Christopher_Williams_Theme_Park_Design_Final

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Themed Entertainment Design
North Carolina State University Special Project
Department of Mechanical and Aerospace Engineering
Written By Christopher Williams
Advised by Dr. Gregory Buckner
I. INTRODUCTION
New inventions and innovations made within the last century have afforded individuals a significant
amount of leisure time. With that new found time, people are spending a significant amount of money
entertaining themselves. The music, film, and television industries are booming with record sales almost
every year, and consumers look towards these industries as a form of escape from their day‐to‐day
activities. As another form of entertainment and escape, families are using their free time and money to
vacation. Many families are taking multiple trips every year, and they are looking to travel new places
and have unforgettable experiences. Media giants such as the Walt Disney Company and NBCUniversal
are able to appeal to a wide base of these vacationers by incorporating their music, film, and television
assets into their Theme Parks. This unique type of Themed Entertainment Design allows vacationers to
experience the environments of their favorite movies and television series through rides and attractions.
A detailed investigation into these theme park rides and attractions is the main focus of this report,
which covers the current climate of the theme park industry, an investigation into the current industry
standards for theme park design, a trade study of the Disneyland Matterhorn Bobsleds ride vehicle, and
a new original concept for a theme park ride vehicle.
II. THEMED ENTERTAINMENT OVERVIEW
Themed Entertainment Design has become a broad topic that encompasses many different types of
entertainment. Although this report focuses solely on theme park experiences, there are many themed
entertainment companies such as The Thinkwell Group and Garner Holt Productions that work to design
and create compelling exhibits for museums, unforgettable moments for live performances/events, and
exciting environments for restaurants. Even sports teams have contracted out to these companies to
design their sports stadiums to draw in fans and entertain them with the desire to keep them coming
back. Themed Entertainment Designers utilize their highly technical design skills in a creative way to
appeal to large audiences. When this attention is turned to theme park design, the newest technologies
become utilized to create the most awe‐inspiring experiences possible.
A. TYPES OF THEME PARK RIDES
All theme park rides can be classified into one or more categories listed below. For the purposes of this
report, the term “ride” is defined as a theme park experience that is able to physically move or transport
the guest. Therefore, walkthrough exhibits and standard theater showings are not included in the list
below.

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1. Train Ride – A traditional train ride or similar experience
2. Coaster—Motion created from the conversion from potential to kinetic energy
3. Bumper Car Vehicle—Vehicle controlled by guests
4. Water Ride/Log Ride—Floating vehicle
5. Drop/Freefall Tower—Ascending/Descending Vertical Based Track
6. Ferris wheel—Based on the design from the 1893 World Columbian Exposition
7. Motion Simulator—simulates motion through the use of accelerations
8. Dark Ride—an vehicle guided through animation, sound, and special effects
9. Omnimover/Mass Transit System—nonstop loading and unloading vehicle
10. Orbiter—a ride vehicle attached to a central support that rotates 360‐degrees

Usually, a newer theme park attraction will incorporate the latest technologies to expand on one of the
categories listed, or even combine different concepts from the different categories to create hybrid of
attractions. An example of this hybrid combination is the famous Haunted Mansion of Disney Park fame,
which combines characteristics of a classic Dark Ride with an Omnimover ride vehicle system.
III. THEME PARK SAFETY – DESIGNING FOR SAFETY AND HUMAN
FACTORS
For a brief time In the United States, there was a national government commission that oversaw theme
park safety standards. This occurred when Congress passed the Consumer Product Safety Act in 1972.
This Act established the Consumer Product Safety Commission (CPSC). The CPSC held a broad
interpretation of their power, and believed that amusement park rides should be under their jurisdiction
as “consumer products.” The federal court system later upheld this belief when it was challenged in
court. Therefore, under the provisions of this act, the CPSC were able to regularly inspect permanent
theme park rides as well as mobile amusement rides that travel from state to state. This lasted until
1981, when Congress passed the federal Omnibus Budget Reconciliation Act in 1981. One of the
features of this act removed the CPSC’s jurisdiction over permanent theme park attractions. Therefore,
the ability to regulate theme parks has since been left up to the state and local governments where
permanent theme parks reside.
Currently there are 44 out of the 50 states in the US that regulate theme parks. It should be noted that
the six remaining states have few if any theme parks. The most recent published findings show that as of
1986, around eighty‐percent of injuries that take place in amusement parks are caused by rider error.
The results of this research coupled with significant incidents at local theme parks caused ten different
states to adopt “rider responsibility legislation” to help protect theme parks from liability to rider error.

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At the very least, most states have laws that allow amusement parks the ability to detain and eject
anyone that is suspected of violating any theme park rules.
The overall rules and regulations that a theme park must follow varies from state to state, but some
states such as California, have little to no regulations on permanent theme parks with the exception of
making theme parks comply with local building codes. Some states have strict inspection requirements
that require inspections multiple times a year from an independent party. In addition to the state and
local government oversight, the insurance companies of theme parks are able to leverage their own
rigorous inspections on theme parks in order to provide insurance coverage.
Overall, the theme park industry is largely self‐regulated through the standards set by the American
Society for Testing and Materials (ASTM) F‐24 Committee on Amusement Rides and Devices. The ASTM‐
24 committee is made up of consumer advocates, government officials, amusement park operators, ride
manufacturers, and industry suppliers. The committee establishes voluntary standards on design and
manufacture, testing, operation, maintenance, inspection, and quality assurance for the theme park
industry. All of the standards are reviewed regularly in order to stay current and up to date with the
latest technologies and have been adopted by thirty‐two states, as well as in countries around the world.
The standards are all published in the ASTM Annual Book of Standards and can be found in Section
15.02. Many of the ASTM standards are very specific, such as stating that 175 lb. shall be the assumed
weight of an adult passenger for design purposes, although there are not currently any ASTM standards
for software.
A. DESIGNING FOR SAFETY
There are four different aspects of safety to consider when designing a theme park attraction
1. Designing Rides for Safety
Designing a ride to be safe goes beyond the structural analysis of the ride, or determining if the ride will
be safe during normal operation. There should be a human factor analysis that will determine if there is
any way a rider could potentially use the ride that is unsafe, such as reaching out of the ride vehicle and
hurting themselves.
2. Manufacturing Rides for Safety
Manufacturing the rides for safety is determining whether the ride was built according to the safe
design. All of the design plans been followed accordingly.
3. Maintaining Rides for Safety
Maintaining rides for safety means that all rides receive the necessary and proper maintenance in order
to continue safe operation.
4. Operating Rides for Safety
Operating rides for safety means that the ride operator controls the ride according the proper
maintenance requirements, and the ride operator knows and follows all passenger safety requirements
and assures that the passengers use the ride in a way that is consistent with the original designed safety
requirements.

