Designing a Curved Highway Exit Ramp

In summary, the engineer must bank the curve at an angle of theta with respect to the horizontal in order for the car to round the curve without skidding.
  • #1
BuBbLeS01
602
0
Hi everyone, I just need some help on setting up a free body diagram with the appropriate forces acting on it.

The question is:
An engineer must design a curved exit ramp for a highway in such a way that a car, exiting at the posted speed limit of 17.88 m/s (40 mi/hr), does not depend on friction to round the curve without skidding. The radius of the curve is 208.0 m. At what angle with respect to the horizontal must the curve be banked (in degrees)?

I m confused as to whether to draw the angle theta with respect to the x-axis or y-axis? I already got the answer I am just reviewing for a test I am having.

Thank you!
 
Physics news on Phys.org
  • #2
I've seen questions like this, and when I drew a FBD I always drew it lengthwise to the car, so on a graph, looking from the front or back of the car, the x-axis is the ground, and the car's direction is headed in or out of the page. Therefore, the angle theta would be with respect to the x axis. In any case, the other angle WRT the y-axis is just 90 degrees - theta!
 
  • #3
Thats what I thought, the x-axis, but then the normal force becomes ncos(theta) and its supposed to be sin. So what am I doing wrong?
 
  • #4
The normal force is just directional , and how you calculate it you will not necessarily use sin always... you may have to use cos sometimes, depending on how you drew your component forces, and as long as you can prove in your FBD that it is cos, then that's what it is. It's not necessarily wrong, it just so happens that in most examples the instructor may have used sin.
 
  • #5
Then again you did say you have the answers...does it show a diagram of how the FBD was presented? if so then obviously it should show why sin was used.
 
  • #6
No it doesn't, that's why I am confused about it.
 
  • #7
Maybe the angle was of the one not to the x axis, but the angle up that forms with the line perpendicular to the x axis. If that's so then it'd be sin theta. But like I said, as long as you end up with the right answer - regardless of which angle you used and whether you used sin or cos, as long as it makes sense and you get the correct value of the normal force, then you know you did it correctly.
 
  • #8
How would I go about solving this same problem, only with a different radius?
 

1. How do you determine the appropriate curve radius for a highway exit ramp?

The appropriate curve radius for a highway exit ramp is determined by several factors, including the design speed of the ramp, the angle of the curve, and the size and type of vehicles that will be using the ramp. The design speed is typically determined by the posted speed limit for the ramp, while the angle of the curve is based on the curvature of the road and the desired vehicle speed. The size and type of vehicles can also affect the curve radius, as larger and heavier vehicles may require a wider radius for safe navigation.

2. Are there any safety guidelines or standards for designing a curved highway exit ramp?

Yes, there are safety guidelines and standards that must be followed when designing a curved highway exit ramp. These guidelines are set by organizations such as the Federal Highway Administration and the American Association of State Highway and Transportation Officials. They include recommendations for the design speed, curve radius, lane width, and superelevation (banking) of the ramp to ensure safe and efficient navigation for all vehicles.

3. How do you account for different weather conditions when designing a curved highway exit ramp?

When designing a curved highway exit ramp, different weather conditions must be taken into consideration to ensure safe and reliable operation of the ramp. This can include designing for proper drainage to prevent water buildup on the ramp, as well as providing adequate lighting and signage for visibility during inclement weather. Additionally, the materials and construction methods used for the ramp may need to be adjusted for different weather conditions to ensure durability and stability.

4. Can a curved highway exit ramp be designed for both high-speed and low-speed vehicles?

Yes, a curved highway exit ramp can be designed to accommodate both high-speed and low-speed vehicles. This can be achieved through the use of lane width transitions, which gradually widen or narrow the lanes to accommodate different vehicle speeds. Additionally, the superelevation of the ramp can also be adjusted to provide a more comfortable and safe curve for low-speed vehicles, while still allowing high-speed vehicles to navigate the curve efficiently.

5. How do you ensure proper merging onto the main highway from a curved exit ramp?

Proper merging onto the main highway from a curved exit ramp is crucial for the safety and efficiency of traffic flow. To ensure this, the design of the ramp should include a sufficient acceleration lane, which allows vehicles to reach the desired speed before merging onto the highway. The design of the ramp should also consider the sight distance for merging vehicles, as well as the design of the merge area to minimize conflicts with other vehicles on the highway.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top