Super elevation Formula Derivation and Explanation

in this post we will complete Superelevation Formula Derivation i m solving step by step read this post you will bitter understand you and you can design super elevation formula.

Superelevation Formula Derivation and Explanation

the outer edge of a curved road or a railway track is some what at higher level than the inside edge. so that a vehicle may not tilt at the curve . the difference in elevation between both edges is called super elevation . the more the vertical distance between the two edges of a track the more is the magnitude of the super elevation.
in fact when a vehicle is running on a straight path it does not feel the centrifugal force . As soon as the vehicle reaches the curve then the centrifugal force begins to act upon it . this force pushes the vehicle on to the external side . this causes a danger of tilting the vehicle. the more speed of a vehicle the more is the danger of its tilting. in the same way the less the radius of a curve the more is the danger of its tilting this means that the magnitude of super elevation is directly proportion curve . two forces one the weight W of the vehicle and second the centrifugal force P are acting on the vehicle. Both of these pass through the center of gravity of the vehicle.These are perpendicular to each other the weight of the vehicle acts vertically downward while the centrifugal force act horizontally . the surface of a track is set perpendicular to the resultant of these two forces , so the vehicle may not slip away the track of the curve.
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Method of superelevation formula derivation.

                     

                        Figure 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
0 = angle of inclination
h =super elevation
B = breadth of the road
G =gauge of railway track
in this diagram , 0 is the inclination of the road or rail surface , according the geometry of the figure the inclination of the resultant to the vertical also equal to 0 .
There for ;
                         tan0 = bc/ac

                 and also tan0 = P/W

so          P/W = bc/ac  ......(1)

we know that  P/W =  v2/gR ….(2)

it is called centrifugal ration . its maximum value is taken as 1/10 comparing eq . (1) and (2)
bc/ac  = v2/gR            = bc = (ac)v2/gR

h = (ac)v2/gR           =          h = Bv2/gR   (For road)

h = Gv2/gR   (For railways)
                                       in image type Superelevation Formula Derivation

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