Road Curve Design Calculator: Minimum Radius, Maximum Speed, Superelevation and Side Friction

The basic equation of a road curve, solved for the part you need.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose what you want to find: the minimum radius, the maximum speed, the superelevation or the side friction.

Enter the other values. You can give the radius or the degree of curve.

The calculator gives the answer with the centrifugal ratio, the banking angle, the centrifugal force and the degree of curve.

Formulas used

  • R_{min} = \frac{v^2}{g(e + f)}
  • R_{min} = \frac{V^2}{127.1376(e + f)}
  • CR = IF = \frac{v^2}{gR} = e + f = \frac{F}{W}
  • \theta = \tan^{-1}(e)
  • D = \frac{1145.9156}{R}

Worked example

With the default numbers in the calculator above:

  1. Speed in metres per second: 19.44 m/s
  2. Minimum radius of the curve: 164.00 m
  3. Same radius with the speed in km/h: 164.00 m
  4. Centrifugal ratio (impact factor): 0.235
  5. Centrifugal force on the vehicle: 9.40 kN
  6. Banking angle of the road: 4.86 degrees
  7. Degree of curve (arc definition): 6.99 degrees

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? The maximum speed; Degree of curve (type 0 to use the radius above instead) 4 deg; Superelevation (the rise across the road) 18 %; Side friction factor 0.12.

  1. Radius used: 286.48 m
  2. Maximum speed in metres per second: 29.04 m/s
  3. Maximum speed in kilometres per hour: 104.53 km/h
  4. Centrifugal ratio (impact factor): 0.3
  5. Centrifugal force on the vehicle: 12.00 kN
  6. Banking angle of the road: 10.20 degrees
  7. Degree of curve (arc definition): 4.00 degrees

Common questions

What is the centrifugal ratio or impact factor?

The sideways force on a vehicle on a curve divided by its weight. It equals v squared divided by g R, and on a curve it is carried by the superelevation plus the side friction.

Why is the number 127 used?

It is g times 3.6 squared. It lets you put the speed in km/h and the radius in metres: R = V squared divided by 127 times (e + f). With g = 9.81 it is 127.1376.

What is the degree of curve?

The angle at the centre for a 20 metre arc, so R = 1145.9156 divided by D.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any highway engineering text (horizontal curve design). Use the road design standard that applies (for example Austroads) for the side friction factors and the largest superelevation.

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