Need help finding the banking angle of a curved road please

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In summary, the correct banking angle for a highway curve of radius 500m designed for traffic moving at 90 km/hr is 89.8 degrees. The calculation involves finding the net forces in the x and y directions and solving for theta using the equations Nsin(theta)=mv^2/R and mgcos(theta)=0. A potential error could be converting the speed from km/h to m/s.
  • #1
Coronita
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A highway curve of radius 500m is designed for traffic moving 90 km/hr. What is the correct banking angle of the road?




I made a force diagram and wrote out the sums of the forces in the x and y then tried to solve for theta I got:

sumFx= -nsin theta=ma=mv^2/r

and

sumFy= -mg+ncos theta=0 --> n=mg/cos theta

then substituted n into the first


I ended up getting 89.6 degrees though...did I just make an algebra mistake or did I go about it the wrong way?
 
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  • #2
I suspect you made an arithmetic mistake. Show the final steps where you solved for theta.
 
  • #3
Your net Fx is incorrect, it should be Nsin(theta)=mv^2/R not -Nsin(theta)=mv^2/R
 
  • #4
mg/cos(theta)*sin(theta)=mv^2/r

mg sin(theta)/cos(theta)=m(90^2)/500


10tan(theta)=8100/500

tan(theta)=162

theta=arctan 162

theta=89.6
 
  • #5
Coronita said:
mg/cos(theta)*sin(theta)=mv^2/r

mg sin(theta)/cos(theta)=m(90^2)/500
Wrong units for the speed. Convert km/h to m/s.
 
  • #6
Thanks! You're right on that one but now I get 89.8 degrees :P
 
  • #7
Coronita said:
Thanks! You're right on that one but now I get 89.8 degrees :P
What's the correct speed?
 

Related to Need help finding the banking angle of a curved road please

1. What is the banking angle of a curved road?

The banking angle of a curved road refers to the angle at which the road is tilted or slanted from the horizontal. It is also known as the superelevation angle and is measured in degrees.

2. Why is the banking angle important for curved roads?

The banking angle is important for curved roads because it helps vehicles maintain stability and prevent skidding or slipping while navigating the curve. It also helps reduce the amount of friction between the tires and the road, allowing for smoother and safer travel.

3. How is the banking angle of a curved road calculated?

The banking angle of a curved road can be calculated using the radius of the curve, the speed of the vehicle, and the coefficient of friction between the tires and the road. There are also online calculators and formulas available for determining the banking angle.

4. What factors affect the banking angle of a curved road?

The factors that affect the banking angle of a curved road include the speed of the vehicle, the weight and size of the vehicle, the radius of the curve, the type of road surface, and the coefficient of friction between the tires and the road. These factors can vary and may require different banking angles for optimal safety and stability.

5. How can I find the banking angle of a curved road?

To find the banking angle of a curved road, you can use a protractor or an inclinometer to measure the angle. You can also consult road design guides or seek assistance from a civil engineer or transportation expert who can analyze the road and calculate the appropriate banking angle based on its specific characteristics.

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