Machine Design
Formal Report
Anooj Chamakala
Ari Novick
Executive Summary
The goal of this design project was to come up with a solution to the problem of loose
article policies for roller coasters. Amusement parks have certain codes and standards that
restrict the guest from carrying personal belongings onto large attractions. Additionally, items
may be prone to theft if left on the station, or even required to be placed in a purchased locker. In
order to avoid this situation, a compartment composed of a standard piston-cylinder mechanism
and a memory foam lining, called MemoryBox, was designed. The piston-cylinder is located in
back of the compartment and its purpose is to push the top wall down so that the accessories are
nicely cushioned and secure. It is attached to a compressed air line that connects with the station
when parked.
The MemoryBox design was affirmed to be fully working by using analysis techniques
through Pro/Engineer. Pro/Mechanica was used in order to calculate and visualize Von Mises
stress distributions on all the stressed components of the links. For the pins, the highest factor of
safety was found to be 69.0, while the lowest was found to be 1.23.
NoLimits Coaster Editor was also utilized in order to better understand the magnitude
and the duration of the maximum vertical and lateral forces. Utilizing this, the minimum factor
of safety for the screw connection of the compartment was found to be 58.8. The drag force per
car was also calculated to be 21.8lbf, decelerating the car by only .0394%.
In order to make this a working storage compartment, necessary calculations were taken
and put into this report. These included the amount of thrust required by the piston, found to be
approximately 243lbf. High density memory foam also requires a certain amount of force to be
thoroughly compressed, found to be 45lbf for .5 inch deflection of 2 inch thick sheet. Combined
with these calculations, graphs of strain energy and Von Mises stress distributions are located in
the appendices along with the assembly drawings and detailed drawings.
In this report, one will find everything necessary to manufacture and assemble a
MemoryBox. This device will revolutionize the amusement park industry, for it holds the key to
efficiency, convenience, and security.
Project Report
Introduction …………………………………………………………………….2
Results, Description of Final Design ………………………………………..... 3
Discussion, Advantages and Disadvantages of the Design ………………….. 9
Summary and Conclusion ………………………………………………….…11
Calculations ………………………………………………………………..12
Finite Element Analysis..……………………………………………25
Amusement parks are known for their great rides and joyous environment. Roller
coasters are the most popular ride ever developed for amusement parks. The ride is composed of
feelings of free fall, weightlessness, and may even contain various dives and inversions.
Unfortunately, the industry has is becoming harsher in terms of what can and cannot be brought
on a ride.. Even though amusement parks provide great high speed rides in what they hope is a
family friendly atmosphere, they fall short in terms of easily storing away accessories before
entering the larger attractions. This leads to lost cell phones, keys, and wallets during the ride.
This is especially frustrating when the guests learn that they cannot hold onto such items in their
hands and that they must be placed in a pocket for safety reasons. Often, the only alternative is
an expensive one. It consists of a onetime use locker system, purchased prior to entering the
queue line. These are extremely inconvenient and aggravating. The few rides that still have free
cubbies for personal belongings are prone to theft. The system’s overall riders per hour are
decreased since there is simultaneous loading and unloading, slowing down the ride process and
making it difficult for the ride operators.
Results/Description of Final Design
In order to solve this problem, an on-ride storage compartment has been designed to
safely and securely store passengers’ items. This simultaneously eliminates the cluster of people
shuffling back and forth from the platform to place their loose articles on the side and the forced
locker policy. The design also allows for overall happier guests as they can now have their
wallets and cell phones in the queue, without the worry of the items falling out of their pockets
or getting stolen from the platform.
The design created, deemed MemoryBox®
may be seen in Figure 1. It was designed for one of
the most popular kinds of roller coasters; they are
Bolliger and Mabillard designed and manufactured
hypercoasters. The non-inverting roller coasters
always have an initial drop of over 200 feet, and
typically reach 75 miles per hour. Popular models
include Nitro at Six Flags Great Adventure, and
Figure 1. MemoryBox
Raging Bull at Six Flags Great America. While
detailed dimensions were not able to be found for this ride, patented rough drawings were.
Having visited the park, the exact dimensions were referenced and scaled appropriately.