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IV. REDESIGNING A CLASSIC – REDESIGN OF THE MATTERHORN BOBSLED
After looking at the various requirements for theme park ride vehicles, it was determined that the
Matterhorn Bobsleds in Disneyland Park in California would be an excellent case study for this project.
The Matterhorn Bobsleds opened in 1959, and it is credited to be the world’s first tubular steel roller
coaster. There have been several plans to replicate The Matterhorn at other Disney theme parks;
however, the one built in California is still the only on in existence. The Matterhorn is an excellent
example of themed entertainment design, because the ride vehicle helps communicate the theming and
story behind the attraction. After stepping into the bobsled and putting a seatbelt on, guests are pulled
up to the top of a snowy mountain using a drive‐chain. Once at the top, gravity takes over to race the
bobsled down to the bottom of the mountain. Construction details and other facts regarding the
Matterhorn are included in Figure 1.

Figure 1.Informational graphic published in The Orange County Register August 21,2013.

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A. MATTERHORN RIDE VEHICLE HISTORY
Several enhancements have been made to the Matterhorn since its opening, including the addition of
projections, sound effects, show scenes, and Abominable Snowmen audio‐animatronics. The
Matterhorn ride vehicle has had a total of three iterations during the life of the attraction. The original
ride vehicle seated up to four guests (two seats that allowed up to two people each with lap sitting) as
shown in Figure 2.

Figure 2. The original Mattherhorn Bobsleds ride vehicle after opening in 1959.
Original design continued until 1978, when two cars were joined together to allow up to eight guests to
ride (four seats that allowed up to two people each with lap sitting). This new design leveraged the
Space Mountain ride vehicle design from Disneyworld and was able to adhere to the Bobsled theming by
repainting the ride vehicles. This design is shown in Figure 3.

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Figure 3. The second iteration of the Matterhorn Bobsled ride vehicle.
The ride vehicles were updated again most recently in 2012. The original dual tandem seating was
replaced with three individual seats per car. As shown in Figure 4, cars were once again joined together
to have a total capacity of six guests.

Figure 4. Current Matterhorn Ride Vehicles updated in 2012.

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The current iteration of the Matterhorn has a total capacity six guests, which is technically less than the
previous capacity of the former ride vehicles; however, the change was almost certainly made for
operational reasons. Although the total vehicle capacity is now less, the hourly throughput has most
certainly increased. The tandem seating was not always popular among guests and many groups would
ask for individual seats for personal comfort in order to avoid lap sitting in the vehicles shown in Figure 3.
Therefore, if two groups of two asked for individual seating, the capacity of the ride vehicle drops in half
from eight guests to four guests. By ensuring that six guests are able to experience the attraction every
time the vehicle leaves the station, the overall hourly capacity is able to increase.
B. CURRENT MATTERHORN RIDE VEHICLE AREAS OF IMPROVEMENT
Ideally the new design of the ride vehicles would have been extended to allow for eight individual seats
to be included in the ride vehicle. However, the original tubular steel track remains largely unchanged
since opening, and the ride vehicles were designed to remain compatible with the original track. The
cost to modify the structure of the track is almost prohibitively expensive when the option to remain
within the original vehicle envelope is available.

Figure 5. A close up view of the current Matterhorn Bobsleds after the redesign in 2012.
The latest vehicle design, as shown in more detail in Figure 5, divided the existing space into three even
sections in order to allow for three individual seats. The addition of the third seat takes up a significant
amount of overall space in the vehicle, especially considering that the new design also lowered the
position of the seats and attached them directly to the floor of the vehicle. Physical sizes as well as
flexibility now play a significant role in the overall comfort of experiencing the attraction. As shown in
Figure 6, even average sized guests must squeeze into the space allotted and straddle the individual

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bucket seats of the attraction. If guests sit in the front of the vehicle, their legs don’t have a seat to
straddle and they must conform to the shape of the nose of the vehicle. The sides of the bucket seats
are attached to the vehicle at its sides, which prevents guests that are larger, or even slightly above
average height, from comfortably sitting in the vehicle.

Figure 6. The current Matterhorn Bobsled vehicle depicting the tight fit required for average sized guests.
Another overall concern regarding the design of the ride vehicle is that the original track provides a very
uncomfortable experience—especially now that guests are seated directly on the floor of the ride
vehicle in an already uncomfortable position. The Matterhorn’s tubular steel track was the first of its
kind in the world, and was originally designed as a smoother alternative to the popular wooden roller
coasters of its time. Today, the original intentions of the track design are still appreciated; however the
fifty‐six year track is starting to show its age when compared to modern roller coasters. The current
industry utilizes computer simulations to digitally build a roller coaster track well before it is ever
constructed in order to accurately predict the body forces experienced by guests during the ride. This
allows for the track to be changed and optimized, providing the most thrilling experience while also
keeping the uncomfortable vibrations and accelerations to a minimum.
For an update for the Matterhorn Bobsleds ride vehicle, and for the design of any other theme park
attraction, guest comfort and safety should always be the number one concern. However, there is
another important reason to update the current Matterhorn ride vehicle to a more comfortable
experience. Theme parks, by definition, design and theme their attractions to tell a specific story or
convey a specific message to their audience. In order for good themed entertainment design to work,
the guest and all of their senses must be fully convinced that what they are experiencing is real. This
important detail is what sets “theme parks” above generic “amusement parks,” even though both types
of parks can offer similar rides and attractions. For the Matterhorn Bobsleds in particular, if the guests
are able to experience a smoother ride quality, their attention will be more on the theming and detail of
the Matterhorn instead of on their own personal discomfort. In addition, the smoother ride quality will

