Calculate critical curve speed, the fastest a vehicle can take a curve before sliding, from curve radius, road surface and banking, or solve for radius.

Typical tireโ€“road friction used in crash reconstruction. Real values vary with tires, speed and pavement.

0% is a flat road. Banked highway curves are typically 2โ€“8%; negative means banked away from the turn.

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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 = โˆš(gR(e + f))
f = (Vยฒ) / (gR) - e
R = (Vยฒ) / (g(e + f))
e = (Vยฒ) / (gR) - f
  • V = critical curve speed
  • g = acceleration due to gravity, 9.80665 m/sยฒ
  • R = radius of curve
  • e = superelevation as a decimal
  • f = signed side-friction demand factor; positive is toward the curve center

If you enter superelevation as a percent, it is converted to a decimal before calculation.

e = (superelevation percent) / (100)

If you enter superelevation in degrees, it is converted using the tangent of the angle.

e = tan(ฮธ)
  • Critical curve speed: select speed, then enter the curve radius, pick a road surface (or Custom friction factor) and the superelevation.
  • Friction factor: select friction factor, then enter speed, radius, and superelevation.
  • Radius of curve: select radius, then enter speed, pick a road surface (or Custom friction factor) and the superelevation.
  • Superelevation: select superelevation, then enter speed, pick a road surface (or Custom friction factor) and the radius.

Illustrative Superelevation and Friction Values

These are illustrative numerical examples, not universal road-design limits. 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 1.15ยฐ Low banking
4% 0.04 2.29ยฐ Moderate banking
6% 0.06 3.43ยฐ Illustrative higher banking
8% 0.08 4.57ยฐ High banking
Friction Factor f Relative Side Friction Use as a Check
0.05 Low More conservative, lower speed support
0.10 Moderate Illustrative side-friction demand
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 = โˆš(9.80665(120)(0.06 + 0.15))
V โ‰ˆ 15.72 m / s

That is about 56.59 km/h or 35.17 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 = (25ยฒ) / (9.80665(0.04 + 0.12))
R โ‰ˆ 398.33 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 model 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.