How To Derive Formula For Full Super Elevation Of Highway
Super elevation is one of the most vital terms in the field of highway engineering. So what is this super elevation in highway engineering? The answer that comes directly by analyzing the term is the internal crosswise slope dispensed all over the length of the horizontal curves to thwart the centrifugal force and as a result to verify the propensity of the vehicle to turn turtle or skid.
External edge of the pavement is lifted in compliance with the internal edge of the pavement, the ratio of the height elevated to the width of the pavement is termed as super-elevation. It is symbolized by "e".
See the image below to get an idea of super-elevation in highway engineering
Procedure Of Superelevation Formula Derivation:
W= Weight of the vehicle
P = centrifugal force
V = speed of the car explanation
g = Acceleration due to gravity
R = radius of the curve
θ = angle of inclination
h =super elevation
B = breadth of the road
G =gauge of railway track
In this diagram , θ is the inclination of the road or rail surface , in accordance with the geometry of the figure the inclination of the resultant to the vertical also equal to θ .
Hence,tanθ = bc/ac
and also tanθ = P/W
so, P/W = bc/ac ......(1)
we know that, P/W = v2/gR ......(2)
It is addressed as centrifugal ration. Its maximum value is considered as 1/10 comparing equation (1) and equation (2)
bc/ac = v2/gR = bc = (ac)v2/gR
h = (ac)v2/gR = h = Bv2/gR (For highways)
h = Gv2/gR (For railways)
Now in this detailed demonstration we will find out the step by step method of the derivation of super elevation in highway engineering delivered by Engineer SL Khan.
Video Courtesy : SL Khan