Superelevation

Superelevation is the transverse slope provided to prevent the effect of centrifugal force and decrease the tendency of the vehicle to overturn and to skid laterally outwards by raising the pavement outer edge with respect to the inner edge. Superelevation is generally indicated by “e”.

Advantages of Superelevation

1. Superelevation increases the speed of vehicles on the highway.
2. It reduces the stresses on-road foundation.
3. It provides stability to vehicles.

Derivation of Superelevation

We have to find the angle of elevation or superelevation

   tanθ  = ^E⁄_B ( Refer above figure )

As we know that, there are three forces acts on any vehicle

Weight of the vehicle     = W kg (↓) ; 

Centripetal force             = P (→);

Frictional forces              = F₁ & F₂ (← ); 

By solving,

 e + f = V²/ 127R

Where,

e= Rate of super elevation

f= Lateral friction factor

V= Velocity of vehicle

R= Radius of circular curve

Thus, P.Cosθ  = W.Sinθ+F₁+F₂
where              F = fR

P.Cosθ = WSinθ + fR₁ + fR₂

= W.Sinθ + f(R₁ + R₂)

= W.Sinθ + f(PSinθ+WCosθ)

P.Cosθ-f.PSinθ = W.Sinθ+f.WCosθ

Divide by “W.Cosθ”;

^{(P.Cosθ-f.PSinθ)}⁄_W.Cosθ  = ^{(W.Sinθ+f.WCosθ)}⁄_W.Cosθ

             ^P⁄_W -(^f.P⁄_W)tanθ = tanθ + f

                 ^P⁄_W (1-f.tanθ) = tanθ+f

                                       ^P⁄_W = ^(tanθ+f)⁄_1-f.tanθ       

                                       ^P⁄_W = e + f

But, ^P⁄_W = V²/ gR

Hence,            e + f = V²/ gR

Where,

e = rate of Super elevation in percent

V = velocity of vehicle in m/s

f = lateral friction factor = 0.15

g = acceleration due to gravity = 9.81 m/s²

R = radius of circular curve in meters.

If velocity is in KMPH then  e + f = V²/ 127R

Super Elevation formula:-

This formula is utilized only to find out one of the missing values either e or f or V or R for design purposes consider the below procedure.

Design procedure of Superelevation:-

The design procedure includes the following steps

Step – 1:-

Find out the Superelevation (e) necessary for 75% design speed [0.75V] and assume no lateral friction is developed.

As per practical conditions, it is suggested that superelevation should be provided to fully counteract the centrifugal force because 75% of the Design Speed (V) by neglecting lateral friction (f=0) developed.

Super Elevation formula = e + f = [V²]/127R

Consider lateral friction f = 0;

75% of design speed which means V= 0.75V

As per formula,

e + f = [V²]/127R

e + 0 = [0.75V]²/127R

e = V² / 225R

Note: e value should not be more than 0.07 

If the calculated value (ecal) is less than (emax) then consider the value of (ecal) if not proceed to the next step,

if  (e_cal<e_max) then e = e_cal  

If the calculated value (e_cal) is greater than (e_max) then consider the value of (e_max)

if  (e_cal<e_max) then e = e_max  

Step – 2:-

Lets assume e = e_max   = 0.07 and proceed to next step.

Step-3: Calculate the value of friction for ‘e’ Value

Super Elevation formula = e + f = [V²]/127R

= 0.07 +f = [V²]/127R

f = [V²]/127R – 0.07

Step – 3:-

From the above step, we found the value of e. Now let’s find the value of the lateral friction (f) for the known value of e_max Value

Super Elevation = e_max + f = [V²]/127R

= 0.07 + f = [V²]/127R

f_cal   = [V²/127R] – 0.07 

If f_cal < f_max (0.15)

Then f_cal = f ;

If f_cal  > f_max (0.15)

Then e = 0.07 is safe.

But if f_cal > 0.15

Then f_cal =f_max (0.15)

Step – 4:-

Lets calculate the value of Restricted Speed (V_a)

Therefore V = V_a

Super Elevation = e + f = [V²]/127R

= 0.07 + 0.15 = (V_a)²/127R

V = [127R(0.22)]^1/2

If V_a > V then e = 0.07, f = 0.15

If V_a < V still e = 0.07 and f = 0.15 but the speed restriction board is provided along with consists the value of V_a.