Calculate horizontal curve radius from design speed, superelevation, and side friction. Follow the equation in SI or US units for coursework.
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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
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
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
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.