Civil & Transportation Engineering, Highway Geometric Design (AASHTO)
AASHTO Curve Superelevation Radius & Stopping Sight Distance
Calculate AASHTO Green Book Minimum Horizontal Curve Radius V^2 / (127*(e + fs)), Perception-Reaction Distance 0.278*V*tr, Grade-Adjusted Braking Distance, and Total Stopping Sight Distance (SSD).
Design safe highway alignments for wet-pavement friction and downhill braking grades!
Highway geometric engineers follow the AASHTO Green Book to prevent vehicles from skidding off horizontal curves or overrunning hazards on steep downgrades! Banking the pavement inward by Superelevation Rate e (decimal cross-slope, e.g., 0.06 = 6%) works together with Wet-Pavement Side Friction Factor f_s to resist centrifugal acceleration, setting Minimum Horizontal Curve Radius R_min = V_kmh^2 / (127 * (e + f_s))! Simultaneously, Stopping Sight Distance (SSD) sums Perception-Reaction Travel 0.278 * V_kmh * t_r (standard t_r = 2.5 s) plus Grade-Adjusted Braking Distance V_kmh^2 / (254 * (f_brake + G)), where downhill roadway grade G is NEGATIVE (lengthening braking distance because gravity pulls the vehicle forward)!
Verify on a 100 km/h Mountain Arterial—Design_Speed V = 100 km/h (B2), Max_Superelevation e = 0.06 (6.0%, B3), Side_Friction_Factor f_s = 0.10 (B4 -> R_min = 10,000 / (127 * 0.16) = 492.13 m in E2), Driver_Reaction_Time t_r = 2.5 s (B5 -> Reaction Distance = 0.278 * 100 * 2.5 = 69.50 m in E3), Deceleration_Friction_Ratio f_brake = 0.35 (3.43 m/s^2, B6), and 3% Downgrade G = -0.03 (B7): Downhill Braking Distance is 10,000 / (254 * (0.35 - 0.03)) = 123.03 m (E4), requiring a Total Stopping Sight Distance SSD = 69.50 + 123.03 = 192.53 m (E5)!
| AASHTO Alignment Metric (V=100 km/h, e=6%, fs=0.10, tr=2.5s, fb=0.35, G=-3%) | Formula | Verified Output |
|---|---|---|
| Min Horizontal Curve Radius (m) | V_kmh^2 / (127 * (e + f_s)) | 492.13 m |
| Perception-Reaction Dist (m) | 0.278 * V_kmh * Reaction_Time_s | 69.50 m |
| Grade-Adjusted Braking Dist (m) | V_kmh^2 / (254 * (f_brake + Grade_G)) | 123.03 m (112.49 m @ Level 0%) |
| Total Stopping Sight Dist SSD | Reaction_Dist + Braking_Dist | 192.53 m (181.99 m @ Level 0%) |
AASHTO Grade-Adjusted Stopping Sight Distance (SSD) Formula
Validate Design_Speed > 0, non-negative e and f_s with (e + f_s) > 0, t_r > 0, f_brake > 0, and net deceleration (f_brake + G) > 0.05!
=LET(v_kh, B2, sp_e, B3, fr_s, B4, tr_s, B5, fb_g, B6, gr_d, B7, IF(OR(v_kh <= 0, sp_e < 0, fr_s < 0, sp_e + fr_s <= 0, tr_s <= 0, fb_g <= 0, fb_g + gr_d <= 0.05), "Invalid AASHTO Alignment Input", LET(d_pr, ROUND(0.278 * v_kh * tr_s, 2), d_br, ROUND((v_kh ^ 2) / (254 * (fb_g + gr_d)), 2), ROUND(d_pr + d_br, 2))))Level Roadway Grade Baseline Check (Set Grade G = 0.00)
Set Roadway_Grade B7 = 0.00 (flat alignment): Braking Distance E4 shortens by 10.54 m to 112.49 m, reducing Total Stopping Sight Distance E5 to 181.99 m!
=IF(ISTEXT(E5), E5, ROUND((B2 ^ 2) / (254 * (B6 + B7)), 2))Try the example
Use the original values or change them to test your understanding.