Purdue University | Fluid Power Vehicle Challenge

A DESIGN REPORT FOR THE PURDUE UNIVERSITY HYDRAULIC VEHICLE, 2018 – 2019
SUBMITTED BY:
CHANDLER FAIRFIELD
TIMOTHY WILLIAMS
COREY FLETCHER
SHANE KOPPOLD
PROJECT ADVISORS:
DR. ANDREA VACCA
DR. JOSÉ GARCIA-BRAVO
AGRICULTURAL & BIOLOGICAL ENGINEERING
PURDUE UNIVERSITY
WEST LAFAYETTE, IN 47906
APRIL 22, 2019
PURDUE UNIVERSITY
NATIONAL FLUID POWER ASSOCIATION
FLUID POWER VEHICLE CHALLENGE

2019
RESTRICTED INFORMATION
Any reference required by University.

To our teammate and friend, Tommaso Greco. We couldn’t have done it without you.
Thank you for all your support along the way.

CONTENTS
Executive Summary...................................................................................................................... 1
Introduction................................................................................................................................... 2
1 Objectives ............................................................................................................................... 3
1.1 Hydraulic Efficiency ........................................................................................................ 3
1.2 Energy Storage................................................................................................................. 3
1.3 Alternative Power Transfer .............................................................................................. 3
1.4 Create a Natural Riding Experience................................................................................. 3
2 Problem Definition.................................................................................................................. 4
2.1 Success Definition............................................................................................................ 4
3 Background Research ............................................................................................................. 4
3.1 Existing Solutions ............................................................................................................ 4
3.1.1 Purdue University ..................................................................................................... 4
3.1.2 Murray State University............................................................................................ 5
3.2 Similar Problems.............................................................................................................. 6
3.3 Related Companies........................................................................................................... 6
3.4 Standards.......................................................................................................................... 7
3.5 Ethical & Professional Considerations............................................................................. 7
3.6 Impact............................................................................................................................... 7
3.6.1 Economic .................................................................................................................. 8
3.6.2 Global........................................................................................................................ 8
3.6.3 Cultural & Social ...................................................................................................... 8
3.6.4 Environmental........................................................................................................... 8
3.6.5 Public Health, Safety, and Welfare........................................................................... 8
4 Problem Scope ........................................................................................................................ 9
4.1 Constraints........................................................................................................................ 9
4.1.1 General...................................................................................................................... 9
4.1.2 Sprint Race................................................................................................................ 9
4.1.3 Efficiency Challenge............................................................................................... 10
4.1.4 Endurance Challenge .............................................................................................. 10
4.2 Criteria............................................................................................................................ 10
4.2.1 Sprint Race.............................................................................................................. 11
4.2.2 Efficiency Challenge............................................................................................... 11
4.2.3 Endurance Challenge .............................................................................................. 11
5 Alternative Solutions ............................................................................................................ 11
5.1 Frame.............................................................................................................................. 12
5.1.1 Two-Wheeled Bicycle ............................................................................................ 12
5.1.2 Recumbent Bicycle ................................................................................................. 12
5.2 Pumps............................................................................................................................. 13
5.2.1 Two-Chamber Gear Pump...................................................................................... 13
5.2.2 Single Gear Pump ................................................................................................... 14

5.2.3 Piston Pump ............................................................................................................ 15
5.2.4 Pneumatic System................................................................................................... 15
6 Proposed Solution Path......................................................................................................... 16
6.1 Introductory Analysis..................................................................................................... 16
6.2 Design Matrices.............................................................................................................. 16
6.2.1 Frame ...................................................................................................................... 16
6.2.1.1 Solution: Recumbent Frame............................................................................ 17
6.2.2 Pumps...................................................................................................................... 18
6.2.2.1 Solution: Dual Hand Pump & Rotary Pump ................................................... 19
6.2.3 Charging Method .................................................................................................... 19
6.2.3.1 Solution: Foot Pump........................................................................................ 20
6.2.4 Electronics............................................................................................................... 20
6.2.4.1 Solution: Raspberry Pi..................................................................................... 21
7 Overall Project Proposal Summary....................................................................................... 22
7.1 Final Design Specifications............................................................................................ 22
7.1.1 Circuit Design ......................................................................................................... 25
7.1.2 Frame ...................................................................................................................... 26
7.1.3 Propulsion Method.................................................................................................. 28
7.1.4 Hydraulic Circuit .................................................................................................... 28
7.1.5 Manifold Design ..................................................................................................... 28
7.1.6 Electronic User Interface ........................................................................................ 29
7.2 Sizing Objectives............................................................................................................ 32
7.2.1 Free Body Diagram................................................................................................. 32
7.2.2 Sizing the Circuit .................................................................................................... 33
7.2.3 AMESim Optimization........................................................................................... 34
7.2.3.1 Genetic Algorithm ........................................................................................... 34
7.2.3.2 Nonlinear Programming by Quadratic Lagrangian ......................................... 34
7.2.3.3 AMESim Models............................................................................................. 34
7.2.3.4 System Parameters........................................................................................... 35
7.2.3.5 Outputs to be optimized................................................................................... 35
7.3 Budget Requirements..................................................................................................... 35
8 Lessons Learned.................................................................................................................... 37
9 Conclusions........................................................................................................................... 38
9.1 Industry Experience........................................................................................................ 38
9.2 Learning Outside the Classroom.................................................................................... 38

Appendix...................................................................................................................................... 39
9.3 References Cited ............................................................................................................ 40
9.4 Project Gantt................................................................................................................... 42
9.5 Supporting Material........................................................................................................ 43
9.5.1 Introduction to System............................................................................................ 43
9.5.1.1 Accumulator .................................................................................................... 43
9.5.1.2 Hydraulic Pump/Motor.................................................................................... 47
9.5.1.3 Reservoir.......................................................................................................... 47
9.5.1.4 Connecting Lines............................................................................................. 47
9.5.2 Network Integration................................................................................................ 49
9.5.2.1 Continuity........................................................................................................ 49
9.5.2.2 Equation of Motion.......................................................................................... 50
9.5.3 Fluid Folks’ Modes Vision ..................................................................................... 50
9.5.3.1 Charging .......................................................................................................... 51
9.5.3.2 Boost................................................................................................................ 51
9.5.3.3 Pumping........................................................................................................... 52
9.5.3.4 Regen............................................................................................................... 52
9.6 Final Competition Photos............................................................................................... 53

LIST OF FIGURES
Figure 1: The Purdue Tracer 2017.................................................................................................. 5
Figure 2: Murray State's Bicycle .................................................................................................... 5
Figure 3: Road Bicycle ................................................................................................................. 12
Figure 4: Recumbent Bicycle........................................................................................................ 12
Figure 5: Components of a Dual Gear Pump System................................................................... 13
Figure 6: Components of a Single Gear Pump System................................................................. 14
Figure 7: Components of a Piston Pump System.......................................................................... 15
Figure 8: Components of a Pneumatic Piston Pump System........................................................ 15
Figure 9: Frame Pugh Matrix........................................................................................................ 16
Figure 10: Pumps Pugh Matrix..................................................................................................... 18
Figure 11: Charging Method Pugh Matrix.................................................................................... 19
Figure 12: Electronics Pugh Matrix.............................................................................................. 20
Figure 13: Fluid Folk's Bicycle Model ......................................................................................... 22
Figure 14: Complete Hydraulic Circuit Schematic....................................................................... 25
Figure 15: Base Frame Model....................................................................................................... 26
Figure 16: Loads Placed on Frame for FEA ................................................................................. 26
Figure 17: FEA with Von Mises Stress ........................................................................................ 27
Figure 18: Frame Deflection......................................................................................................... 27
Figure 19: Manifold Schematic .................................................................................................... 28
Figure 20: Dashboard Display ...................................................................................................... 29
Figure 21: Charging Mode Display .............................................................................................. 30
Figure 22: Boost Mode Display.................................................................................................... 30
Figure 23: Pumping Mode Display............................................................................................... 31
Figure 24: Regeneration Mode Display........................................................................................ 31
Figure 25: Bicycle Free Body Diagram........................................................................................ 32
Figure 26: AMESim solution path to finding the best component size........................................ 34
Figure 27: AMESim Schematics .................................................................................................. 35
Figure 28: Schematic diagram of a typical hydraulic energy storage system............................... 43
Figure 29: Pressure drop coefficient (k) in the schema. ............................................................... 47
Figure 30: Conservation of mass using continuity equation example.......................................... 49
Figure 31: Hydraulic Circuit Schematic Symbol Key................................................................. 50
Figure 32: Charging Mode Schematic .......................................................................................... 51
Figure 33: Boost Mode Schematic................................................................................................ 51
Figure 34: Pumping Mode Schematic........................................................................................... 52
Figure 35: Regen Mode Schematic............................................................................................... 52
Figure 36: Team with Vehicle ...................................................................................................... 53
Figure 37: Front, dual foot pumps ................................................................................................ 54
Figure 38: Front steering assemblage, featuring disc break and tie rod ....................................... 54
Figure 39: Regenerative Braking System ..................................................................................... 55
Figure 40: Rear Motor & Hub ...................................................................................................... 55
Figure 41: Hall Sensor for Speed.................................................................................................. 56

