Introduction to Rollercoaster Engineering
http://www.mrwaynesclass.com/ap/coaster/web/index08.html
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Tyler Demyan - 07/28/2019
Introduction
This instruction set will show college students the introductory steps behind engineering a
rollercoaster from a technical perspective. When a rollercoaster is being designed, the park
coordinates with the rollercoaster manufacturer to decide on the location of the proposed ride.
We will assume this step has already been completed. Designing and engineering a complex
rollercoaster, can take weeks to months to complete. Throughout this instruction set, we will
use numbers by means of example, please substitute your own numbers in for accurate results.
These introductory steps should take approximately one hour.
Below is a list of vocabulary in order to help you become proficient in the art of rollercoaster
engineering.
• Schematic: Rendering typically done in a computer software that shows the
configuration of the rollercoaster from multiple viewpoints.
• Feeder Velocity: The speed at which a transportation device sends the train to the next
block.
• Block: The spaces between sections of track where a train can stop. Often, there must
be at least 2 blocks open between two trains for the ride to work safely.
• Lift Hill: The location where the train is pulled up to its maximum height.
• Crown: The top of the lift hill, which is typically the maximum height of the ride.
• Airtime Hill: A flat, unbanked hill, where riders sustain 0 G or lower. They have the
sensation of flying out of their seats.
• Inversion: Any point of the ride where the track inverts past 135°.
• Loop: A clothoid shaped inversion where riders are flipped upside down.
• G-Force: The force the riders feel while the train maneuvers throughout the layout.
Typically these forces will range between -2 Gs and +4 Gs.
Instruction to Rollercoaster Engineering
STEP 1
Acquire the schematic of what the rollercoaster will look like from your design team. This is an
important step so you can begin your engineering analysis. Throughout this instruction set, the
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images below will be referenced.
Figure 1: Ride Top View
Figure 2: Ride Side View
Instruction to Rollercoaster Engineering
STEP 2
Assign a speed that the train leaves the station at (Location #1 in Figure: 2). This is called the
feeder velocity. For purposes of demonstration, we will use 5.24 m/s in the following equations.
This speed is important as it will factor into the force needed to pull the train up the lift hill, as
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well as have an impact on the ride’s overall duration.
STEP 3
Calculate the force needed to pull the train up the lift hill (Location #2 in Figure: 2). This can be
done by using the following equation set.
Note: In order to demonstrate this, we will use a train mass of 4410 kg, a lift hill angle of 42°,
and a height of 102m. Be sure to get the correct numbers from your design team.
Lift hill length = 102/(sin42°)
Lift hill length = 152.4 m
ET(OUT OF STATION) + Work = ET(TOP OF LIFT HILL)
KE + PE +W = KE +PE
(1/2)mv2 + mgh + Fd = (1/2)mv2 + mgh
(1/2)4410(5.24)2 + 4410(9.8)(22.5) + F(152.4) = (1/2)4410(8.26)2 + 4410(9.8)(124.5)
60544.008 + 972405 + F(152.4) = 150441.858 + 5380641
F(152.4) = 4498133.85
F = 29515.314 N
Figure 3: Force needed to pull the train up the lift hill
Finding this value will help calculate the maximum velocity of the ride in step 5.
Instruction to Rollercoaster Engineering
STEP 4
Calculate the time it will take to reach the top of the lift hill, otherwise known as the crown.
This can be done by using the following equation set.
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The acceleration of the train is found from
(vf)2 = (vo)2 +2ad
(8.26)2 = (5.24)2 + 2(a)d
a = 0.134 m/s2
vf = vo + at
8.26 = 5.24 + 0.134(t)
t = 22.537 sec
Figure 4: Time it will take to reach the top of the lift hill
This time comes in handy when calculating the overall ride duration, it is not necessarily related
to the following steps.
STEP 5
Calculate the maximum velocity of the ride, which typically occurs after the drop off the crown
of the lift hill (Location #3 in Figure: 2). This can be done using the following equation set.
ET(LOCATION #2) = ET(LOCATION #3)
KE + PE = KE +PE
(1/2)mv2 + mgh = (1/2)mv2 + mgh
(1/2)4410(8.26)2 + 4410(9.8)(124.5) = (1/2)4410(v)2 + 4410(9.8)(0)
150441.858 + 5380641 = 2205(v)2
2508.428 = (v)2
v = 50.084
v = 50.1 m/s
Figure 5: Maximum velocity of the ride
Finding this velocity comes in handy in the step 7 where you will analyze the g-forces felt by the
rider while entering a loop.
Instruction to Rollercoaster Engineering
STEP 6
For any loop, you need to know the velocity as the train enters the loop, at the top of the loop,
and at the exit of the loop.
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• For simplicity, the velocity as the rider enters the loop, and as the rider leaves the loop,
is considered the same as the velocity at the bottom of the first hill. This is because all
three locations are at the same height.
• The velocity at the top of the loop is not the same as at the bottom. As the coaster
travels up the loop it will lose kinetic energy and gain potential energy.
• The height of the loop is simply double the radius. h = 2(31.2) = 62.4 m
First, calculate the velocity of the train as it enters the bottom of the loop.
ET(LOCATION #2) = ET(LOCATION #4)
KE + PE = KE +PE
(1/2)mv2 + mgh = (1/2)mv2 + mgh
(1/2)4410(8.26)2 + 4410(9.8)(124.5) = (1/2)4410(v)2 + 4410(9.8)(62.4)
150441.858 + 5380641 = 2205(v)2 + 2696803.2
1285.388 = (v)2
v = 35.852
v = 35.9 m/s
Figure 6: Velocity of the train when entering the loop
This will help calculate the g-force felt by the riders in step 7.
STEP 7
To calculate the g-force felt by the rider, calculate the centripetal acceleration as the train
enters the loop.
Warning: This is a critical step as too high of a g-force can cause riders to grey-out or potentially
black-out.
v = 35.852 m/s
r = 31.2 m
𝑣𝑣 2
Ac=
𝑟𝑟
ac = 4.2 Gs
ac = 4.2 Gs – 1 G
ac = 3.2 Gs
Figure 7: G-Force felt by the rider as the train enters the loop
(Note: Ended steps after 5 pages)
Instruction to Rollercoaster Engineering
Sources
Wayne, Tony. “Introduction to Roller Coaster Design.” Roller Coaster Design,
www.mrwaynesclass.com/ap/coaster/web/index08.html.
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Instruction to Rollercoaster Engineering
