Engineering surveying; two-way principle application

Engineering surveying is the branch of surveying done for engineering works. It covers all the measurements and setting out needed for the planning, design, construction and monitoring of projects such as roads, bridges, dams and buildings. The accuracy is chosen to suit the work.

The survey principles used here are "make a check on every measurement" and "fix a quantity by at least two independent measurements".

Two-way linear distance measurement

A line AB is measured twice, once from A to B (forward) and again from B to A (backward), with the same tape and tension.

1. Forward measurement: $L_f$; backward measurement: $L_b$.
2. The difference $d = |L_f - L_b|$ is compared with the allowable limit (for example, 1 in 1000 to 1 in 5000, depending on the ground and the class of work).
3. If it is within the limit, the mean is adopted:

$$L = \frac{L_f + L_b}{2}$$

4. If the difference is large, a mistake exists (a miscounted tape length or a wrong reading), so the line is measured again.

The second measurement is independent of the first, so a blunder is caught and random errors are reduced by averaging.

Single angle measurement

An angle $\angle AOB$ is measured with a theodolite by:

1. Observing on face left and then on face right, and taking the mean (this removes instrumental errors such as collimation and trunnion-axis errors).
2. Measuring the angle several times (method of repetition), or in sets with different initial circle readings, and taking the mean. This gives a check on the reading and a smaller error.
3. As a further check, the explement ($360^\circ - \theta$) can be measured on the other side and the two values added to see that they total $360^\circ$, or the angle can be compared with a value calculated from measured sides.

Thus every distance and angle is obtained from two independent observations, and the survey is checked.