• The “Clothoid Loop: why roller coaster loop the loops are NOT circular

When we look at the roller coasters now in the amusement parks, we will notice that the loops are not perfect circles but instead clothoid loops like the picture below. The perfect loops existed 200 years ago, but they all lasted very shortly, (passengers will literally pass out or break their neck ;() and there’s a physics reason behind that. Through this activity, I learned how the physics concepts we are learning are everywhere in our daily lives.
Modern roller coaster loops are all shaped as clothoid loops. For clothoid loops, the radius for the bottom part closer to the ground is larger than the top as the photo below. We know that when an object is in vertical circular motion, it experiences a force of gravity and normal force (ignoring friction) and these two forces will result in a centripetal force depending on the position of the object. Centripetal force, Fc, could be calculated through the equation Fc = 4π²mr/T² = mv²/r. We know that vertical circles require a certain speed to overcome/make it because we need a positive normal force. To prepare for that speed, the passengers also need a high speed at the bottom of the loop, but humans cannot stand the high speed with rapid changes in directions. Before the passenger enters the loop, fn = fg, when they enter, fn increases to provide fc. So the passenger will feel heavy and pressed down to their seat in less than one second. But with clothoid loops, while maintaining the necessary speed for the top, a higher radius at the bottom will make the centripetal force lower! This allows the whole process of entering and completing the loop to become smoother since fc increases more smoothly as the radius decreases. Decreasing and increasing the radius in the clothoid loop would give the passengers a safer ride.