Max Design Speed from Sight Distance
The fastest safe design speed given the available sight distance.
Example
You enter
- Available sight distance (ft) 492.4
- Perception-reaction time (s; default 2.5) 2.5
- Friction coefficient f (set from condition or enter directly) 0.348
You get
- Max safe design speed 55 mph
Checked against published worked examples from: Illinois Department of Transportation (IDOT), Bureau of Local Roads and Streets.
Details, formula, and sources
ScopeThe positive root of 1.075 v^2/(32.2 (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.
Formula or tablev is the positive root of 1.075 v^2 / (32.2 (f + g)) + 1.47 t_pr v - SSD = 0, i.e. v = (-b + sqrt(b^2 + 4 a SSD)) / (2 a) with a = 1.075/(32.2 (f+g)), b = 1.47 t_pr. The inverse of SSD = 1.47 t v + 1.075 v^2/(32.2 (f+g)), the Green Book form.
Source and editionAASHTO Green Book (Policy on Geometric Design of Highways and Streets, 7th ed.) Chapter 3.
Free accesstransportation.org for TOC; AASHTO design SSD tables are licensed.
What governsMath aid for personal verification. The ELD on the truck and the carrier tariff are the legal record. State limits may be lower than federal.
API field namessight_distance_ft, reaction_time_s, friction, design_speed_mph
- Quadratic inverse v = (-b + sqrt(b^2 + 4 a SSD))/(2 a), a = 1.075/(32.2 (f+g)), b = 1.47 t_prAASHTO Green Book Chapter 3
- Friction coefficient 0.348 AASHTO design (11.2 ft/s^2 / 32.2, already a wet-pavement basis) / 0.20 poor wet surface or worn tires (not an AASHTO value) / 0.10 ice or packed snowAASHTO Green Book Chapter 3 for 0.348; engineering practice for 0.20 and 0.10
- Grade decimal; + uphill, - downhill lowers the safe speedstandard convention