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Engineering Senior Design Reports Engineering Science Department
5-7-2025
Final Project Report: Custom Rocket Motor Final Project Report: Custom Rocket Motor
Simeon Gantt
Austin Parcell
Saif Saleh
Kailey Tubbs
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Gantt, Simeon; Parcell, Austin; Saleh, Saif; and Tubbs, Kailey, "Final Project Report: Custom Rocket Motor"
(2025).
Engineering Senior Design Reports
. 98.
https://digitalcommons.trinity.edu/engine_designreports/98
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Final Project Report
Custom Rocket Motor
Simeon Gantt, Austin Parcell, Saif Saleh, and Kailey Tubbs
Dr. Eliseo Iglesias, Team Advisor
May 7, 2025
Executive Summary
This report outlines the design, fabrication, testing, and evaluation of a custom composite-propellant
rocket motor developed by the Custom Rocket Motor Team. The primary goal of this design project was
to overcome the limitations of off-the-shelf rocket motors by creating a system capable of delivering
tailored impulse and burn profiles within a highly constrained geometry. Specifically, the team targeted a
motor with a 3.125-inch diameter and a total impulse between 3,000 and 5,120 N-s, aligning with Tripoli
High-Power Rocketry Level 2 requirements while allowing for improved control over rocket altitude [1].
The final design successfully met or exceeded all core objectives. A custom pressure vessel and nozzle
assembly were developed and validated using analytical calculations and finite element analysis (FEA),
ensuring a minimum structural safety factor of 2.0 across all components. The nozzle featured a
bell-shaped contour optimized for isentropic flow, designed using MATLAB tools and OpenMotor
simulations. The team also formulated and cast their own composite propellant, based on the “Reliant
Robin” Ammonium Perchlorate Composite Propellant (APCP) formulation. This process included
multi-stage mixing, vacuum degassing, and a controlled curing process to ensure consistency and safety.
To manage extreme thermal conditions, the team implemented a phenolic liner, which was selected due to
challenges in achieving uniform results across the full motor length while spin-casting. Additionally, a
simple relay ignition system was developed to ensure safe and reliable motor ignition.
The full-scale static fire test, conducted at the Law family ranch in Pipe Creek, TX, served as the project’s
primary test. The motor was mounted on a modified test stand equipped with a 500 kg load cell and a
2500 psi-rated pressure transducer. A remote ignition system with a 300-foot safety zone and 100-foot
DAQ clearance distance was implemented to ensure safety for the team and equipment. During the test,
the motor delivered an estimated 5,250 N-s of total impulse, exceeding the targeted performance range
and technically qualifying the motor at Level 3 (L-3). Comparing this impulse to the mass of propellant
suggested a delivered specific impulse of 251.2 seconds, substantially higher than the initially predicted
236.6 seconds. This performance increase is attributed to high chamber pressures and beneficial
erosion-chamber pressure relationships during the burn in the nozzle.
While the pressure transducer failed to record data during the test, likely due to thermal or wiring issues,
chamber pressures were estimated indirectly through the load cell data, visual indicators, and CEA. These
methods suggested average internal pressures between 1600 and 2000 psi, significantly above the design
target of 1250 psi. The nozzle showed measurable erosion, with a 17% increase in exit diameter and 8%
increase in throat diameter, validating the material choices made during the design. Thermal protection
systems functioned effectively, as evidenced by external case and nozzle temperatures remaining below
the 200°C limit for 6061-T6 aluminum.
All essential objectives of the project were met in addition to one optional objective. This project clearly
demonstrated the team’s ability to design, build, and validate a high-performance solid rocket motor.
Possible improvements include, but are not limited to, increasing the design pressure, refinements to the
manufacturability of motor components, and higher aluminum content propellant. Future iterations of this
project could improve upon it by mixing and spin-casting a custom thermal liner and by acquiring
pressure transducer data during a static fire test. Farther into the future, teams may be able to improve
manufacturability of both hardware and propellant, as well as redesign the nozzle to be optimized at the
higher chamber pressures.
Final Project Report Custom Rocket Motor
May 7, 2025 Page 1 of 70
Introduction
The Trinity University Rocketry Club seeks to overcome the limitations of commercially available rocket
motors, which are restricted to standardized impulse and diameter specifications. These constraints limit
customization, making it challenging to optimize rocket designs for specific altitude objectives. By
developing a custom rocket motor, the team aimed to achieve precise control over critical design
parameters, including impulse and burn profile, to meet mission-specific performance requirements.
To accomplish this, the team designed and produced a composite-propellant rocket motor compatible with
the club’s high-powered rocket. The motor aims to deliver an impulse within the range of 3,000 to 5,120
N-s, adhering to FAA limitations while exceeding the performance of the previous 3,000 N-s design. The
motor was designed to integrate seamlessly with the rocket’s airframe, with a maximum case diameter of
3.125 inches. Various tests were performed on each component, culminating in the assembly and a static
fire of the motor. The static fire test was intended to verify that impulse requirements for an L2 motor
have been met in accordance with Tripoli safety code [1] and that the TURC would be delivered a more
powerful motor than their present design.
In addition to enhancing rocket motor customizability for the TURC, this project provides a valuable
learning opportunity. Developing, testing, and validating the motor allowed the team to gain hands-on
experience in engineering design, manufacturing, and experimental analysis in a field outside of the
department’s curriculum. Data collected from testing verified that the motor met its design objectives,
which will ensure a successful launch in the near future with the TURC.
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Overview of the Final Design
The custom rocket motor was developed with several objectives in mind, the primary of which was to
satisfy an impulse in the range of 3,000 N-s to 5,120 N-s while also restricted to a maximum tube
diameter of 3.125 inches. The design adhered in its material choice and maximum impulse to the Tripoli
Rocketry Association Safety Code, ensuring compliance with relevant standards. A focus on safety and
reliability guided the design process, with critical components such as the pressure vessel and forward
closure incorporating a minimum safety factor of 2.0 over the design pressure.
Testing and validation are also integral to the project, ensuring that the design meets all performance and
safety criteria. Testing hardware and protocols were designed to validate the system’s functionality and
reliability under controlled conditions. For example, multiple full-scale static fires were planned before
the motor was to be integrated into the rocket.
Figure 1. Rendering of full motor assembly
Figure 2. Cutaway view of completed assembly. See Appendix 2 for parts list.
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Manufacturing limitations shaped the selection of materials and components, particularly in regards to the
thermal liner and ablative parts of the nozzle. Cost considerations of the rocketry club also played a role,
leading to a preference for long-term cost-effective solutions over more expensive commercial
alternatives.
The design itself was supported by extensive research into theoretical principles and practical
applications. For the pressure vessel, analyses of hoop stress, bolt shear stress, bearing stress, and tear-out
stress ensured that the design would remain structurally sound under operational loads. The nozzle
assembly design was informed by research into isentropic flow behavior and the method of
characteristics. Thermal liner thickness calculations were also conducted after research of similarity
solution approaches. The ignition system required the development of a relay circuit..
Key components include the pressure vessel, nozzle assembly, graphite insert, phenolic carrier, thermal
liner, and propellant formulation. Each subsystem was designed with careful attention to its integration
into the overall system notably through designed tolerances, aiming to achieve optimal performance while
meeting the defined constraints.
Pressure Vessel
The pressure vessel, which forms the structural core of the propulsion system, was designed to withstand
the high internal pressures generated during operation. The subsystem was designed to contain a design
pressure of 1200 psi, with a minimum safety factor of 2.0 in yield. The pressure vessel was subdivided
into three parts, the case, forward closure, and nozzle carrier as seen in Figure 3. All components were
manufactured out of 6061-T6 aluminum alloy as per Tripoli specifications. Both nozzle carrier and
forward closure were fastened into the motor case with eight ¼-20 bolts made from Grade 8 steel. This
ensured shear of the frangible bolts would not be the primary mode of failure. Analyses of hoop stress,
axial stress, bolt shear stress, bearing stress, and tear-out stress ensured that the design would remain
structurally sound under operational loads.
Figure 3. Pressurized load-bearing components of the motor
The forward closure was given particular attention due to its critical role in maintaining structural
integrity of not just the motor, but the rocket itself. If the forward closure failed and was ejected, the
motor would separate from the rest of the rocket during flight. To mitigate the risk of unplanned
disassembly, the forward closure was equipped with dual O-rings, as shown in Figure 4, offering
redundancy in case one O-ring fails. O-rings are necessary to ensure a pressure seal, as parts cannot retain
even the most perfect tolerance under 1200 psi. Failure at the seal between the forward closure and case
could result in thrust opposing the nominal direction, which would, in the worst case, destructively eject
the motor from the test stand.
Final Project Report Custom Rocket Motor
May 7, 2025 Page 4 of 70
Figure 4. Engineering cutaway drawing of the forward closure (left), and forward closure in
assembly (right)
Like the rest of the case, the forward closure, as seen in Figure 5, was made using 6061-T6 aluminum
turned into shape on our CNC lathe. Multiple fit checks were performed during machining to ensure
proper interface between the case and forward closure.
Figure 5. Machined forward closure with two high-temperature silicone O-rings
The process of drilling the holes took more time than initially anticipated. Originally, the case/forward
closure and case/retaining ring holes were going to be drilled at the same time to ensure they lined up
perfectly. This posed many challenges but the most significant was that the forward closure and retaining
ring would move while inside the case during drilling. The small amount of movement created an uneven
ring of holes which increased the stress concentrations at certain bolts. This problem was resolved by
drilling each part separately. Figure 6 shows the drill guides for the forward closure, retaining ring, and
case, respectively.
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May 7, 2025 Page 5 of 70
Figure 6. Drilling guides for forward closure, retaining ring, and case
Once the bolt holes were drilled, the forward closure and retaining ring were tapped while sitting inside
the case for the alignment of the threads. The specific orientations were marked on both parts and the
case. Figure 7 shows the forward closure and nozzle set inside the case and securely bolted in place. Both
parts sit just inside the case and are not flush with the edge.
Figure 7. Forward closure and nozzle integrated with case after hole drilling and tapping
Nozzle Assembly
The nozzle assembly was designed to optimize the exhaust velocity of the exhaust gases. For the
diverging section, a bell-shaped nozzle was chosen over a conical design, not only for its slight
improvement in efficiency but also for the novelty of its design. As the team had access to a CNC lathe,
manufacturing of a bell-shaped phenolic nozzle was of equal difficulty as manufacturing of a conical one.