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help convey the message that they are plummeting down a snowy mountain through fresh powdered
snow.
The final concern that came up after the most recent 2012 design of the ride vehicles was the change in
height requirement. Both the original and second iterations of the Matterhorn Bobsleds (shown in
Figures 2 and 3) had a 35‐inch height requirement, thus making it the first roller coaster experience for
multiple generations of guests. The updated bobsleds have a 42‐inch height requirement, which is 2‐
inches taller than comparable newer roller coasters such as Space Mountain and Big Thunder Mountain.
Ideally, the height requirement should be changed back to 35‐inches, or at the very least dropped down
to 40‐inches to make the height requirement comparable to Space Mountain or Big Thunder Mountain.
As a summary of the important improvements that should be made to the design:
1. The human factors and ergonomics for the ride vehicle need to be revisited in order to allow a
comfortable experience for the widest range of guests possible
2. The ride quality (comfort, not theming) needs to be improved to allow guests a better overall
experience
3. Similar to designing for human factors, the height requirement should be able to be reduced
back to the original 35‐inches instead of the current 42‐inch height requirement
C. IMPORTANT DESIGN DETAILS TO KEEP
There are a number of features that have been included in Matterhorn Bobsled design that must be
included in order to allow for the ride vehicle to remain compatible with the current track.
1. As part of the original wheel assembly, a lift‐hill hook is included to allow the ride vehicle to be
taxied up to the top of the mountain before it can begin its decent.
2. The Matterhorn track currently has sensors with pacer motors and air‐brakes as shown in Figure
1. A “strike‐plate” is included on the undersides of the chassis and the wheel assemblies that
allow for the ride vehicles to move at a consistent speed while also preventing any vehicle
collisions.
3. The underside and outside of the ride vehicle is able to stand up to weather, particularly water,
because the vehicle dives into a pool of water during the ride finale.
4. There is a universal linkage that is included in the design to be able to connect two of the ride
vehicles in series.
5. The wheels and wheel assemblies will largely remain unchanged to allow for their compatibility
with the existing track. Most roller coaster wheels are made from either Nylon or Polyurethane.
Nylon is wheels tend to make the ride faster, but also tend to vibrate more and cause more
wear onto the track. Therefore, it is assumed Polyurethane wheels are used in the wheel
assemblies.
6. The body material that bonds to the ride vehicle chassis is likely fiberglass. This is assumed for
the design.
D. RESEARCH ON RIDE VEHICLE SUSPENSION SYSTEMS
The original plan for this project was to keep the wheel assemblies untouched, and only change the
chassis and the seating for the redesign of the Matterhorn Bobsleds. Therefore, vibration isolators were

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investigated to be able to directly isolate the ride vehicle seats from any rough forces or vibrations
induced by the track. Wire rope isolators, elliptic leaf spring mounts, and air springs as shown in Figure 7
were investigated as a good option to use in between the ride vehicle seats and the chassis. Of these
options, the air springs and the elliptic leaf spring mounts were the most promising; however, the spring
rates for the elliptical leaf spring mounts could not provide isolation for a broad range of weights sitting
in the seats. Statistical data shows that if the height requirement dropped back down to 35‐inches, then
a child that is 35‐inches tall would weigh an average of 35 lb. There is no maximum height or weight
requirements, which means that guests seven feet or taller and guests weighing up to 350 lb. will also
ride the attraction. This means that vibration isolators for the seat needed to be able to comfortably
respond to a wide range of weights, and after a significant amount of research, it was determined that
only the air springs could be installed and adjusted to be able to meet this requirement. However, in
order for this to work, either an employee would have to change the air pressure within the air springs
prior to the departure of every ride vehicle (an operational nightmare), or an autonomous system could
be set up to inflate or deflate the air springs based on sensor inputs placed on the seat. Of these two
choices, the autonomous system would be the better choice, although this requires an air compressor to
be added to the Matterhorn Bobsleds. This could be done, although the excessive and unexpected noise
of the air compressor would immediately ruin the illusion of being in a bobsled. With all of these options
off the table, the option of adding a chassis suspension system seemed like the most likely option for
ride comfort.

Figure 7. Mechanical vibration isolators in order from left to right: air springs, wire rope isolators, and elliptical leaf springs.
After a significant amount of research, it was evident that it is very uncommon to use suspension
systems on theme park vehicles of any kind. Adding a suspension system to a roller coaster wheel
assembly and integrating it with the chassis of the roller coaster has likely never been done before. As
mentioned previously, the roller coaster ride vehicle is always attached rigidly to the wheel assemblies
as shown in Figure 8, and the track is usually designed to allow for the roller coaster to smooth and
controlled maneuvering. With that being said, the Matterhorn Bobsled track is already in place with a lot
of the original track attached to the structure of the mountain. This prevents the track from easily being
modified in order to make the ride experience more enjoyable.

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Figure 8. The roller coaster from Six Flags Magic Mountain, showing the connection of the wheel assembly chassis.
Luckily, the use of suspension systems in vehicles has been prevalent for as long as passenger vehicles
have been around. Suspension systems avoid a rigid connection between a vehicle chassis and its
wheels, and allow relative motion between the two for either ride handling reasons or passenger
comfort. Suspension system components generally include the wheels, springs, dampers, and linkages
that connect a vehicle to its wheels. The linkages control the relative motion between the chassis and its
wheels, while the springs and dampers allow for wheels to react to changes in the road conditions.
Springs determine how a vehicle will respond to changes in the road conditions or how it will respond to
changes in the vehicle loading caused by accelerations and cornering. Springs need to be chosen with
the suitable spring rate that is soft enough to handle bumps and stiff enough to avoid excessive pitching
while accelerating or braking. While springs determine how far the chassis will move during
accelerations and road conditions, damping determines how long it takes to get there, and how quickly
it will return to its original position. Overall, damping has a huge influence on comfort, handling, and
vehicle traction, and while spring force is determined by the amount a spring is compressed, damping
force is determined by the change in velocity of the damper. This damping force is almost always
created by forcing oil through an orifice from one chamber to another, and the viscosity of the oil
creates the resistance to flow.
After looking at all of the different designs for suspension systems, a 4‐bar suspension system was
chosen because it prevents a lot of “kick‐up” when compared to other configurations, and it has a
relatively compact installation design. Specifically, a Satchell Link was chosen, because the roll center
could be lowered while using a minimum amount of space. After adjusting the geometry of a Satchell
Link suspension within the existing envelope available near the wheel assemblies, the configuration
shown in Figure 9 was developed. This suspension system will work better than the current design
without any tuning of the suspension system, however, one of the goals of this design was to maximize
the comfort level for the guests experiencing the attraction. Therefore, new technologies were
investigated in order to provide the most comfortable experience to the widest audience available.
Active and semi‐active suspension systems are becoming very popular because they are able to
overcome the trade‐off between comfort and handling.

