Angle Distance Traverse and Leveling Errors Angle Errors

Angle, Distance, Traverse, and Leveling Errors

Angle Errors • • • Reading errors – repetition and direction Pointing errors – lining up the crosshairs Combined reading and pointing errors Target centering errors Instrument centering errors Leveling error (alignment of vertical axis)

Reading and Pointing Reading - repetition Reading - direction Pointing Reading and pointing – total station (DIN)

Target Centering For two targets at D 1 and D 2 distance away: NOTE – RESULT IS IN RADIANS!

Instrument Centering Given a backsight distance D 1, a foresight distance D 2, and a distance D 3 between targets: NOTE – RESULT IS ALSO IN RADIANS! For leveling error, see textbook pp. 108 -110.

Combined Angular Errors Note: Some values are in arc-seconds and some in radians. They must be converted to a consistent unit. Also, leveling error is not considered.

Interior Angles of a Polygon Error propagation is error of a sum. With all interior angles measured once, there is one (1) degree of freedom. If angles are measured multiple times, they are correlated (in practical cases). Use t statistic for testing closure.

EDM Errors Given instrument specifications where a is the constant portion, and b is the parts per million value …

Error Propagation in a Traverse Error propagation for any type of horizontal network (including traverse) can be conveniently and properly determined through a full least squares analysis. Therefore, we will not cover traverse as a special case.

Fuzzy Traverse

Errors in Differential Leveling • Systematic – Collimation – Earth curvature and refraction – Both can be avoided by balancing BS & FS • Random – Reading (usually given in ft/ft or mm/m) – Instrument leveling – Rod leveling • In practical cases, random error is relative, based on distance or number of setups

Trigonometric Leveling

Propagation of Random Error

Estimated Error in a Measured Zenith Angle

Zenith Angle Error With Total Station