LIST OF TABLES
Table 3.2:1 Other Engineering Student Design Competitions........................................................ 6
Table 5.1:1 Two Wheeled Bicycle | Advantages & Disadvantages ............................................. 12
Table 5.1:2 Recumbent Bicycle | Advantages & Disadvantages.................................................. 12
Table 5.2:1 Dual Gear Pump | Advantages & Disadvantages ...................................................... 13
Table 5.2:2 Single Gear Pump | Advantages & Disadvantages.................................................... 14
Table 5.2:3 Piston Pump | Advantages & Disadvantages............................................................. 15
Table 5.2:4 Pneumatic System | Advantages & Disadvantages.................................................... 15
Table 7.1:1 Hydraulic Components.............................................................................................. 23
Table 7.1:2 Mechanical Components ........................................................................................... 23
Table 7.1:3 Bicycle Components.................................................................................................. 24
Table 7.2:1 Sizing objectives for competitions............................................................................. 32
Table 7.2:2 Assumptions made for bicycle free body diagram .................................................... 33
Table 7.3:1 Cost analysis FY18 & 19........................................................................................... 36
Table 11.4:1 Project Gantt for Fall 2018 ...................................................................................... 42
Table 11.4:2 Project Gantt for Spring 2019.................................................................................. 42
LIST OF EQUATIONS
(1) Efficiency Challenge Scoring Ratio........................................................................................ 11
(2) Forces on Bicycle.................................................................................................................... 33
(3) Torque Needed for Pull........................................................................................................... 33
(4) Motor Torque Needed for Pull................................................................................................ 33
(5) Desired Motor Displacement .................................................................................................. 33
(6) Flowrate of Fluid into Accumulators ...................................................................................... 44
(7) Gas Mass Relationship to Gas Expansion............................................................................... 44
(8) Internal Energy per Unit Mass ................................................................................................ 45
(9) Benedict-Webb-Rubin............................................................................................................. 45
(10) Energy Equation for Gas....................................................................................................... 45
(11) Torque Value for Equation (10)............................................................................................ 45
(12) Specific Heat of Gas.............................................................................................................. 46
(13) System Losses ....................................................................................................................... 46
(14) Pressure Differences in Accumulator.................................................................................... 46
(15) Polytrophic Relationship....................................................................................................... 47
(16) System Pressure Drop ........................................................................................................... 48
(17) Reynold’s Number ................................................................................................................ 48
(18) Laminar Flow Friction Coefficient ....................................................................................... 48
(19) Turbulent Flow Friction Coefficient ..................................................................................... 48
(20) Continuum Mechanics Analysis............................................................................................ 49
(21) Mechanical to Hydraulic System Equation of Motion.......................................................... 50

1 | N F P A F l u i d P o w e r V e h i c l e C h a l l e n g e
EXECUTIVE SUMMARY
Efficiency is one of the primary reasons why cycling is one of the most widely used methods of
human transportation. Fluid power is mankind’s way of manipulating forces to move great loads.
The marriage of these two disciplines presents a unique engineering challenge. The National Fluid
Power Association’s (NFPA’s) Fluid Power Vehicle Challenge asks the question, how does an
individual combine these two engineering feats in order to make a human-powered hydraulic
system work?
The method used by this past year’s team was simple: design a bike using findings from prior years
to design a novel vehicle that uses innovative technology by means of a hydrostatic transmission.
A hydrostatic transmission is a type of power transmission where power is transferred by means
of a fluid connection to a hydraulic motor; often through a hydraulic pump. The term hydrostatic
refers to the transfer of energy from flow to pressure, from kinetic energy of the flow. The pump
receives mechanical energy from a rotating shaft connected to the prime mover and transfers it to
the fluid in the form of flow and pressure; i.e., hydraulic energy. The fluid then carries the
hydraulic energy into the motor where it is transformed back into mechanical power at the output
shaft connected to a mechanical device. Thus, the bare-bone elements of a hydraulic transmission
are, therefore, the pump, the fluid and the motor, whose detailed roles are as follows:
Pump : converts mechanical energy into hydraulic energy.
Fluid : transports hydraulic energy from the pump into the motor.
Motor: converts hydraulic energy into mechanical energy.
The hydraulic components were sized on the basis of preliminary calculations and a numerical
optimization strategy based on an AMESim model used to simulate the various drive cycles of the
vehicle during operation.
In all, the vehicle was designed according to the rules of the Fluid Power Vehicle Challenge and
uses a hydrostatic transmission in place of a classical chain transmission. This fluid transmission
uses energy storage devices (accumulators) that are capable of capturing energy while (1)
stationary, (2) in motion, and (3) while braking.
The team’s work is significant due to the increasing demand for low-cost transportation vehicles
worldwide, the use of hydraulics in the biomedical industry and any other sector that is focused on
the scaling down of hydraulics through green, energy-efficient modes.
The present report details all the mentioned aspects of the design, while pointing out the elements
of originality that characterize the proposed solution.

INTRODUCTION
Efficiency is one of the main reasons as to why cycling is one of the most widely used methods of
human transportation. Fluid power is mankind’s way of manipulating forces to move great loads.
The marriage of these two disciplines presents a unique engineering challenge.
The National Fluid Power Association (NFPA) asks students the question: How does one combine
these two engineering feats to make a human-powered hydraulic system? To engage others on the
topic, the NFPA began the Fluid Power Vehicle Challenge to stimulate education in practical
hydraulics, pneumatics, and sustainable energy devices for motion control; and provide students
with experience in real-world engineering under a strict timeline of designing, simulating,
ordering, building, testing and demonstrating their designs.
This STEM competition challenges college engineering students to redesign a traditional bicycle
using hydraulics as the mode of power transmission. By combining this unlikely pair, the Fluid
Power Vehicle Challenge hopes to create an environment that results in uncommon connections
and breakthroughs, while supporting learning and the growth of fluid power industry knowledge.
Additionally, the Fluid Power Vehicle Challenge easily embeds into Purdue University’s capstone
design course most engineering students take in their senior year and includes exclusive
opportunities to connect with industry professionals through the design and competition process.
For Purdue’s 2018/19 team – Fluid Folks – the chainless bike’s design is simple; engineer a vehicle
using our knowledge gained from previous years to make the most efficient fluid driven bike
possible. This will result in a vehicle that is lightweight and utilizes hydraulic circuitry to propel
the machine forward.
Upon the end of the spring semester, the team achieved a redesign of a traditional, trike bicycle
using hydraulics as the mode of power transmission and competed at the national competition,
sponsored by IMI Engineering in early April. With this redesign, the team scored high marks
across the board, prior to a competition-ending structural failure.

1 Objectives
With an initial philosophy of designing and building a bicycle that used fluid instead of a chain, it
quickly became obvious that the team’s design could include so much more. Although the vehicle
is modeled off a recumbent bicycle and maintains some of the standard features like steering with
one’s hands, using one’s legs for power input, and varying speeds; the group added many new
features which, with the right technology, have the potential to be included on most modern-day
bicycles.
To achieve project success, the team has four primary objectives to achieve.
1.1 Hydraulic Efficiency
Since the vehicle is to be completely human powered, all sources of resistance need to be
minimized. This was achieved by decreasing pressure loss and maximizing fluid flow since it
directly related to the increased efficiency of our hydraulic components. The system uses two
connected hydraulic hand pumps as the primary charging circuit. Power is generated when foot
pumps are pressed which transmits fluid to the hydraulic accumulators. This power is transferred
to the rear wheel via a hydraulic motor (located on the rider’s right, at the rear of the vehicle). A
separate regeneration circuit uses a second hydraulic pump (located on the rider’s left, at the rear
of the vehicle). This second hydraulic pump can be used to charge the accumulators in addition
to the two primary foot pumps (located at the front of the vehicle). The whole regeneration circuit
is controlled via directional control valves which are located in the hydraulic manifold (located
under the seat).
1.2 Energy Storage
The option to store energy onboard the vehicle presented a unique opportunity in the design. The
separation of the drive and regenerative circuit allowed us to recover the energy lost due to braking.
As the resistance of the regeneration hydraulic gear pump is negligible, due to the fact that it only
overcomes the circulation of fluid flow in the lines as well as the friction from the pump and
driving gears, this allows the drive circuit to operate as the primary method of charging the
accumulators. Now, the rider only needs to overcome the mechanical resistances of pressurizing
the accumulators through the foot pump and has the added benefit of utilizing the onboard
regeneration system.
1.3 Alternative Power Transfer
There are several ways to transmit power without the use of chains. The need for tight packaging
and dual power input are enough of a reason to avoid using chains, but the point penalty also
provides a considerable incentive. Placing the hydraulic components in a similar location to a
typical recumbent bicycle was used to further showcase for the switch to fluid power.
1.4 Create a Natural Riding Experience
Riding a bike is second nature for most people and is second only to walking as far as human-
powered transportation is concerned. A natural experience is defined by predictable input
resistance that directly correlates to the motor and torque at the drive wheel. Braking, maneuvering,
and the ergonomics of a bicycle are all part of the natural riding experience as well. These were
the performance attributes we wanted to include in our design.

2 Problem Definition
This year’s problem is the same as in years past:
There is a need to design and build a human-powered vehicle that uses fluid
power to transfer and store energy using novel approaches and innovative
technology.
Furthermore, for additional points, the vehicle should include an energy recovery system or a
renewable energy source. The bike must be able to race in three different competition events: a
sprint race, efficiency challenge, and a time trial.
2.1 Success Definition
Upon completion of the project, the team will have achieved a measure of success if project
objectives have been achieved and compete at the competition in Littleton, Colorado.
3 Background Research
The NFPA Fluid Power Vehicle Challenge has been in existence for the last eleven years, with the
only differences being modifications to some of the rules. Upon the project’s inception, the team
met with their technical advisors, Andrea Vacca and José Garcia-Bravo, to discuss expectations
and their experience(s) with the project. Vacca, a seasoned veteran, was able to provide a list of
companies that were used in years past as well as those which prior teams wanted but weren’t
necessarily able to obtain for the Challenge.
The next research step was to explore these companies and the NFPA website – taking notes of
deadlines to assist in making a Gantt and requirements, aiding in formulating constraints and
criteria.
Finally, the last preliminary method of research involved studying prior year’s designs with
Purdue’s being the last to avoid unintentional bias and/or dampening creative thoughts.
3.1 Existing Solutions
During the research phase of design, the team spent a great deal of time focusing on what went
well for teams and what did not. During the initial construction conversations, the team was set on
creating a two-wheeled design as it seemed to be the purest route. But, during one of the mid-way
frame reviews, realized that taking the commoner’s route was not the best way to win the
Challenge. With a desire to win, the team shifted its focus to create a vehicle that had similarities
to Murray State’s 2018 design – often referred to those on the team as a “rocket” – with improved
upon concepts.
3.1.1 Purdue University
A solution which allowed the Purdue team to achieve a first place for the first time in the school’s
history, the Purdue Tracer was a starting point for this year’s design. From a design standpoint, a
two-wheeled design was the best solution on paper as based on optimization of frame designs;
Section 5.1: Frame.

