How to Create a Hot Wheels Loop in Real Life

Hot Wheels has been considered one of the classic toys of all time. The original vehicles were miniature versions of real models like the Chevy Camaro, and tracks could be built for them to perform astonishing stunts, all powered by gravity. However, were those stunts really impossible? It turns out that some are viable, although perhaps not advisable.

Let's imagine a situation: a human gets into a large toy car to descend a track. At the end of this track, there is a vertical loop that allows for a complete 360-degree turn. If this were attempted in real life (which is not recommended), one shouldn't proceed by trial and error like when assembling those orange track segments. Instead, it would be necessary to model the physics to determine the correct size of the loop and the height from which the car should be launched.

Let's start with the calculations. Suppose we set up a ramp that descends into a loop, with the top of the loop being approximately 4 meters above the ground. The question is: at what height should the car be released on the ramp? For this, we can visualize it in terms of energy. At the top of the track, the car possesses gravitational potential energy (U), which depends on its height (h) and the gravitational force, calculated as mass (m) multiplied by the gravitational field (g). As the car descends, its height decreases and, therefore, its potential energy also decreases.

However, for the Earth-car system as a whole, the total energy remains constant, which we know as the conservation of energy. Thus, when potential energy decreases, the car must acquire energy of another type, which is kinetic energy (KE), determined by its mass and velocity (v). Upon reaching the ground, the car has zero potential energy and a certain amount of kinetic energy. As it ascends the loop, it slows down and increases its potential energy.

We can consider three key points on this track: point 1 is the top, point 2 is the bottom, and point 3 is the top of the loop. As we mentioned, total energy remains constant at all three points. Therefore, one might think that for a loop of 4 meters in height, the car should start its journey from that same height. However, this is not advisable. Even though the car would reach the highest point of the loop, its kinetic energy would fall to zero, causing it to plummet straight down.

To complete the loop, the car must maintain a certain speed at the top. What is the minimum speed required? Let's assume the loop is a perfect circle with a radius R. At the top of the loop, there are two forces acting on the car: the gravitational force (mg) downward and the contact force from the track (FT), also downward. If both forces act downward, why doesn’t the car fall? It is important to remember that forces do not directly cause motion; rather, they produce changes in that motion, which we call acceleration.

In fact, the acceleration is directed toward the center of the circle. When an object moves in a circle, the direction of its velocity vector changes, meaning it is accelerating even if it maintains a constant speed. This acceleration is known as centripetal acceleration (ac), and its magnitude depends on the object's speed (v) and the radius (R) of the circular motion.

Newton's second law states that a net force (Fnet) equals mass times acceleration. By considering only the vertical component of the motion, we can derive the necessary relationship for the car to remain in motion. If the speed decreases too much, the centripetal acceleration would be insufficient, and the only way to balance the equation would be for the force from the track to push the car upward, something that doesn’t happen, as the track only provides an outward force.

We can calculate the minimum speed by setting the track force equal to zero. Once we have this minimum speed, we can use it in our energy equation to determine the initial height from which the car should be released at the start of the ramp. Since the loop is circular, the height of the loop will be twice the radius (2R). If the loop is 4 meters high (with a radius of 2 meters), the car should be released from 5 meters above the ground to complete the loop properly, assuming no energy loss due to friction; it might be wise to start a little higher.

On the other hand, it is not advisable to release the car from an excessively high height. As the car speeds up, the G-forces experienced by the driver during the loop also increase. If the car is released just at the minimum speed, there will be no force from the track, leading to a temporary sensation of weightlessness. However, if the car is released from a height greater than 2.5R, the speed at the top of the loop would exceed the minimum required. In this case, the gravitational force would not be enough to maintain circular motion, and the track would have to exert additional downward force, generating G-forces greater than zero.

By observing the video of the stunt, it can be estimated that the loop has a radius of 2 meters and the car is released from a height of about 8 meters. The force at the top of the loop, divided by the weight to get the measurement in G-forces, turns out to be 3 G's, which is within the limits tolerable for humans. However, experiencing a height of 20 meters with a loop radius of 1.5 meters could generate dangerous forces of up to 21 G's. Although it may seem impressive, it also represents a serious risk.