The MemoryBox is a storage compartment that uses memory foam that is two inches
thick on the top section, and .2 inches thick on the bottom. The memory foam that is lined on the
top and bottom has a density of approximately 4𝑓𝑑 3 , which is more than enough to withstand any
force on the items during ride operation. A typically secured item rises no more than one inch
thick. This includes almost all models of phones and music players. Therefore, every
compartment compresses one inch consistently. This compression is sustained throughout the
entire ride duration. There is an extra inch available on top to account for possible wear and tear,
and negative gravitational forces experienced on the ride. This is available mainly for the items
rising above 1-inch. The firmness of the memory foam is determined by the foam’s indentation
force deflection rating, or simply IFD. IFD determines the force that is needed in order to make a
25% thick compression on a 20x20x4 inch foam specimen by an 8-inch diameter disc. It was
decided that shock absorbing memory foam would be necessary. Thus, to compress the top layer
by 1 inch, a 90lbf would be necessary. These
calculations may be seen in appendix III. The
memory foam is not shown in the 3-d Pro/Engineer
model of the MemoryBox.
The device has a sliding top plate that
comes down to compress the accessories prior to
departing the station. This is made possible by a
pneumatic piston-cylinder mechanism in back of
the compartment, as seen in Figure 2. The cylinder
Figure 2. Pneumatic Piston/Cylinder
was chosen to be CRE0805P x 050. This implies an 8 millimeter (.314in) bore, an adjustable air
cushioned cylinder, and a possible stroke of 50 millimeters (.197in). This system is connected to
a flexible tube that rides along the back of every row. When the train is parked in the station, the
tube connects to the compressed air compartments located under the station. The gas runs
automatically after all restraints have been checked by the operators, but prior to dispatch. This
allows all the articles to be in place by the time of compression, and will not compress
prematurely. This also eliminates possible injury should someone decide to utilize the drawer
while it is in motion. When the ride completes its circuit, the connection is once again made with
the station and the cylinders are decompressed. The guests are then free to gather their
belongings and exit the ride area. The process then repeats for the next influx of guests.
The drawer is a unique property
of the device. It is pinned to the front
part of the compartment, and is made of
polyvinyl chloride (PVC). When the
drawer is pulled open, items may be
placed in. When it is closed, the items
slide down to the base of the drawer,
and are readily compressed by the
plate. The reverse occurs when articles are
Figure 3. Tilting Drawer
picked up; the drawer is opened and the articles can slide forward. There is .2 inches of memory
foam lined on the flat inside surface of the drawer for extra padding. If this happens to provide
too much friction for the items to slide correctly, the items will still be within reach inside the
compartment. The drawer can tilt 30° forward. The flatbed of the drawer also serves as the
locking mechanism. The top plate, when the piston is fully compressed, keeps the drawer and the
items from tilting forward.
Four screws are secured down onto the floor of the car on each corner of the
compartment. The standard screw selected for this connection was ¼-20 UNF x 1 ½ comprised
of AISI 1044 carbon steel, with a yield strength of 60,000 psi. This allows for a minimum factor
of safety of around 58.6 during ride motion. The MemoryBox itself is made of AISI 302 stainless
The piston-cylinder mechanism is connected to a link designed to pivot around the
compartment; this mechanism can be seen in Figure 4. This is then connected to a shorter link
which is pinned directly to the memory foam plate. There are three custom pins and two custom
links involved in the connections, all of which are made from low carbon steel, except for pin C.
Pin C, connecting the piston to the center link, is
comprised of AISI 302 stainless steel. There was
a much higher stress on Pin C during
compression, so a material with a higher yield
strength of 75,000 psi was necessary. The carbon
steel for the other pins, however, is ideal because
it is relatively cheap and is neither ductile nor brittle.
Figure 4. Plate Top Sliding Mechanism
This design may be seen in Figure 3. In Pro/Engineer,
a servo motor was attached to the piston to simulate an actual compression and decompression.
Both of these have a duration of approximately 2.5 seconds. The reaction forces for each of the
pin connections were graphed as a function of displacement of the piston, as see in Appendix III.
This helped us to understand how each of the reaction forces behaved with every displacement of
the piston. The maximum reaction force was located on the compartment, and had a value of
1,117 lbf. The minimum force was 54 lbf, located on Pin A. While these reactions had a large
range, they still had high factors of safety. All of these graphs and calculations may be seen in
Appendix III.
