Physics Behind Design and Action of Roller Coasters


The study aims at discussing the Physics behind the design and action of roller coasters by first stating the definition of a roller coaster. A roller coaster is a type of amusement ride that employs a form of elevated railroad track design with tight turns, steep slopes, and sometimes inversions (Wikipedia). The study tries to answer which Physics concepts apply to the action and design of roller coasters and tries to explain them. The study tries to explain which forces are involved and how they apply in relation to physics knowledge. The study explains the various Physics laws applied too.

History of Roller Coasters

Roller coasters originated from the Russian Ice Slides. The slides first appeared during the 17th century throughout Russia; with a concentration in the area that would become St. Petersburg. The structures were built out of lumber with a sheet of ice several inches thick covering the surface. Riders climbed the stairs attached to the back of the slide, sped down the 50-degree drop, and ascend the stirs of the stairs that lay parallel (and opposite) to the first one. It is known that by 1817 two coasters were built in France known as the Russian Mountains of Belleville and The Aerial Walk. Several upgrades have been made and now there are several types of steel roller coasters. 

The Aerial Walk featured a heart-shaped layout with two tracks that flowed in opposite directions from the central tower. They then went around the course, came together at the bottom, and ascend parallel lift hills.

The first looping coaster was located in Frascati Gardens in Paris, France. The hill was 43 feet high, had a 13-foot wide loop, and was tested with everything under the sun before humans were allowed on. The layout was simple: the rider rode down the gentle slope on a small cart and through a meal small circle. 

The Physics behind Design and Action of Roller Coasters

One’s body feels accelerated in a funny way when a coaster car is speeding up and pulled into the seat as stated by this applies the Newton’s First Law of motion which states that a body remains in its state of rest or motion in a straight line unless acted upon by an external force-Law of Inertia.

Similarly, if the coaster accelerates down fast enough, the upward acceleration force exceeds the downward force of gravity, making you feel like you are being pulled upward if you are accelerating up a steep hill; the acceleration force and gravity are pulling in roughly the same direction, making you feel heavier than normal as stated by.

That explains the laws of Physics related to the roller coaster and one’s body.

As you go around a loop-the-loop, your inertia not only produces an exciting acceleration force but also keeps you in the seat when upside down.

The main principle behind all roller coasters is the law of conservation of energy, which states that energy can neither be created nor destroyed but transformed from one form to another. In roller coasters, the two forms most important forms of energy are gravitational potential energy and kinetic energy. Gravitational potential energy is the energy that an object has due to its height and is equal to the object's mass multiplied by the height multiplied by the gravitational constant(PE=mgh).

Gravitational potential energy is always greatest at the highest point of a roller coaster and least at the lowest point. Kinetic energy on the other hand is the energy an object has due to its motion hence the name kinematics means the study of motion and is equal to a half multiplied by the mass of the object multiplied by its velocity squared.( KE= 1/2mv2).

KE = Kinetic Energy, m= mass of the body, v= velocity of the body.

The kinetic energy is greatest at the bottom and lowest at the top. This implies that the roller coaster is fastest at the bottom. Potential energy and kinetic energy can be exchanged for one another, so at certain points, the car of the roller coaster may just have potential energy (at the top), Just kinetic energy (bottom), and a combination of both at all the other points as illustrated in figure 2 above. The first hill of the rollercoaster is always the highest part of the roller coaster because friction and drag immediately begin robbing the car of energy. At the top of the first hill, the car's energy is almost entirely gravitational potential energy (because its velocity is zero or almost zero). This is the maximum energy that the car will have during the ride as stated by.

Friction force which hinders motion exists in all roller coasters, and it takes away from the useful energy provided by the roller coaster. Friction is caused in roller coasters by the rubbing of the car wheels on the track and by the rubbing of air (and sometimes water) against the cars. Friction turns the useful energy of the roller-coaster to heat energy, which is unnecessary. Friction is also the reason that roller coasters can never regain their maximum height after the initial hill unless a second chain lift is incorporated somewhere on the track, and they can’t go forever as stated by.

Cars can only make it through loops if they have enough speed at the top of the loop. This minimum speed is referred to as critical velocity and is equal to the square root of the radius of the loop multiplied by the gravitational constant (vc= (rg) 1/2).

Where vc= critical velocity, r= radius, g=gravitational constant, as stated by (Liddle. S, 2013.

Most roller coaster loops are not perfectly circular in shape but have a teardrop shape called clothoid. Roller coaster designers discovered that if a loop is circular, the rider experiences the greatest force at the bottom of the loop when the cars are moving fastest, following the principle of maximum tension in a vertical circle at the bottom of uniform circular motion. After many riders sustained neck injuries, looping roller coasters were abandoned in 1901 and revived in 1976 when Revolution at Six Flags Magic Mountain became the first looping roller coaster using a clothoid shape. In a clothoid shape, the radius of curvature of the loop is widest at the bottom, reducing the force on the riders when the cars move fastest and smallest at the top when the cars are moving relatively slowly as stated by.

Riders also often feel weightless at the hilltop and heavy at the bottom. This feeling is caused by the changing direction of roller coasters.


In conclusion, Roller coasters in Amusement Parks are upgraded and designed basically taking into account Physics laws practically in their motion, design shapes, and safety. They borrow Physics concepts of gravity, uniform circular motion in the loop types, Newton’s First Law of Motion- Inertia Law, friction, and the backbone concept being The Law of Conservation of Energy. Numerous forces are involved in the daily motion of roller coasters too to ensure the perfect functioning of the roller coaster and to keep it in balance. Work and energy are mainly potential energy and kinetic energy, gravity, and some uniform circular motion too in cases where the roller coasters take circular paths. Gravity plays a huge part in roller coaster physics. As the coaster gets higher the cars are pulled down faster by gravity and move faster along the tracks. Friction forces also play a role in roller coasters and Newton’s First Law of Motion as well which states that a body remains in its state of rest or motion in a straight line unless acted upon by an external force which answers the question of Physics behind roller coasters from the study. In the coming 100 years


  1. (Sandy. A, 2007. The beginning of roller-coasters. Article (online) Available at: Accessed (25/1/19).
  2. Harris. T, 2010.
  3. Palmer, 2015.
  4. Gunn. L, 2015. (Liddle. S, 2013.
01 August 2022
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