Engineering and Construction Surveying: Curves, Staking, and Earthwork
Horizontal curves
Know both degree-of-curve definitions. Arc definition: R = 5729.578 / D (100-ft arc). Chord definition (railroads) gives a slightly larger radius. From R and intersection angle delta: T = R tan(delta/2), L = R x delta (radians) or 100 x delta / D, LC = 2R sin(delta/2), and M = R[1/cos(delta/2) - 1]. Trap: mixing arc and chord definitions, or reporting the long chord as arc length.
Vertical curves
A symmetrical parabola with K = L / A, where A is the algebraic grade change in percent. Offset from tangent at distance x from the BVC = (A x^2) / (200 L). The high or low point lies at x = g1 L / (g1 - g2) from the BVC. Grades are usually in percent, so elevation change = grade x horizontal distance / 100.
Layout and earthwork
Construction layout uses stationing (station 12+50 = 1,250 ft), offset hubs, grade stakes, slope stakes, and cut/fill notation. Watch sign conventions: cut is excavation below grade, fill is embankment above. Volumes come from average end area or the prismoidal formula; borrow and shrink/swell factors adjust in-place versus compacted quantities. As-built surveys compare design to constructed position against stated tolerances.
Worked example
Grades g1 = +2.0% and g2 = -3.0%, L = 600 ft. A = 5.0, so K = 600/5 = 120. High point distance from BVC = (2.0 x 600) / (2.0 + 3.0) = 240 ft.