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Figure 9. The analysis of the Satchell Link suspension design when added to one of the wheel assemblies.
After a significant analysis between the two technologies, it was decided that a semi‐active dynamic
suspension could be easily implemented. Accelerometers will be installed on the sprung and unsprung
portion of the vehicle and potentiometers that can measure the travel of the suspension will also be installed.
The damping and spring preload can then be adjusted based on the riding scenario. Servo motors would be
too slow to make the adjustments to a sensed disturbance, so fast‐moving solenoids will be utilized to quickly
alter the oil flow though dampers. This will allow the vehicle to be perfectly damped depending on the
situation. The other advantage that this design has over a standard vehicle suspension is that the track the
vehicle is on is not completely random and will not regularly change. Therefore, the entire track can allow the
solenoid responses to be “scripted” with the only thing changing being the passenger load. A model can be
Material Selection:
Upper Links Lower Links
Outside Diameter 1.500 in Outside Diameter 1.750 in
Wall Thickness 0.120 in Wall Thickness 0.188 in
Material Used Steel 1018 Material Used Steel 4130T
Rod End Rated Load 32,000 lb Rod End Rated Load 55,000 lb
Modulus of Elasticity 29,000,000 psi Modulus of Elasticity 29,700,000 psi
Yield Strength 50,000 psi Yield Strength 110,000 psi
Density 0.2840 lbm/in^3 Density 0.2840 lbm/in^3
Moment of Inertia 0.125 in^4 Moment of Inertia 0.285 in^4
Area 0.520 in^2 Area 0.923 in^2
Pyield 26,012 lb Pyield 101,480 lb
Pbuckling 271,515 lb Pbuckling 351,184 lb
Pbending 2,901 lb Pbending 9,299 lb
Link Length 11.4690 in Link Length 15.4353 in
Link Weight 1.69 lb Link Weight 4.04 lb
Link Force -14 lb (Compression) Link Force -841 lb (Compression)
F.S. Yield -1,909.36 (link stretching) F.S. Yield 120.62 (link compressing)
F.S. Buckling -19,929.75 (link buckling under braking) F.S. Buckling 417.41 (link buckling under acceleration)
F.S. Bending 4.84 (somewhat irrelevant for an UPPER link) F.S. Bending 15.50 (link bending w/ 1/2 the vehicle weight on it)
F.S. Rod End -2,348.86 (rod end breaking) F.S. Rod End 65.37 (rod end breaking)

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developed by instrumenting each of the passenger seats and having a “dummy load” that will place the
Center of Gravity at a different location on the ride vehicle. After instrumenting a handful of different loading
scenarios, including the most extreme cases such as a bobsled loaded with three 350 lb. passengers or one
filled with two 35 lb. children and a petite 100 lb. adult, any loads that are between the instrumented cases
can be interpolated to achieve a comfortable response to the attraction. Therefore, with this system, even a
classic roller coaster can receive an upgrade in ride quality, and for the Matterhorn Bobsleds in particular, the
theming can even be improved.
E. UPDATED MATTERHORN BOBSLED DESIGN
The new design of the Matterhorn Ride Vehicle improves upon quite a few of the features of the existing
ride vehicle, including keeping the individual bucket seats. With the new design in particular, the seats
were designed to be able to be separated from the chassis of the ride vehicle, allowing the seats to be
replaced individually for maintenance reasons. The seats are attached to the chassis with steel rails that
fasten directly to the vehicle chassis as shown in Figure 10. Seatbelts are not included directly into the
seat design, and instead interface with the seats by fitting up through the steel rails on either side of the
seat. As part of ASTM F2291, seatbelts are required to have a manual override that allows them to be
unlocked during an emergency situation. By including the seatbelts with the chassis, a ride operator will
be able to unlock all three seatbelts from outside the ride vehicle.

Figure 10. A picture depicting the updated Matterhorn ride vehicle bucket seat design.

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With the seats slightly elevated, not only are the seats more ergonomic, but it allows for natural sitting
for the passenger sitting in the seat behind it by allowing their feet to pass under the seat. The seats are
designed specifically to be able to fit individuals up to 6’ 5” in height, as shown in Figure 11, which was
chosen because it is the 99th
percentile of the population. For individuals taller than this, the seats were
narrowed to open up aisles on either side of the seats to provide even more leg room for the middle and
rear seats. A portion of the rear of the vehicle was also removed to allow the rear seat to sit further back
in the ride vehicle. The seats were also designed to allow children to comfortable be seated on the ride.

Figure 11. A model showing a 6’ 5”, 99
th
percentile male sitting in the updated Matterhorn Ride vehicle.

Figure 12. An isometric view of the updated Matterhorn Bobsled ride vehicle.

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The underside of the vehicle shown in Figure 13 shows the integration of the Satchell Link Suspension
system, along with the electronics compartment that has also been integrated into the chassis. The
electronics compartment will house the signal conditioners for the suspension sensors, as well as the
onboard computer that will set the scripting for the damping parameters and communicate to the ride
controller computer to confirm position along the track and verify a safe ride through. To remain
compatible with the track, the wheel assemblies remain largely unchanged from before. More images of
the final design offering different perspectives are included in Figures 14‐17.

Figure 13. An underside view of the vehicle showing the Satchell Link semi‐active suspension design and other important
components.

Figure 14. Front view of the newly designed Matterhorn Bobsled ride vehicle.

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Figure 15. Top view of the newly designed Matterhorn Bobsled ride vehicle.

Figure 16. Side view of the newly designed Matterhorn Bobsled ride vehicle.
The final design accomplishes all of the goals that were set for this design process, including adding a
suspension system that allows for guests 35‐inches and taller to be able to comfortably ride this
attraction. New technology is included as part of the attraction to allow for variable damping in the
suspension for an optimized amount of ride quality regardless of the loading of the vehicle and the
resultant location of the center of gravity. The new seat design allows for a combination of increased
ergonomics and increased leg room to be able to enjoy the attraction, and all of the existing features
that were required in order to remain compatible with the current Matterhorn track are still part of the
design. The design presented will allow guests to better enjoy the theme and story of this classic ride.

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Figure 17. An image depicting the assembled Matterhorn ride vehicle with six 6’ 5” passengers.
F. FUTURE WORK
It was decided that the semi‐active suspension system was the best possible option for the existing ride
vehicle, however, if a significant overhaul to the Matterhorn track and technology were made, the best
candidate for the ride vehicle would be a fully active hydraulic suspension as shown in Figure 18. This
would require that in addition to all of the existing sensors added for the semi‐active suspension, a
hydraulic fluid reservoir and filter would have to be added to the ride vehicle, as well as hydraulic pumps
and hoses that would create a hydraulic network connecting the hydraulic reservoir to the suspension
spring‐dampers located at the four corners of the ride vehicle. With this system, in addition to “scripting”
the ride experience for comfort, the Matterhorn Bobsled would be able to be fully controlled by the
suspension system and its controller. This means that the Bobsled could feel like it is floating on fresh
snow powder, and gently lean into turns for the most realistic simulation possible. This solution would
be the most expensive and would be the most difficult to implement; however, it would be able to
provide the best experience overall.

Figure 18. (a) A quarter model of a passive suspension. (b) A quarter model of the semi‐active suspension designed. (c) A quarter
model of the fully‐active hydraulic suspension proposed for future work

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V. DESIGN OF AN ORIGINAL RIDE VEHICLE
Looking at the most recent attractions that have opened within the last five years, it is evident that the
most popular attractions are the most immersive. For example, the Radiator Springs Racers attraction in
Disney’s California Adventure Park utilizes show scenes combined with animatronics to recreate the
environments shown in the popular Cars movies as shown in Figure 19. This attraction is located in a
themed portion of the park that also recreates the environments from the Cars movies.