Finite element analysis, also known as FEA, was performed on the stressed components
in order to be sure they would not fail. FEA aids in the verification of how a product will behave
prior to manufacturing. Areas of the object that will receive a high amount of stress have greater
node density and the opposite occurs for areas with a low amount of stress. In the design of the
MemoryBox, one FEA was performed on every stressed component in order to have a better
visual understanding of where the stresses occurred. The stressed components included all pins
and the hinges of the compartment for the drawer. The maximum force on each pin was used to
conduct finite element analysis for that pin. This was done with careful consideration of each pin
connection. Pins in the assembly were constrained
over the width of one pin connection, while the force
was placed on one half of the surface area covered by
the other link. This analysis was consistent for all of
the pins. Color coded visual displays of the Von
Misses stress distribution may be seen in the
appendix for each of the pins; an example of this may
be seen in Figure 5. It was also performed for the
Figure 5. Example of Von Misses Stress
hinge connection with the drawer of the compartment, in
case of someone stepping on it accidentally.
Over the top of the compartment is a strip of steel protruding directly between the two
adjacent seats. This is strategically placed to prevent guests from tampering with the inner
workings of the box. The design feature combined with the already close proximity of the seats
make the moving components of the device unreachable, and therefore considered safe. The only
standard codes found for amusement park rides were those concerning how a person should be
restrained; none considering the restraint of loose articles nor that of what may or may not go on
a coaster train.
The drawer of the MemoryBox is manually operated due to liability issues. Every door
will have a label explaining that it is the guests’ responsibility to close the drawer as much as
possible. If the doors are not closed and the machine compresses, the articles may not be
completely secured by the memory foam, even though the drawer will close. This subjects the
articles to possible strikes against the side of the steel compartment. The internal sides need not
be lined with memory foam because this creates unnecessary friction between the drawer and the
compartment. This would have greatly increased the wear and tear of the foam lining.
Every car on the train has three storage compartments; one is located in between each of
the four seats. While this allows three compartments to every four people, it is estimated that this
should be sufficient. The area of the holding surface on the drawer is 6.5 x 5.74 inches. This is
enough for three items to have their individual space on the surface of the drawer. Because the
estimated number of items per rider is two, mainly a wallet and a cell phone, the compartments
combined will hold enough items for four people. Additionally, many people have wallets in a
buttoned or zippered compartment on their pants, and will therefore not require a compartment
for their wallet.
Discussion/Advantages and Disadvantages of
the Final Design
There are many advantages and disadvantages to this design. Guests can freely open and
close the compartment when the ride is stationary, but it automatically locks down when it starts
to move. In this way, passengers can store their items at the start of the ride and take them back
at the end. This cycle repeats throughout the operating period. This eliminates all chaos and
hassle involved with storage, and therefore increases efficiency. The location of the box is also
very ideal; people can walk freely onto the ride and have the convenience of placing their items
right next to their seat. The compartment is very safe in terms of holding accessories in place; the
memory foam that is inside is of high quality and ensures proper compression. The stainless steel
compartment also provides long lasting duration. A more aesthetic and professional appeal of the
coaster is allowed with AISI 302. There is minimal drag force on the box due to its curved shape;
this makes it aerodynamic and insignificantly interferes with ride performance. This is proved in
Appendix III with thorough fluid flow calculations.
Like any design, there are a few disadvantages that come with it. The compartment
cannot hold an excessive amount of accessories due to the tightly placed seats on the roller
coaster. The amount of workable space was extremely limited. While cell phones, wallets, music
players and other small personal items are allowed in the compartment, only three of them can fit
at one time. These items cannot have a thickness (height above the ground) of over 1 inch.
Additionally, air for the piston is provided through a tube that runs in the back of a car, and goes
to all three compartments. If for some reason there is something wrong with the air compressors
or the connection, then all compartments in that row will have complications with memory foam
compression. In order to prevent this, the MemoryBox connections and the compressed air
compartment should be checked on a daily basis to ensure proper air flow and connections.
Difficulties with the automated air flow may also cause a problem. If for some reason the
compressors do not engage after completion of the ride cycle, passengers may have to wait to get
their valuables back. There is also a slight possibility that items placed in the compartment prior
to compression by the guest may fall out the back by accident. While this is unlikely because of
the memory foam friction and the length of the compartment, it is still a possibility.
