Slope Stake Catch Point on a Cross Slope

The design slope leaves the hinge point at the shoulder and runs out at its ratio until it daylights. If the ground were level the catch would sit at the half-width plus the depth times the ratio, and no correction would be needed -- but the ground is never level, and a cross slope that rises away from centerline pushes the catch point FARTHER out on a cut, because the ground is climbing toward the slope while the slope is climbing toward the ground and they take longer to meet. The denominator carries the whole correction and it also carries the warning: as the ratio times the cross slope approaches one -- a ground cross slope as steep as the design side slope -- the denominator goes to zero and the slope never catches at all. That is a real condition on side-hill work and the answer is a retaining structure or a slope change, not a longer tape. A 24 ft roadway in a 6 ft cut at 2:1 with the ground rising 10% away from centerline catches at 27.0 ft out and 7.5 ft down, three feet past the 24.0 ft the level-ground form would give; at 20% cross slope it is 32.0 ft, eight feet past. At 50% the 2:1 slope runs parallel to the ground and never daylights. A field calculation; the grading plan, the surveyor of record, and the existing-ground breaks between shots govern.

d = half_width_ft + depth_ft x side_slope_ratio / (1 - side_slope_ratio x g), where g is the ground cross slope taken positive when it works against the section; vertical at the catch = depth_ft + g x (d - half_width_ft).

Slope-stake catch point with the ground cross-slope correction, by name -- standard construction-surveying practice. The level-ground form is the zero-cross-slope case and is reported alongside for comparison. The grading plan, the surveyor of record, and the existing-ground breaks between shots govern.

The correction is plane geometry on the section's own dimensions; nothing is reproduced from any standard.

Estimate. AHJ and licensed professional govern.

Field names used by the API: half_width_ft, depth_ft, side_slope_ratio, ground_cross_slope, section, catch_distance_ft, run_ft, vertical_at_catch_ft, flat_ground_distance_ft

• Cross-slope correction the (1 - s g) denominator; the level-ground answer is the g = 0 caseconstruction surveying practice
• Never daylights when s x g reaches 1 the slope runs parallel to the ground; the section needs a retaining structure or a slope changeconstruction surveying practice
• Planar ground one constant cross slope between the hinge and the catch; existing-ground breaks between shots change the true catchconstruction surveying practice