# Analysis of Superelevation

Let, W = Weight of the vehicle,

v = Speed of the vehicle in m/sec,

g = Acceleration due to gravity in m/sec²,

f = Coefficient of friction,

e = rate of superelevation (tanθ),

F = Frictional force resistance due to centrifugal force,

P = Centrifugal force.

Now, **P = Wv****²/gR**

Analysis of Superelevation Formula as Per I.R.C |

**
**For equilibrium, resolving the forces parallel to the inclined plane, are

**P Cosθ = W Sinθ + F**

Or,

**P Cosθ = W Sinθ + f(W Cos**

**θ**

**+ P Sin**

**θ**

**)**

**After putting the value of P(P = Wv²/gR) we get,**

**Wv**

**²**

**Cos**

**θ**

**/ gR = W Sin**

**θ**

**+ f(W Cos**

**θ**

**+ Wv**

**²**

**Sin**

**θ**

**/ gR)**

**Or, v**

**²**

**Cos**

**θ**

**/ gR = Sin**

**θ**

**+ f(Cos**

**θ**

**+ v**

**²**

**Sin**

**θ**

**/ gR)**

**Now, both side divided by Cosθ, After that we get the following equation:**

**v**

**²**

**/ gR = tan**

**θ**

**+ f(1**

**+ v**

**²**

**tan**

**θ**

**/ gR)**

**Or,**

**v**

**²**

**/ gR = tan**

**θ**

**+ f**

**+ fv**

**²**

**tan**

**θ**

**/ gR**

The term fv² tanθ / gR being too small and can be neglected.

Now,

**v**

**²**

**/ gR = tan**

**θ**

**+ f**

**Or,**

**v**

**²**

**/ gR = e**

**+ f …………(1)**

**Superelevation Formula**

**²**/ 9.81 R = e + f

**e + f = V**

**² / 127R**

Superelevation Formula |

**Formula Of equilibrium Superelevation **

**If we provide e =**

**V**²

**/ 127R,**then the value of f will be equal to zero and the lateral friction will not be considered. This superelevation is called equilibrium superelevation.

**V**²

**/ 127R**

Equilibrium superelevation Formula |

**Design Formula of Superelevation as Per IRC**

Design Formula of superelevation as per IRC |