CHAPTER 4 – ANGLES & DIRECTIONS. 4/27/03. Read Kavanagh Ch. 4 Angles and Directions. Read all of chapter 4. 4.1 Horizontal Angle Review Horizontal angle is the angle in the horizontal plane, even if measured from uphill point to downhill point, etc.
Read all of chapter 4.
4.1 Horizontal Angle Review
Horizontal angle is the angle in the horizontal plane, even if measured from uphill point to downhill point, etc.
Common methods of measuring horizontal angles = transit, theodolite, total station. Can also lay out angles by taping or measuring distances (trilateration).
Horizontal angles have a direction or sense: L or R, clockwise or counterclockwise
Common angles: angles to right, interior angles, deflection angles (L or R)
Horizontal directions must be tied to a fixed line of known or assumed direction defined as a reference meridian. There are four basic types:
1. Astronomic meridian = true meridian = geographic meridian = points to North pole = line of longitude
2. Magnetic meridian = direction of a magnet = points to magnetic north pole = varies with location
3. Grid meridian = parallel with central meridian of a State Plane Coordinate System
4. Assumed meridian
In the field, horizontal directions and angles are determined relative to a line of known or assumed direction called a baseline.
Bearings = angle of a line from N or S reference meridian; always < 90E
Azimuth = angle measured clockwise from any reference meridian (usually from N); ranges from 0E to 360E
Magnetic Meridian (Magnetic North)
Declination = horizontal angle between direction of a compass needle and true (geographic) north
Procedure for determining directions:
1) Set local declination
2) Sight on object
3) Rotate compass housing to center magnet in housing’s N arrow
Reverse Bearings Reverse Azimuths
Example: Calculate Azimuths in Counterclockwise Direction
Example: Calculate Azimuths in Clockwise Direction
Example: Retrace an old magnetic bearing
A magnetic bearing of N 15E40’ E was recorded on a lot line survey dated January 1, 1903. The bearing represented the direction from the property corner Pt. A to the property corner at Pt. B. On June 1, 2003, you find Pt. A, and want to find Pt. B. What compass bearing should you use to find Pt. B? The location of the survey is shown on the following isogonic map.
1985 Isogonic Map
Survey "calls" = statement of direction and distance
Example of Bearing + Distance call: N 01E13'24" E 213.46'
Basis of bearing or basis of azimuth must be known
To be able to determine a call, you must have a base line
Base Line = survey line between two known points used as a reference
line for the rest of the survey or map area
Trilateration = method of computing angles by measuring distances
Laying out a building: Match the diagonals
1) Law of Sines
2) Law of Cosines
These two equations can be used to solve just about any soluble geometric problem. Other “methods” are just special cases of these two equations.