TRANSPORTATION ENGINEERING - Superelevation on Highways

Dear readers, today I am going to discuss about the term 'Superelevation' that is frequently used in Transportation Engineering.
Transportation Engineering is the branch of Civil Engineering that mainly deals with design, construction and analysis of highways. That is why it is sometimes also known as Highway Engineering.
While designing the highways the safety of passengers is of utmost importance followed by comfort of passengers while travelling at high speeds. For designing the highways many different studies are carried out like speed study, traffic volume study, accident study etc. The main problem lies in designing the highway on curves when it should be designed such that no skidding of vehicle should take place. Skid is the term that is used when longitudinal movement of vehicles is more than circumferential movement of the tires. Slip is the term that refers to the condition when circumferential movement is more than longitudinal movement of vehicle. So skidding is the main problem that can occur on the curves when vehicle is moving in circular motion at high speed due to centrifugal force. To clear your doubts regarding circular motion there is a video below that will explain the circular motion and basic terms related to it.

(Clip showing basics of Circular Motion)

So now we will continue to the technical part that is involved in providing superelevation on highways. Superelevation is the rise provided to the outer part of the road on curves to prevent skidding of vehicle due to centrifugal force. The figure shown below represents various forces that are involved while vehicle is moving along the curve on highway.

Figure 1.1 : Showing direction of frictional force along the tires

Figure 1.2 : Showing various forces and their components

As shown in the figure 1.1 "e" is the superelevation provided. e multiplied by total width of road will give you total rise "E" required on highways. W=m×g and P=mv²/r 

where W - Weight, m - Mass, g - Acceleration due to gravity, P - Centrifugal force, v - Velocity of vehicle, r - Radius of curve.

Now as depicted from figure Pcosθ=Wsinθ+F_b, where F_b is frictional force and is equal to 

f(Wcosθ+Psinθ).

Therefore Pcosθ=Wsinθ+f(Wcosθ+Psinθ), where f is frictional coefficient. Putting values of W and P we get,

(mv²/r)cosθ-(mg×sinθ)=f(mg×cosθ)+f(mv²/r)sinθ. 

Reducing the equation after dividing by gcosθ  we get,

v²/gr - tanθ = f + f(v²/gr)tanθ, from figure 1.2 tanθ= E/B= e

v²/gr(1-fe)= f+e. Since f i.e frictional factor's maximum value is 0.14 and maximum value of e i.e. superelevation 0.07 so f×e being very small can be neglected. Hence we get

v²/gr=f+e.

Where v is design velocity

g is acceleration due to gravity

r is radius of curve

f is frictional coefficient subject to maximum of 0.14

e is superelevation provided subject to maximum of 0.07

From the above equation we can decide superelevation or we can determine new design velocity if value of superelevation is exceeding its maximum value i.e 0.07.

Therefore while designing highway on curves we should provide designed superelevation so that vehicles can take turn at design speed without skidding. The rise so provided is introduced by different methods that will be discussed in other post. Hope the topic was helpful to you.

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