Figure 19. A show scene and the ride vehicle from Radiator Springs Racers in Disney’s California Adventure theme park.
Universal Studios has also seen a lot of success recreating the environments from the Harry Potter films
in their Orlando theme parks with themed portions of the parks as well as immersive attractions such as
the Harry Potter and the Forbidden Journey attraction in the Islands of Adventure theme park shown in
Figure 20.

Figure 20. Ride loading area for Harry Potter and the Forbidden Journey at Universal Studios Islands of Adventure Park.

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An extensive patent search was also completed in order to accomplish the goal of creating an original
theme park ride vehicle. A select number of related patents are documented in Appendix A of this
document.
Ultimately, a suspended ride vehicle on a track that allows for motion simulation was chosen because it
allows for the most versatile use in multiple theme parks. The following sections outline the design
decisions made for the original ride vehicle and how it could be implemented into a theme park
attraction.
A. RIDE VEHICLE CONCEPT
Motion simulators are very common in theme parks today, because they allow attractions to be built
utilizing a fraction of the amount of space that ride vehicles on a track utilize. However, there are a
significant number of guests that experience called Simulator Sickness when riding a motion simulator.
Simulator Sickness occurs when the body senses discrepancies between its perceived motion and its
actual motion. The ride vehicle shown in Figure 21 is intended to be a smooth and subtle motion
simulator that is able to be controlled on a track with a Dual Sided Linear Induction Motor (DLIM). The
DLIM allows for the vehicle to be driven forward or backward depending on the frequency that the
induction loops are turned off and on. The vehicle is not intended to be “launched” utilizing the DLIM
like many roller coasters are. Instead, the DLIM is utilized for a controlled and steady pace throughout
the ride.

Figure 21. Original ride vehicle design concept.

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As shown in Figure 22, the suspended chassis is able to tilt forward and backward by controlling two
linear actuators that apply a moment couple about the vehicle central pivot. Above the central pivot, a
large turntable allows for the ride vehicle to rotate up to 360‐degrees. Welded Aluminum tubing is the
primary material utilized in the chassis because it is lightweight, some tempers are able to be formed
easily, and it is inexpensive and readily available.
Another feature shown in Figure 22 is the decorative shroud. The decorative shroud obstructs the view
of both the ride vehicle and track from riders and is also able to contain cooling fans to continuously
blow air on guests to aid in preventing Simulator Sickness. Lighting can also be installed in the
decorative shroud to assist with guest loading and unloading, as well as lighting in the case of a
breakdown of the ride. The Center of Gravity (CG) of the ride vehicle was also intentionally placed just
behind the pivot point to always allow for the ride vehicle to tilt slightly backwards instead of forwards if
the ride vehicle happened to lose power while it was operating regardless of how it is loaded.

Figure 22. Motion control mechanisms of the ride vehicle.

21 | P a g e

In order to cut down on the overall weight of the vehicle, a high tensile (HT) Nylon mesh netting (Type
TP21) was utilized to be able to support the individual riders on the ride vehicle. A sample of the mesh
netting is shown in Figure 23. The mesh netting is rated for a 325 lb. individual, and weighs 10.2 ounces
per square yard. The total weight of the mesh netting is 4.78 lb. once installed on the ride vehicle.

Figure 23. Nylon mesh netting sample.
The overall structure of the ride vehicle chassis is shown in Figure 24, which is used to create the finite
element analysis (FEA) model of the ride vehicle.

Figure 24. The aluminum structure (skeleton) of the ride vehicle, which is converted to a mesh for a Finite Element Analysis.

22 | P a g e

B. FUTURE WORK
The original intention with this design was to allow full motion control of the ride vehicle. The attraction
presented is not able to roll, which is fairly important for a simulation experience. After researching
different ways to accomplish this, the two most attractive solutions were to add another motor that
allowed for rolling articulation or to add five more electric linear actuators to be able to create an
inverted Stuart Platform. Adding another motor would have added a lot of complexity to the model, as
well as added a significant amount of weight to the overall structure of the chassis. Adding the Stuart
Platform would have added even more complexity to the model, although it would not have the same
weight consequences as adding another motor would. Both solutions also present issues if power is lost
while guests are in the ride vehicle. A significantly more complicated chassis would have to be
developed in order to allow for the guests to remain comfortable when the power is lost. Ultimately, an
inverted Stuart Platform would be the preferred choice of the two options because of the weight savings
afforded. An image of a Stuart Platform is shown in Figure 26.

Figure 25. Image of a Stuart Platform being used to tilt in a full 360‐degree.
Although it is a little out of scope for this project, a concept of how spherical projection could work for
this ride vehicle is shown in Figure 25. The concept prevents the ride vehicle from crossing into the
direct path of the projection on spherical walls.

Figure 26. Spherical Projection Concept

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VI. ANALYSIS OF AN ORIGINAL RIDE VEHICLE
The design intent for this ride vehicle is to allow as many different people to be able to ride it as
possible. This is accomplished by designing the maximum load for the chassis to be able to seat six 99th

percentile males—each weighing 250 lb. With this in mind, the total weight of the chassis including the
passengers is 2114 lb. As previously mentioned, the chassis is designed to have the center of gravity
behind the central pivot to prevent the chassis from tipping forward in the event of a loss of power. This
holds true regardless of the loading of the chassis.
Figure 27. The maximum chassis load with the CG shown as a magenta reference frame.
The following section of the report provides stress analysis and margin of safety calculations for
expected load cases for the original ride vehicle. Analysis methods in this report use finite element (FE)
models to calculate stress as a result of the various load cases. The intent of this report is to provide
analysis substantiation for the ride vehicle chassis, which will be subjected to the most stringent load
cases.