Purdue’s 2017 model was different than most bicycles at the competition because it featured a tank
integrated into the bicycles’ frame as seen in Figure 1. Additionally, the bicycle had an
accompanying smartphone app that was attached to the vehicle’s handlebars. This app measured
how much pressure existed in the hydraulic lines, how fast the rider was pedaling and their
heartbeat, and other things like weather and geolocation.
Figure 1: The Purdue Tracer 2017
3.1.2 Murray State University
Unlike other teams which relied heavily on mechanical gearbox designs, Murray focused on
efficient energy usage with a massive amount of overall fluid storage. As seen in Figure 2, the
large, white cylinder is one of two PVC reservoirs (each holding ~1.84 gals. of fluid) which were
used to power the substantial main accumulator (2.5 gals. weighing 14 lbs.).
Figure 2: Murray State's Bicycle

3.2 Similar Problems
From art and design to science and math, there are a number of opportunities in the United States
which suit a plethora of interests and ambitions. One of the ways the team utilized external
resources was through studying the Human Powered Vehicle Challenge and the various design
methodologies used in the design process. Some other engineering student design competitions
can be found in Table 3.2:1. What is important to grasp from this table is the idea of similar
problems, solutions, and paths to get there.
Table 3.2:1 Other Engineering Student Design Competitions
Competition Description Sponsor
¼ Scale Tractor Design
Competition
Design and build a ¼ scale
tractor
American Society of
Agricultural and Biological
Engineers (ASABE, 2018)
Human-Power Helicopter
Competition
$250,000 prize for controlled
flight
Vertical Flight Society (VFS,
2018)ª
AGCO National Student
Design Competition
Design and engineering
project useful to agriculture
American Society of
Agricultural and Biological
Engineers (ASABE, 2018)
Human Powered Vehicle
Challenge
Design, build and race a
streamlined bicycle
American Society of
Mechanical Engineers
(ASME, 2018)
Formula SAEᵇ
Conceive, design, fabricate
and compete with small
formula-style racing cars
Society of Automotive
Engineers (SAE, 2018)
ªOriginally is known as the American Helicopter Society (AHS)
ᵇOther SAE related competitions include: Baja, Formula Electric, Supermileage, etc.
3.3 Related Companies
The International Fluid Power Conference (IFK) is one of the largest scientific events on the topic
of fluid power. Every other year, it brings representatives of science and industry from throughout
the world together to exchange information and views on the latest developments in hydraulic and
pneumatic applications.
At last year’s event in Aachen, a small western German city, it wasn’t the world’s largest producer
of X, Y, or Z that gave the closing speech but Aaron Saunders, VP of Engineering at a small1
company in Massachusetts: Boston Dynamics.
Similar to the team, the company has a fundamental focus on the basic principles of mechanics
with relation to the various robots they are developing – especially Atlas.
1
Boston Dynamics is a designer and developer of robots for the defense and military sector and is headquartered in
Waltham, Massachusetts. Boston Dynamics has a revenue of $12.3M, and ~100 engineers with three main
competitors: Clearpath Robotics, Endeavor Robotics and Energid.

Started in 2009, the company began with a working quadruped – to which they literally sawed in
half – and went from there. Shortly after work began on this new project, a new competition started
in the United States to design mobile robots to use in disaster response scenarios. The U.S.
government then asked Boston Dynamics to build 10 robots and give them to universities to learn
how to access the trends in 2012.
These robots were 6.5 ft. tall, self-contained, and weighed nearly 440 lbs.
After an acquisition by Google, the company was given a new opportunity to evaluate its work
and use new methods (e.g., additive manufacturing through 3D printing), to develop an Atlas
model that was ~5 ft. tall, still self-contained, and 176 lbs. Additionally, the company was able to
increase the robot’s strength density to near-human levels, operate completely autonomously
(running between 30-60 minutes, depending on what it was doing) and have 28 degrees of freedom.
Saunders often laughs when he is asked, “What’s the purpose? Are you making any money with
this?” because the short answer is “no.” Yes, the aforementioned achievements are outstanding
given the short time period and small team, but they are not meant to generate short-term profit for
the company – it’s about facing a pragmatic problem (Heney, 2018).
While this year’s fluid power team isn’t facing the design challenge of a disaster response robot
that uses hydraulics, they are facing a pragmatic problem: designing a bike with hydraulics.
Meaning, just like Boston Dynamics, the team does not strive to sell millions of trikes on the global
market, but instead, build on and add to work being done in the fluid power industry today.
3.4 Standards
During this project, the team used and referred to various NFPA administered and maintained fluid
power standards. The primary resources include the following:
A. ISO 1219
Part 1: Graphic Symbols
Part 2: Circuit Diagrams
3.5 Ethical & Professional Considerations
When beginning the design process, one of the key steps is considering which factors will be most
influential to the design. It is crucial to highlight these considerations as well as the various impacts
that will result from the design. Acknowledging these aspects of the design process will ensure
that the overarching goals of the bike are accommodated for and will drive the decision making
for individual features.
3.6 Impact
Highlighting the different impactful categories will provide an understanding of the thought
process behind the decisions made for the design. Emphasizing the factors that are more relevant
to the design will place the focus on the more impactful areas. These considerations and impacts
were the variables in the equation of success for the bicycle.
Accommodation for each variable and the desired capabilities of each will ensure the prosperity
of the bicycle and enlighten the beneficial outcomes the team expects. The following subsections
pertain to various factors the team considered while formulating a plan to design the vehicle.

3.6.1 Economic
Unfortunately, Purdue and other sponsors will not be funding the team with millions of dollars. As
a result, the bike must be designed with consideration to the overall cost. It must be produced
within a reasonable price range that doesn’t exceed the donation and sponsorship support provided.
Since there are no intentions on manufacturing and selling the design and bike, there was little
consideration placed on producing a bike that would be affordable for the public. Instead, the focus
was placed on designing and fabricating the bike within the financial limits given.
3.6.2 Global
One of the main objectives of the competition is to enhance one’s understanding of hydraulics and
fluid power. This is not constrained to the teams involved, but the world’s comprehension of the
topic and its applicability. Using hydraulics and fluid power, not to replace a current mechanism
or system, but instead to show its capabilities as an alternative solution. This may not result in any
revolutionary changes as to how a bike is operated but sheds light on substitutes that can be used.
3.6.3 Cultural & Social
The cultural and societal impact that the team intended on having was like that of the global impact
but within a smaller range. Increasing individual knowledge of fluid power as well as gaining
experience in the design process, provided a more developed understanding of the topic. This is
the NFPA’s main goal behind holding this competition with hopes of shedding light on the
significance of this development. This symbolizes the outcome that the team wants to reiterate
with the bike. The ability to demonstrate this development and understanding, as well as relay it
onto others, will equate to an increase with societal understanding pertaining to hydraulics and
engineering design. By doing so, society and culture will be able to intensify the ideology of
incorporating hydraulic power and lead to new discoveries and technologies beneficial to the
advancement of society.
3.6.4 Environmental
Given that the final competition will be held in Colorado, it is essential to determine how this may
cause an effect on the bike’s performance. Colorado’s environmental conditions, such as climate,
pressure, and altitude, could pose negative, unforeseen results that vary from those conditions in
West Lafayette, Indiana. To eliminate the unpredictability, these factors must be considered
throughout the simulation process to give the most accurate predictions.
3.6.5 Public Health, Safety, and Welfare
When designing any product that engages and associates public surroundings, the top priority is
maintaining a safe environment. Keeping individuals operating the product as well as those around
the trike safe, is the most important constraint of the design. If it poses any safety hazards, the bike
design will immediately be eliminated neglecting all the time and work put forth into the design.
Public well-being is the primary concern and should be considered when making any decisions
that may have resulting consequences. This consideration is of utmost significance and must be
kept in mind throughout the entirety of the design process from start to finish.
The primary way the team considered this factor was in the overall bicycle stability. By having
two foot pumps and accumulators, total weight ratios can be equalized on either side of the central
axis.

