Minimum Radius of a Horizontal Curve at a Design Speed (AASHTO)

Also known as minimum curve radius · minimum radius horizontal curve AASHTO · sharpest curve for a design speed · Rmin = V squared over 127 (e + f) · minimum radius superelevation and friction · design speed curve radius · AASHTO minimum radius · maximum superelevation side friction minimum radius · curve radius from design speed · horizontal curve design speed radius

R_{min} = \frac{V^{2}}{g\,(e_{max} + f_{max})}\qquad \left(\text{AASHTO metric: } R = \frac{V^{2}}{127\,(0.01\,e + f)},\ V\text{ in km/h}\right)

sig figs

Worked example: 100 km/h, 8 %, f 0.12 → 393.4 m. Press Try an example to run it live, then adjust anything.

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g_{n} = 9.80665\ \text{m/s}^{2}

Standard acceleration of gravity · exact

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Minimum Radius of a Horizontal Curve at a Design Speed (AASHTO) explained

A vehicle going round a curve needs a sideways force toward the centre, and a road has two ways to supply it: the banking of the road, called superelevation, and the sideways friction between tyre and surface. The minimum radius is the sharpest curve for which these two together just supply the force the design speed asks for: $R = V^{2}/(g(e + f))$ , with $e$ the maximum superelevation rate as a fraction and $f$ the maximum side friction factor for that speed. Because the speed is squared, a higher design speed calls for a much larger radius, and anything that lowers $e$ or $f$ does the same.

The friction factor is not a constant: the design manual tabulates it against speed, and it falls as the speed rises, from 0.32 at 15 mph to 0.20 at 30, 0.16 at 40, 0.14 at 50, 0.12 at 60, 0.10 at 70 and 0.08 at 80. At high speed, then, less of the sideways force is allowed to come from friction, so more has to come from banking or from a larger radius. The same relation appears in several unit forms: the AASHTO metric $R = V^{2}/(127(0.01\,e + f))$ with $V$ in km/h and $R$ in metres; US units with 15 in place of 127, miles per hour and feet; and the Washington State Department of Transportation design manual's exhibit 1250-2, $R = 6.68\,V^{2}/(e + f)$ with $e$ in percent.

The manual's minimum radii at a maximum superelevation of 10 percent are 205 ft at 30 mph, 700 ft at 50 mph and 1 095 ft at 60 mph. At 60 mph, lowering the maximum superelevation to 8 percent raises the minimum radius to 1 205 ft, and 6 percent raises it to 1 340 ft: less banking has to be made up by a gentler curve. The page reproduces the rows from 40 mph up to within 1 percent; the table is rounded to 5 feet, and the Green Book adjusts the lower speeds. For example, the page gives 1 094.0 ft where the table prints 1 095.

The page's own example is metric: 100 km/h, a maximum superelevation of 8 percent and a friction factor of 0.12 give 393.4 m. The relation is the library's superelevation-rate page solved for the radius, carried here with the design-speed framing and the table of friction factors; set $e = 0$ and it becomes the flat-curve speed limit. The manual takes it from the AASHTO Green Book.

Minimum Radius of a Horizontal Curve at a Design Speed (AASHTO) formula

R_{min} = \frac{V^{2}}{g\,(e_{max} + f_{max})}\qquad \left(\text{AASHTO metric: } R = \frac{V^{2}}{127\,(0.01\,e + f)},\ V\text{ in km/h}\right)

Where

$R$ = Minimum radius of the curve (m)
$V$ = Design speed (km/h)
$e$ = Maximum superelevation rate (%)
$f$ = Maximum side friction factor

Where this comes from

Washington State Department of Transportation, Design Manual M 22-01.23 (September 2024), chapter 1250, Cross Slope and Superelevation, read 23 Oct 2026 (the pdf, with the exhibits checked on the rendered pages): Exhibit 1250-2, 'Minimum Radius for Existing Curves', R = 6.68 V^2 / (e + f) with R in ft, V in mph, e the superelevation rate in percent and f the side friction factor from Exhibit 1250-3; Exhibit 1250-3, side friction factor by design speed, 0.32 at 15 mph, 0.27 at 20, 0.23 at 25, 0.20 at 30, 0.18 at 35, 0.16 at 40, 0.15 at 45, 0.14 at 50, 0.13 at 55, 0.12 at 60, 0.11 at 65, 0.10 at 70, 0.09 at 75, 0.08 at 80; Exhibit 1250-4, minimum radius at a 10 percent maximum superelevation: 40 ft at 15 mph, 75 at 20, 130 at 25, 205 at 30, 295 at 35, 415 at 40, 545 at 45, 700 at 50, 880 at 55, 1 095 at 60, 1 345 at 65, 1 640 at 70, 1 980 at 75, 2 380 at 80; Exhibit 1250-5 (8 percent) 1 205 ft at 60 mph; Exhibit 1250-6 (6 percent) 1 340 ft at 60 mph; the manual points to the AASHTO Green Book as its source. Read it

Revised 30 October 2026

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formula.expert. (2026, October 30). Minimum Radius of a Horizontal Curve at a Design Speed (AASHTO) Calculator. https://formula.expert/solvers/minimum-horizontal-curve-radius-aashto

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