Ferris Wheel Math

  Just about any traveling amusement entertainment or amusement park has at least one Ferris wheel.  I remember living in the middle of a flat dusty part of New Mexico over near the Texas boarder and the carnival arrived in town with a large number of rides including the Ferris wheel.

I am the member of the family who hated going up on those rides because I had a horrible fear of heights and I still do.  I end up gripping the bar, closing my eyes, and praying till the ride is over.  I love looking at them from a distance and the math is so elegant but please don't make me get up in one.

Fortunately for me, there is a nice amount of math associated with a Ferris Wheel.  As you can tell from the weekend warm-ups, there is always the circumference and area.  Students could also design a scale model of a Ferris wheel complete with seats and everything.  They could determine how far apart the seats are either in feet or in degrees since the wheel has 360 degrees.

A Ferris Wheel has quite a lot of trig associated with it so its possible to use this topic in Geometry, Trigonometry, or Algebra II. For Geometry, you can calculate circumference, area,  and surface area.  The Ferris Wheel provides a great way of applying sine and cosine functions.  For Trig and Algebra II student can calculate rates for the Ferris Wheel

 If you have students create a Ferris Wheel out of paper and a brad, they can play with it to determine the height of a passenger car from the ground as it turns.  Students can take readings every 15 degrees.  Once done, the heights can be placed on  a graph so students are able to see the graph resembles a sine wave.

Students can also relate the unit circle to sine and cosine waves if the student places the sine and cosign values as riders in each car.  As the car hits the bottom where people get off, the values can be graphed showing the relationship between the unit circle and the graphs of both the sine and cosine.  

Another activity would be to place a circle on graph paper to determine which parts of the ride would have positive values, negative values, a mixture in respect to the x and y axis.  Let the student know they begin at the positive x axis.

In addition, its possible to include the math an engineer or designer might use to design a Ferris wheel. This site has a lovely write up on what parts are used to create one.  It is good to relate the application to the theory so students see practical applications for the math they are learning.  Its only due to teaching that I've found real life applications for much of the theory I'd learned at school. I love that but wish they'd covered it when I was in school.

Let me know what you think.  I'd love to hear.  Have a great day.