Calculate critical curve speed, friction factor, radius, or superelevation for road curves using any three known values and selectable units.
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Critical Curve Speed Formula
The critical curve speed calculation is based on the balance between speed, curve radius, superelevation, and side friction. The calculator uses SI base units internally: speed in meters per second, radius in meters, and superelevation as a decimal.
V = \sqrt{gR(e + f)}f = \frac{V^2}{gR} - eR = \frac{V^2}{g(e + f)}e = \frac{V^2}{gR} - f- V = critical curve speed
- g = acceleration due to gravity, 9.80665 m/s²
- R = radius of curve
- e = superelevation as a decimal
- f = friction factor
If you enter superelevation as a percent, it is converted to a decimal before calculation.
e = \frac{\text{superelevation percent}}{100}If you enter superelevation in degrees, it is converted using the tangent of the angle.
e = \tan(\theta)
- Critical curve speed: leave speed blank, then enter friction factor, curve radius, and superelevation.
- Friction factor: leave friction factor blank, then enter speed, radius, and superelevation.
- Radius of curve: leave radius blank, then enter speed, friction factor, and superelevation.
- Superelevation: leave superelevation blank, then enter speed, friction factor, and radius.
Typical Superelevation and Friction Values
Use these values as general reference points. Actual design values depend on road type, standards, pavement condition, drainage, vehicle type, and safety requirements.
| Superelevation | Decimal e | Approx. Angle | Common Interpretation |
|---|---|---|---|
| 2% | 0.02 | 1.15° | Low banking |
| 4% | 0.04 | 2.29° | Moderate banking |
| 6% | 0.06 | 3.43° | Common higher roadway value |
| 8% | 0.08 | 4.57° | High banking |
| Friction Factor f | Relative Side Friction | Use as a Check |
|---|---|---|
| 0.05 | Low | More conservative, lower speed support |
| 0.10 | Moderate | Common for simple curve checks |
| 0.15 | Higher | Requires more side friction demand |
| 0.20 | Very high | May be unsuitable for design unless justified |
Example Calculations
Example 1: Calculate critical curve speed
Suppose the radius is 120 m, the friction factor is 0.15, and the superelevation is 6%.
e = 6/100 = 0.06
V = \sqrt{9.80665(120)(0.06 + 0.15)}V = 15.71 \text{ m/s}That is about 56.56 km/h or 35.14 mph.
Example 2: Calculate radius of curve
Suppose the speed is 25 m/s, the friction factor is 0.12, and the superelevation is 4%.
e = 4/100 = 0.04
R = \frac{25^2}{9.80665(0.04 + 0.12)}R = 398.02 \text{ m}FAQ
What does critical curve speed mean?
Critical curve speed is the speed associated with a given curve radius, superelevation, and friction factor. In this calculation, it is the speed at which the combined effect of roadway banking and side friction balances the centripetal demand of the curve.
What happens if superelevation plus friction is too low?
The value of e + f must be greater than zero to calculate speed or radius. If the sum is very small, the calculated allowable speed will be low or the required radius will be very large. If the sum is zero or negative, the formula cannot produce a valid positive curve speed.
Is superelevation in degrees the same as superelevation percent?
No. Superelevation percent is a slope ratio multiplied by 100. Superelevation in degrees is an angle. The calculator converts degrees using tan(angle). For small angles the values may look similar, but they are not the same unit.