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A. FINITE ELEMENT (FE) MODEL
The finite element model of the original ride vehicle consists of dimensionally reduced meshing elements
throughout, representing all contributing mass, inertia, and stiffness of the ride vehicle. Dimensionally
reduced elements essentially comprise mesh elements that possess one less dimension than the
structural components that they represent. For mesh elements like fasteners, 2‐D beam elements are
used. A beam element has two nodes with a line in between. The line that ties the two points together is
the reduced dimension element, as it’s infinitely small in diameter, yet it contains the cross‐sectional
characteristics of the structural member it represents (as calculated numeric constants). The same holds
true for large, flat sections of machined parts or sheet metal. Plate elements are employed to represent
those metal pieces; the net shape, curvature and contributing structural details are captured with
infinitely thin surfaces that have thickness applied as numeric constant once more. This is a significant
enabler for the analysis as it utilizes roughly 1/5 the number of nodes and elements of a fully‐meshed
tetrahedral model (thus reducing run times), and allows the modification of the design (such as
increasing or decreasing machined thickness, sheet metal gage or fastener size) without having to re‐
mesh. Likewise, the reduced overall amount of nodes and elements allows for a complete assembly
model to be analyzed with one analysis, adding to the fidelity and accuracy of the product. Each element
is also defined with a material and a property. Properties allow for the same material to be used for
different element types, and help define various element parameters. With plate elements, the plate
thickness is a numeric constant that is assigned within the property state. For mass elements, a specific
mass is assigned. For beam elements, the material and cross sectional properties are assigned.
As shown in Figure 28, the FE model captures all structural components with simplified geometry. Figure
29 shows a representation of the FE model with the thickness and cross sectional areas of dimensionally
reduced elements shown. The FE model’s center of gravity (CG) is located is within .15” of the 3D CAD
models CG location. This is important, because the expected load cases are all body‐load cases—where
the chassis acts as the primary inertial reference frame and any dynamics that act on it externally are
able to affect the reference frame through accelerations. The accelerations are applied on a per element
basis which results in forces being applied to elemental nodes. A great example of this is a constant
gravitational acceleration acting downward. The only external forces that are applied to the system are
utilized to represent the controlling forces from the linear‐actuators utilized to tilt the chassis while
controlling it.

Figure 28. Comparison of the 3‐D CAD to the Dimensionally reduced Finite Element (FE) Model.

25 | P a g e

Figure 29. The Finite Element (FE) Model with thicknesses represented.
B. MODEL ELEMENTS
Figure 28 shows the FE model of the ride vehicle chassis, which is comprised almost entirely out of plate
elements. Plate elements are able to be used primarily because the entire chassis design takes
advantage of structural tubing and machined thin walled structures. The 99th
percentile passengers that
are on the ride vehicle are able to be modeled as mass elements. These mass elements possess the mass
and inertial properties of the corresponding passengers, but are represented in the analysis as a single
node collocated at the component’s geometric CG. As shown in Figure 30, these single‐node elements
tie into parent FE structure via rigid elements at the same locations where actual fasteners are used to
secure the components in place. These rigid mounting points are, in themselves, conservative when
used for the static analysis, because they do not account for any internal damping that would occur
when transferring loads from the CG to the structure. The handles for the chassis are modeled utilizing
beam elements, also shown in Figure 30. The various element counts and their descriptions are shown
in Table 1 for reference.

Figure 30. Mass elements being shown directly tied to the structure with rigid elements.

26 | P a g e

Table 1. Types of FE Elements Used to Model the Chassis.

C. MODEL MATERIAL
All of the elements within the FE model have assigned material properties. The material used in the
model is 6061‐T651 aluminum, which is an isotropic material with the material properties defined in
Table 2. A more detailed summary of material properties is included Appendix C.
Table 2. Isotropic Material Properties‐Used in the model for beam elements of varying cross‐sections and plate elements of
varying thicknesses.

For isotropic materials, the yield stress, , and ultimate stress, , determine the allowable limit of
the material. More details regarding the material limits of the materials and calculated margins can be
found within the individual load case sections of this report.
Fatigue is also an important topic to cover in this analysis, because the load cases presented will occur
hundreds or even thousands of times daily. The fatigue curves for 6061‐T6 aluminum are included in
Figure 31 to allow a comparison between the results of the analysis and the fatigue life of the chassis.
Although aluminum is a light structural material, it generally has very low fatigue strength when
compared to other structural materials such as steel. An unnotched curve without a stress concentration
factor is able to be utilized because FEA accurately calculates stresses at specific locations where
stresses may be concentrated.

Figure 31. The Unnotched 6061‐T6 aluminum S/N curve from MMPDS‐8.
Element Type Element Count Description
Beam, Linear 49 Used to model fasteners or long structures with constant cross sectional area
Plate, Linear 124342 Used to model simple isotropic geometry‐‐efficient use cuts down element count
Mass 6 Used to accurately represent the mass and inertia of nonstructural objects
Rigid 8 Used to secure mass elements to the corresponding structures that bear their load.
Material Alloy Ftu (ksi) Fty (ksi) E (Msi) ν ρ (lb/in^3) REF.
Aluminum 6061‐T651 42 35 9.9 0.33 0.098 MMPDS‐08

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D. FINITE ELEMENT MODEL QUALITY
The choices of the type of element, as well as the quality of the elements are very important when using
Finite Element methods to calculate accurate results. Misuse of elements can dramatically change
results; therefore, a conservative approach should always be used. In creating a model, the element
quality should always be checked to confirm that the results provided by the Finite Element code are
accurate. A significant amount of time was spent to verify that the mesh quality was appropriate, and as
shown in Figure 32, the mesh quality of the Finite Element model is excellent. A more detailed
discussion of element quality is included in Appendix B of this report.

Figure 32. The Jacobian contoured on the mesh of the Finite Element model, showing that all of the elements have a Jacobian of
less than 0.6.

28 | P a g e

E. CONSTRAINTS OF THE MODEL
In order to constrain the model and allow for the stiffness matrix of the Finite Element model to be
invertible, the FE model must be properly constrained in its degrees of freedom. For this model, the
internal bearing surfaces were constrained translationally and rotationally about its axis as shown in
Figure 33.

Figure 33. The two internal bearing surfaces where the constraints are applied to prevent axial translation and rotation.
F. VIBRATIONAL MODES OF THE MODEL
The vibrational modes or natural frequencies of the model are an important consideration during the
design process, especially when designing around any motors or other machinery. If a structure is
excited by an oscillatory input that is very close to its dominant natural frequencies, it is possible for the
entire structure to fail catastrophically. Finite Element analysis is an excellent method of predicting at
what frequencies vibrational modes will occur, as well as what the mode shapes look like. Being able to
see the mode shapes during the design process is a significant advantage, because it allows the designer
to stiffen up the structure in problem areas if necessary. The first natural frequencies of the model are
shown in Table 3. After observing the mode shapes of the model, the first natural frequency in Table 3
can be discounted because of the loading conditions and chosen constraints. The first natural frequency
shown at 5.07 Hz corresponds to the rotation of the chassis about the axis of its bearings, which
currently has constraints applied to it for this analysis. This rotation about the axis should correspond to
a rigid body mode (natural frequency = 0 Hz) being controlled by the linear actuators of the system. The
linear actuators are represented as forces in this analysis, and are therefore not accurately represented

29 | P a g e

in a vibrational modes analysis, which is a function directly related to the mass and the stiffness of the
model. The subsequent mode shapes correspond to various “twistings” of the ride vehicle chassis, as
shown in Figure 34 which shows the exaggerated deflections of the second and third mode shapes. It is
important to note that the natural frequencies of the system can also be utilized to perform random
vibration analysis or sinusoidal response analysis with the Finite Element model.
Table 3. The natural frequencies of the Finite Element model.

