Tunnel lateral displacement (breakthrough) error

The standard displacement error (sigma) of a geodetic station in tunneling in a direction normal to the axis of the tunnel (lateral error).

The standard displacement error (sigma) of a geodetic station in tunneling in a

direction normal to the axis of the tunnel (lateral error). This error describes tunnel

breakthrough error (offset), and can be used in tunnel geodetic network pre-analysis.

Vectorized.

Version: 13 Jun 22

Input: n - the number of the traverse legs

s - the length of the open tunnel traverse [meter]

sigma_angle- the standard deviation (uncertainty) of angle measurements [radians]

Output: sigma - standard error (sigma) of a geodetic station in the tunnel [meter]

Reference: Chrzanowski, A., 1981. Optimization of the breakthrough accuracy in tunnelling surveys. Canadian Surveyor 35 (1), 5 – 16.

Keywords: tunneling, surveying, standard accuracy, breakthrough error