Tools › Civil and Geotechnical › Surveying and Earthwork › Horizontal and Vertical Curves and Sight Distance › Example

Simple curve R 1,000 ft, Δ 30°, PI 12+50: elements, PC / PT and the 100-ft staking table; the 600-ft crest at 50 mph against stopping sight distance

Tool	Horizontal and Vertical Curves and Sight Distance
Source	Department of the Army (1985). Construction Surveying. FM 5-233, pages 3-4 to 3-8 (simple-curve formulas and the deflection-angle staking); Donnell, E. T., et al. (2009). Speed Concepts: Informational Guide. FHWA-SA-10-001, pages 10 to 14 (stopping sight distance assumptions, Table 2, equations 1 and 2); Bureau of Land Management (2011). Road Design Handbook H-9113-1, Illustrations 5 and 6 (crest and sag curve-length forms).
Level	Undergraduate

Problem

A highway alignment deflects Δ = 30° at PI station 12+50 and is to be fitted with a simple circular curve of radius 1,000 ft (arc definition). Find the degree of curve, T, L, E, M and LC, the PC and PT stations and the deflection angles and chords for staking at full 100-ft stations. A 600-ft equal-tangent crest curve joins +3 % to −2 % at PVI 25+00 (elevation 500.00 ft) on a 50-mph road: find K, the high point, the stopping sight distance (2.5 s, 11.2 ft/s²), the minimum crest length for it with 3.5-ft eye and 2.0-ft object heights, and the sight distance the curve provides.

Inputs to Enter

Simple curve: Δ 30°, R 1,000 ft (arc definition), PI 12+50, staking interval 100 ft
Vertical curve: g_1 +3 %, g_2 −2 %, L 600 ft, PVI 25+00 at 500.00 ft, table interval 100 ft; V 50 mph, t 2.5 s, a 11.2 ft/s², G 0, h_1 3.5 ft, h_2 2.0 ft

Open the Horizontal and Vertical Curves and Sight Distance tool (loaded with this example)

Answers

D = 5,729.58/1,000 = 5.7296° (chord definition would give 5.7320°); T = R tan 15° = 267.95 ft; L = R Δ = 523.60 ft; E = 35.28 ft; M = 34.07 ft; LC = 517.64 ft; PC = 12+50 − 267.95 = 9+82.05; PT = 9+82.05 + 523.60 = 15+05.65
Staking: d = (D/2)(C/100): 0°30.85′ to 10+00 (C 17.95 ft), 2°51.89′ per full station, 0°09.71′ to the PT (C 5.65 ft); cumulative 15°00.00′ = Δ/2 at the PT; true full chord 2R sin d = 99.96 ft
Crest: PVC 22+00 at 491.00, PVT 28+00 at 494.00, e = L(g_2 − g_1)/8 = −3.75 ft, K = 600/5 = 120 ft per percent, high point 25+60.00 at 496.40 ft
SSD = 1.47 (50)(2.5) + 50²/(30 (11.2/32.2)) = 183.8 + 239.6 = 423.3 ft (AASHTO design value 425 ft, FHWA Table 2); C = 200(√3.5 + √2.0)² = 2,158.3; S > L so L_min = 2 S − C/A = 846.7 − 431.7 = 415.0 ft (K_min 83.0); the 600-ft curve provides S = √(L C/A) = 508.9 ft, r = 423.3/508.9 = 0.832, M.S. = +0.20

Notes

The tool's default inputs are this curve and this crest; press Submit (the simple-curve sub-tool first, then the vertical-curve sub-tool). Both cases are illustrative (stated on the page); every value is a closed form checked by test_road_curves_sight_distance.php (658 checks) against an independent numpy / scipy script (References/Road-Curves/checks/), and the method is checked on the FM 5-233 and NAVEDTRA 14337 printed examples (chord-definition curve PI 18+00, the Figure 11-22 compound curve, the reverse and spiral examples, the Q3 / Q4 vertical curves).