Figure 34. The second and third mode shapes plotted with their corresponding strain energies.
Mode Number Frequency [Hz]
1 5.07
2 8.44
3 22.85
4 26.76
5 50.77
6 75.43
7 81.87
8 95.75
9 113.11
10 120.65

30 | P a g e

G. FIRST LOAD CASE OF THE MODEL
The first load case analyzed corresponds to a standard fully loaded chassis with the six 250 lb.
passengers with a factor of safety of 1.5. This load corresponds to six 375 lb. passengers. The von Mises
stress results, as well as an exaggerated deflection of the model is shown in Figure 35. Knowing that this
type of load is dynamic (guests loading and unloading), the maximum stress must be compared to the
fatigue stress chart in Figure 31. Looking at the chart, it is evident that the fully‐reversing cycling has a
run out of roughly 12,000 psi. This corresponds to a safety margin of 0.18, showing that the design is
suitable for this load condition.

Figure 35. The von Mises stress [psi] contour plot results after the first load condition is applied.

31 | P a g e

H. SECOND LOAD CASE OF THE MODEL
The second load case analyzed corresponds to a standard fully loaded chassis with the six 250 lb.
passengers with a rotational acceleration of 8π rad/s2
. This load corresponds to the maximum rotational
acceleration/deceleration allowed by the structure to stay within the fatigue limits. It is important to
note that even though this load corresponds to a margin of safety of 0.16 for a fully reversing load with
run out of 12000 psi, it also corresponds to a linear acceleration of 3.8g’s for the outside passengers.
Therefore, this load case is chosen only as a theoretical limit that could be applied as a rotational
acceleration due to an applied torque to the system. This load would make even the hardiest of guests
uncomfortable and likely sick. Even though this rotational acceleration will likely never be used in
practice, the analysis shows that the current design is suitable for the load condition. The von Mises
stress contour plot results are shown in Figure 36.

Figure 36. The von Mises stress [psi] contour plot results after the second load condition is applied.

32 | P a g e

I. THIRD LOAD CASE OF THE MODEL
The third and final load case analyzed corresponds to a fully loaded chassis with the six 250 lb.
passengers with a factor of safety of 3 combined with the necessary control forces provided by the
linear actuators. The linear actuators are required to provide the necessary forces to create the moment
couple required to keep the chassis in its maximum tilted position. The force required to be applied by
the linear actuators is 2013 lb. in opposing directions. A large factor of safety was chosen for this
situation, because of the importance of the stabilizing actuator forces. Even though the chassis is
designed to “fail safely” in the event of a loss of power, if the linear actuator causes a structural failure,
the safety of the passengers is at risk. The actuator forces will provide dynamic loading to the chassis,
therefore, the maximum stress must be compared to the fatigue stress chart in Figure 31. The maximum
stress for this load case is 10674 psi as shown in Figure 37, which corresponds to a margin of safety of
0.11. The analysis shows that the current design is suitable for the expected load conditions.

Figure 37.The von Mises stress [psi] contour plot results after the third load condition is applied.

33 | P a g e

VII. CONCLUSIONS
An introduction to Themed Entertainment Design has been presented through research into current
industry standards, a redesign of an existing theme park ride vehicle, and through the original research,
design, and analysis of an original theme park ride vehicle. It is the intention of this paper to properly
display the broad knowledge base required to design a theme park attraction, as well as the depth of
knowledge required to support the design of theme park attractions. During the process of this
investigation, there were numerous difficulties, including numerous changes to the designs of both ride
vehicles. Many of the original design concepts are vastly different than the original concepts planned,
such as the fully‐active suspension for the Matterhorn ride vehicle concept and the fully articulating ride
vehicle concepts presented in the future work sections of this report. The detailed FEA analysis has
proven the feasibility of the original theme park ride vehicle with a significant amount of margin when
compared with the dynamic loading cases of the chassis and the fatigue life of the chosen materials. The
analysis was completed assuming that six 99th
‐percentile males were the passengers, which allows for a
significant percentage of the population to be able to experience the original ride vehicle design. Now
that the original ride vehicle structure is proven, it can be integrated into a Theme Park Attraction.
VIII. SOURCES
https://www.library.ca.gov/CRB/97/12/97012lr.html
http://www.iaapa.org/safety‐and‐advocacy/safety/amusement‐ride‐safety/astm‐standards
http://www.astm.org/COMMITTEE/F24.htm
http://www.iaapa.org/safety‐and‐advocacy/safety/amusement‐ride‐safety/regulations‐standards
http://www.vibrationmounts.com/WireRopeIsolators.htm
http://www.carbibles.com/suspension_bible_pg2.html

34 | P a g e

APPENDIX A – PATENTS RESEARCHED FOR THIS PROJECT
A. PATENTS RELATED TO ORIGINAL THEME PARK DESIGN
1. Theme Park Ride with Ride‐Through Screen System
a) https://www.google.com/patents/US7905790?dq=theme+park+ride+v
ehicles&hl=en&sa=X&ved=0CBwQ6AEwADgKahUKEwjSup3TibbHAhXHTIg
KHQ2MAH8
2. Dynamic Ride Vehicle
a) https://www.google.com/patents/US5623878
3. Amusement Apparatus and Method
a) https://www.google.com/patents/US6354954?dq=suspended+theme
+park+ride+vehicles&hl=en&sa=X&ved=0CE0Q6AEwBzgUahUKEwj2yoaMk
LbHAhUMl4gKHV0yCBw
4. Amusement Ride
+park+ride+vehicles&hl=en&sa=X&ved=0CEYQ6AEwBjgUahUKEwj2yoaMk
LbHAhUMl4gKHV0yCBw
5. Ride Vehicle Control System
+park+ride+vehicles&hl=en&sa=X&ved=0CBwQ6AEwADgeahUKEwj7gdTK
k7bHAhXFlYgKHSepA90
6. Flying Roller Coaster With Vertical Load and Launch
a) https://www.google.com/patents/US20140165868?dq=suspended+th
eme+park+ride+vehicles&hl=en&sa=X&ved=0CCoQ6AEwAjgoahUKEwj2isG
cmbbHAhWIn4AKHY36Bg0
7. Motion‐based Attraction
+park+ride+vehicles&hl=en&sa=X&ved=0CCMQ6AEwATg8ahUKEwic78CT
mrbHAhVFnYAKHcqPC2o
8. Amusement Ride
+park+ride+vehicles&hl=en&sa=X&ved=0CDgQ6AEwBDg8ahUKEwic78CT
mrbHAhVFnYAKHcqPC2o
9. Motion Simulator Theater With Suspended Seating

