## 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 (tanÎ¸),

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 CosÎ¸ = W SinÎ¸ + F**

Or,

**P CosÎ¸ = W SinÎ¸ + f(W Cos**

**Î¸**

**+ P Sin**

**Î¸**

**)**

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

**Wv**

**²**

**Cos**

**Î¸**

**/ gR = W Sin**

**Î¸**

**+ f(W Cos**

**Î¸**

**+ Wv**

**²**

**Sin**

**Î¸**

**/ gR)**

**Or, v**

**²**

**Cos**

**Î¸**

**/ gR = Sin**

**Î¸**

**+ f(Cos**

**Î¸**

**+ v**

**²**

**Sin**

**Î¸**

**/ gR)**

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

**v**

**²**

**/ gR = tan**

**Î¸**

**+ f(1**

**+ v**

**²**

**tan**

**Î¸**

**/ gR)**

**Or,**

**v**

**²**

**/ gR = tan**

**Î¸**

**+ f**

**+ fv**

**²**

**tan**

**Î¸**

**/ gR**

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

Now,

**v**

**²**

**/ gR = tan**

**Î¸**

**+ f**

**Or,**

**v**

**²**

**/ gR = e**

**+ f ............(1)**

###
**Superelevation Formula**

If the speed of the vehicle is given as V Km/h, then

v = V⨯1000 / 60⨯60 m/Sec

Or, v = 0.278V

Then the equation (1) becomes

(0.278V)

**²**/ 9.81 R = e + f
Or,

**e + f = V****² / 127R**Superelevation Formula |

###
**Formula Of equilibrium Superelevation
**
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**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.

Equilibrium superelevation (e) =

**V**²**/ 127R**Equilibrium superelevation Formula |

###
**Design Formula of Superelevation as Per IRC**

As per I.R.C, superelevation is calculated at three fourth the design speed

e = (0.75V)² / 127R

Or e = V² / 225R

Design Formula of superelevation as per IRC |

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