The piston must be manufactured with the compartment piece. This is because the
compartment contains the connection to the piston, and was not designed to be removable. When
a piston needs to be changed, the entire compartment will need to be replaced. The steel for each
compartment is also somewhat expensive. Ideally, this piece is made out of PVC plastic, which
allows for a cheaper and lighter design. Unfortunately, for now this must remain steel, as the
connection reaction on the cross bar was greater than PVC’s yield strength.
Summary and Conclusion
Given the task of designing a device to eliminate the worry of having personal items in a
queue line, our team was not sure of the best way to comprise a solution at first. However, it was
soon realized that an on ride compartment was the only way to have the optimal efficiency while
still being able to have small loose articles inline. While the safety rules of no items in hands
while riding a roller coaster still holds, one now has the worry-free convenience of cell phones
and wallets in the line ride.
MemoryBox consists of several types of material and several moving parts. Ranging
from PVC to stainless steel, the box meets all the stress requirements to securely hold most loose
articles. Pneumatic piston cylinders that attach to air compressors in the station were well
utilized, and seemed to be the safest solution. The pistons extend after all the restraints are
checked, prior to dispatch. While the first prototype might be a bit expensive, the future costs
will be reduced significantly.
The on-ride storage compartment is a much-needed device in the amusement park
industry. Roller coasters are meant to be a great experience for everyone, and they should not be
hindered by a required locker purchase or the risk of losing a cell phone. With the MemoryBox,
not only can passengers access the ride quicker and with more confidence, but it also ensures the
safety of articles that are onboard due to the high quality memory foam being utilized. The
compartment increases the efficiency of the loading system by causing less confusion when
people are getting on and off the ride. Memory compartment is just the beginning of the
possibilities of on-ride item storage.
The entire compartment assembly was
estimated to weigh 50 lb with a live load.
The maximum lateral g forces experienced on a
typical Bolliger and Mabillard coaster can reach
2.5 times the force of gravity. With 4 screws to
hold down the compartment, the maximum
shear force is thus calculated below:
𝑔 =
Figure 5. Typical Maximum Positive Vertical Gravitational Force,
Located At Bottom of First Hill
50𝑙𝑏 ∗ 2.5
= 637 𝑝𝑠𝑖
4πœ‹(. 25𝑖𝑛)2
The maximum vertical positive g force can reach up to 4 times the force of gravity; this can be seen in
Figure 5. With 4 screws to hold down the compartment, the maximum tensile stress is calculated:
= 1020psi
πœŽπ‘¦ (πΆπ‘Žπ‘Ÿπ‘π‘œπ‘› 𝑆𝑑𝑒𝑒𝑙) = 60,000 𝑝𝑠𝑖
Factor of safety for tensile stress:
Factor of safety for shear stress:
= 58.8
= 94.2
Memory Foam Calculations:
Although IFD, indentation force deflection, is usually measured as an amount of lbf for a 25%
deflection of a 50 𝑖𝑛2 cross section on a 20x20x4 in piece. The area doing the compressing is the
surface area of the loose articles, approximated to be 4.5x5inches (the surface area of two cell
phones side by side). This is pushing on the 6.5x5.74inch area of memory foam on the ceiling.
= .03125/𝑖𝑛
20𝑖𝑛 ∗ 20𝑖𝑛 ∗ 4𝑖𝑛
4.5𝑖𝑛 ∗ 5𝑖𝑛
= .603/𝑖𝑛
6.5𝑖𝑛 ∗ 5.74𝑖𝑛 ∗ 2𝑖𝑛
Because the ratios are off by so much, it is difficult to predict how much force is required to
compress the necessary 1 inch of foam. Thus, this situation is unique for memory foam
calculations. Typically, these calculations are done so that the outer most edges remain
stationary, and only the area of interest is compressed. A typical IFD value for shock absorbing
foam, measured in lbf, is 45. Our value will therefore have to approximate this model.
