VectorExpertWhen it is used
- Setting out levels. For each peg you know the design R.L.; the reverse calculation gives the staff reading the leveller should see when the peg is at the right height.
- A level book for finished levels. After sections have been adjusted, a level book whose readings reduce exactly to the final levels, laid out like the original, for checking on site.
A reverse level book is a calculation aid. A level book that records a survey must hold the readings actually taken on site.
The method
It is the height of instrument method run backwards:
- Set up on the bench mark: choose a back sight that suits the ground; H.I. = R.L. of the bench mark + B.S.
- Each point: reading = H.I. − R.L.
- Watch the staff limits. If the next reading would be more than the staff can show (more than 4.000 m on a 4 m staff), or uncomfortably close to its foot, make the last point a change point: book its reading as a fore sight, then choose a new back sight on the same point and work out the new H.I. = R.L. + B.S.
- Close with the last reading as a fore sight.
Worked example
Bench mark R.L. 100.000, a 4 m staff, and these final levels along a falling route:
| Chainage | 0+000 | 0+020 | 0+040 | 0+060 | 0+080 | 0+100 | 0+120 |
|---|---|---|---|---|---|---|---|
| R.L. | 99.900 | 99.200 | 98.300 | 97.600 | 97.100 | 96.800 | 96.450 |
Back sight 1.500 on the bench mark gives H.I. 101.500. The readings at 0+000 to 0+060 are 1.600, 2.300, 3.200 and 3.900. At 0+080 the reading would be 101.500 − 97.100 = 4.400, off the 4 m staff, so 0+060 becomes the change point: fore sight 3.900 there, then the instrument moves down the slope and takes a back sight of 0.600 on the same point. New H.I. = 97.600 + 0.600 = 98.200.
| Point | B.S. | I.S. | F.S. | H.I. | R.L. |
|---|---|---|---|---|---|
| BM | 1.500 | 101.500 | 100.000 | ||
| CH 0+000 | 1.600 | 99.900 | |||
| CH 0+020 | 2.300 | 99.200 | |||
| CH 0+040 | 3.200 | 98.300 | |||
| CH 0+060 (C.P.) | 0.600 | 3.900 | 98.200 | 97.600 | |
| CH 0+080 | 1.100 | 97.100 | |||
| CH 0+100 | 1.400 | 96.800 | |||
| CH 0+120 | 1.750 | 96.450 |
Check it like any level book
- Σ B.S. = 1.500 + 0.600 = 2.100; Σ F.S. = 3.900 + 1.750 = 5.650
- Σ B.S. − Σ F.S. = −3.550 = last R.L. − first R.L. = 96.450 − 100.000 ✓
- Every R.L.: 4 × 101.500 + 3 × 98.200 − Σ I.S. (9.600) − Σ F.S. (5.650) = 685.350 = the sum of the seven R.L.s after the bench mark ✓
(The checks are explained in how to reduce a level field book.)
Choosing the back sights
- On falling ground, a small back sight after each change point leaves the most room on the staff for the readings that follow, which grow as the ground falls.
- On rising ground it is the other way round: readings shrink as the ground rises, so take a larger back sight.
- Keep a margin at both ends of the staff. Readings at the very top or the very foot are the hardest to read accurately.