Theoretical principles, including the Prandtl-Meyer equation and isentropic flow equations for pressure
and area ratios were applied during its design. This design was modeled in MATLAB with the goal of
avoiding over-expansion and under-expansion of the exhaust plume under ideal chamber pressure
conditions. The engineering schematic in Figure 8 shows the bell shape of the nozzle.
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Figure 8. Engineering drawing of the nozzle assembly
Linen phenolic was selected for the diverging section of the nozzle because of its manufacturability, its
ablative properties, and its ability to withstand temperatures up to 3000 K. Ablation is a crucial property
of the phenolic as it allows for the absorption and dissipation of the high energies experienced at the
nozzle.
To address the high thermal stresses and erosive nature of the flow experienced during operation, a
graphite throat insert was incorporated instead of phenolic at the nozzle throat. This ensured durability
during static fire testing as well as predictable performance over the course of the burn as a larger
diameter throat would cause a significant drop in chamber pressure. The graphite insert was made conical
in profile due to machining concerns, as graphite produces electrically conductive dust upon machining,
and cannot be used in a CNC machine. After machining, sharp edges were subsequently sanded down to
reduce stress concentrations. The graphite insert is shown in Figure 9 (left) and the phenolic component
with the aluminum ring and graphite insert are shown in Figure 9 (right).
Figure 9. Machined Nozzle Components
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An aluminum ring with threaded holes was used to secure the nozzle to the motor case, and a single
o-ring was integrated into the phenolic portion of the nozzle to provide a pressure seal when the nozzle
was inserted into the case. All components of the nozzle were RTV silicone-cured together to ensure a
proper seal was formed. An engineering drawing of all components of the nozzle assembly is shown in
Figure 8, and a completed assembly is seen in Figure 9.
Thermal Liner
The main purpose of the thermal liner was to prevent hot combustion gases (temperatures in excess of
2900K) from damaging the pressure vessel. At these temperatures, ablative solutions were the only
reasonable approach within our budget. The team initially chose to insulate both the case tube and the
forward closure using a custom-cast HTPB-based liner. The bulk of the liner, along the case wall, was to
be spin-cast, meaning that the liner would be poured into the case as a liquid and then spun into shape
before curing. The thermal liner was formulated as a composite of Kevlar®, titanium dioxide powder,
HTPB binder, and carbon black opacifier.
The thermal liner would theoretically carbonize as the motor fires, resulting in a hard char layer on the hot
surface, while the inner portions of the liner remain soft. This hard char layer massively reduces the
thermal conductivity of the liner, as the trapped air and titanium dioxide have incredibly low conductivity,
while the dark pigmentation results in radiation being primarily absorbed at the surface rather than
absorbed deeply into the material. The Kevlar® serves to affix the char layer onto the surface for as long
as possible, before it too burns away, allowing the char layer to shear away and renew.
Due to high viscosities during casting, the team pivoted to the backup liner solution. This involved
purchasing a premade paper phenolic tube of 0.06” thickness and cutting it down to size as needed. Figure
10 demonstrates the thermal management approach implemented in the final motor, where propellant was
cast into the phenolic tube with an HTPB-based liner insulating the forward closure. RTV silicone, a
temperature resistant adhesive, seals together the three components pictured.
Figure 10. Thermal management of the custom rocket motor
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The team was confident in the reliability of the phenolic liner because of the widespread use of this
material in similarly-sized motors. In motors under 1000 psi, a simple layer of grease is known to
sufficiently shield the forward closure from the heat of the combustion due to the lack of mass flux, since
all of the exhaust products flow toward the nozzle in the opposite direction. For this custom motor, whose
average design pressure is around 1250 psi, we therefore chose a fairly conservative forward liner
thickness of 0.2 inches.
Propellant Formulation
Propellant formulation selection was a key aspect of the design. The team selected “Reliant Robin”, an
APCP with bimodal particle distribution, with several small modifications. This formulation ensured high
impulse density and pourability while maintaining compatibility with the liner through a shared binder
composition. APCP propellants are known for their high specific impulse (a measure of impulse delivered
per unit mass of propellant and normalized to gravity, commonly shortened to Isp), especially when
aluminized. This choice unfortunately results in a significantly higher flame temperature, complicating
thermal management. Various additives were added to modify viscosity and blowing properties to ensure
pourability, as well as increase propellant strength and resistance to vibration.
The propellant was composed of an oxidizer, fuel, binder, and other additives. Each component of the
propellant has its own unique role or function in the burning or casting process, and will be explored
sequentially. The full list of propellant components is seen in Table 1.
Table 1. Propellant components and their function
Binder
HTPB
Polyol
IDP
Plasticizer
MDI
Crosslinking Agent
Additives
HX-878
Bonding Agent
Lecithin
Surfactant
PDMS
Anti-foaming Agent
Oxamide
Burn Rate Suppressant
Fuel and Oxidizer
Aluminum
Primary Fuel
Ammonium Perchlorate
Oxidizer
The oxidizer used in this propellant is ammonium perchlorate, an industry standard for solid propellants.
This is due to its power as an oxidizer, impact insensitivity, cost, and availability in various particle sizes.
The selected formulation uses three different particle sizes, 400 um and 90 um AP particles, and the
aluminum powder is approximately 5um. The various sizes allow for the smaller particles to “nest” in the
gaps between the larger spheres. This ensures high overall propellant density, a key metric of efficiency in
propellant design.
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The primary fuel is crystalline aluminum, which aggressively reacts with the ammonium perchlorate,
oxidizing into alumina gas. This reaction also massively increases the combustion temperature of the
combustion gases, up to 3000K in our formulation. Aluminum has a significantly higher energy density
than almost all other metals, and more than the other components of the propellant. To this end, in
propellant formulations, aluminum concentration is maximized when high performance is the driving
factor in the design.
Notably, aluminum concentration has an effective upper limit that changes depending on the size of the
motor. Aluminum reacts relatively slowly compared to the rubber binder, due in part to its naturally
passivated oxide shell around the particles, which results in the aluminum primarily reacting off of the
burning surface. This fundamentally limits the aluminum concentration in a motor as a function of the
motor’s physical size, as the longer the motor is, the longer the aluminum has to react in the gas before it
reaches the nozzle. Large quantities of aluminum in the nozzle should be avoided to prevent two-phase
flow losses in the diverging section. The aluminum also acts to stabilize the combustion, as slow burning
aluminum droplets in the gas dampen unstable acoustic waves in the combustion chamber. Adding
aluminum also helps to opacify the propellant, ensuring burning only happens at the surface of the
propellant due to UV and infrared radiation from the combustion gas being absorbed in the top surface of
the propellant. If this were not present, radiation from the high temperatures could spontaneously ignite
pockets of propellant deep inside the grain, leading to a rapid breakup of the entire grain, and thus
overpressure of the case.
The rubber binder was designed to hold both solid oxidizer and fuel particles together in a well mixed
manner to ensure as even burning as possible. This rubber is a type of polyurethane known as HTPB, or
hydroxyl-terminated polybutadiene. This rubber has been used in spaceflight since the 1960s, liked for its
high solids loading capabilities, along with its relatively high Isp when burned. High performance solid
propellants have solids loading between 80% and 90%, as the solid particle combustion contributes
significantly more to the reaction than the burning of the rubber binder, with the only source of oxidizer
being in solid form. Solids loading is the weight percent of the entire propellant that is a solid particle. As
solids loading increases, manufacturing becomes significantly more difficult. The team has struck a
balance in the propellant formulation that they chose, with a solids loading of 83%, just maintaining
pourability. The rubber in the team’s propellant is crosslinked with methylene diphenyl diisocyanate
(MDI) as a balance between toxicity and performance.
The propellant the team chose also contained various additives to ease synthesis, manufacturability, and
improve mechanical performance. Small quantities of lecithin and PDMS were added to improve
manufacturability. These additives reduce the viscosity and surface tension of the propellant respectively,
both necessary for ensuring pourability and gas detrainability. Oxamide was also added to reduce the burn
rate of the propellant as a chemical reaction suppressant. The original Reliant Robin propellant also
contained CAO-5 as an antioxidant, but this was deemed to be unnecessary by the team and SWRI
advisors, as the propellant would be fired within a short period of time after manufacture.
The most important additive was HX-878, also known as Tepanol, an ITAR regulated chemical bonding
agent. Tepanol is a three molecule mixture that works together to bond ammonium perchlorate to HTPB.
When propellant has large particles in it, it is common to have slight stratification of the particles, with
large particles rising to the top of the mixture. This upsets the delicate balance in particle sizes that keeps
propellant density high. If the particles are large enough, it is likely that a high solids loading will be
unachievable due to the relatively high surface tension of the propellant. This is because with high surface
tension, the binder will not be able to adequately coat the large particles as it would with smaller particles.
Final Project Report Custom Rocket Motor
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HX-878 counteracts this by chemically bonding the ammonium ion in the ammonium perchlorate to the
Tepanol. According to Orbital ATK, the HX-878 also electrostatically coordinates the rest of the
ammonium perchlorate after forming a Tepanol perchlorate salt from an acid/base reaction with
ammonium perchlorate. During this process, an ammonia molecule is released, requiring extended
degassing time for around 48 hours after mixing [3].
The team decided to select a propellant instead of formulating one for a number of reasons. First, ensuring
pourability on a new propellant is complicated and requires a significant number of iterations. Second,
and more importantly, if the team formulated their own propellant the team would have to characterize its
pressure-burn rate behavior onto Saint-Robert’s law, as seen in Equation 1. Chamber pressure is
represented by P, and r denotes burn rate. The a and n values are known as the burn rate coefficient and
exponent, respectively. They cannot be determined analytically and must be determined empirically.
𝑟 = 𝑎𝑃𝑛
(1)
This task would take multiple years of successive static firings or strand burning tests, something
significantly outside the scope of this project. To add a sense of novelty to the project, and to improve
performance, the motor was designed to operate at slightly higher pressures than previously tested with
this propellant previously. Instead of burning at 800 psi, this motor was designed to burn at around 1200
psi. This higher pressure slightly changed the burning characteristics of the propellant, but it almost
certainly still followed the general pattern laid out and characterized in Saint-Robert's law, as the pressure
is not close to where a slope break could become a concern.
The team modified a hand-mixing procedure from Purdue University to get a solid starting point for our
mixing process. As will be detailed later, this mixing process evolved as tests were performed. Ultimately,
a good mixing process leaves the finished product as close to the theoretical density of the propellant as
possible, which, in our case, primarily involved refining the degassing process that we used to remove any
air incorporated during the mixing process.
