Super Elevation
The inward transverse inclination provided to cross section of carriage way at horizontal curved portion of the road is called as Super Elevation. It is also referred as to Cant or Banking.
Objectives :
- To counteract the effect of centrifugal force acting on moving vehicle.
- To help a fast moving vehicles to negotiate a curved path Without overturning and skidding.
- To ensure smooth and safe movements of passengers and goods on the road.
- To prevent damaging effect on the road surface due to improper distribution of load.
- The maintenance cost of road on curve is reduced.
How to Calculate Super Elevation ?
For Example : Calculate the super elevation required for road of 7 m wide on a curve of 250 m radius for permissible speed of 80 kmph. Let the coefficient of friction be 0.15.
The formula for calculating is given below :
Where,
e = Super elevation.
f =coefficient of friction.
v = speed in kmph.
R = Radius of the curve in metre.
Putting all the values in the formula we get,
∴ e = 0.201 – 0.15 = 0.051 per meter of carriage way.
∴ Super elevation = 0.051 * 7 = 0.357 m or 35.7 cm above the inner edge of the road.
Minimum and Maximum Super Elevation.
- If the elevation is less than the value of camber of a road, it should be kept equal to the camber of the road for drainage purpose.
- In case of flat curves with large radius, the super elevation will be negligible, as the centrifugal force which will be developed will be very small. Under such condition, the normal camber may be retained also on the curve.
- But, such a practice will result into negative elevation on the outer half of the road.
- The centrifugal force combined with negative elevation will be less than allowable friction coefficient.
- Below shows the recommended radius of horizontal curves beyond which normal cambered section may be maintained without the provision of super-elevation.
- For mixed traffic pattern where there is fast moving vehicles as well as slow moving vehicles like bullock cart.
- High value of superelevation is in convenience. Hence the maximum value of elevation in plain and ruling terrains and in snow bound areas has been fixed by IRC as 6.7 percent i.e. 1 in 15.
- However for hill roads not bound by snow, a maximum limit of super elevation is upto 10% i.e. 1 in 10 has been recommended by the IRC values.
- Thus the maximum allowable value of (e + f) works out to (0.067 + 0.15) = 0.217.
- From this the minimum value of radius R given to a curve when the speed is known can be obtained.
Also Read : Fiber as a construction material.
Methods for Providing Super Elevation
Following are the two stages involved in providing super elevation :
1. First Stage :
The above fig shows the road camber is gradually neutralized by changing the cross section from straight portion to circular portion with the help of a transition curve.
The step involved are marked as step 1, step 2, step 3, step 4.
2. Second Stage :
After the entire road surface forms a straight fall from outer to the inner edge, full super-elevation is provided by following two methods.
Method 1 :
In this case crown is made the pivot point about which the road is rotated.
Thus full super elevation is provided by lowering the inner edge by half the total amount of super elevation and by raising the outer edge by same amount by which the inner edge is lowered.
Advantage of this method is that earthwork involved is less. But this method is not favoured in practice because lowering of the inner edge of road interferes seriously with the drainage system of the road.
Method 2 :
As shown in above fig, the inner edge of road is made the pivot point. And crown as well as the outer edge are raised in such a way that full amount of superelevation is achieved.
Disadvantages of this methods are :
- The center of the pavement is raised.
- The entire pavement width and the outer shoulder are to be raised with respect to the inner edge by additional filling of earth.
Inspite of above two disadvantages this method is favoured because it does not involve any drainage problems.
In this equation what is ‘g’, it is not explained. Please explain.
‘g’ is represented as the ‘acceleration due to gravity (9.81 m/s^2)’. The formula (e+f= v^2/g.R) is used for the problems when the speed of the vehicle is in ‘m/s’. But generally the speed of the vehicles is calculated in ‘kmph’, hence we use the formula (e+f= v^2/127.R)
g is the force due to gravity. 32.6 ft/sec/sec in English units
if g is equal to 9.81m/s2 how do we get 127 in the formula?
In both the formulas,
e + f = v2 / g.R …(eqn 1)
or
e + f = V2 / 127.R …(eqn 2)
The value of g = 9.81 m/s2 in both the formula and this will not change. Just to simplify the formula the value of acceleration due to gravity (g) is multiplied by the the converting factor of ‘kmph’ to ‘m/s’.
You can use the first equation when the speed of vehicle is in ‘m/s’, but generally the speed of vehicle is mentioned in ‘kmph’, so you have to use the second equation in this case. In second equation the value of ‘V’ i.e speed of vehicle is converted to ‘kmph’. Below we have explained how the value 127 has been occurred in the formula.
e + f = v2 / g.R
The convert the value from kmph to m/s, the speed value must be divided by 3.6.
In the above formula we have to convert the value of ‘v’ from kmph to m/s. To do this we have to divide the speed value by 3.6 and simplify the formula.
e + f = (v/3.6)2 / g.R
e + f = V2 / (3.6)2.g.R
e + f = V2 / 12.96*9.81.R
e + f = V2 / 127.R (after multiplying 12.96*9.81 we get 127.1376. Round off the value to whole number)
This is how you get the value 127 in the super elevation formula used for the speed of vehicles in kmph.
Thank you so much for explaining!
it mean, is 3.6 constant?
Regards
Yes, to convert the value from km/h to m/s, you have to divide the speed value by 3.6, which is a constant. Alternatively, you can also convert the value by multiplying it by 0.28. Both methods are correct.
how did you solve to multiply 3.6square with gR?
Do you mean how to simplify this: (v/3.6)^2 / g.R
I want to conclude it with feet
are you talking about the radius unit?
If you have your road width and radius dimensions in feet then convert it to meter before using this formula. These formulas are standard for meter/kmph units.
My total curve length (i.e tangent to tangent) itself is 77m only. But i get length of transition as 72m. How can i provide transition on both sides (i.e 144m) in 77m total length of curve.? How much should be minimum length of Horizontal or actual curve without (after deducting) transition length?
In your case, with a total curve length of 77 meters and transition lengths of 72 meters on each side (totaling 144 meters), the transition curves would overlap or completely occupy the curve length, leaving no room for the circular arc. This situation is not possible in practical design.
Here’s what can be done:
Re-Evaluate the Curve Design:
1. Transition Length Adjustment: Consider reducing the transition lengths to fit within the 77 meters. However, keep in mind that this may impact the curve’s design speed and overall safety.
2. Increase Curve Length: If possible, extending the total curve length (tangent to tangent) would allow for the required transition lengths while still accommodating the circular arc.
Minimum Circular Curve Length:
Ideally, after deducting the transition lengths, there should be a remaining length for the circular curve. If not, the curve design might need to be adjusted to ensure safety and functionality.
It’s crucial to balance transition lengths and the circular curve within the available space to maintain the curve’s integrity and ensure a safe design.
Note: It’s crucial to consult with a road engineer or site engineer who is familiar with the specific site conditions. They can provide detailed guidance tailored to the actual terrain, traffic, and design requirements.