Slope stake (catch point)
Where a road template's cut or fill slope meets existing ground on one side, its offset and the cut or fill to the shoulder, found by iteration and written in stake notation.
Experimental: not yet fully verified. How results are checked
Set the stake at 25 ft from the centerline: C 4.5 / 25.0 R.
- Cut or fill
- Cut or fill
- Stake notation
- Ground elevation at the catch point
Provenance
- Computed by
- survey.earthwork.slope-stake 1.0.0, core 0.1.0
- Model
- Design line from the shoulder: grade + (x − w)/s_cut in cut, grade − (x − w)/s_fill in fill; ground linear between the points given; the catch point solves ground(x) = design(x) by Brent's method to 1e-6 of the unit (Ghilani & Wolf 2021, ch. 26)
- Accuracy
- The iteration converges far inside 0.01 of the unit; the answer is as good as the ground points and the template
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Design line from the shoulder: grade + (x − w)/s_cut in cut, grade − (x − w)/s_fill in fill; ground linear between the points given; the catch point solves ground(x) = design(x) by Brent's method to 1e-6 of the unit (Ghilani & Wolf 2021, ch. 26)
Accuracy: The iteration converges far inside 0.01 of the unit; the answer is as good as the ground points and the template
Worked example: A cut on ground rising 10% to the right. Source: add-survey-suite catch-point scenario on planar ground. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Cut slope
- 2
- Fill slope
- 3
- Grade elevation
- 100 ft
- Existing ground
- 0 ft, 102 ft 60 ft, 108 ft
- Half width
- 16 ft
- Side
- right
You get
- Catch point offset
- 25 ft
- Cut or fill
- 4.5 ft
- Cut or fill
- cut
- Stake notation
- C 4.5 / 25.0 R
- Ground elevation at the catch point
- 104.5 ft
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapter 26 (volumes: slope staking and catch points).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.