Propellant Geometry
The propellant geometry was designed to maximize performance within the specified impulse range.
Simulations accounted for shifting specific impulse (Isp) during the duration of the simulation, ensuring
stable performance throughout the burn. This design also prioritized stability during initial ignition and
pseudo-steady state combustion, ensuring safe and reliable operation during launch. This was achieved
through a high initial Kn ratio, the ratio between burning surface area and throat cross sectional area,
which was maintained throughout the burn.
Another key objective of the propellant geometry was to establish a relatively constant chamber pressure
for the duration of the burn. This would ensure that the motor was at its design pressure for as long as
possible, effectively making the safety factor of the motor as uniform as possible throughout the length of
the burn. A constant chamber pressure also ensures that the nozzle performs optimally for the duration of
the burn, further improving efficiency.
Propellant geometry also ensured that erosive burning would not be a major concern in motor operation.
Erosive burning occurs when high velocity combustion gases induce shear stresses at the burning surface
that result in small (or sometimes large) pieces of propellant being liberated from the surface. This greatly
reduces efficiency and can sometimes result in motor overpressure. Erosive burning can be reduced by
ensuring that the mass flux of the combustion gases remains as low as possible inside the combustion
Final Project Report Custom Rocket Motor
May 7, 2025 Page 11 of 70
chamber. The team accomplished this by designing a one-degree taper into the cylindrical section, as well
as placing the finocyl (fins on a cylinder) at the end of the motor near the nozzle as seen in Figure 11.
This increase in cross sectional area will decrease the velocity of the gases as they move towards the
nozzle, as the flow inside the combustion chamber should remain subsonic until reaching the nozzle. To
this end, no sections of the grain were designed to have a core diameter smaller than the nozzle throat to
ensure that the flow would never choke before the nozzle. The propellant geometry was modified in the
spring semester to ensure manufacturability and to change the total impulse as different density values
were measured in the propellant tests.
Figure 11. Engineering drawing of the propellant grain. Finocyl is visible on the left of the image, close
to the nozzle
The mandrel was split into three different sections for manufacturability — two cylindrical and one
finocyl. Since the Bambu printers could not print the entire mandrel on one build plate due to build height
restrictions, each part was roughly six inches long and made out of PLA. They were attached to each
other by the mechanism shown in Figure 12. This was designed so one part would go into the next section
and twist to lock. These were then superglued together to make it one piece, sanded, and waxed. The final
result is shown in Figure 12.
Figure 12. Isometric views of mandrel components, clearly showing the interlock used to keep pieces
aligned after gluing.
Figure 13. Finished and waxed mandrel, directly before casting
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The mandrel was used with a PLA printed base and the phenolic liner to mold the propellant. The
propellant was poured into the mold via a funnel. The mandrel screwed into the funnel to keep it centered
during pouring and curing. The propellant was then left to cure and the mandrel was pushed out with an
arbor press. The left side of Figure 14 is a cross section of the Fusion model and the right side is the actual
propellant inside the liner and casing.
Figure 14. Section view of the propellant grain and full scale cast in the thermal liner
Design Evaluation
Essential Objective #1: Design and build a motor with more impulse
than the current TU Rocketry Club’s motor design (3000 Ns)
Open-Motor Verification of Impulse
Test Overview
This test involved simulating the motor’s performance using the Open-Motor software. The simulation
ran from 0 to 4 seconds and evaluated key parameters such as thrust, chamber pressure, and Kn (the ratio
of burning surface area to nozzle throat cross-sectional area).
Purpose of Test
To maintain a consistent motor performance, this simulation would ensure the thrust curve was relatively
flat and verify that the Kn ratio was large enough to prevent combustion instability.
Feature(s) Evaluated
The features evaluated in this test include the stability of the thrust curve over the 4-second burn time at
atmospheric pressure, as well as the Kn ratio to confirm that combustion remained stable during the
motor's operation.
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Test Scope
The scope of the test covered the simulated motor performance over the full 4-second burn duration. The
focus was on the behavior of the thrust curve, chamber pressure, and Kn ratio throughout the burn.
External factors such as ambient environmental conditions were not included in the model.
Test Plan
The test plan utilized the Open-Motor software to simulate thrust, chamber pressure, and Kn as functions
of time. Built-in data logging tools were used to record performance metrics for later analysis. Successful
execution of the test required proficiency with the Open-Motor software, knowledge of how motor design
parameters influenced thrust and combustion stability, and familiarity with interpreting thrust curves and
Kn ratio profiles. The team assumed that the simulation accurately reflected real-world motor behavior
and that ambient conditions would not significantly impact the results. Data collected included thrust
curve values over the 0 to 4 second interval and Kn ratio measurements throughout the burn for
evaluating combustion stability.
Acceptance Criteria
The chamber pressure was required to remain stable, without oscillations or deviations exceeding 5%.
The Kn ratio was required to meet or exceed a threshold value of 100 to prevent combustion instability.
The total impulse delivered by the motor had to fall within the range of 3000 to 5120 N-s.
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Test Results and Evaluation
The propellant characteristics were entered into OpenMotor, taking into account Saint-Robert’s law of
propellant burn rates. The simulation assesses the thrust curve, chamber pressure behavior, and Kn ratio
across the burn time.
Fundamentally, this test was to ensure that the designed motor would have an impulse within the required
range. It uses shifting specific impulse methods to determine the impulse. Notably, as seen in Figure 15.
The thrust remains lower than the average during the start of the burn. The team designed it this way to
preemptively take into account erosive burning behavior increasing the burn rate at the finocyl. Chamber
pressure peaks at around 1200 psi, consistent with the design of the pressure vessel.
Figure 15. Open-motor test displaying chamber pressure, Kn, and thrust
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Essential Objective #2: The team should be able to mix and cast their
own pourable, composite propellant.
HTPB Casting Test
Test Overview
This test involves casting samples of our HTPB-based rubber binder to evaluate our process performance
during mixing, degasing, and curing.
Purpose of Test
The purpose of the test was to verify that the MDI-HTPB hydroxyl ratios were correct to achieve
complete curing. The test also ensured that the vacuum chamber effectively removed air bubbles to create
a uniform, void-free material and that the mixture exhibited proper pourability for smooth casting.
Feature(s) Evaluated
The features evaluated included the accuracy of the MDI-HTPB hydroxyl ratios for proper curing, the
qualitative uniformity of the rubber, and the ease of pourability.
Test Scope
The scope of the test included mixing HTPB with MDI curative under controlled environmental
conditions such as temperature and humidity. A vacuum chamber was used to remove air bubbles from
the mixture. The evaluation focused on the consistency of the mixture during pouring and the curing
process, with non-conforming batches, such as those with incorrect ratios or visible air bubbles, excluded
from further analysis.
Test Plan
The test setup included a digital scale for precise component measurements, a vacuum chamber for
degassing the mixture, and a timer to track mixing times. Proper personal protective equipment (PPE) was
used throughout the process. The procedure required familiarity with vacuum chamber operation and
safety, knowledge of chemical ratios and curing behaviors for MDI-HTPB systems, and experience
interpreting the results of rubber casting.
The team assumed that small-scale sample behavior would be representative of full-scale performance
and that the vacuum chamber would effectively remove significant air bubbles. It was also assumed that
environmental conditions would remain consistent throughout mixing and curing. Data collected included
mass and ratio measurements, observations of pourability and consistency, and notes on curing
characteristics such as tackiness or voids. The actual quantities of HTPB, IDP, Tepanol, Lecithin,
Oxamide, aluminum powder, and ammonium perchlorate (AP) used were documented, and a detailed
propellant manufacturing procedure is included in Appendix 1B.
Acceptance Criteria
The pourability of the mixture must allow smooth casting without interruptions. The mixture must cure
fully within the expected time frame with no tackiness or incomplete areas, and no visible air pockets or
voids should be present in the cured samples. Repeatability is confirmed with at least three successes.
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Test Results and Evaluation
HTPB and MDI were mixed under controlled conditions, degassed in a vacuum chamber, and observed
for curing consistency. Component weights were calculated per the Mixing Ratios in Appendix 1C for a
53 cm³ batch to fit four small test molds. Significant void formation was observed during the mixing
process for the four tests, but was mostly removed with the vacuum process. A more powerful vacuum
system was necessary for the full propellant, which had a high solid loading of 85%. Ultimately, this test
served to test procedures for not just the mixing process, but allowed the team to gain experience with
waste disposal procedures and chemical acquisition. Detailed mixture ratios can be found in Appendix
1C.
No-Load Liner Density Test
Test Overview
This test involved casting small sections of thermal liner to evaluate density, mixing ratios, and the overall
mixing process.
Purpose of Test
It is imperative to verify that the MDI-HTPB ratios are correct for proper curing and ensure that the
density of the mixture aligns with expected values, or otherwise obtain a new, repeatable density value.
Feature(s) Evaluated
The team evaluated the curative hydroxide ratio by qualitatively assessing the cure of the liner. A sample
cross-section helped determine the effectiveness of the vacuum degassing setup.
Test Scope
This test involved mixing a small batch of the thermal liner material with a specific MDI-HTPB ratio of
33 parts HTPB to 5 parts MDI by mass. A vacuum chamber was used during the process to degas and
improve material uniformity. Measurements were taken to determine the density of the cured samples and
compared against target values. The team excluded faulty data (e.g., incorrect ratios or improper curing
conditions) from the analysis.
Test Plan
The test setup included a digital scale for precise component measurements, a vacuum chamber for
degassing, and calipers and a mass scale for calculating cured liner density. The process required
knowledge of HTPB-based mixing procedures, proper use of the vacuum chamber, and an understanding
of how chemical ratios impact curing behavior. The team assumed that the behavior of small-scale
samples would reflect full-scale performance and that the vacuum process would eliminate all significant
voids. Data collected included mass and volume measurements for density calculations, visual
observations of curing quality, and documentation of the mixing ratios used. The detailed liner
manufacturing procedure is provided in Appendix 1A.
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Acceptance Criteria
The measured density of the cured liner was required to fall within ±10% of the target value of 920 kg/m³.
The mixture had to cure fully, with no tackiness or signs of incomplete chemical reaction. The vacuum
chamber process was expected to yield samples with voids no larger than 2 mm. At least ten samples were
required to ensure statistical reliability in density measurements.
