roller coasters?

Question

Does any one know any good websites i can use to find information on how math is important with roller coasters? I need info on like angles and diagrams and construction and formulas and other things.

Answer 1

I don't know of any websites, but I can tell you in general:

You need the math in order to be able to calculate all of the forces involved in the roller coaster, in order to make sure that it works and works safely BEFORE you try to build it -- you can just imagine what a disaster it would be if you first built the roller coaster, then found out it either didn't get all the way up the second hill or else it broke peoples' necks when it went around the first curve.

Math is the "language" of physiscs, and physics is the study of moving things. Since a roller coaster is a moving thing, math is needed to understand and describe what forces will operate in it and how it will function.

So for example you will need math to understand how strong of a motor you will need in order to hoist the roller coaster up to the top of that first big hill. This will be a formula based on the weight of the roller coaster cars, their rolling friction, the angle of the climb, and the efficiency of the motor.

Next you will need math to describe how fast the cars will be moving when they get to the bottom of the first hill -- this is an equation that is based onthe angle of the hill (which will determine how much the cars will accelerate) and the distance of the downhill part of the hill.

Then you will need math to make sure that the way the tracks come back up at the bottom of that downhill section is not too sudden --there is a formula for "centripedal accelleration" which converts the speed of the cars and the diameter of the curve into a vlaue for the accelleration the riders will feel or in other words "how many gees they will experience" -- if you make them accellerate too hard, all those gees will make them black out.

Now we have got up and down the first hill and are heading up the second one: we need more math to figure out how big of a second hill we can climb just from our momentum, so there is a formula for converting the cars speed (from two calculations ago) into a maximum height based on the accellertaion due to gravity and the friction of the wheels -- we want to make sure the car does not slow all the way down to zero speed, or it will get stuck.

But after climbing that hill, there is a sharp turn -- and if we hit it too fast, we are going to break peoples' necks. So we use more math to calculate the ideal speed to enter that turn (this is centripedal acclleration again) without hurting anyone, and that is the fastest we ever want to enter that turn. This information then feeds back to the calculation about how high this second hill should be, because if it is not high enough then we enter this fast turn too quickly and people get hurt, but if we make that second hill too tall we will enrter the turn too slowly and it will be boring (or worse yet the coaster will come to a stop in the middle of the curve).

Beyond that there are math formulas for making sure we "bank" the turns at the right angle so that the riders only feel gee forces pressing them down in thei seats and not slamming them into the side of the car, and so on -- this goes on and on for every hill and curve of the coaster.

When all of this is worked out, math helps calculate how to make the roller coaster structures strong enough to withstand all the forces acting on it.

And finally, math helps the owners of the amusement park figure out how much to charge to ride the roller coaster. By adding together the cost to operate the roller coaster from day to day (operators, repair people, advertising, electricty, and so forth) and dividing that by the number of people expected to ride the roller coaster each day, they can figure out how much they must charge just to keep the coaster running from day to day. Add on to that the total cost of building the coaster, plus the cost of repair parts needed throughout the life of the coaster, and divide that by the total number of people EVER expected to rde the coaster, and you have the amount that must be added to actually pay for the coaster itself. Finally you need to add on the amount needed to pay for other people and things at the amusement park that are not directly making money (trash collecting, the people in costumes, and so on) and then a profit margin, and you can finally calculate how much you must charge each person who wants to ride the roller coaster.

Answer 2

There are many good websites out there. Here is one.

http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html

Engineers design roller coasters. They need to know the alignment and profile and mass of the roller coaster to conduct the calculations. You are asking how to engineer a roller coaster. I assume you are no engineer, nor is your audience.

Let me summarize. Roller coasters are designed by engineers. Engineers communicate in mathematical calculations and to scale drawings. The web site above has some great discussion and illustrations of the physics involved in a roller coaster. F = m v^2/r for instance. But to understand this simple formula, you need to understand coordinate systems, vectors and dimensional analysis.

Please note: There is no such thing as a construction formula.