Theme Parks and Mathematics 

This is one of a new type of web page we are introducing to give you examples of where mathematics is used outside the classroom. This one shows the type of mathematics you will find in theme parks and fairgrounds.

<<<<----- To download the ALGEBRA 2 Higher level worksheets, click on the diagram on the left.

Why not also view the trial videos available from the link on the home page?


If you are really looking for examples of mathematics that you can observe and 'feel' in the flesh, as it were, theme parks and fairgrounds are the place to go.


Here you see the world's very first Ferris Wheel or Big Wheel as it is often called. It was built for the World's Columbian Exposition, 1893.


At the time it was one of the world's largest rotating structures and you will see many triangles have been used in its design as triangles provide a very strong basic unit from which other, larger structures may be made. So the first thing you need to design a ferris wheel like this for a theme park is a good knowledge of forces and inherent strength of materials such as steel. When you visit a theme park such as Thorpe Park, Chessington or Alton Towers, take a look at any similar structures you may see and work out how you would go about designing them.





Roller Coasters

Look carefully at this structure and you will see that the roller coaster (often called a 'switchback' in days of old) is built from rectangular supports, but the supports are strengthened with cross struts, making many triangles that add the rigidity and strength such a structure needs. Older versions of roller coaster were very tough on a person's back and other vulnerable parts of the body, because as the trains reached the joins between the various parts of the track, it would be swung violently from side to side, giving a very uncomfortable ride.

Modern rides use things special curves called 'cubic splines' which are based on cubic graphs in three dimensions. The great advantage of these is that they join together without any sudden jerks, so the ride is much smoother (although no less frightening!).




In this design of rollere coaster, you can see the ride is very smooth, but there are those triangles again!






Up to now, we have seen static structures, with the exception of the ferris wheel, of course. Here we have a carousel which represents one of the simplest types of motions, but even this is more complex than it looks as each horse is going around and around as well as up and down. Above each horse is a mechanism for lifting the horse and rider and this is normally a rotating shaft linked to the central column around which the whole ride rotates. It is fascinating to watch a small piece of the lifting mechanism as it rotates in a vertical plane and goes around the ride in a horizontal plane. Can you work out its equation of motion?

I have not seen one of these at Thorpe Park or Alton Towers, but I have not been to Chessington, so cannot comment on that.

They are plentiful in travelling fairgrounds.


Super Star

This type of ride has many names depending on where in the world it
originates. It is sometimes called a 'Super Star' ride.

Now this is where the mathematics really starts to kick in. Not only do we have structures to support the ride, but we now have high speeds and accelerations to contend with. The engineers that design these rides must be very highly qualified with excellent mathematics qualifications (GCSE, A level, Degree etc) so that they can calculate how the rides may designed to withstand the loads and include a substantial safety margin to protect the passengers. Thorpe Park, and the other major theme park sites such as Chessington and Alton Towers have excellent safey records, which is in part due to professional design of the rides and also to constant surveillance and regualr checking of rides.



Blackpool Big Dipper

Some years ago, my daughter challenged me to a ride on the Blackpool Big Dipper, which we both thoroughly enjoyed.

As you can see, it a pretty complicated design and every piece had to be fitted into the whole, with due allowance made for imposed force, vibration etc. Quite a fete, really.





Thorpe Park

Thorpe Park is one of the largest theme parks in the south east of England (Chertsey) and was begun in 1979. The park's first roller coaster was added in 2002.

Chessington World of Adventures

Situated south west of London, Chessington World of Adventures was originally just a zoo. When zoos declined in popularity due to an increase in excellent television programmes, it was decided to revamp the site, which was a valuable asset in its own right. The zoo remains, but the main attractions now are the fairground rids, making Chessing World of Adventures the third most visited theme park in the UK.

Alton Towers

Alton is situated in the midlands in Staffordshire and there provides easier access for the people living in the north of the country. Rita, a launched roller coaster accelerates to 100 km/h (62 mph) in approximately 2.5 seconds. Most cars take about 8 - 10 seconds to reach this speed from a standing start, so watch out for the acceleration if you decide to give it a go!