Test Results and Evaluation
The samples were easily demolded, and the mixture cured as expected. However, the test revealed
significant issues with bubble and cavity formation, with large voids observed throughout the cured
samples as shown in Figure 16. These defects prevented an accurate density measurement and indicated
shortcomings in the vacuum degasing process. Despite these issues, the team decided to proceed to the
short spin-cast liner test, considering this an opportunity to further refine the process. The observed
problems suggested improvements were needed in the degasing procedure. To address this concern, a new
vacuum chamber with a lower absolute vacuum was acquired.
Figure 16. Thermal liner test samples, showing white specks of titanium dioxide powder and Kevlar®
fiber
Propellant Sample Test
Test Overview
This test involved preparing and casting small propellant samples to verify the general procedure and
evaluate key material properties, including density and pourability.
Purpose of Test
In addition to confirming that the propellant preparation and casting procedures function as intended, the
sample test allowed for the assessment of propellant density, verifying that voids were drawn out of
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propellant during degasing, as well as demonstrating that the propellant mixture had the proper
pourability for smooth and consistent casting.
Feature(s) Evaluated
The team measured propellant density, performed a qualitative characterization of remaining voids, and
ensured that the propellant could be degassed and poured within its pot life.
Test Scope
The test focused on the consistency and accuracy of the mixing, pouring, and curing processes.
Measurements were taken to determine the density of the cured propellant and compared with target
values. Pourability was assessed during the casting process to ensure the mixture flowed smoothly
without separation or air pockets. Environmental conditions such as temperature and humidity were
controlled to avoid variability.
Test Plan
The test setup included a digital scale for accurate mass measurements of ingredients, molds for casting
small samples, a vacuum pump and chamber capable of reaching 0.1 psia, and tools such as calipers and a
scale for density calculations. The procedure required experience in mixing and safely handling energetic
materials, the ability to measure density accurately, and the use of proper personal protective equipment
(PPE). The team assumed that the behavior of small-scale propellant samples would reflect that of
full-sized batches and that environmental conditions such as temperature and humidity would remain
constant during the test. The team recorded mass and volume measurements, monitored whether the
propellant deflated appropriately during degassing after MDI was added, and documented observations
related to pourability, including smoothness and the presence of air bubbles. The detailed mixing ratios
and procedures are redacted due to ITAR concerns, as recommended by the senior design administrator.
The remaining procedural information is available in Appendix 1B.
Acceptance Criteria
The cured propellant was required to have a density greater than 5% under the target value 1550 kg/m³,
ensuring the motor remained within the Tripoli impulse limit [1]. The mixture needed to exhibit consistent
pourability, free from air pockets or material separation during casting. The propellant was also required
to fully deflate during degassing once the MDI was added. All procedures had to run smoothly,
confirming that the process was both reliable and repeatable. Results had to be consistent across multiple
batches to validate the reliability of the manufacturing method.
Test Results and Evaluation
This test presented the team with a few key pieces of information. Primarily, it taught the team that the
vacuum pump previously used was insufficient for high density propellant. Voids larger than 1 mm were
observed throughout the propellant grain. This is clearly visible in Figure 17. Due to the small batch size,
the mixture also failed to pour easily, especially considering its shear-thickening properties. These factors
led us to significantly different density results between each test sample. The team moved on to the small
finocyl test after securing a new vacuum chamber.
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Figure 17. Propellant sample and cross section with voids clearly visible
Finocyl Mandrel Tests
Test Overview
This test involved pouring a small quantity of propellant into a mold containing a section of the finocyl
mandrel. A finocyl refers to a section of the propellant grain geometry. It is essentially a cylindrical hole
with fin-like cut-outs around its circumference. This shape was chosen to temporarily increase burning
surface area at the start of the burn. The mandrel is the positive form for the designed finocyl to be used in
molding the propellant grain.
Purpose of Test
The purpose of the test was to ensure that the mandrel could be removed easily without damaging the
propellant. The test also verified whether the surface preparation procedures for the mandrel worked as
expected and whether the propellant cured properly with minimal void formation. Additionally, the team
used the test to evaluate the paddle mixing procedure.
Feature(s) Evaluated
The features evaluated included the functionality and design of the finocyl mandrel, the ease of mandrel
removal after curing, and the solidity and structural integrity of the cured propellant.
Test Scope
The test focused on evaluating whether the mandrel could release cleanly from the cured propellant
without requiring tools. It included the use of a paddle mixer and involved visual inspection of the
propellant for deformation, cracking, or voids after demolding. Environmental conditions such as
temperature and humidity were controlled to ensure consistent curing behavior. If the propellant failed to
cure or the mandrel could not be removed, adjustments to the process or mandrel design were to be made.
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Test Plan
The test setup included short and mid-scale finocyl mandrels and molds, a digital scale for accurate
ingredient measurements, a vacuum pump and chamber capable of reaching 0.1 psi, and tools for density
measurement such as calipers and a mass scale. A paddle mixer was used for uniform mixing. The
procedure required knowledge of safe propellant handling and pouring methods. The team allowed the
propellant to flow under gravity into the space between the mold and the mandrel and expected the
mandrel to break away cleanly after curing. It was assumed that the small-scale molds would replicate
conditions for larger-scale applications. Observations included the quality of mixing, the force required to
remove the mandrel, and the condition of the propellant surfaces. The team also recorded ambient
conditions such as temperature and humidity.
Acceptance Criteria
The mandrel was required to be removable without damaging the propellant or mold. The cured
propellant had to be solid with no visible cracks or large voids. The team needed to observe consistent
results across multiple casts before accepting the process as reliable.
Test Results and Evaluation
The team completed one short finocyl mandrel test to assess both density of propellant and ease of
mandrel removal. The test was widely successful in all regards. The team mixed about 100 g of propellant
(following the procedure given in the propellant sample test) and attempted to pour the resulting batch
into the pre-prepared 3d-printed mold. The mixture was found to be incredibly shear thickening and quite
viscous, resulting in the propellant being unable to flow at this scale. The completed propellant before
cure is seen below in Figure 18.
Figure 18. Completely degassed propellant with noticeable bubble at the bottom
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After 48 hours, the propellant was removed from the mold and density measurements were taken. The
propellant separated cleanly, with little debris being left on the mandrel and mold, giving the team
confidence in the method for future tests. We found the density to be 1640 kg/m³, approximately 4%
higher than the previously expected value of 1550 kg/m³. Furthermore, minimal void formation was
observed, due to the new vacuum setup being able to reach 0.01 atm absolute. A picture of the propellant
sample is seen below in Figure 19.
Figure 19. Completely cured small-scale finocyl propellant sample
After completing the short finocyl test, the team completed two full finocyl tests. These tests finalized our
propellant density, as well as helped us verify that a full finocyl could be removed from the propellant.
The first test resulted in a complete cure and density measurement, but the mandrel proved to be too weak
to be removed cleanly, resulting in the sample having to be halved to remove the mandrel. The halved
samples are seen below in Figure 20.
Figure 20. Half of the full finocyl propellant test after cure
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To correct this problem, the team increased the infill percentage on the mandrel from 15% to 65%. The
second full finocyl test resulted in an incomplete cure due to excessively high humidity in the lab (>80%)
for several days during the cure. This caused the MDI in the binder to crosslink into the water molecules
in the air, reducing its ability to cure the propellant. However the partially cured propellant did release
from the mandrel.
This test also allowed the team to verify the new mandrel design; even with the full pressure of the arbor
press that destroyed the previous mandrel test, it exhibited little deformation as shown in Figure 21.
Ultimately, this test taught the team to be much more careful about scheduling the curing times of the
propellant casts around weather conditions.
Figure 21. Propellant after better mandrel was removed
Essential Objective #3: Design and manufacture a custom nozzle
optimized for the motor.
MATLAB/OpenMotor Analysis of Nozzle Performance
Test Overview
This test involved the use of MATLAB and OpenMotor to model nozzle performance under a chamber
pressure of 1200 psi and for a selected geometry. The analysis focused on optimizing the nozzle shape for
isentropic flow conditions, ensuring efficient performance by matching exit pressure to atmospheric
pressure.
Purpose of Test
The purpose of this test was to model the characteristics of isentropic flow through the nozzle. It
evaluated flow properties such as velocity and pressure distributions along the nozzle to ensure alignment
with theoretical predictions.
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Feature(s) Evaluated
This test evaluated the nozzle design’s ability to prevent over-expansion and under-expansion.
Over-expansion can be identified when the theoretical pressure at the nozzle exit is less than atmospheric
pressure. Under-expansion can be identified when the theoretical pressure at the nozzle exit is greater than
atmospheric pressure. MATLAB-generated geometry was coded to ensure that the exit pressure matched
atmospheric pressure.
Test Scope
The scope of this test was to identify nozzle geometries that avoided over-expansion and under-expansion
when a chamber pressure of 1200 psi was applied. The focus was on isentropic flow behavior;
non-isentropic effects (e.g., turbulence) were excluded in this analysis.
Test Plan
MATLAB and OpenMotor software was used to perform flow modeling and analysis. Familiarity with
isentropic flow principles and proficiency in MATLAB and OpenMotor were required for this test. This
test made the following assumptions: Flow through the nozzle was isentropic flow; chamber pressure at
3000 K was 1200 psi; atmospheric pressure was 1 atm; and specific heat ratio was constant and known.
This test was intended to produce nozzle geometries that avoided both over-expansion and
under-expansion. For these geometries, this test would also plot flow speed and pressure distributions
along the length of the nozzle. See detailed nozzle contour design in Appendix 1D for more information.
Acceptance Criteria
The nozzle geometry would produce exit pressure equal to atmospheric pressure to avoid over-expansion
or under-expansion and to maximize nozzle efficiency.
Test Results and Evaluation
At the entrance of the converging section, flow accelerates and pressure drops. As seen in Figure 22, the
contour of the linear section of the nozzle starts to curve around x = 1.5 cm.
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Figure 22. Full nozzle contour
The flow velocity curve shows an irregularity in their behavior, as seen in Figure 23. This cusp is caused
by the abrupt change in shape of the contour as it transitions from conical to bell-shaped, which was
somewhat mitigated by manually sanding the graphite as it transitions between the converging and throat
sections.
Moving along the contour of the nozzle, the diverging section begins past the throat, consisting of an
expanding and straightening section. As expected, the Mach number continues to increase and the
pressure continues to drop. A pressure ratio of unity ensures that both over-expansion and
under-expansion are avoided. Atmospheric pressure at the nozzle exit is achieved with a flow velocity of
Mach 3.3.
