You are to design a roller coaster using the knowledge you have learned from physics and the book Roller Coaster Physics.(A few copies of the book in the class room. An online version of the book can be accessed at http://vip.vast.org/BOOK/HOME.HTM.) You are to make a scaled drawing on graph paper. You will create 3 copies of the design.
Main Drawing is on large graph paper (see below). It is what visitors would see when they show up to your coaster minus trees and any scenery elements. You do not need to draw the support system for the track. No numbers are on this copy.
Plastic layer 1is drawn on a piece of plastic. Use a Sharpie(tm)to draw on the plastic. It shows all the information of copy one plus speeds as hill peaks, hill dips, loop tops and curves. Show the accelerations in g’s felt by the rider at the bottom and top of the loops, around horizontal curves (banked and flat). When in doubt, calculate. This copy shows all the numbers without the math.
Plastic Layer 2is drawn on a piece of plastic. Use a Sharpie(tm)to draw on the plastic. shows all the information from copy one and two plus examples of how you calculated the speeds and accelerations. (You may need to split, “Copy 3” up into 2 sheets of plastic, “Copy 3A” and “Copy 3B.”
Plastic Layer 3 (Extra Credit) See the rubric for points shows any and all cool scenery like trees, bushes, background, or anything else that is deemed cool.
You will be supplied with plastic drop cloth in class. (The cheapest drop cloth works the best.)
How to get organized...
Sketch out a basic design. If you are going to have a theme, now would be a good time to decide on it.
Make a list of what the coaster will have in the order the rider will experience it. For example, The Shock Wave at Virginia's King's Dominion amusement park would have the following list.
leave the station
small dip
pulled up hill
flat 180 turn
big drop
irregular loop
smaller hill
small drop
small hill
horizontal corkscrew
series of small hills
flat hill
stopping force
Most people make the mistake of starting with the ride heights and using energy to calculate the velocities. But velocity determines the cetripetal accelerations and velocity is the transitioning variable between sections. Instead of stating with heights, determine velocities in between sections and calculate heights using energy.
I would annotate the list above like the one below.
leave the station Start at 3 m/s
small dip speed at the bottom is 5 m/s
pulled up hill Speed at the hill top is 6 m/s
flat 180 turn Maintain speed at 3 m/s
big drop gets to 35 m/s
irregular loop no change in entrance and exit height
smaller hill Speed at the bottom is 15 m/s
etcetera
This list allows one person to work on the hill leaving the station; one person to work on the next dip and one person to work on the pulled up hill ALL AT THE SAME TIME. Otherwise one person would wait until the next person finishes. this is not good use of time.
Place all your work in a folder. Do not take anything home until the end. If you have free time in another class, you are welcome to come to my room and pick up your work to add to.
Leave notes to other about what you have done and what need to be done in case you are not here. Fill out the daily log on Google Apps.
If you miss a class, do not redo anything someone else has done unless it is wrong. Accept it and move on. You do not have time to second guess other people's work.
Guidelines for Full Credit:
You may work in groups of up to three. Your team members must be from your class.
You may not use a piece of paper or poster board smaller than 11” x17 “ or larger than 26” x 42.” Paper may be taped together.
Must work on it during every class AP physics class period you are present.
The track should NOT be drawn in pencil. It should be drawn in ink, marker, or crayon.
The project is due May 23, by 3:50 PM -even if you do not have class that day. No late projects will be accepted.
All accelerations must be less than 5.5 g’s.
Heights and loops are to be scaled appropriately.
The lengths and heights on speed runs are scaled appropriately.
The angles on banked curves are correctly calculated and labeled.
Centripetal accelerations felt by the riders on banked curves must be calculated.
Horizontal curves do not need to be scaled on your 2d’ish drawing.
The horizontal lengths not mentioned above must look appropriate but do not have to be scaled.
Friction is ignored unless your stipulate its existence over a piece of track to use it to make a calculation.
Data from a free fall hill must be presented in small data table on, “Copy 3.”The transition angle from free fall curve to recover curve must be calculated and shown on copies 2 and 3.
The recover section of the free fall hill can be drawn with plotting any points. See the section on free fall hills to see what the recover section should look like
Springs must have a calculation showing the average acceleration during compression and extension of the spring and it’s force constant.
Correct calculations with proper SI units and accelerations in g’s.
Include all three copies as mentioned above.
Show all calculations for changes in velocity at extremes like hill/loop tops and bottoms and after outside forces are applied.
Show all calculations for flat and banked curves.
Show calculations for free fall shaped hills.
Show calculations for additional non-conventional pieces.
Responsibilities for design and calculations must be divided up and put on a calendar before beginning. Responsibilities include, but are not limited to:
Design of the track's shape (Including unique track element for extra credit.)
Calculations of heights, lengths, velocities, g's and other accelerations.
Scaled drawing of the track on the graph paper.
Scaled dimensions of the track added to a piece of plastic (layer 1).
Scaled calculated numbers for the physics of the track added to a piece of plastic (layer 2).
Scenery (extra credit) added to a piece of plastic (layer 3).
The design must have
At least two hills that follows free fall path. One high and one no higher than half the height of the other.
At least loop where a rider feels between 1.5 and 5.5 g’s.
At least one banked curve where the rider feels la centripetal acceleration less than 3.0 g’s if the curve is banked and less than 2.0 g’s if it is flat.
Banked curves must be designed for the optimum angle with minimal
At least one power calculation showing the power to pull a 15,000 kg train up the first hill or get it up to speed depending on your initial launching method.
Cool design element not mentioned above. Be creative.
Below is an PARTIAL example showing what the different copies of plastic overlays could look like.
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)
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