Max Design Speed from Sight Distance

The positive root of v^2/(30(f+g)) + 1.47 x t x v - SSD = 0 (AASHTO Green Book). With 490 ft of sight distance on dry level pavement (f 0.35, t 2.5 s) the max is 55 mph; a -6% downhill drops it to 51 mph. Sets a curve/crest advisory speed or checks a design speed against the sight line, instead of the distance for one speed. A design aid; the AASHTO Green Book and the state DOT govern.

v is the positive root of v^2 / (30 (f + g)) + 1.47 t_pr v - SSD = 0, i.e. v = (-b + sqrt(b^2 + 4 a SSD)) / (2 a) with a = 1/(30(f+g)), b = 1.47 t_pr. The inverse of SSD = 1.47 t v + v^2/(30(f+g)).

AASHTO Green Book (Policy on Geometric Design of Highways and Streets, 7th ed.) Chapter 3.

transportation.org for TOC; AASHTO design SSD tables are licensed.

Math aid for personal verification. The ELD on the truck and the carrier tariff are the legal record. State limits may be lower than federal.

Field names used by the API: sight_distance_ft, reaction_time_s, friction, design_speed_mph

• Quadratic inverse v = (-b + sqrt(b^2 + 4 a SSD))/(2 a), a = 1/(30(f+g)), b = 1.47 t_prAASHTO Green Book Chapter 3
• Friction coefficient 0.35 dry / 0.20 wet / 0.10 iceengineering practice; AASHTO design values
• Grade decimal; + uphill, - downhill lowers the safe speedstandard convention