Figure 23. Mach number along nozzle
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Essential Objective #4: Ensure that all motor components are designed
within an appropriate factor of safety (2.0).
Pressure Vessel Analytical Design
Test Overview
This test involved using analytical formulas to determine the safety factor of the motor case in regards to
bolts and general hoop and axial stress.
Purpose of Test
The purpose of this test was to assess the motor case’s ability to withstand mechanical stresses during
operation, ensuring it could handle the pressure profiles expected during firing. It also ensured that the
appropriate safety factor was reached, and that the primary failure mode would not be causing hoop stress
failure.
Feature(s) Evaluated
The features evaluated included the structural integrity of the motor case in bearing, screw shear, tensile
failure, and screw tear out.
Test Scope
The scope of the test identified primary failure modes, but did not account for stress concentrations that
could have been induced through the machining process.
Test Plan
The test used a modified version of the “Half-Cat Rocketry” pressure vessel calculator [5]. Sourced
component yield and shear stresses were added to ensure it accurately reflected the designed and built
motor.
Acceptance Criteria
Minimum safety factor was to be 2.0, with casing tensile failure to not be the critical failure mode.
Test Results and Evaluation
The test results are shown in Figure 24. It can be seen that bearing fails in yield at a minimum safety
factor of 2.0, followed by screw tear out at a safety factor of 2.3. Various values including the screw type,
screw shear strength, and center-edge distance were modified until these results were achieved. These
results were then incorporated into the design before the following test simulated the nozzle in more detail
with FEA.
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Figure 24. Spreadsheet for theoretical margins of safety of the custom rocket motor
FEA of Nozzle Assembly
Test Overview
This test involved conducting a Finite Element Analysis (FEA) on the nozzle assembly to evaluate its
structural integrity and performance under operational conditions.
Purpose of Test
The purpose of this test was to assess the nozzle's ability to withstand mechanical stresses during
operation, ensuring it could handle the pressure profiles expected during firing.
Feature(s) Evaluated
The features evaluated included the structural integrity of the nozzle design under the anticipated flow and
pressure conditions expected during operation.
Test Scope
The scope of the test included identifying stress concentrations and deformations and analyzing potential
failure modes across the nozzle assembly. All conditions were simulated, and no physical testing was
performed.
Test Plan
The test was conducted using Fusion 360. The analysis required proficiency with FEA modeling tools and
accurate interpretation of the results. The team defined material properties to reflect the actual materials
used in the nozzle, including graphite, phenolic, and aluminum components. Flow conditions were
selected to represent worst-case scenarios during operation. The team collected data on stress
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concentration locations and deformations, and calculated factors of safety across the nozzle components.
The results were used to confirm that stress levels remained within safe limits and that no critical failure
points existed under expected load conditions.
Acceptance Criteria
The maximum stress in the graphite insert was required to remain below 50 MPa, while the phenolic
component was limited to 58.1 MPa, and the aluminum ring was not to exceed 369 MPa. Deformations
had to remain small enough to preserve the nozzle’s designed geometry. The analysis needed to identify
no critical failure points that could compromise the nozzle during firing..
Test Results and Evaluation
The simulation results, shown in Figure 25, demonstrated that the nozzle design met the acceptance
criteria. The lowest simulated safety factor, which occurred near the O-ring grooves, was 1.69 and
therefore greater than the design criteria of 2.0. Deformation levels were minimal and well within
acceptable limits. No critical failure points were identified, confirming the design's structural integrity.
While the analysis revealed no immediate design concerns, minor adjustments to manufacturing
tolerances could further enhance ease of assembly and integration.
This test also determined that the principal failure would be bolt tear out, as expected. This type of failure
results when the bolts that hold the retaining ring pull straight out towards the end of the motor. It is
shown in the bottom left of Figure 25 in yellow and green.
Figure 25. Safety factor distribution of nozzle assembly, with stress directions shown as arrows
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Optional Objective #1: Design and manufacture a spin-cast thermal
liner.
Short Spin-Cast Liner Test
Test Overview
This test involved applying a spin-casting process to a short section of thermal liner to evaluate its density
and ensure the process ran smoothly. The goal was to verify the liner’s uniformity and validate the
effectiveness of the spin-casting method. See Appendix 1A for detailed procedure.
Purpose of Test
The purpose of the test was to evaluate the density of the spin-cast liner to confirm that it met design
specifications. The test also aimed to ensure that the spin-casting process produced consistent, void-free
results and could be reliably used for manufacturing larger-scale components.
Feature(s) Evaluated
The features evaluated included the density of the spin-cast liner, the consistency and uniformity of the
liner’s thickness, and the ability of the spin-casting process to eliminate air bubbles and defects.
Test Scope
The test covered both the spin-casting and curing stages of the liner material. Observations focused on the
liner’s density and surface uniformity after curing. The evaluation was performed under standard room
temperature and humidity conditions (40%–60%) to ensure repeatability of the process.
Test Plan
The test setup included a spin-casting machine to apply the liner evenly, a digital scale for measuring
component ratios and final liner mass, and precision tools such as calipers to assess liner thickness and
uniformity. The manual lathe used during the test operated at rotational speeds of 250 and 1350 rpm. The
procedure required experience with spin-casting equipment, knowledge of polymer-based materials, and
an understanding of material behavior during curing. The team assumed that the small-scale test would
accurately reflect full-scale performance and that the spin-casting process would evenly distribute the
liner material with minimal voids. Data collected included density measurements compared to target
values, visual assessments of surface uniformity, and records of process conditions such as spin speed and
ambient temperature.
Acceptance Criteria
The density of the cured liner was required to fall within ±2% of the target value of 920 kg/m³. The liner
surface had to be uniform, with no air pockets, cracks, or voids. The spin-casting process needed to
produce consistent results across multiple trials, and any deviations had to be minor enough not to affect
the liner’s performance in the final motor configuration.
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Test Results and Evaluation
The thermal liner was poured into a short section of aluminum tubing and then spin-cast on the CNC
lathe. Figure 26 shows the tube along with the 3D printed plugs that prevented the liner from spilling out
while spinning on the lathe. The test aimed to validate the process for larger-scale applications and
evaluate its ability to prevent defects such as air pockets or uneven thickness.
Figure 26. Small spin-casting tube for the test, with two 3D-printed plugs
Figure 27 shows the uneven distribution and exposed aluminum suggest potential issues with liner
viscosity, casting speed, or rotation parameters. Further trials would focus on refining these variables to
improve material flow and ensure uniformity. The team also considered modifying the material
formulation to enhance spreadability or adjusting the spin-casting technique to achieve better coverage.
These challenges, however, pushed against the scope and schedule limitations of the project, and the team
decided to pivot to the backup liner plan until the first successful static fire of the motor. This allowed the
main project objectives to be met while leaving open the possibility of returning to a spin-cast liner.
Figure 27. Test of the spin cast liner, with clear irregularities visible in the surface texture
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Optional Objective #2: Manufacture a custom pressure vessel (forward
closure, retaining rings, case) that can withstand the operating pressure
range of the motor with an appropriate factor of safety (2.0).
Ignition System Test
Test Overview
This test was meant to confirm that the custom-built ignition circuit was properly designed and built and
that it could reliably ignite a propellant batch without the addition of a pyrogen.
Purpose of Test
The purpose of this test was to verify electrical performance and ignition capability of the system,
particularly without a pyrogen
Feature(s) Evaluated
The circuit was expected to receive 600 mA, and all components (LEDs, switches, relay, etc…) were
expected to function properly in order to ignite the propellant.
Test Scope
The igniter was to be placed in contact with a propellant sample and initiated from a safe distance.
Test Plan
The ignition circuit, a 5g propellant sample, an ammeter, and safety goggles were required for completion
of this test. This test also required some familiarity with electrical testing and safe handling of energetic
materials. It was assumed that the propellant was properly prepared and dry, and that the circuit was
successfully built according to the full circuit schematic shown in Appendix 1H.
Acceptance Criteria
The circuit was to function properly to provide more than 600 mA to the electric match and ignite the
propellant.
Test Results and Evaluation
To prepare for the static fire test, the team briefly tested the ignition system of the motor disconnected
from the propellant. Initial results found a fault in the ignition battery connection which was then
replaced. After this adjustment, the ignition system worked as intended, lighting an electric match with
little to no ignition delay. The circuit successfully delivered more than 600 mA and ignited the propellant
samples on the second attempt. The test confirmed both the ignition circuit and the E-match were
sufficient for the static fire test.
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Load Cell Calibration Test
Test Overview
This test determined the calibration factor needed to convert load cell voltage readings to force
measurements.
Purpose of Test
The purpose of this test was to correlate voltage vs time and force vs time measurements in order to
calculate a calibration factor for the load cell in Newtons per Volt.
Feature(s) Evaluated
The linearity of both DAQ and Instron outputs were evaluated.
Test Scope
To attach the load cell to the Instron machine, it was necessary to design and manufacture a custom rig.
Once the custom rig was built, a linear loading force was applied by the Instron while voltage and force
readings were recorded.
Test Plan
This test required the following instruments: a 5960 Series Instron machine, a custom-built calibration rig,
Windaq software for voltage logging, Bluehill 3 for Instron data, and Excel for calibration analysis and
calculation. Experience with the Instron and Bluehill 3 was provided by Joshua King. Knowledge of DAQ
configuration and load cell wiring was required for load cell set up. Additionally, experience with the drill
press and vertical bandsaw were required for construction of the custom rig.
The results of this test relied on proper wiring and accuracy of the Intron’s load cell. These results
included voltage vs time and force vs time curves which in turn provided a N/V calibration factor.
Acceptance Criteria
A successful test would show a clear, linear relationship between voltage and force.
Test Results and Evaluation
This test was run twice, once with 100 ft insulted DAQ wire and once without. Both tests confirmed
linear behavior of the load cell with R2 values of one. Dividing the slope of the force-time curve in Figure
28 by the slope of the voltage-time curve in Figure 29 provided a calibration factor of 584.77 2.93 N/V.
±
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Figure 28. Calibration curve from Instron machine (Bluehill 3)
Figure 29. Calibration curve from DAQ (Windaq)
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Full-Scale Static Fire Test
Test Overview
The full assembly was placed in a test stand and fired down, while pressure and force data was collected.
Video evidence was also collected to aid in data analysis.