In order to have 2 inches of memory foam compressed to 1 inch:
𝐴𝑑 25% π‘‘π‘’π‘“π‘™π‘’π‘π‘‘π‘–π‘œπ‘›:
45π‘™π‘π‘“π‘€π‘œπ‘’π‘™π‘‘ π‘π‘œπ‘šπ‘π‘Ÿπ‘’π‘ π‘  .5 π‘–π‘›π‘β„Žπ‘’π‘ 
45𝑙𝑏𝑓 ∗ 2 = 90𝑙𝑏𝑓
90lbf would compress 1 inch
Air flow for one car moving at 75 miles per
𝐹𝐷 = ( ) πœŒπ‘£ 2 𝐢𝑑 𝐴
Drag Coefficient for Long Cylinder: .82
Drag Coefficient for Cube Cross Section:
Drag Force for 3 compartments (for density
simplicity, this calculation was performed in
metric units)
π‘š 2
𝐹𝐷 = 3 ∗ ( ) ∗ ( 3 ) ∗ (33.53 ) ∗ (1.05)(.1814π‘š ∗ .2489π‘š)
π‘š 2
+ 3 ∗ (2) ∗ (1.2 π‘š3 ) ∗ (33.53 𝑠 ) (. 82) ∗ (.0381π‘š ∗ .0884π‘š)=
= 95.94 𝑁 + 5.59𝑁 = 102𝑁 = 22.8 𝑙𝑏𝑓
Approximate weight of one loaded car: 1800 lb
Approximate maximum horizontal acceleration: 1g = 32.2 𝑠2
F = 32.2
∗ 1800𝑙𝑏 = 57960lbf
∗ 100 = .0394%
The drag force will decelerate the train by, at most, approximately .0394%. While this is
something to be considered, the train will definitely be able to continue on its path without
It is important to note that the airflow calculation only considers the drag force horizontally.
While a rider may experience up to four times that of gravity on a ride, this is only due to a
sudden change in direction. In the horizontal component, the one parallel to the track, the car
only experiences acceleration of up to one times the force of gravity, unless a launch mechanism
is utilized.
The back piece of the cross section may appear to be significant, but is not. The majority
of the quick moving air has already been displaced by the time it reaches the thicker back cross
Force required to push the piston so that the memory foam compresses was calculated to be 90 lb. For
simplicity, let us call this F. This as a whole may be considered a 5 bar linkage with a slider. After
searching far and wide for such equations, none were able to be located. Because the compressor is
designed to compress 1 inch every cycle, the exact position of the slider is not needed to be known for
any given displacement of the piston. However, the thrust output of the cylinder is. This was best
approximated by taking moments about the center axis of the compartment. This was done by taking
the horizontal distance from point b to the center of the slider connection, and the horizontal distance
from point b to the piston connection. Only the vertical components of the forces were necessary. In
the calculations to follow, F is the force of the memory foam on the top plate, and all angles are in
∑ 𝑀𝑏 = 0
5.6𝐹 = (2.5) ∗ cos(9.88) ∗ 𝐹2 ∗ sin(75.94) − 𝐹2 cos(75.94) ∗ 2.5 ∗ sin(9.88)
𝐹2 =
= 2.45𝐹
2.5 ∗ sin(75.94°) − cos(75.94) ∗ 2.5 ∗ sin(9.88)
Using a value of 90 lbf for 𝐹2 the thrust would be 221 lbf.
This was an approximation neglecting the smaller link. The smaller link directly above F was assumed to
only move vertically, parallel to the same axis as F, for this calculation. Because of this and additional
frictional forces from the pins, an additional factor of 10% will be added on to the final thrust.
221𝑙𝑏𝑓 ∗ 1.10 = 243lbf
Fs = Sm / Sw
Sm = Working Stress (psi)
Sw = Allowable stress (psi)
Fs= Factor of Safety
AISI 1044 (Carbon
AISI 1044 (Carbon
Pin B
AISI 302 (Stainless
Pin C
AISI 302 (Stainless
Compartment Steel)
Pin A
Yield Strength
Factor of
While the factor of safety for Pin C and the Compartment connection are relatively
low, it is important to remember that these reactions are only for the in-station
compression and decompression. They will not undergo such stress during the ride
circuit. The pins are considered safe, and therefore allowable.
Pin A
Pin B
Pin C
Appendix IV
Computer or Spreadsheet Program Listings
Microsoft Word
Microsoft Excel
NoLimits Coaster Simulator