Grade Rod, Cut, and Fill from One Setup
The cut or fill at a shot, from one grade rod that carries the whole design for the instrument setup.
Example
You enter
- Benchmark elevation (ft) 100
- Backsight rod reading (ft) 5.2
- Design (finished grade) elevation (ft) 98.5
- Ground rod reading at the shot (ft) 4.9
You get
- Height of instrument 105.20 ft
- Grade rod for this setup 6.70 ft
- Ground elevation at the shot 100.30 ft
- Cut fill (ft) 1.8
Details, formula, and sources
Set the instrument, shoot the benchmark, and the height of instrument is fixed: it is the benchmark elevation plus the backsight. From then on a single number does all the work -- the grade rod is the height of instrument less the design elevation, which is the rod reading that WOULD be observed if the rod were standing on finished grade. Every subsequent shot is compared against it and the difference is the cut or fill, with no elevation arithmetic at all. The sign is where crews go wrong and it is worth stating plainly: a rod reading SMALLER than the grade rod means the rod is standing HIGHER than design, because the rod reads downward from a fixed instrument. Smaller reading, higher ground, cut. It reads backward the first hundred times. A benchmark at 100.00 with a 5.20 backsight fixes the height of instrument at 105.20, and a design grade of 98.50 makes the grade rod 6.70; a ground shot reading 4.90 is therefore a cut of 1.80 ft, which checks independently because the ground sits at 100.30 against a design of 98.50. A shot reading 7.55 on the same setup is a fill of 0.85 ft. One grade rod, every shot on the setup, until the instrument moves. A field calculation; the grading plan, the benchmark of record, and a checked level circuit govern.
hi_ft = benchmark_elev_ft + backsight_ft; grade_rod_ft = hi_ft - design_elev_ft; ground_elevation_ft = hi_ft - ground_rod_ft; cut_fill_ft = grade_rod_ft - ground_rod_ft, positive being cut.
The grade-rod method of differential leveling, by name; standard construction-surveying practice. A smaller rod reading means higher ground and therefore a cut. The grading plan, the benchmark of record, and a checked level circuit govern.
Four subtractions on the crew's own benchmark, rod readings, and design elevation.
Estimate. AHJ and licensed professional govern.
Field names used by the API: benchmark_elev_ft, backsight_ft, design_elev_ft, ground_rod_ft, hi_ft, grade_rod_ft, ground_elevation_ft, cut_fill_ft
- One setup the height of instrument and therefore the grade rod are fixed until the instrument movesdifferential leveling practice
- Sign a SMALLER rod reading than the grade rod means higher ground and a cutdifferential leveling practice
- Reachable design if the design elevation is at or above the instrument, no rod reading reaches it and the setup must movedifferential leveling practice