Purpose of Test
The purpose of this test was to ultimately validate the impulse requirement with empirical data. To this
end, the team aimed to measure the thrust and pressure produced by the motor over time and to then
integrate the thrust over the burn duration, giving the team the motor’s delivered impulse. This delivered
impulse could then be compared to both simulated values and the design requirements to determine if the
essential impulse objective was satisfied.
The team also aimed to measure the temperature at several points on the motor, verifying proper
functioning of the thermal liner in keeping the aluminum components under 200 ℃ (to avoid significant
reduction in strength). The case was videographed during the test to collect transient temperature data.
Feature(s) Evaluated
The static fire tests the motor's thrust and pressure profiles and overall impulse delivered during the firing
event. The pressure vessel’s external temperatures are also observed over time using maximum
temperature labels. A qualitative assessment of the exhaust plume is performed to evaluate nozzle
effectiveness throughout the burn.
Test Scope
The motor was securely mounted in a static test stand, with a load cell, pressure transducer, and
temperature indicator labels installed to measure thrust traces, pressure traces, and maximum
temperatures during the firing.
Test Plan
The static fire test took place in Pipe Creek, TX, on the Law family ranch. The team ordered a 2500 psi
pressure transducer and 500 kg load cell from Aerocon systems. A custom test stand, provided by the
sponsor, was modified to fit the motor. The detailed DAQ setup procedure is seen in Appendix 1F and the
stand is seen below in Figure 30. Additionally, the team had to design and manufacture a load cell
interface adapter, which was intended to allow both the load cell and pressure transducer to act on the
forward closure. The previously tested ignition system was also used in this test, allowing the team to
light the motor from the safe 300 foot clearance radius. The DAQ system was set to record data around
100 feet from the test site, far enough to ensure a failed test would damage more equipment than
absolutely necessary. The full test procedure for the test is written in full in Appendix 1G.
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Figure 30. Test stand as configured during the static fire test
The test involved one main assumption that being the load cell’s calibration curve. To ensure there was
little error involved here, the load cell was calibrated with the full length of the signal wire (the full 100
feet) to ensure wire resistance was accounted for.
Acceptance Criteria
For the motor to be accepted and for the test to be called a complete success, the motor must produce
enough thrust to meet the impulse goal (3000 to 5120 Ns). Additionally, no structural failures or abnormal
behaviors should occur during the static fire test that would affect the operation of the motor in flight.
Finally, all data should be successfully recorded by the various test apparatus, including pressure
transducer data, load cell data, and various camera angles and speeds.
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Test Results and Evaluation
Introduction
This test acquired all data needed to validate the impulse objective. Before analyzing any numerical data,
it was clear that the motor had not behaved exactly as predicted. The total burn time was 2.5 seconds,
significantly shorter than the expected 3.75 seconds predicted by OpenMotor in the earlier test. Once the
load cell data was processed, the team observed that the thrust delivered by the motor was significantly
higher than expected. The pressure transducer failed to record data, as it was impossible to verify the
transducer was operating correctly on the test stand, unlike the load cell. From the load cell data however,
it is possible to estimate the chamber pressure of the motor. From these values, it is clear that the chamber
pressure in the motor was significantly higher than expected. This pressure led to an increased burn rate,
which increased the thrust delivered by the motor.
Performance Parameters
To evaluate the performance of the motor, load cell data was processed into a usable thrust-time
relationship. We first imported the four seconds of relevant WinDAQ voltage-time relationship into
Microsoft Excel. This resulted in a data file with 20,000 data points, as the sampling rate was set to 5000
samples/second. We then used the previously calculated voltage-force conversion factor of 584.77 N/V to
calculate the force at each time step. The trapezoidal integration rule was then used to calculate the total
impulse of the burn, taking into account that each data point had a 0.2ms time step. This impulse can be
seen in Table 2. Before the test, the team measured the mass of propellant in the phenolic liner to be
2.132kg. This mass was then used to calculate the theoretical average exhaust velocity needed to generate
the previously calculated impulse with our measured propellant mass. This was done by dividing the mass
by the total impulse. This exhaust velocity could then be compared to the theoretical exhaust velocity
from the MATLAB nozzle test.
Table 2. Motor performance parameters
The exhaust velocity was then normalized to the acceleration due to gravity to calculate delivered specific
impulse. This specific impulse was determined to be 251.2 s, significantly higher than the 236.6 s
predicted by OpenMotor. This higher efficiency is likely due to several constructive factors. First, the
motor’s faster burning propellant led to a significantly higher pressure than intended. Higher pressures
lead to both higher combustion efficiency and exhaust velocity, which both are positively correlated to an
increase in efficiency. As described earlier, the nozzle was also eroding at such a rate that the increase in
the chamber pressure was matched by an increase in the expansion ratio of the nozzle, ensuring the nozzle
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fully developed the exhaust for as long as possible in the burn. The nozzle itself was also a more efficient
shape than the OpenMotor simulations were using, that being an optimized bell-shape instead of the
simplified conical approximation that we used for grain geometry design purposes.
This increased specific impulse led to the motor delivering more impulse than intended, ultimately
increasing the impulse beyond the L2 limit of 5120N-s. While this did technically put our motor outside
of the specifications, reducing the total impulse solely requires a shortening of the propellant by
approximately a 0.1 in in the conical section.
To determine how close to the theoretical maximum performance we had designed the motor, in other
words, our overall efficiency, we needed to first know the average chamber pressure during the burn. To
do this, we first assumed a nozzle efficiency, then used the delivered exhaust velocity to find the
isentropic exhaust velocity. This isentropic exhaust velocity was then divided by the sonic velocity of the
combustion products as they left the nozzle, as determined by the CEA program Rocket Propulsion
Analysis (RPA). This mach number was then taken as the end point in the iteration of our MATLAB
nozzle code, which determined a chamber pressure. This chamber pressure was then fed back into RPA,
which gave us new values for the ratio of specific heats and sonic velocity at the exhaust. This process
was repeated until the pressure converged. Once we had reached convergence, a new nozzle efficiency
was chosen, and the process repeated. From this iteration of nozzle efficiencies from 0.95 to 0.98, we
determined that the average chamber pressure was likely between 1600 and 2000 psi. Once the team had a
chamber pressure estimate, overall efficiency was determined from comparing the RPA derived
theoretical Isp and the delivered Isp. All of these values are seen in Table 1. This efficiency is quite high,
and decreases to a more realistic value if the chamber pressure was on the higher end of the possible
chamber pressure range.
RPA determined the reaction efficiency of the propellant to be 98.50% at 2000 psi. We took this value as
the true value, but it seems reasonable. This is due to the translucent nature of the plume, which does not
occur if large amounts of aluminum is still combusting in the nozzle. Figure 31 is a comparison of the
same propellant being burned at 400 psi and the team’s.
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Figure 31. Comparison of the Reliant Robin propellant being burned at 400 psi and ~1800 psi [4]
OpenMotor Simulation Comparisons
To determine a possible cause for the increased pressure than expected, we looked at OpenMotor
simulations of the burn. With the published burn rate values, the theoretical thrust curve is relatively short
and long, as seen in Figure 32.
Figure 32. Comparison between load cell measured thrust data and original OpenMotor simulation results
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Our theory for the increased pressure was a deviation from the theoretical burn rate exponent from
Saint-Robert’s Law. Several alterations to this value were performed, and the results simulated and
compared to the measured thrust curve. This comparison is seen in Figure 33.
Figure 33. Comparison between load cell measured thrust data and OpenMotor simulation results with
two modified burn rate exponent values
These burn rate exponent values were chosen due to the burn behavior at the first “peak,” seen at around
0.8 seconds in the measured thrust curve. Importantly, this peak is evidence that the motor burned as
expected, without a major deviation caused by the mechanical failure of the propellant grain. The
existence of this behavior is caused by the grain geometry of the propellant, with time position in the
course of the burn determined by the burn rate of the propellant. The burn rate exponents displayed in
Figure 33 are the two bounds of a reasonable placement of this peak, accounting for different durations of
the startup transient, a behavior which is not modeled by OpenMotor. The fact that the curve matches so
closely in terms of amplitude and duration indicates that a pressure dependent burn rate error was the
cause of the accelerated burning. These two burn rate exponent values were higher than the published data
by 8.8% and 6.3% respectively.
The team has considered two possible, but not mutually exclusive, causes for this increase. The first is the
incomplete mixing of the Oxamide burn rate suppressant into the propellant. Over time, lab humidity
caused the Oxamide to “clump,” making it difficult to effectively mix. During degassing, small clumps of
Oxamide were observed floating to the top of the batch, though the small quantities of the unmixed
oxamide led the team to not rule out other causes. The other possible factor is the extrapolation of
Saint-Robert's law to the higher pressures that the team designed the motor for. It is entirely possible that
due to limited data at higher pressures, the Reliant Robin propellant exhibits a slightly different empirical
relationship at higher pressures than at lower pressures. Note that the propellant was not pressurized to a
level close to possibly reaching a sharp slope break in the pressure-burn rate relationship.
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Nozzle Erosion and Expansion
The chamber pressure can also be qualitatively analyzed through the shape of the exhaust plume. In
Figure 34, the nozzle, which was designed to an average chamber pressure of 1250 psi, appears to be
optimally expanded the moment after the flow chokes. It is difficult to identify the exact point of
maximum chamber pressure due to ongoing nozzle erosion. Therefore, the point of maximum pressure
represented in the figure was determined to occur at the time of maximum thrust as recorded by the load
cell. At this peak pressure, the flow is clearly underexpanded, indicative of a chamber pressure higher
than the design pressure. This conclusion was further cemented by nozzle erosion having already widened
the exit diameter. At the end of the burn, the nozzle has eroded considerably, so, as the pressure decreases
toward the end of the burn the flow again appears to be optimally expanded. Around a quarter of a second
later, pressure and nozzle conditions are such that the flow is finally overexpanded before the motor
depressurizes entirely.
Figure 34. Static fire plum profile over burn time
(left to right: start of burn, 0.2 s; peak pressure, 0.8 s; 2.2 s; end of burn, 2.5 s)
Figure 35 shows the pre- and post-test views of the diverging section of the nozzle. Erosion at the nozzle
exit increased the exit diameter from 1.58” to 1.85”. Accounting for erosion at the throat, which increased
throat diameter from 0.50” to 0.54”, the nozzle’s area expansion ratio increased from 10.02 to 11.78. Two
observations here evidence a much higher chamber pressure than was designed for. First, the nozzle
eroded faster than expected, indicating significantly higher shear forces and heat transfer rates. Second,
even through the elevated erosion rate and expansion area ratio, the flow remained underexpanded for the
majority of the burn.