4 Problem Scope
4.1 Constraints
At the competition, each team must have a safety inspection, design assessment, compete in
various challenges, and a final presentation. The general project constraints are listed in Section
4.1.1 with each event’s constraints to follow.
4.1.1 General
• Each team starts with storage device void of hydraulic fluid. Maximum 10 minutes allowed
to manually pressurize the storage device.
• The pre-charge of the accumulator may not exceed 50 PSI if the vehicle is being shipped.
The Technical Liaison and Judges will gas charge the accumulator to the safe, desired pre-
charge pressure.
• No mechanical, hydraulic, or pneumatic failures are allowed due to poor design or
application of components. Vehicle failures during the Sprint Race and Efficiency
Challenge will result in elimination.
• Reservoirs, components, and plumbing must meet reasonable industry standards. No duct
tape or other examples of insufficient workmanship. There is zero tolerance for active leaks
in the system.
• Maximum weight of the vehicle is 210 lbs. without rider.
• Be sure to include instrumentation (pressure gauge).
• The manufacturer’s size and rating of the accumulator must be easy to read. If air is used,
the size of the receiver and pressure must be known.
• All course competitions will begin with a standing start.
• The vehicle system configuration does not need to remain the same for all races. Teams
may modify the configuration as long as there is no loss of oil during the change-over,
other than a few drops.
• Teams that need to make repairs will have that option only until their specified race start
time. No additional grace period will be provided.
• All repairs need to be done in the designated “shop area,” not in the field or on the race
track.
• The event race schedule is final unless teams agree to swap start times on their own. Judges
and program staff will not make accommodations.
• Drivers must maintain a safe speed and adhere to all instructions from the course marshals.
Failure to comply will result in penalties, disqualification of event races or elimination.
• The decisions of the judging panel are final. This includes tie-breaking decisions. All ties
will be broken based on adherence to the design criteria and performance.
• Spending budget for parts which can be acquired/donated through the Association should
not exceed $2,000.
4.1.2 Sprint Race
• Heats of multiple bikes at a time on a course that is 600 ft.
• Standing start, one rider on the vehicle, no pushing.
• Each team is allowed up to two attempts and must use the same rider in both attempts.
• Best time for places 1st, 2nd, and 3rd.
• Timing in Minutes: seconds: tenths of seconds: hundredths of seconds.

4.1.3 Efficiency Challenge
• The vehicle that goes the farthest is NOT necessarily the most efficient. Similarly, the most
stored energy does not automatically indicate the winner either.
• The vehicle must travel a minimum distance of 100 ft. braking is not required. The vehicle
will go as far as it can before coming to a complete stop.
• The vehicle, rider, and safety gear will be weighed at the track, immediately before starting
the event.
• Each team is allowed up to two attempts and must use the same rider in both attempts.
• Standing start, one rider on the vehicle. There can be no assistance in making the machine
move on its own. No windshields or wiggling of handlebars is allowed. Rider must remain
on the vehicle for the entire event. If a foot touches the ground, this distance will be
measured from the starting point.
• The rider will not be allowed to operate the pedals or any other mechanical input device
from the start of the event until the vehicle comes to rest. Braking is allowed for energy
recovery, but not required.
• The vehicle’s pre-charge pressure used in the calculation below will be the pre-charge that
is requested by the team and deployed by approved Technical Liaison only.
• The volume of the storage device used in the calculation will be as stated on the vessel by
the manufacturer (Pressure storage devices manufactured other than by Parts Supplier must
be approved by the Technical Liaison).
4.1.4 Endurance Challenge
• Two bikes leave every two minutes.
• The course may consist of laps in a slalom fashion and will total no more than 1 mile.
Maximum time to complete will be 30 minutes. The specific course will be determined and
communicated prior to the Competition Event.
• To test the regenerative braking circuits of the vehicles, the course will require at least one
stop and restart of the vehicle.
• Standing start, one rider on the vehicle, no pushing.
• Teams are allowed up to two drivers, as an option, although not a requirement to complete
the course. Driver changes will only be allowed in a designated area. For safety sake, the
vehicle will come to a complete stop to change drivers, no pushing.
• If the vehicle breaks down during the Endurance Challenge, it must be moved to a safe
distance from the track. The team will have 15 minutes to repair. The clock is not stopped
for repairs.
• Best time for places 1st, 2nd, and 3rd. Timing in minutes: seconds: tenths of seconds.
4.2 Criteria
As in Section 4.1: Constraints, project criteria are unpacked within each of the competition’s
challenges; sometimes in bullet form. Based on the theme of the event and the considerations
mentioned previously, the team has constructed an overall criterion of obtaining the best scores in
each of the challenges; thus, leading to the first prize for Purdue.
Overall, the most important criterion of this project is how many points the team can earn at the
competition. Derivative to this criterion pertains to utilizing large accumulator storage for the
sprint, having easy energy input during long races, and maintaining high system efficiency.

4.2.1 Sprint Race
This event will demonstrate the ability of the vehicle to move a distance where the weight of the
vehicle is proportional to the human propulsion with a primary criterion of obtaining the fastest
time on a 600-foot course. Limits from this challenge are the 10-minute charging period and the
maximum weight of 210 lbs. A boundary that the team placed on vehicle design relates to storage.
That is, the vehicle should store all of the energy it needs for the race prior to the race’s start.
4.2.2 Efficiency Challenge
This event will demonstrate the ability of the vehicle to effectively store and most efficiently use
the smallest amount of stored energy to propel the unassisted vehicle the greatest distance
proportional to the vehicle’s weight. The winner will be determined based on Equation 1 and its’
parameters.
𝑆𝑐𝑜𝑟𝑖𝑛𝑔 𝑅𝑎𝑡𝑖𝑜 =
𝑊 𝑥 𝐿
𝑃 𝑥 𝑉
(1)
Where,
W = Weight of the vehicle and rider (lbs.)
L = Total distance traveled from the starting point (in.)
P = Gas pre-charge pressure (PSI)2
V = Volume of gas in storage device (in³)
Equation (1) is a dimensionless ratio and is meant to provide an objective measurement to judge
the vehicle to system ratio efficiency. It quantifies the winning vehicle as providing the most work
with the smallest amount of stored energy with components being used efficiently.
4.2.3 Endurance Challenge
This event will demonstrate the reliability, replicability, and durability of the fluid power system
design and assembly. The goal of this challenge is to obtain the best time on a 1-mile course with
a vehicle that features a regenerative braking circuit with no malfunctions or breakdowns. The
biggest limit on the design for this challenge is that it must demonstrate regenerative braking.
Placed lower on the team’s priority list, regenerative braking was a secondary focus to the primary
propulsion because there is no score for how well the regenerative brakes are designed – it just
must be included.
Therefore, for this challenge, the highest importance factor is how much energy the bike can store
during the 10-minute charging period. Second highest importance is for the rider to be able to
power the vehicle while it is moving at a competitive rate of speed after the boost runs out.
5 Alternative Solutions
When solving a design problem, there are always several possible solutions. By focusing on one
solution prior to looking at alternatives, a group risks overlooking a better solution. As mentioned
by Purdue’s Professor John Lumkes, “A good rule to live by when thinking of solutions is not
settling on your first idea” (Lumkes, 2018).
2
The minimum accumulator gas pre-charge pressure during filling must be 100 PSI.

5.1 Frame
As mentioned in Section 3: Background Research, Fluid Folks spent a great deal of time focusing
on the frame of the vehicle. This section contains basic pros/cons for two primary design focuses:
(1) typical, two-wheeled and (2) recumbent.
5.1.1 Two-Wheeled Bicycle
Figure 3: Road Bicycle
Table 5.1:1 Two Wheeled Bicycle | Advantages & Disadvantages
Advantages Disadvantages
• More maneuverable
• Handles like a traditional bike
• Internal tank is easy to include
• Less space for components
• Top heavy
• Hard to start and keep balance
• Force input limited to riders' weight
5.1.2 Recumbent Bicycle
Figure 4: Recumbent Bicycle
Table 5.1:2 Recumbent Bicycle | Advantages & Disadvantages
• More stable
• Low center of gravity
• More space for components
• Safer at high speeds
• Harder to steer
• Less conventional riding position
• Internal tank not as feasible

5.2 Pumps
Another bone of contention was the pumping method. As a baseline, Fluid Folks generated a list
of pros/cons to assist in the development of a Pugh.
5.2.1 Two-Chamber Gear Pump
Figure 5: Components of a Dual Gear Pump System
Table 5.2:1 Dual Gear Pump | Advantages & Disadvantages
• Flexible fluid flow rate by using one or
both pumps (Acts as a 2-speed gearbox)
• Hydraulic fluid is incompressible and
transmits force efficiently
• Less volume than a pneumatic system
• Rotary pumps are easily modified to fit
bike kinematics
• ‘Additional’ pump and hydraulic
fluid; i.e., more weight
• Must use pipe due to the fact that
hydraulic tubes have a large radius of
curvature, which is bad for space-
confined designs.

5.2.2 Single Gear Pump
Figure 6: Components of a Single Gear Pump System
Table 5.2:2 Single Gear Pump | Advantages & Disadvantages
• Rotary pump is easy to integrate into
bicycle kinematics
• Less volume than a pneumatic system
• Easy user-adjustable input force
• Complications with “clutch”
mechanism, possible point of failure
• Much larger space requirement, more
gears, bearings and shafts, and
complexion
confined designs.

