What is the ruling radius of a horizontal curve?
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The maximum degree of curve or smallest radius for a railroad is 3 degrees on a new main line track with a maximum grade of 1% compensated at 0.04% per degree of curve; therefore a grade in a 3 degree curve would actually be 0.88%. For a highway it depends on what kind, where, typical traffic, speed limits, etc. Degree of curve is the angle between the radii of a curve of a 100 foot chord which is chord definition. Highway departments usually use Degree of Curve as the angle between the radii of a curve of an arc of 100 feet. For curves 3 degrees or under, the difference between the definitions staked on the ground is inconsequential.
The minimum radius of a horizontal curve by considering maximum superelevation and coefficient of friction is called ruling minimum radius.
For Ruling design speed, Ruling minimum radius is given by
R=Ruling minimum radius in m
v = ruling design speed in m/s
e = superelevation (0.07)
f = coefficient of friction (0.15)
g = acceleration due to gravity in m/s²
The maximum comfortable speed on a horizontal curve depends on the radius of the curve. It is possible to design with maximum superelevation and coefficient of friction. If the design speed is increased in the future. So the radius of the curve is not desirable. Therefore a ruling minimum radius can be derived by assuming maximum superelevation and coefficient of friction.
Ruling Radius = v^2/g(e+f)
Generally, the radius of the curve is higher than the ruling radius