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Figure 35. Diverging section before (left) and after (right) static fire test
Figure 36 shows the pre- and post-test views of the converging section of the nozzle. The relatively minor
erosive at the throat, around an 8% increase in throat diameter, validates the team’s decision to use a
composite nozzle with graphite as the throat material. The thermal and machining advantages of phenolic
are well-complemented by the strength of graphite here.
Figure 36. Converging section before (left) and after (right) static fire test
As shown in the pictures on the right side of Figures 36 and 37, the perpendicular phenolic surface of the
nozzle formed a thin char layer, approximately 0.050” thick as it was exposed to the exhaust products
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head-on. Figure 37 additionally shows the widened throat profile with obvious deformation. Slag is also
seen to have accumulated around in and around the throat.
Figure 37. Nozzle throat (left) side profile of nozzle (right) after static fire test
Thermal Management
The thermal management of the motor was not overtly affected by these higher chamber pressures,
though. As shown in Figure 38, the phenolic liner developed eroded slightly, and a thin char layer is
present. The inside edge of the liner where it was in the nozzle remains relatively untouched, having
retained its original burnt orange color. This indicates that the O-ring served as an adequate seal for the
pressure vessel throughout the burn.
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Figure 38. Thermal liner after static fire test. Cross-shaped erosion pattern is visible
The temperature-indicating labels placed along the motor case demonstrated the effectiveness of the liner
well. The label placed near the nozzle, shown in Figure 39, should have experienced the highest
temperature increase due to the fact that the end of the motor experiences the highest throughput of the
combustion products, especially where adjacent to a finned propellant grain like in this motor. This is
reflected in the collected temperature data: the junction between the liner and the nozzle, past which there
is no insulation, had the greatest temperature increase, reaching between 93° and 121°C within the minute
after combustion ceased. The rest of the case never exceeded 66°C, and the entire motor was below 66°C
while it was pressurized. Since the motor exterior remained well below the glass transition temperature of
the case material, between 160° and 200° C for 6061-T6 aluminum, the liner did function as intended.
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Figure 39. Two temperature labels that activated several seconds after the test
The forward closure liner also functioned as intended, preventing the heat of the combustion from melting
the forward closure. A flaked char layer from the insulting disk is shown in Figure 40, where several
globules of aluminum solidified after the burn.
Figure 40. Forward closure liner char layer that separated during disassembly. Aluminum slag is visible
on the surface.
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Pressure Transducer Results
As previously mentioned, the pressure transducer did not output any data. This may have occurred due to
a number of reasons. As shown in Figure 41, the pressure transducer itself appeared fully intact after the
test. However if the thermal liner failed to protect the sensor from the high temperatures within the
chamber, it is feasible that the pressure sensor was fried by the high temperatures from the chamber. It is
more likely that failure was caused by improper wiring between the DAQ and pressure transducer. The
pressure transducer voltage regulator may have been fried as well. Despite failure of the pressure
transducer to record data, maximum chamber pressure was able to be calculated by analyzing the load cell
data and combining it with CEA as described earlier.
Figure 41. Pressure transducer as seen after static fire test
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Conclusions
This project met all essential objectives set forth in the Project Charter. As demonstrated in the analysis of
the static fire test, a total impulse of approximately 5250 N-s was achieved. This exceeds the impulse
range of 3000 to 5120 N-s allowed for an L2 motor and pushes our motor into the range of an L3 motor.
The specific impulse was higher than expected by approximately 10 seconds. The team was also able to
successfully mix and pour their own composite propellant. In fact, the team’s propellant had a density of
1640 kg/m³, exceeding the Reliant Robin propellant’s density by 6%. The nozzle was also successfully
designed and manufactured to achieve optimal efficiency. During the static fire, the nozzle showed
near-optimal expansion for the entirety of the burn by inadvertently matching the the erosion rate with the
increase in chamber pressure.
Of the two optional objectives, only one was fully met. The custom pressure vessel, including the forward
closure, retaining ring, and case were designed and built to handle a design pressure of 1200 psi with a
safety factor of 2.0. The team used a bolted pressure vessel and considered various failure modes. The
nozzle and forward closure were designed with internal safety factors higher than the 2.0 limit for the
case. The effectiveness of these designs was tested during the static fire test, which produced an
approximately 30-40% larger average chamber pressure than expected. Due to time constraints and
difficulties in mixing and casting procedures, the team was unable to implement a spin-cast thermal liner
for the full case. Though the team resorted to a commercially available phenolic liner for the case, they
did succeed in casting the forward closure insulator.
If this project were repeated, or given more time, the team would seek to make a few changes. First, the
team would have liked to modify the motor to be more manufacturable. During fabrication, the team
noticed that the drilling and tapping process was very time consuming and unreliable, so alternate
methods such as retaining clips or case threading would be considered. The team would also seek to
acquire direct pressure transducer readings in addition to the indirect calculations made from observing
the exhaust plume. To do this, the wiring to the DAQ would have to be reevaluated and functionality of
the voltage regulator would have to be confirmed. Furthermore, in order to empirically determine the
minimum safety factor, the team could perform a hydrostatic test to failure on the spent motor.
Additionally, as the motor performed well nearning 2000 psi, it would be possible to increase the design
pressure of the motor to the tested value, increasing delivered specific impulse, maintaining the derided
impulse of the motor while decreasing its weight. With lessons learned from the static fire, the nozzle
could be redesigned to take advantage of heightened erosion at these elevated chamber pressures and
temperatures, further improving the motor’s efficiency.
Overall, not only was this project a success in delivering on its primary objectives, it was successful
beyond expectations in allowing the senior design team to learn about the many facets of rocket motor
design. The project sponsor, the Trinity University Rocketry Club, is now well-equipped with the
resources to manufacture an L2 motor for their rocket in a well-documented and cost-effective way.
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Appendix 1. Operations Manual (Collection of Procedures)
Appendix 1A. Procedure for mixing of an HTPB-based Liner
Goal
The goal of this procedure is to provide instructions for researchers to safely mix, cure, and store a
composite liner.
Hazards
The following hazards are of concern for this project:
1. Ignition of oxidizer(s), fuel(s), and/or energetic material(s).
2. Exposure to hazardous materials.
3. Heating during propellant curing.
Care should be taken to minimize the risk of any of the above dangers. Materials that build up static
charge should be avoided during the mix procedure. After mixing, the propellant should be stored in a
secure location until needed. To avoid exposure to hazardous materials, appropriate PPE should be worn.
This includes, but is not limited to, appropriate, compatible gloves and safety glasses.
NOTE: This procedure is only to be performed by authorized personnel. Contact your supervisor
with any questions.
Formula:
13.00% Thermacels Ceramic Powder
5.50% Carbon Black
1.50% Kevlar Pulp
68.95% HTPB + Curative
11.00% IDP
0.05% Lecithin
1 drop / 100 g propellant PDMS
Density = 920kg/m^3
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Required Equipment
The following equipment is required for this process:
1. Small weigh boats for the solid powders
2. 1-2 large plastic cups.
3. Weighing scale.
4. Plastic spoon/other measuring device.
5. Compatible spatula.
6. Stand Mixer.
7. 3-4 plastic pipettes for measuring liquids.
8. Molding forms.
9. Vacuum chamber.
10. HTPB (E.W. 1234)
11. Lecithin
12. IDP
13. MDI (E.W. 172)
14. PDMS
15. Thermacels Ceramic Powder
16. Carbon Black
17. Kevlar pulp
Procedure
1. Ensure another person nearby knows what you are doing.
2. Measure required mass of Thermacels ceramic powder, carbon black, and kevlar pulp into weigh
boats. There should be a separate cup for each component. Record actual amount.
3. First by pouring, then by pipette, measure the required mass of HTPB into a cup. Record actual
amount. Tare scale.
4. Using a pipette, measure the proper amount of IDP into the cup. Record actual amount. Tare
scale.
5. Add required number of drops of PDMS into the cup
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6. Degas Binder x2
7. Add solids to one new plastic cup
8. Add ⅔ of the binder into the stand mixing bowl
9. Add remaining binder to the solids and pre-mix by hand for 5 min
10. Degas premixture x2
11. Add premix into stand mixing bowl and mix with mixer for 15 min
12. Degas mixture x2
13. Using a pipette, measure the proper amount of MDI curative into a separate plastic cup. Record
actual amount.
14. Add contents to stand mixer and mix on low speed for a further 5 minutes
15. Remove bowl from mixer and fill aluminum case with solid plug attached with contents of bowl
16. Bring the filled tube to the lathe and attach the hollow cap.
17. Affix tube with steady-rest, lubricate steady rest
18. Turn lathe on at low speed (~200rpm)
19. Let spin for 5 min
20. Power off lathe and move to high speed, lubricating steady rest as needed.
21. Let spin for 6-7 hours, or until the mixture is no longer tacky.
22. Let cure in fume hood for 2 days before removing plugs
Emergency Procedures
Scenario
Response
Fire
Extinguish fire with appropriate fire-fighting
equipment
Respiratory tract irritation
Remove person to fresh air. If person is not
breathing, administer artificial respiration.
Follow appropriate MSDS procedures for
component causing issues
Skin contact with propellant component(s)
Follow appropriate MSDS procedures
Eye contact with propellant component(s)
Follow appropriate MSDS procedures
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Appendix 1B. Procedure for mixing of an HTPB-based Propellant Grain
Goal
The goal of this procedure is to provide instructions for researchers to safely mix, cure, and store a
composite solid propellant.
Hazards
The following hazards are of concern for this project:
1. Ignition of oxidizer(s), fuel(s), and/or energetic material(s).
2. Exposure to hazardous materials.
3. Heating during propellant curing.
Care should be taken to minimize the risk of any of the above dangers. Materials that build up static
charge should be avoided during the mix procedure. After mixing, the propellant should be stored in a
secure location until needed. To avoid exposure to hazardous materials, appropriate PPE should be worn.
This includes, but is not limited to, appropriate, compatible gloves and safety glasses.
Formula
Redacted due to ITAR concerns
Procedure
1. Using a pipette, measure the required mass of HTPB into a large plastic cup. Record actual
amount. Tare scale.
2. Using a pipette, measure the proper amount of IDP into the large plastic cup. Record actual
amount. Tare scale.