5.2.3 Piston Pump
Figure 7: Components of a Piston Pump System
Table 5.2:3 Piston Pump | Advantages & Disadvantages
• Very efficient with regard to intended
bicycle layout
confined designs
• Linear motion pump is more difficult
to integrate into bicycle kinematics
5.2.4 Pneumatic System
Figure 8: Components of a Pneumatic Piston Pump System
Table 5.2:4 Pneumatic System | Advantages & Disadvantages
• Most components are very lightweight
• Tubing is very flexible
• Air is compressible and pneumatic
systems transmit forces less efficiently
• Takes up a large volume
• Linear motion pump is more difficult
to integrate into bicycle kinematics

6 Proposed Solution Path
6.1 Introductory Analysis
Prior to generating a hydraulic schematic, Fluid Folks spent time reviewing prior year’s work as
well as other Universities’ hydraulic componentry layouts.
When performing analysis, a two-wheeled bicycle was the design focus to fit with the theme of
the competition and an overall aesthetically appealing vehicle. Propulsion was going to be
comprised of a hydraulic pump directly linked to a motor. After performing system optimizations
and utilizing those concepts found in the Appendix, Fluid Folks discovered that the hydraulic
pumps could be used to fill the hydraulic accumulators and then fix the accumulators to the motor.
6.2 Design Matrices
Many complex decisions have certain constraints and considerations that must be considered when
making a choice. A constraint is a limitation or restriction. Contrary to this are considerations,
which are factors that should be considered but are not necessarily deal breakers.
The following subsections show the various Pugh matrices that Fluid Folks used, thoughts after
analyzing the results, and the intended solution path.
6.2.1 Frame
Figure 9: Frame Pugh Matrix

The criteria within each category were determined based on the individual challenges pertaining
to the overall competition. When generating responses to the various parameters and using a
townie as the datum, the following were considered:
a. Performance
One of the team’s criteria for the Challenge is to win. For the team, winning will be possible
through performing the best in each of the competitions. Stability was selected as a crucial
subcategory due to the fact that rider position will have to be evenly balanced to meet the
time constraint of 10 minutes during vehicle charging.
b. Efficiency
Although not a primary goal for the team, the NFPA has a desire for students entered into
the Challenge to not only learn fluid power material but also look at the problem as if it
were applicable to the rest of the world. Meaning, the design should be different but similar
to vehicles (i.e. bicycles) on the market today. Rolling resistance was selected as an
important subcategory because of friction’s effect on overall propulsion. Since competitors
are using human input power, it is of primary importance to reduce overall stress and
energy exertion going into the system.
c. Manufacturing
Building the physical vehicle is a large linchpin in the Fluid Folk’s plan. Therefore, the
design must be feasible and able to be built within a specified time. The team also has a
limited budget which means a stringent balance sheet must be used when looking at
componentry and alternative solutions.
d. Miscellaneous
Appearance is not a scoring category for the competition, but the group would like to focus
on aesthetics to a degree due to the fact a majority of the bicycles that typically place high
also look nice. Features that contributed to this include things like small componentry,
specific bends or placement of hydraulic connections, etc. Additionally, vehicle
ergonomics are an important subcategory that contribute to points during the safety
inspection.
6.2.1.1 Solution: Recumbent Frame
Upon successful analyzation of scores and factors making up those values, the group determined
that a recumbent bicycle would be the best option. Although not the highest score, Fluid Folks
believes that the design will help eliminate bias during judging,3
allowing for better placement of
hydraulic components, and provide greater stability at high speeds.
3
During 2018’s competition, Purdue’s team was given a lower score when it came to the innovation category –
described by some as a “bad replica of 2017’s bike.”

6.2.2 Pumps
Figure 10: Pumps Pugh Matrix
The criteria within each category was determined based on prior knowledge of pump usage and
Purdue’s/Other’s successes and failures while using the apparatuses. When generating values for
the system and using a hand pump as the datum, the following were considered:
a. Performance
Like considerations made for the frame, proper balancing of components is a primary
concern when looking at overall stability. Pumps, typically heavy objects,4
have the
potential to create undesirable weight ratios about the center of mass. The team’s initial
plan was to use a smaller, axial piston pump5
which would have saved the group a lot of
weight but ended up using a different pump due to the frame layout and propulsion method.
b. Efficiency
This criterion is evenly split into two subcategories: (1) Rideability and (2) Component
Routing.
c. Manufacturing
As with other manufacturing considerations, the time required to make modifications was
the primary area of focus.
4
Eaton V10’s weigh ~ [10, 15] lbs. (Eaton).
5
Vivolo TFH-040 which weighs ~0.5 lbs. (Takako).

d. Miscellaneous
Innovation was an important consideration due to the scoring category relating to prior
year’s work.
6.2.2.1 Solution: Dual Hand Pump & Rotary Pump
that a Dual Hand Pump (for the primary) and Rotary Pump (for regeneration) would work best.
Although not a first choice, Fluid Folks decided to use a rotary pump for regeneration instead of
charging due to the limited modifications that would need to occur for the pump’s mounting and
overall low cost.6
6.2.3 Charging Method
Figure 11: Charging Method Pugh Matrix
Like the selection of pumps, the criteria within each category was determined based on prior
knowledge of successes and failures while using the apparatuses by others and Purdue. When
generating weighting values for the system and a standard cycle motion as the datum, the following
were considered:
a. Performance
Like considerations made for the frame, stability was the biggest concern. When generating
flow to the accumulators in a limited amount of time, individuals will have to exert a high
amount of energy in a short amount of time.
6
The group was able to obtain a pump from the Italian manufacturer Vivolo for $0.

b. Efficiency
Rideability was an important consideration because it relates to charging. Meaning if riders
are unable to charge the system while moving, it will not be as efficient as it could be.
c. Manufacturing
As with other manufacturing considerations, the time required to make modifications was
the primary area of focus.
d. Miscellaneous
Closely tied to the system efficiency, ergonomics is an important consideration because,
pending on the competition within the Challenge, the rider should remain comfortable to
avoid getting fatigued.
6.2.3.1 Solution: Foot Pump
to choose the solution which scored the highest among other options. Originally designed to be
used as hand pumps, the group plans to modify two, Hydac MP10 Hand Pumps to be used by one’s
legs.
6.2.4 Electronics
Figure 12: Electronics Pugh Matrix

Prior Purdue teams used electronic systems to actuate valves and display a user interface, but none
of these teams used a Raspberry Pi. Realizing that this avenue may provide new successes for the
group, certain members of the team spent a majority of their time criticizing and evaluating various
systems. Referring to Figure 12, the selection criteria include the following:
a. Performance
This area was a key topic the group was intending to optimize due to the overall system
design. Valves, pressure levels from the accumulators and other hydraulics inputs were
meant to be controlled and feed into the overall system display; i.e., the timing was crucial.
To solve this, mechanical engineers on the team looked at items that would improve
processing time while avoiding too many cores.7
b. Efficiency
As hinted in the performance criteria, there are many components that need to be energized
to allow for smooth and efficient operation. Thus, a lean system that provides ample energy
is of utmost importance.
c. Connectivity
While not a burning platform per se, this area was promoted to the pugh for the implications
it could have on the overall scoring of the vehicle design. Long-term plans were to integrate
the heart rate sensor to the system, and use it as an input to regulate speed, fluid flow being
supplied to the various pumps, and an alert system in case of spikes in the system.
d. Miscellaneous
This criterion was added to capture and analyze data in order to constantly improve upon
the system design – leading to something which could be used to make trends or expose
bottlenecks.
6.2.4.1 Solution: Raspberry Pi
to choose the solution which scored the highest among other options. While not listed as a factor
on the pugh, the biggest deciding factor was the group’s familiarity with the hardware which
became very important given the small timeframe.
7
Clock speed becomes more nebulous when you consider speed to multiple cores due to the fact the processors will
be crunching various data threads, which will have to run at lower speeds because of thermal restrictions.

7 Overall Project Proposal Summary
Figure 13: Fluid Folk's Bicycle Model
7.1 Final Design Specifications
The overall hydraulic schema can be found in Section 7.1.1: Circuit Design.
There are many hydraulic components that are generic and can be bought through Sun Hydraulics,
but the optimized components need to be bought from a specialty company that will carry the
specific sizes needed for the application.
The optimized accumulators were determined to be 1.3 gallons each. Steelhead Composites, Inc.
was chosen as an accumulator supplier because they make accumulators out of carbon fiber
material which reduces the overall weight to only 12.8 lbs. each. The team was able to gain
sponsorship for the accumulators which made them free when they are originally estimated to be
$500.00 per unit. The accumulators chosen were the Micromax series and had a manufacturer’s
part number of AB30CN010G3N. Additional hydraulic parts can be found in Table 7.1:1.

Table 7.1:1 Hydraulic Components
Item Quantity Manufacturer
Accumulator 2 SteelHead
Hand Pump 2 Hydac
Motor 1 Vivolo
Regenerative Pump 1 Vivolo
Relief Valves 2 Sun Hydraulics
Check Valves 4 Vonberg
Manifold 1 Sun Hydraulics
Hose Assembly 10 Gates
Reservoirª 1 --
Spare Components TBD Sun Hydraulics
ª The team will be designing their own reservoir using the methods mentioned in the Appendix.
The regeneration pump8
and motor9
also had to be purchased from a manufacturer; shown in Table
7.1:2. Vivolo is a hydraulic motor company in Italy that was recommended to the team by their
academic advisor. The team contacted Vivolo with the specifications for each component and the
company agreed to a sponsorship. The pump and motor will also be donated. The second
optimization results came in with a motor displacement of 3.2 cc/rev and a pump displacement of
7.8 cc/rev. Based on that information, the team chose the closest motor and pump to the
recommended size. The closest matched motor had a displacement of 3.12 cc/rev and a
manufacture number of X1U2362BGFA. The pump had a displacement of 7.54 cc/rev and a
manufacture number of X1P3462BBBA.
The NFPA provided the team an industry sponsor as well. The industry sponsor works for a
company that manufactures hydraulic hose assemblies. They agreed to donate the hose assemblies
to the team if the team includes their logo on the vehicle.
Table 7.1:2 Mechanical Components
Tie Rod 1 Catrike
Motor Spur Gears (3.45:1) 2 Misumi
Regen Spur Gears (3.45:1) 3 Misumi
Dog Gears 2 AndyMark
Additional components were required to fit with the theme of the vehicle; i.e., recumbent bicycle.
A list of these parts can be found in Table 7.1:3.
8
Appendix – Figure 39: Regenerative Braking System
9
Appendix – Figure 40: Rear Motor & Hub

