I learned that modern roller coasters do not use perfect circular loops. Instead, they use a Clothoid loop, which has a changing radius that starts wide at the bottom and gets smaller near the top. This design is based on physics circular motion principles and makes the ride safer, smoother, and more efficient (allows for longer roller coaster carts, which means more capacity)
Perfect Circular Loops Create Dangerous G-Forces
In a circular loop, the radius stays the same throughout. Since roller coasters move the fastest at the bottom of the loop, this creates a very high centripetal acceleration and g-forces on the rider when entering and exiting the loop.
Example Calculation:
If the coaster is moving at 20 m/s and the loop radius is 8 meters:
This is equal to 5.1g, which is a lot of g force for the human body to handle. Therefore, this loop would be an unsafe and uncomfortable ride.
The Clothoid Loops adjusts the radius to control g-force
Clothoid loops start with a large radius at the bottom (where speed is highest) and a smaller radius at the top (where speed is lower).
- At the bottom of the loop, the increased radius leads to less g-force when entering and exiting the loop, as g force depends on the radius. Bigger radius with same speed = less g-force
- At the top of the loop, the decreased radius means that it needs less speed into the loop to still have Fc ≥ Fg and make it around the loop.
These two factors in changing the radius allow for a smoother ride, with a more consistent force throughout the loop. This makes the ride more enjoyable and safer.
Example Calculation:
If a roller coaster is moving at 20 m/s at the bottom of a loop with a radius of 13 meters, and then reaches the top of the loop, where the radius is 6 meters and they are traveling at 12 m/s.
This is equal to 3.1g at the bottom and 2.4g at the top, which is an acceptable amount for the human body to handle during the loop and gives a more consistent amount of g-force spread throughout the loop.
Core Competencies
To complete this project, I used my Critical and Reflective Thinking by using physics formulas and applying them to real-world roller coaster designs. I had to think carefully about how changing variables like speed and radius affected the outcome, and why engineers design loops the way they do. I also used the Communication Competency by clearly organizing my ideas and using examples to explain complex concepts in a way that others can understand. These skills helped me understand the science behind roller coasters and explain it effectively in my blog post.
Conclusion
- Circular loops are dangerous due to the high g-forces at the bottom.
- Clothoid loops reduce these forces by adjusting the radius to match how speed changes throughout the loop.
- Engineers use physics, including centripetal acceleration to create rides that are thrilling and safe.