The Math Of Roller Coasters.

  The other day my students were discussing the seniors and if they'd be going on a trip.  In past years they've gone to Hawaii or to Los Angeles.  The last group who went to Los Angeles visited six flags and did a bit of sight seeing. 

The nice thing about roller coasters is you can find them as huge creatures or a more portable one that although small is nice. 

The other thing is these amusement park landmarks require a lot of math.  The designer needs to know the maximum velocity a train can go while still thrilling people but not hurting them to the maximum height determined by the building materials. You can build a higher one with steel but it might be cheaper using wood.  On the other hand, if you go for height you have to decide if you want a launch coaster or a crank coaster.  If the coaster is designed to be too extreme, the designer might put a loop in the middle.  This site has a great introduction on the topic.

Just from the introduction, its possible to see that it isn't only the shape of the ride but way more factors.  In addition, information and projects can be found for almost any level of mathematics.  The Mathematical Association of America has a wonderful project on designing roller coasters using derivatives from Calculus.  The project is designed to have students work their way through several modules from start to finish and has everything needed.

NCTM has a nice unit on this topic which begins with students applying a standard equation to a coaster to determine the height of the coaster at a certain point in time. The results are used to find average velocity.  The second activity has students matching results with possible graphs so they have to turn the initial results into ordered pairs.  The final activity has them take their new knowledge to design their own coaster. 

They have a second activity on coasters in which they compare several roller coasters from around the country based on pictures from the web.  Once they've made predictions on fastest, highest, etc, they go to another site to check their predictions.  They repeat this activity a couple of times working to improve their extimates.

The futures channels has a lovely technology based activity which begins with the student being given and equation to work on either a graphing calculator or on a spread sheet.  The activity has students change various coefficients on the 6th degree polynomial and record their results.  Most activities us a second degree equation so this is more complex.

For the upper level math classes Mathspace has an activity which has students choosing the coefficients for a series of polynomials.  They are expected to identify domain, range, zeros, max and min, increasing and decreasing, zeros and other things after graphing each of the four functions.  The nice thing about this activity is that it can be done without a knowledge of Calculus so Algebra classes can do it.

RAFT or  Resource Area For Teaching has a lovely final hands on project to end this by having students build their own roller coaster using slope, rates, ratios, velocity, and speed while working in groups of four.  Students will carry out experiments once the roller coaster is completed.

I think I'm going to have my Algebra II class use the activity from Mathspace to finish out the semester.  I think they'll like knowing how to use the graph information from this unit.  Let me know what you think.  I'd love to hear.