Table 7.1:3 Bicycle Components
Front Tires 2 Schwalbe
Front Wheels with Disc Brakes 2 Catrike
Front Fender Set 1 Fluid Folks
Rear Tire 1 Schwalbe
Read Wheel with Disc Brake 1 Zipp Speed Weaponry
Rear Fender 1 Fluid Folks
Axles 2 Catrike
Front Brakesª 1 Avid
Rear Brakesᵇ 1 Avid
Handlebar Mirrors 1 Catrike
Arm Rests 2 Fluid Folks
Handlebar Grips 2 Fluid Folks
Handlebar Assemblies 2 Catrike
Spindles 2 Catrike
Headset 2 Full Speed Ahead (FSA)
Seat 1 Fluid Folks
ª Includes cables, housing, and brake levers
ᵇ Includes cables, housing, and brake levers

7.1.1 Circuit Design
Figure 14: Complete Hydraulic Circuit Schematic

7.1.2 Frame
Previous year’s bikes were used as a basis for the design of this year’s frame. The dimensions and
other support structures have been modified specifically for this year’s circuit and power mode of
pumping. The base frame, shown in Figure 15, was designed primarily with 1.75” square, 6061
aluminum tubing, but another dimension aluminum tubing is used as well. This size was used
because it is readily available in the marketplace; i.e., lead times/costs are especially low compared
to other metals of similar properties. All the aluminum structural members are a quarter inch thick
for strength, though as will be discussed below, this could be reduced to 3/16” or 1/8” in future
iterations.
Figure 15: Base Frame Model
The frame is a simple design that features two circular journals – slightly forward of the middle –
which retain the steering handles. At the back, there are two flanges that hold the rear wheel in
place, to allow for operation similar to a typical bicycle. The portion protruding from the front is
where the foot pumps are mounted as seen in Figure 13. This length has not been optimized for
all heights but will ideally be comfortable for all the members on the Purdue team.
The specific CAD model in Figure 15 was run through a finite element analysis (FEA) to determine
its strength. This was important to make sure that the frame is well within its working stress range
and will be able to perform well in the competition.
Figure 16: Loads Placed on Frame for FEA

The FEA on the bike frame was completed using Creo Simulate. As can be seen in Figure 16, the
vehicle was constrained on the front two journals, and at the rear flanges. The inside surfaces of
the journals were constrained in all directions, and the inside top surface of the flanges was
constrained in the same way.
A total force of 350 lbs. was decided to be enough for testing the frame. The max weight of the
bike is 210 lbs. without a rider but considering that the weight of the frame is already considered
in the FEA, and the wheels will not put any downward force on the frame, those weights were
excluded. So, assuming the weight of all the hydraulic components and the rider are 350 lbs. is
very reasonable. The weight was distributed with 275 lbs. in the middle of the frame where the
force of the rider, tank, and accumulators will be. A force of 75 lbs. was placed in the rear due to
component placement; e.g., motor, pump, and gearbox. This weight is a high value, but with a
theme of safe design, is sufficient compared to lesser values.
Figure 17: FEA with Von Mises Stress
The results of the analysis were very promising for the strength of the frame design. There were
very low stresses (blue) throughout most of the frame, with the highs (orange and red) being
located at the model constraints. The highest stress in the frame was 8,700 psi, located on the rear
flange. This was expected since this location had the smallest cross-section of the whole frame.
Even still, the yield stress of aluminum is at a minimum 45,000 psi, so the design is well within
the working range of aluminum. In addition, the deflection of the model was low as seen in Figure
18. The max (red) was 0.021”, which is considered negligent.
Figure 18: Frame Deflection

In conclusion, the current frame design for the fluid power vehicle has sufficient strength to support
the rider and all components. The thickness of the tubing may be reduced to save on cost and
weight but only after further FEA and additional shock loading tests. In the end, the frame is
plenty strong for its application, but not over-designed.
7.1.3 Propulsion Method
As discussed in Section 3: Background Research, the majority of prior bicycle designs feature
underutilized accumulators – instead, relying on the pump to motor connection. Fluid Folks’
solution is different because the group plans to focus solely on the accumulators for propulsion
through (1) leg powered pumps and a (2) regeneration pump on the rear wheel. Once fully charged,
the system’s accumulator tanks will operate at a pressure equal to 3,000 psi. Further calculations
which led to this pressure and other conclusions can be found in the Appendix relating to the
Accumulator and Hydraulic Pump/Motor.
7.1.4 Hydraulic Circuit
As mentioned in the sections pertaining to the componentry analysis, Fluid Folks chose to use two
hand pumps to create a balanced input force, paired with two accumulators (each 1.3 gallons) –
increasing overall stability.
The overall hydraulic circuit is designed to charge the accumulators to a specified level and then
control the upstream motor pressure through the use of pressure transducers and 2-way, 2 position
valves.
Finally, as a means to create a modular system, Fluid Folks have devised a way to create multiple
modes, described further with their associated schematics in the Appendix.
7.1.5 Manifold Design
Contrary to a pair of iPhone headphones waded up in a backpack or Los Angeles’s four-level
interchange, a manifold is a component from which various connections in a hydraulic circuit can
be connected. Meaning, primary sources of fluid can be split off into secondary circuits, or
conversely, to join exhausted fluids. Manifolds can also have pressure transducers, check, relief
and other valves attached inside/outside of the body. Figure 19 is a representation of Fluid Folks
manifold, which is intended to be mounted to the 1.75” square aluminum tubing by means of a
bracket. The surrounding, pink, dashed line represents the manifold’s boundary.
Figure 19: Manifold Schematic

7.1.6 Electronic User Interface
The purpose of the user interface was to track and show the energy flow through the system
while acting as an educational tool for students. Riders start with the primary dashboard and have
the ability to select a flow or race type, thereby advancing them to a new screen.
The following figures are screenshots of the various displays that are available to the user.
Figure 20: Dashboard Display

Figure 21: Charging Mode Display
Figure 22: Boost Mode Display

Figure 23: Pumping Mode Display
Figure 24: Regeneration Mode Display

7.2 Sizing Objectives
In order to size all of the components, Fluid Folks studied the various competitions within the
Challenge and created a list of objectives, which could be achieved through the system’s various
modes; shown in Table 7.2:1.
Table 7.2:1 Sizing objectives for competitions
Competition Objective Mode
Sprint Maximize Speed and Acceleration Pump
Efficiency Maximize Scoring Ratioª Boost
Endurance Maximize Speed Pump
ª Discussed in Section 4.2.2 Efficiency Challenge
7.2.1 Free Body Diagram
The initial design was based off a free body diagram; shown in Figure 25. Based on that
information, the group reached out to Hodson Bay10
to acquire a value for the wheel size and use
a total vehicle weight, rider included, of 500 lbs. Although the group does not plan to have a 300
lb. rider for the competition, the goal was to design a system that was adequately rated based on
information obtained through trike bikes on the market today.
Figure 25: Bicycle Free Body Diagram
10
Local bicycle shop in West Lafayette, Indiana serving many students at Purdue University and the surrounding
area.

Three more key assumptions were made relating to pressure, gearing and the motor, based on prior
years’ work which allowed the group to size the circuit. All input variables factoring into free body
equations can be found in Table 7.2:2.
Table 7.2:2 Assumptions made for bicycle free body diagram
Subject Value
Slope (a) 1.14ª
Rolling Coefficient (f) 0.002
Mass (M) 500 lbs.
Radius of Wheel (r) 26 in.
Working Pressure (P) 3000 PSI
Gear Ratio (u) 3
Motor Efficiency (μ) 0.95
ª Based on track conditions in Boulder, CO
7.2.2 Sizing the Circuit
A series of equations were used during the sizing process which helped the group obtain values
for the various components. The first of these set of equations was the pull of the vehicle (𝐹),
which is the force required to move the vehicle – shown in Equation (2) – and equal to 11 lbs.
𝐹 = 𝑀𝑠𝑖𝑛(𝑎) + 𝑀𝑓𝑐𝑜𝑠(𝑎) = 11 𝑙𝑏𝑠.
(2)
The torque needed can be solved for using Equation (3) to obtain that ‘pull’.
𝜏 = 𝑟 ∗ 𝐹 = 259 𝑙𝑏. 𝑖𝑛.
(3)
Using an assumed gear ratio of 3, one can then determine the torque needed – from the motor – to
again, obtain the initial ‘pull’ value using Equation (4).
𝑀𝑜𝑡𝑜𝑟 𝑇𝑜𝑟𝑞𝑢𝑒 (𝜏 𝑀) = 𝜏/𝜇 = 86.4 𝑙𝑏. 𝑖𝑛.
(4)
Finally, assuming a working pressure of 3,000 psi, one can solve for the motor displacement in
cubic inches per revolution using Equation (5).
𝑀𝑜𝑡𝑜𝑟 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 (∆𝑀) = [ 𝜏 ∗ 2𝜋
𝑃 ∗ 𝜇⁄ ] = 0.19
𝑖𝑛.3
𝑟𝑒𝑣.
(5)

7.2.3 AMESim Optimization
As mentioned throughout, unlike a majority of designs, the team’s system does not have the pump
directly linked to the motor. Therefore, it is not possible to size the pump depending on the desired
motor flow.
Instead, the accumulators impose the pressure at which the system works, thereby creating a
pressure coupling on the schema. For this reason and due to the vast number of variables, it is very
challenging to size the system by hand – evening knowing all the aforementioned equations and
circuit/fluid laws.
As a solution to this labor-intensive process, optimizations were made possible through a fluid
power software called AMESim. AMESim allowed the team to develop a dynamic model which
allowed variations with system parameters, hydraulic system layout (including connections) and
outputs to be optimized through a process displayed in Figure 26.
Figure 26: AMESim solution path to finding the best component size.
7.2.3.1 Genetic Algorithm
The first process in using the software was using a genetic algorithm (GA) to find a globally
optimal solution. GA’s are metaheuristic, high-level procedures to find, generate, or select a
heuristic that provides a sufficiently good solution based on the natural selection of a bigger subset
of computer science known as evolutionary algorithms (EA’s).
As a whole, the resultant was a feasible solution that has an objective value that is good or better
than all other feasible solutions to the model. This optimal can then be captured and transferred to
future calculations (The MathWorks Inc., n.d.).
7.2.3.2 Nonlinear Programming by Quadratic Lagrangian
Nonlinear Programming by Quadratic Lagrangian (NLPQL) is a sequential quadratic
programming (SQP) method that solves problems with a smooth continuously differentiable
objective function and constraints (Perez, Jansen, & Martins, 2018).
The final solution is one which is the optimal based on the global optimal solution.
7.2.3.3 AMESim Models
After obtaining the best size for the various components, the team was then able to create
schematics, shown in Figure 27, in AMESim and achieve values for the various competitions
within the overall Challenge.

