’
Length of AC = 306, 818.9 m
3- Explain why a conical projection is used to establish a state plane coordinate system in
Washington. Describe another state plane coordinate system that employs a different
projection. Support your answer by sketches and give reasons.
Answer:
The sate of WA is extended in the east-west direction, the minimum distortion area is
around the secant, which is extended in the east west direction. Other states that
extend in the north-south direction, such as Florida, will use a cylindrical projection.
For further explanations and sketches, refer to the lecture on Coordinate systems.