# How to Calculate and Solve for Superelevation, Guage of Track, Velocity and Radius of a Body in Circular Path Motion | The Calculator Encyclopedia

To calculate the Superelevation, four essential parameters are needed and these parameters are the Gauge of the track (G), the velocity of the body (v), the radius of the curve (r), and acceleration due to gravity (g).

The formula for calculating the circular path motion:

S = GvÂ² / gr

Where:
S = Superelevation
G = Gauge of the track
v = velocity of the body
r = radius of the curve
g = acceleration due to gravity

Let’s solve an example;
Find the circular path motion when the Gauge of the track is 14, the velocity of the track is 47, the radius of the curve is 21, and acceleration due to gravity is 9.8.

This implies that;
G = Gauge of the track = 14
v = velocity of the body = 47
r = radius of the curve = 21
g = acceleration due to gravity = 9.8

S = GvÂ² / gr
S = 14 x 47Â² / 9.8 x 21
Then, S = 14 x 2209 / 205.8
S = 30926 / 205.8
S = 150.27

Therefore, the superelevation is 150.27 m.

### Calculating the Gauge of the track when Superelevation, Velocity of the body, Radius of the curve and Acceleration due to gravity

G = Sgr / v2

Where;
G = Gauge of the track
S = Superelevation
v = velocity of the body
r = radius of the curve
g = acceleration due to gravity

Let’s solve an example;
With a superelevation of 180, the velocity of the body is 32, the radius of the curve is 12 and the acceleration due to gravity is 9.8. Find the gauge of the track.

This implies that;
S = Superelevation = 180
v = velocity of the body = 32
r = radius of the curve = 12
g = acceleration due to gravity = 9.8

G = Sgr / v2
That is, G = 180 x 12 x 9.8 / 322
G = 21168 / 1024
G = 20.67

Therefore, the gauge of the track is 20.67.

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### Calculating the Velocity of the body when Superelevation, Gauge of the track, Radius of the curve and Acceleration due to gravity

v = âˆšSgr / G

Where;
v = velocity of the body
S = Superelevation
G = Gauge of the track
r = radius of the curve
g = acceleration due to gravity

Let’s solve an example;
With a superelevation of 120, the gauge of the track is 28, the radius of the curve is 7, and acceleration due to gravity is 9.8. Find the velocity of the body.

This implies that;
S = Superelevation = 120
G = gauge of the track = 28
r = radius of the curve = 7
g = acceleration due to gravity = 9.8

v = âˆšSgr / G
v = âˆš120 x 9.8 x 7 / 28
So, v = âˆš8232 / 28
v = âˆš294
v = 17.146

Therefore, the velocity of the body is 17.146.

### Calculating the Radius of the curve when Superelevation, Gauge of the track, Velocity of the body and Acceleration due to gravity

r = Gv2 / Sg

Where;
r = radius of the curve
v = velocity of the body
S = Superelevation
G = Gauge of the track
g = acceleration due to gravity

Let’s solve an example;
With a superelevation of 170, the gauge of the track is 18, the velocity of the body is 9, and acceleration due to gravity is 9.8. Find the radius of the curve.

This implies that;
S = Superelevation = 170
G = gauge of the track = 18
v = velocity of the body = 9
g = acceleration due to gravity = 9.8

r = Gv2 / Sg
r = 18 x 92 / 170 x 9.8
Then, r = 1458 / 1666
r = 0.875

Therefore, the radius of the curve is 0.875.

### How to Calculate Superelevation of a Body in Circular Path Motion Using The Calculator Encyclopedia

Nickzom Calculator â€“Â The Calculator Encyclopedia is capable of calculating the superelevation.

To get the answer and workings of the superelevation using the Nickzom Calculator â€“ The Calculator Encyclopedia.Â First, you need to obtain the app.

You can get this app via any of these means:

To get access to theÂ professionalÂ version via web, you need toÂ registerÂ andÂ subscribeÂ forÂ NGN 1,500Â perÂ annumÂ to have utter access to all functionalities.
You can also try theÂ demoÂ version viaÂ https://www.nickzom.org/calculator

Apple (Paid)Â â€“Â https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to theÂ Calculator Map,Â then click onÂ MechanicsÂ underÂ Engineering

Now, Click onÂ Motion of Circular PathÂ underÂ Mechanics

Click on SuperelevationÂ underÂ Motion of Circular Path

The screenshot below displays the page or activity to enter your value, to get the answer for the superelevation according to the respective parameter which are the Gauge of the track (G), velocity of the body (v), radius of the curve (r) and acceleration due to gravity (g).

Now, enter the value appropriately and accordingly for the parameter as required by the Gauge of the track (G) is 14, velocity of the body (v) is 47, radius of the curve (r) is 21 and acceleration due to gravity (g) is 9.8.

Finally, Click on Calculate

As you can see from the screenshot above,Â Nickzom Calculator â€“ The Calculator Encyclopedia solves for the superelevation and presents the formula, workings and steps too.