Figure 27: AMESim Schematics
7.2.3.4 System Parameters
Due to the fact the team used an optimization strategy, the solution was found by starting with the
desired outputs in order to end with reasonable inputs; i.e. parameters – pertaining to the following:
duty cycle, frequency, pressure, pre-charge, volume, displacement of pump and motor, and gear
ratio.
7.2.3.5 Outputs to be optimized
Following the optimization, the first results obtained always yielded the highest possible value for
the volume and the pressure of the accumulators. This was an issue because the program was not
considering a key Challenge constraint of charging time of 10 minutes.
As a solution, the team spent time at Purdue’s Co-Rec facility to determine a reasonable power
output of 300 W to achieve and maintain.
Equations feeding into the output of this value were manipulated to end at a solution that would
require the use of a larger accumulator or, in the team’s case, the use of two, 1.3-gallon storage
devices.
7.3 Budget Requirements
The National Fluid Power Association allows each team to order up to $2,000 worth of various
hydraulic components from SunSource Hydraulics at no cost to the team. However, many specialty
hydraulic, mechanical, and electrical components must be purchased from outside manufacturers.

Although there is no explicit budget for the competition or at Purdue, the price of the vehicle is
considered during the judging process of the competition. This gives teams incentives to keep the
cost of the fluid vehicle lower. Fluid Folks’ proposed budget is $4,000, shown in Table 7.3:1 Cost
analysis FY18 & 19.
The specialty components will be bought through the Maha Fluid Power Research Center that is
operated by advisor Andrea Vacca; i.e., funded by Purdue University. Even though there is not an
exact budget, the team’s goal is to keep the total cost under $4,000.00. A detailed budget analysis
is shown below.
Table 7.3:1 Cost analysis FY18 & 19
Component Manufacturer
Value
($)
Team Cost
($)
Hydraulic
Motor Vivolo 225.00 0.00
Regeneration Pump Vivolo 229.00 0.00
Hand Pumps Hydac 200.00 200.00
Accumulators SteelHead 1000.00 0.00
Valves, Fittings, Manifolds SunSource 900.00 0.00
Hose Assembly Gates 150.00 0.00
Electrical
Raspberry Pi RS Electronics 35.00 35.00
Transducers RS Electronics 300.00 300.00
LCD Screen Amazon 60.00 60.00
Mechanical
Frame Fluid Folks 1,000.00 1,000.00
Reservoir Fluid Folks 500.00 500.00
Bicycle Components Utah, Inc. 1,910.00 1,910.00
$6509.00 $4,005.00

8 Lessons Learned
The Purdue Chainless Challenge Team has learned many valuable lessons during the course of the
past year while designing the vehicle that competed in the 2019 NFPA Fluid Vehicle Power
Challenge.
The first and most important lesson is the importance of starting everything earlier than one would
think. This project and all those within Purdue University’s capstone experience, are very time
consuming – especially when the bulk of the work is done by those currently enrolled in a Senior
Design Class. If the Team had no form of reference from prior year’s work or crucial resources
like the Maha Fluid Power Laboratory, overall project success and completion would have been a
struggle.
Another lesson learned relates to presenting. During the Fall semester, the team had three key
presentations to give – two for the University and another for the NFPA. Leading up to the
presentation deliveries and submittals, little work was done in prior months to prepare for the event
which created a backlog of work to be accomplished over the course of a week.
Finally, the team owes much credit to the Maha Lab, advisors Andrea Vacca and José Garcia-
Bravo, and especially fellow team member Tommaso Greco. Greco’s help this past year with
design work and optimization held the team together when cracks began to evolve. The team is
extremely grateful for his help and the help of many Maha graduate and Ph. D students.

9 Conclusions
The final product is very close to what the team had envisioned from the beginning. The Purdue
University team’s vehicle is not only robust, strong, solid, and innovative in design and included
features, and was a strong contender at the 2019 Fluid Power Vehicle Challenge.
9.1 Industry Experience
The Fluid Power Vehicle Challenge provides students with a unique opportunity to interact with
industry leading engineers, along with attempting to solve real-world problems and improve upon
the age-old design of the common bicycle. In this competition, the team learned how to set goals
for the project before starting the design. This became key for determining the importance of the
challenges that had to be overcome.
Interacting with school staff and professors to receive input on the problems the group faced
allowed team members to become experts at using online supply websites to purchase materials
and find the cheapest option. Working closely with machine shop specialists, the group developed
an understanding of how to produce parts from raw materials. Most importantly, Fluid Folks
learned how to see a project through from start to finish. These skills will all come in handy upon
graduating and when joining the working world.
9.2 Learning Outside the Classroom
This project involved many different engineering disciplines. The group learned about hydraulic
power and stored energy circuits and how to effectively utilize them. It also provided an
application-based learning style, which allowed for hands-on learning while using the math and
theory behind these power circuits to create a functioning product.
This project also relied heavily on the solid modeling program, Creo, which allowed the group to
piece together the bike using custom, in-house parts while providing part drawings which could
be used to have them produced.
Overall, this project and competition taught the 2019 team many new skills which would have
been hard to understand with basic classroom instructions. It provided challenges that allowed
team members to push themselves and develop methods for overcoming problems encountered
using old skills learned in the classroom.

9.3 References Cited
Ahmadi, D. (2004). Polytropic Process of an Ideal Gas. (C. University, Producer) Retrieved
November 2018, from
https://adweb.clarkson.edu/projects/fluidflow/public_html/kam/courses/2004/es340/chap3-
ext.pdf
Ambrosio, J. A. (2001). Quasi-Static Behavior. In CISM International Centre for Mechanical
Sciences (Vol. 423). Vienna: Springer. doi:https://doi.org/10.1007/978-3-7091-2572-4_2
ASABE. (2018). AGCO National Student Design Competition. Retrieved from American Society of
Agricultural and Biological Engineers: https://www.asabe.org/Awards-Competitions/Student-
Awards-Competitions-Scholarships/AGCO-National-Student-Design-Competition
ASABE. (2018). International 1/4 Scale Tractor Student Design Competition. Retrieved from
American Society of Agricultural and Biological Engineers: https://www.asabe.org/Awards-
Competitions/Student-Awards-Competitions-Scholarships/International-1-4-Scale-Tractor-
Student-Design-Competition
ASME. (2018). Human Powered Vehicle Challenge (HPVC). Retrieved from American Society of
Mechanical Engineers: https://www.asme.org/events/competitions/human-powered-vehicle-
challenge-(hpvc)
Ayalew, B., & Kulakowski, B. T. (2005). Modeling supply and return line dynamics for an
electrohydraulic actuation system. The Pennsylvania Transportation Institute. University
Park, PA: The Instrumentation, Systems, and Automation Society. Retrieved November
2018, from
https://pdfs.semanticscholar.org/8924/3df1c4e2a78a90464730e900447a296c2f24.pdf
Eaton. (n.d.). Vickers® Vane Pump & Motor Design Guide. Brochure, 69. Retrieved 2018, from
http://www.eaton.com/ecm/groups/public/@pub/@eaton/@hyd/documents/content/pll_1409.
pdf
Heney, P. (2018, March 23). Evolution of Boston Dynamics Atlas Robot. Retrieved April 2019, from
The Robot Report: https://www.therobotreport.com/evolution-boston-dynamics-atlas-robot/
Informa PLC. (2012, January 01). Fundamentals of Hydraulic Reservoirs. Retrieved 2018, from
Hydraulics & Pneumatics:
https://www.hydraulicspneumatics.com/200/TechZone/ReservoirsAcces/Article/False/6448/
TechZone-ReservoirsAcces
Irizar, V., Rasmussen, P. W., Olsen, O. D., & Andreasen, C. S. (2017). Modeling and Verification of
Accumulators using CFD. The 15th Scandinavian International Conference on Fluid Power,
(pp. 347-349). Linköping, Sweden. Retrieved October 2018, from
http://www.ep.liu.se/ecp/144/034/ecp17144034.pdf
Lumkes, J. (2018). Purdue University | Professor of Agricultural & Biological Engineering.
Neutrium. (n.d.). Pressure Loss From Pipe Entrances and Exits. Retrieved December 2018, from
https://neutrium.net/fluid_flow/pressure-loss-from-pipe-entrances-and-exits/

