CivilSolve

Transportation & Surveying

Minimum Curve Radius (Superelevation)

The minimum safe horizontal-curve radius for a design speed with maximum superelevation e and side-friction factor f: R = v²/(g(e + f)) — identical to the handbook forms R = V²/[127(e+f)] (km/h, meters) and R = V²/[15(e+f)] (mph, feet), shown for reconciliation. Use for: 'design the minimum radius of the curve', superelevation/side-friction radius problems. For the full curve geometry from a KNOWN radius (T, L, E, M, stations), use horizontal-curve.

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Worked examples

These are the solver's own reference problems — the answers come from published sources or independent hand computation, never from the solver itself. The solution below is the live solver output for each.

Example 1

100 km/h with e = 0.07, f = 0.15 (the motivating exam problem)

Given

design speed
100 km/h
superelevation
0.07
side friction
0.15

Assumptions

  • Point-mass curve model: superelevation and side friction together balance the centripetal demand at the design speed (AASHTO basic curve formula).

Solution steps

  1. Balance the centripetal demand

    On a banked curve, gravity's inward component (e) and tire friction (f) together supply v²/(gR).

    R_min = v²/(g·(e + f)) — the V²/127(e+f) km/h form and V²/15(e+f) mph form are the same equation

    R_min = 100 km/h squared over g × (0.07 + 0.15) = 357.64 m

    = 357.64 m

Results

Minimum curve radius R

357.64m

e + f (total lateral supply)

0.22

Notes

  • This is the MINIMUM radius — designs use the next larger standard radius, and flatter is always safer.
Where this answer was checked
source
R = v²/(g(e+f)); handbook form V²/[127(e+f)] — metric design speed
verified by
hand-recomputed
derivation
v = 27.7778 m/s; R = 771.60/(9.80665·0.22) = 357.65 m (127-form gives 357.9 — the 127 constant is rounded).

Example 2

US: 60 mph with e = 0.08, f = 0.12

Given

design speed
60 mph
superelevation
0.08
side friction
0.12

Assumptions

  • Point-mass curve model: superelevation and side friction together balance the centripetal demand at the design speed (AASHTO basic curve formula).

Solution steps

  1. Balance the centripetal demand

    On a banked curve, gravity's inward component (e) and tire friction (f) together supply v²/(gR).

    R_min = v²/(g·(e + f)) — the V²/127(e+f) km/h form and V²/15(e+f) mph form are the same equation

    R_min = 60 mi/h squared over g × (0.08 + 0.12) = 1203.5 ft

    = 1203.5 ft

Results

Minimum curve radius R

1203.5ft

e + f (total lateral supply)

0.2

Notes

  • This is the MINIMUM radius — designs use the next larger standard radius, and flatter is always safer.
Where this answer was checked
source
R = v²/(g(e+f)); handbook form V²/[15(e+f)] — US design speed
verified by
hand-recomputed
derivation
v = 88 ft/s = 26.822 m/s; R = 719.44/(9.80665·0.20) = 366.8 m = 1203 ft (15-form gives 1200 — rounded constant).

Example 3

low-speed urban curve

Given

design speed
50 km/h
superelevation
0.04
side friction
0.16

Assumptions

  • Point-mass curve model: superelevation and side friction together balance the centripetal demand at the design speed (AASHTO basic curve formula).

Solution steps

  1. Balance the centripetal demand

    On a banked curve, gravity's inward component (e) and tire friction (f) together supply v²/(gR).

    R_min = v²/(g·(e + f)) — the V²/127(e+f) km/h form and V²/15(e+f) mph form are the same equation

    R_min = 50 km/h squared over g × (0.04 + 0.16) = 98.352 m

    = 98.352 m

Results

Minimum curve radius R

98.352m

e + f (total lateral supply)

0.2

Notes

  • This is the MINIMUM radius — designs use the next larger standard radius, and flatter is always safer.
Where this answer was checked
source
R = v²/(g(e+f)) — 50 km/h, e = 0.04, f = 0.16
verified by
hand-recomputed
derivation
v = 13.889 m/s; R = 192.90/(9.80665·0.20) = 98.35 m.