35 | P a g e

a) https://www.google.com/patents/WO2011106488A1?cl=en&dq=susp
ended+theme+park+ride+vehicles&hl=en&sa=X&ved=0CEYQ6AEwBjiWAW
oVChMI24Dyip-2xwIV0fqACh00ng0y
10. Roller Coaster with Articulable Seat Backs
a) https://www.google.com/patents/US8490550?dq=motion+coaster&hl
=en&sa=X&ved=0CD8Q6AEwBTgeahUKEwiJmN2RorbHAhUMmYAKHRf7B
kY

36 | P a g e

APPENDIX B – DEFINITION OF VON MISES STRESSES, MARGIN OF SAFETY,
AND MESH QUALITY
Intentionally, all components and assemblies of the analyses presented herein have been
designed such that peak stresses lie within the linear portion of the elastic regime of the
component’s material properties. A plot of the stress/strain curve is shown in Figure A‐2.
Insufficient strain energy exists in every load case to induce plastic deformation. By doing so,
the linear finite element analysis approach is valid as a tool for forecasting the integrity of an
assembly undergoing emergency landing load accelerations.
The analysis approach allows the von Mises stress criterion to be employed, the main stress
scalar presented within this document. Part of the plasticity theory, von Mises stress is a scalar,
‘maximum stress’ value found with ductile materials, such as aluminum and steel. By definition,
a material is said to start yielding when its von Mises stress reaches the yield stress of the
material. von Mises stress takes into account multi‐axial loading and structural displacement
response. The two images of Figure A‐1 illustrate this; when stress values in any axis approach
the limits of the cylinder of the von Mises surface, yielding occurs.
Figure Error! No text of specified style in document.‐1. von Mises Stress in 3‐d Cartesian Coordinate Space
Note: von Mises Stress in 3‐d Cartesian Coordinate Space is a cylinder about the hydrostatic stress axis
(A) and a circle capturing the more‐conservative maximum shear (Tresca) stress in 2d space (B).
von Mises stress, συ, under multi‐axial loading conditions can be defined as:

     
2
2
12
2
33
2
21 



In the case of pure shear stress, σ12 = σ12≠ 0, while all other stresses, σ12=0, von Mises criterion
becomes:
A B

37 | P a g e

3
12
y
k

 
At the onset of yielding, the magnitude of the shear stress in pure shear, k, is 1.7 ( 3 ) times
lower than the tensile stress of the case of pure tensions. In the case of plane stress
(Figure A-1[B]), where σ3=0, the von Mises criterion becomes:
222
221
2
1 3 yk  
This equation represents an ellipse in the X-Y plane of Figure A-1(B). Typically, von Mises
stresses found within the analysis models comprise some combination of shear and tensile
stresses. As such, the perimeter line about the X-Y stress plot is used as the linear yield point for
all materials in these analyses.
An advantage of utilizing von Mises stress is that a direct correlation between material properties
and loading can be derived based on material yield (and corresponding ultimate) alone, thus
alleviating the need for tensile or shear yield values. This simplification is leveraged in the
generation of a margin of safety (MS); a value that is based on material conditions. MS is defined
as:
1
tu
tu
f
F
MS
Where Ftu is allowable ultimate stress and ftu is the factor of safety on the limit load:
tltu ffFoS 5.1

Figure Error! No text of specified style in document.‐2. Stress versus Strain Curve for Aluminum Alloy
It should be noted that material properties for materials comprising this analysis were taken from
Metallic Materials Properties Development and Standardization (MMPDS-8), with specific
materials cited in Appendix C. As long as the margin of safety is 0 or positive, no detrimental
permanent deformation will result, and the analysis entities meet airworthiness requirements.

38 | P a g e

FEA mesh quality was a prime consideration for the generation of accurate analyses results. A
reason for using a robust, established auto-meshing tool in the FEA software such as
FEMAP/Nastran is that the user can generate sound element meshes. All elements underwent a
distortion check; a modified scale-invariant check based solely on geometric parameters. These
parameters included:
 Aspect ratio. Length to height ratio (maximum allowable ratio of 10:1).
 Taper. Similar to aspect ratio for trapezoidal shapes (max. ratio of 10:1).
 Alternate Taper. Divides the Q-4 element into two triangles, looking at triangular taper
ratio (0.5:1 max allowable).
 Internal angles. Deviation from 90° (rhombus shape investigation, 30° max allowable
angle).
 Warping. Investigates the planarity of the element faces (5° max warping angle).
 Jacobian. Comparison of element shape to ideal shape.
Within the mesh, all elements are evaluated against the maximum values of the aforementioned
parameters. For those elements that did not pass the check, local re-meshing, often at individual
elements, occurred. Once the entire mesh met the criteria, the model was ready for analysis.
Consider the Quad-4 shown in Figure Error! No text of specified style in document.-3. The
level to which mesh element geometry strays from the ‘ideal shape’ will impact its strain
response.

Figure Error! No text of specified style in document.‐3. Four‐point Quadratic (Q‐4) Element
To that end, the intent is to minimize divergent element shapes. In terms of the Jacobian distortion
check, the numerical integration of the 2‐d, Quad‐4 plate element, after the chain rule, gives:
[1]
With the Jacobian being
[2]



















































y
x
yy
yx








 























yy
yx
J

39 | P a g e

The Jacobian, in modified form, is a measure of the amount of difference between the ideal
shape and the actual element shape and is key in the distortion check. The modified Jacobian
provides a normalized constant ranging from 0, for optimal shape, to 1, for the worst-case shape.
Large variations of the determinant of the Jacobian translate into numerical stiffening of the
element. A comparison of the two triangle elements shown in Figure Error! No text of specified
style in document.-4 illustrates the difference between the ‘ideal’ element shape (left side)
versus a less desirable, high aspect ratio element shape (right side); note the values of the
Jacobian.
Figure Error! No text of specified style in document.‐4. Jacobian Distortion Check
Comparison of Meshed Elements to Ideally Shaped Elements

40 | P a g e

APPENDIX C – MATERIAL PROPERTIES

Figure 38. MMPDS‐08 Table 3.6.20(b2), Design Mechanical and Physical Properties of 6061 Aluminum Alloy Plate.

41 | P a g e

APPLICABLE DOCUMENTS‐DOUBLE CLICK TO OPEN
ASTM F2291—Standard Practice for Design of Amusement Rides and Devices

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