Nuclear Power for Everybody. (n.d.). Friction Factor for Turbulent Flow – Colebrook Equation.
Retrieved 2018, from https://www.nuclear-power.net/nuclear-engineering/fluid-
dynamics/major-head-loss-friction-loss/friction-factor-turbulent-flow-colebrook/
Perez, R., Jansen, P., & Martins, J. (2018). pyOpt: A Python-Based Object-Oriented Framework for
Nonlinear Constrained Optimization, Structures and Multidisciplinary Optimization.
doi:45(1):101-118
SAE. (2018). Formula SAE. Retrieved from Society of Automotive Engineers International:
https://www.fsaeonline.com/
SteelHead Composites. (2018). Small Bladder Accumulators. Retrieved October 2018, from
https://steelheadcomposites.com/micromax-series/
Takako. (n.d.). Small Axial Piston Pump / Small Axial Piston Pump Unit. Brochure, 1. Retrieved
2018, from https://www.takako-inc.com/english/products/pdf/pump.pdf
The Engineering Tool Box. (n.d.). Equation of Continuity. Retrieved 2018, from
https://www.engineeringtoolbox.com/equation-continuity-d_180.html
The Engineering Tool Box. (n.d.). Friction Coefficient with Laminar Flow. Retrieved 2018, from
https://www.engineeringtoolbox.com/laminar-friction-coefficient-d_1032.html
The Engineering Tool Box. (n.d.). Laminar, Transitional or Turbulent Flow. Retrieved 2018, from
https://www.engineeringtoolbox.com/laminar-transitional-turbulent-flow-d_577.html
The Engineering Tool Box. (n.d.). Nitrogen. Retrieved 2018, from
https://www.engineeringtoolbox.com/nitrogen-d_977.html
The Engineering Tool Box. (n.d.). Reynolds Number. Retrieved 2018, from
https://www.engineeringtoolbox.com/reynolds-number-d_237.html
The Engineering Tool Box. (n.d.). Specific Heat and Individual Gas Constant of Gases. Retrieved
2018, from https://www.engineeringtoolbox.com/specific-heat-capacity-gases-d_159.html
The MathWorks Inc. (n.d.). What Is the Genetic Algorithm? Retrieved 2018, from
https://www.mathworks.com/help/gads/what-is-the-genetic-algorithm.html
Vestfálová, M. (2015). Thermodynamic properties of real gases and BWR equation of state. EPJ
Web of Conferences 92,02106. EDP Sciences. doi:DOI: 10.1051/epjconf/20159202106
VFS. (2018). Human Powered Helicopter. Retrieved from Vertical Flight Society:
https://vtol.org/awards-and-contests/human-powered-helicopter
Wilson, H. (2012, October). Pressure Drop in Pipe Fittings and Valves | A Discussion of the
Equivalent Length (Le/D), Resistance Coefficient (K) and Valve Flow Coefficient (Cv)
Methods. (Katmar Software) Retrieved November 2018, from AioFlo 1.07:
https://www.katmarsoftware.com/articles/pipe-fitting-pressure-drop.htm

9.4 Project Gantt
The following tables show the design process as separated by physical year/academic semester.
Although not as detailed as the Gantt used by the team, the timeline provides a condensed version
of the major milestones during the project lifecycle.
Table 9.4:1 Project Gantt for Fall 2018
Activity
27
Aug
1
Sep
10
Sep
17
Sep
24
Sep
1
Oct
22
Oct
29
Oct
5
Nov
12
Nov
26
Nov
3
Dec
21
Dec
Team
Development
Brainstorming
Select Final
Design
Evaluate
Alternatives
CAD Model
Model in
AMESim
Midway
Presentation
Order Parts
Table 9.4:2 Project Gantt for Spring 2019
Activity
7
Jan
14
Jan
28
Jan
4
Feb
11
Feb
18
Feb
25
Feb
4
Mar
11
Mar
18
Mar
25
Mar
3
Apr
12
Apr
Order Parts
Build Bicycle
Mechanical
Hydraulic
Electronic
Test Bicycle
Modify
Test Bicycle
Shipping
NFPA Report
Final
Presentation
Competition

9.5 Supporting Material
The following sections come in three parts: (1) an introduction of the system topology, component
functions and affiliated mathematical descriptions, (2) a complete mathematical model,11
and (3)
the group’s hydraulic schematic in addition to the various modes of operation.
9.5.1 Introduction to System
Like many hydraulic systems, the team’s design features a schema comprised of a hydraulic
accumulator, hydraulic pump/motor, reservoir, connecting lines, and a controller. A diagram
depicting these elements are illustrated in Figure 28 with the use of hydraulic oil.
Figure 28: Schematic diagram of a typical hydraulic energy storage system.
Although not an exact replication of the group’s work, the hydraulic energy storage system shown
in Figure 28 is an excellent example to start with. In this instance, the hydraulic input is used to
pre-charge the accumulator to a specified level gas pressure and the mechanical input/output is
linked to a flywheel – a mechanical energy storage device. The flywheel is designed to not only
consume but generate energy from/to (respectively) the entire system, which simulates peaks and
troughs within an energy cycle.
9.5.1.1 Accumulator
A hydraulic accumulator is a pressure storage reservoir in which a non-compressible hydraulic
fluid is held under a specific pressure until being transferred to an external source. As oil and gas
levels increase in the accumulator, overall system pressure will continue to increase until reaching
maximum pressure. In the event the latter occurs, a relief valve is incorporated to prevent surplus
hydraulic fluid from entering the accumulator.
11
Although not explicitly stated in equation descriptions, derivatives are used throughout and denoted by
d[variable].

To incorporate accumulators in a hydraulic system, two fundamental parameters are needed:
(1) actual flow rate of oil entering the storage device (𝑄 𝑎) and (2) oil pressure at the accumulator’s
outlet (𝑝). The mathematical model is described in Equation (6).
𝑄 𝑎 = −𝑚 𝑔
𝑑𝑣
𝑑𝑡
(6)
Where,
𝑄 𝑎 = Flow rate of fluid into the accumulator
𝑚 𝑔 = Gas Mass
𝑡 = Time
𝑣 = Gas Specific Volume
During the compression and expansion processes, gas temperatures can vary dramatically –
creating irreversible heat transfer from the gas accumulator wall to the external environment.12
For
this reason, the team decided to select an accumulator through SteelHead Inc., which has
elastomeric foam. The benefit of such material comes with the large contact surface with the gas
paired with a smaller, carbon fiber, wall thickness. Based on these parameters, an equation can be
devised based on an equilibria relationship of foam and gas shown in Equation (7).
𝑚 𝑔
𝑑𝑢
𝑑𝑡
= −𝑝 𝑔
𝑑𝑉
𝑑𝑡
− 𝑚 𝑓 𝑐𝑓
𝑑𝑇
𝑑𝑡
− ℎ𝐴 𝑤(𝑇 − 𝑇 𝑤)
(7)
Where,
𝑚 𝑔 = Gas Mass
𝑢 = Gas Internal Energy
𝑡 = Time
𝑝 𝑔 = Gas Absolute Pressure
𝑉 = Gas Volume
𝑚 𝑓 = Foam Mass
𝑐𝑓 = Specific Heat of Foam
𝑇 = Absolute Gas/Foam Temperature
ℎ = Heat Transfer Coefficient
𝐴 𝑤 = Effective area of the accumulator for heat convection
𝑇 𝑤 = Accumulator Wall Temperature
The gas’s internal energy change is represented on the left side of Equation (7), and, from left to
right, the first portion of the right side pertains to the gas expansion work; heat absorption of foam;
and heat transfer to the accumulator wall.
12
Thermal loss can be as high as 40 percent of the input energy (Ayalew & Kulakowski, 2005).

For real gases, the internal energy per unit mass (u) is given by Equation (8):
𝑑𝑢 = 𝑐 𝑣 𝑑𝑇 + [𝑇 (
𝑝 𝑔
T
)
𝑣
− 𝑝 𝑔] 𝑑𝑣
(8)
Where,
𝑐 𝑣 = Constant-Volume Specific Heat of Gas
𝑣 = Gas Specific Volume
Through the Benedict-Webb-Rubin (BWR) equation of state, the gas pressure (𝑝 𝑔) can be
calculated, which uses gas temperature (𝑇) and specific volume (𝑣) as inputs as shown in Equation
(9) (Vestfálová, 2015).
𝑝 𝑔 =
𝑅𝑇
𝑣
+
𝐵0 𝑅𝑇 − 𝐴0 −
𝐶0
𝑇2
𝑣2
+
𝑏𝑅𝑇 − 𝑎
𝑣3
+
𝑎𝛼
𝑣6
+ (𝐶 (1 +
𝛾
𝑣2
) 𝑒
−𝛾
𝑣2⁄
)/𝑣3
𝑇2
(9)
Where,
𝐴0, 𝐵0, 𝐶0, 𝑎, 𝑏, 𝑐, 𝛼, and 𝛾 are constants in BWR equation
After combining the aforementioned equations, the resultant is Equation (10), which is the energy
equation for the gas and can be used to determine the approximate temperature of the gas through
integration. For a majority of foam-filled accumulators like SteelHead’s, the thermal time constant
(ℎ), shown in Equation (11), is often several minutes.13
(1 +
𝑚 𝑓 𝑐𝑓
𝑚 𝑔 𝑐 𝑣
)
𝑑𝑇
𝑑𝑡
=
𝑇 𝑤 − 𝑇
𝜏
−
1
𝑐 𝑣
[
𝑅𝑇
𝑣
(1 +
𝑏
𝑣2
) +
1
𝑣2
(𝐵0 𝑅𝑇 +
2𝐶0
𝑇2
) −
2𝑐
𝑣3 𝑇2
(1 +
𝛾
𝑣2
) 𝑒
−𝛾
𝑣2⁄
]
𝑑𝑣
𝑑𝑡
(10)
𝜏 =
𝑚 𝑔 𝑐 𝑣
ℎ𝐴 𝑤
(11)
13
This statement was made possible through using similar experiments (Irizar, Rasmussen, Olsen, & Andreasen,
2017) and information pertaining to SteelHead (SteelHead Composites, 2018).

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