3. Measure required mass of Lecithin into the small plastic cup. Record actual amount.
4. Measure required mass of Oxamide into the small plastic cup. Record actual amount. Crush
oxamide into fine powder
5. Add required number of drops of PDMS into the large plastic cup
6. Mix by hand for 5 min.
7. Degas mixture in vacuum chamber (our chamber only goes down to 0.04atm absolute, so we
cycled the vacuum three times)
8. Measure required mass of aluminum powder into a weigh boat. Record actual amount
9. Add aluminum powder into binder, mix until completely incorporated
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10. Measure the required mass of AP into a weigh boat. There should be a separate weigh boat for
each particle size. Record actual amount.
11. Add ⅓ of the 90μm AP to the large plastic cup
12. Mix until incorporated
13. Repeat steps 12 and 13 until all 90μm AP is incorporated
14. Add ⅓ of the 400μm AP to the large plastic cup
15. Mix until incorporated
16. Repeat steps 15 and 16 until all 400μm AP is incorporated
17. Mix the propellant for 15 minutes by hand
18. Degas mixture in vacuum chamber
19. Hold mixture under vacuum for 24-48 hours for the ammonia to be drawn out
20. Measure required amount of MDI into the large plastic cup and add to bowl
21. Mix the propellant for 10 minutes
22. Degas mixture in vacuum chamber for 15 min
23. Pour propellant into molds.
24. Put the filled molds in a secure, ventilated, dry location and allow the propellant to cure for 2-3
days.
25. Dispose of large and small plastic cups according to proper propellant disposal procedure.
26. Dispose of other waste through proper waste management procedure.
Emergency Procedures
Scenario
Response
Fire
Leave the room as fast as possible. Do not
attempt to fight a propellant fire
Respiratory tract irritation
Remove person to fresh air. If person is not
breathing, administer artificial respiration.
Follow appropriate MSDS procedures for
component causing issues
Skin contact with propellant component(s)
Follow appropriate MSDS procedures
Eye contact with propellant component(s)
Follow appropriate MSDS procedures
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Appendix 1C. Mixing Ratio Tables
Table C1. Binder Sample test
material (in order)
%
mass
units
HTPB
68.77
39.897
g
IDP
20.80
12.070
g
DEGAS ~ 5 min (until bubbling stops)
MDI
10.43
6.053
g
DEGAS ~ 10 min, agitate, 5 min
Total
125
58.020
g
Table C2. Liner Sample test
material (in order)
ideal mass
units
actual mass
units
HTPB
23.33
g
23.31
g
IDP
4.29
g
4.29
g
Lecithin
0.02
g
0.02
g
PDMS
1
drop
1
drop
Carbon black
2.15
g
2.15
g
TiO2 powder
5.07
g
5.07
g
Kevlar pulp
0.59
g
0.59
g
DEGAS ~ 5 min (or until bubbling stops)
MDI
3.54
g
3.60
g
DEGAS ~ 10 min, agitate, 5 min
Total
39.99
g
40.03
g
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Appendix 1D. Bell Shaped Nozzle Design
By: Simeon Gantt, Austin Parcel, Saif Saleh, Kailey Tubbs
Clear Previous Data
clear
clc
Given Parameters
P_ch = 1200 * 6894.75729; % chamber pressure [Pa]
P_atm = 101 * 10^3; % atmospheric pressure [Pa]
g = 1.198; % gamma (specific heat ratio) []
T_ch = 2977; % chamber temperature [K]
mw = 24.98; % molar mass [g/mol]
d_th = 0.0127; % diameter of throat [m]
d_in = 0.0651; % diameter of inlet [m]
Define Angle for Linear Converging Section
cone_angle = 130; % degrees
Define Length of Circular Converging Section
% Note: Actual length of the circular section is given
% by k + k*cosd(cone_angle/2)
k = 0.125; % [in]
Define Maximum Diverging Section Turning Angle
% Note: To achieve a pressure ratio of 1 with g = 1.198, the smallest
% maximum turning angle is 36.4 degrees
theta_maximum = 36.4; % [degrees]
Define Functions
% Prandtl-Meyer Function
PM_fun = @(M) sqrt((g + 1) / (g - 1)) .* atan(sqrt(((g - 1) / (g + 1)) ...
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.* (M.^2 - 1))) - atan(sqrt(M.^2 - 1));
% Subsonic Area Ratio Function
mach_fun_sub = @(M, A_r) (1 ./ M^2 .* (2 ./ (g + 1) .* (1 + ((g - 1) / 2) ...
.* M.^2)).^((g + 1) / ((g - 1))) - A_r^2);
% Supersonic Area Ratio Function
mach_fun_sup = @(M, A_ratio) 1 ./ M .* (2 ./ (g + 1) .* (1 + ((g - 1) / 2) ...
.* M.^2)).^((g + 1) / (2 * (g - 1))) - A_ratio;
Converging Section (Linear & Circular)
% Circular Section
t = 0.0254*k;
x_arc = (0:0.000001:(t + t*cosd(cone_angle/2)))'; % Length along
% circular section
r = t*sind(cone_angle/2)/(1-cosd(cone_angle/2)); % Radius of
% circular section
d_circ = 2*(r-sqrt( r^2 - (x_arc(end) - x_arc).^2)) + d_th; % Diameter
% along circular section
% Linear Section
L = (d_in - d_circ(1))/2/tand(cone_angle/2); % Length of linear section
x_cone = (0:0.000001:L)'; % Length along linear section
d = 2*(L-x_cone)*tand(cone_angle/2) + d_circ(1); % Diameter
% along linear section
% Total Converging Section
d_conv= [d; d_circ]; % Diameter along total converging section
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A_ratio = d_conv.^2/d_th^2;
x_conv = [x_cone; (x_cone(end)+ x_arc)]; % Length along total
% converging section
x_conv_max = x_conv(end); % Total converging section length
% Mach # along total converging section
M_conv = zeros(size(x_conv));
for i = 1:size(x_conv)
M_conv(i) = fzero(@(M) mach_fun_sub(M,A_ratio(i)),[0.000001 1]);
end
Diverging Section (Expanding)
% Initialize Variables
x = linspace(0, 0.5, 10000); % Discretize length along nozzle
d_expand = zeros(size(x)); % Initialize diameter array
M_expand = zeros(size(x)); % Initialize Mach array
theta_expand = zeros(size(x)); % Initialize turning angle array
A_ratio_expand = zeros(size(x)); % Initialize area ratio array
d_expand(1) = d_th+0.000000001; % Start with a small increment
% to avoid zero value
theta_max = pi/180 * theta_maximum; % [rad]
P_x = zeros(size(x)); % Initialize pressure along nozzle
% Iterate to compute Mach number, turning angle, and diameter
i = 1;
while theta_expand(i) < theta_max
i=i+1;
% Calculate Area Ratio
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A_ratio_expand(i-1) = (d_expand(i-1).^2) / d_th^2;
% Calculate Mach #
M_expand(i-1) = fzero(@(M_val) mach_fun_sup(M_val, ...
A_ratio_expand(i-1)), [1 5]);
% Calculate Turning Angle
theta_expand(i) = PM_fun(M_expand(i-1));
% Increment Diameter
d_increment_expand = 2 * (x(i) - x(i - 1)) .* tan(theta_expand(i));
d_expand(i) = d_expand(i - 1) + d_increment_expand; % Update diameter
end
x_expand_max = x(i); % Length of expanding section
d_expand_max = d_expand(i); % Final diameter of expanding section
P_x(1) = P_ch * (1 + ((g - 1) / 2) .* M_expand(i).^2)^(-g / (g - 1)); %
Pressure
% at end of expanding section
M_expand = M_expand(1:i-1); % Mach # along expanding section
d_expand = d_expand(1:i-1); % Diameter along expanding section
Diverging Section (Straightening)
% Initialize Variables
d_straight = zeros(size(x)); % Diameter along straightening section
d_straight(1) = d_expand_max; % Initial diameter of straightening section
A_ratio_straight = zeros(size(x)); % Area ratio along straightening section
M_straight = zeros(size(x)); % Mach # along straightening section
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theta_straight = zeros(size(x)); % Turning angle along straightening section
theta_straight(1) = theta_max; % Initial turning angle of straightening section
i = 1;
while P_x(i) >= P_atm
% Calculate Area Ratio
A_ratio_straight(i) = (d_straight(i).^2) / d_th^2;
% Calculate Mach #
M_straight(i) = fzero(@(M_val) mach_fun_sup(M_val, A_ratio_straight(i)), [1
5]);
% Calculate Turning Angle
theta_straight(i+1) = 2*theta_max - PM_fun(M_straight(i));
% Increment Diameter
d_increment_straight = 2 * (x(i+1) - x(i)) .*tan((theta_straight(i)));
d_straight(i+1) = d_straight(i) + d_increment_straight;
% Pressure along straightening section
P_x(i+1) = P_ch * (1 + ((g - 1) / 2) .* M_straight(i).^2)^(-g / (g - 1));
i = i+1;
end
x_straight_max = x(i); % Length of straightening section
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d_straight_max = d_straight(i); % Final diameter of straightening section
M_straight = M_straight(2:i-1); % Mach # along straightening section
d_straight = d_straight(2:i-1); % Diameter along straightening section
x_div_total = x_expand_max + x_straight_max; % Total length of diverging
section
x_total = x_conv_max + x_expand_max+x_straight_max; % Total length of nozzle
x_plot = linspace(0,x_div_total,size(M_expand,2)+size(M_straight,2)); % Length
along
% diverging section
Pressure Ratio Along Nozzle
P_x = P_ch * (1 + ((g - 1) / 2) .* [M_conv' M_expand M_straight].^2).^(-g / (g
- 1));
Display results
fprintf('Max Angle: %.4f degrees\n', theta_maximum); % Maximum angle [degrees]
Max Angle: 36.4000 degrees
fprintf(['Diameter at transition from expansion section to straightening
section: %.4f ' ...
'cm\n'], d_expand_max * 100); % Final expansion diameter [cm]
Diameter at transition from expansion section to straightening section: 1.8957 cm
fprintf('Diameter at nozzle exit: %.4f cm\n', d_straight_max ...
* 100); % Exit diameter [cm]
Diameter at nozzle exit: 4.0656 cm
fprintf('Converging Section Length: %.4f cm\n', x_conv_max ...
* 100); % Converging section length
Converging Section Length: 1.5392 cm
fprintf('Expanding Section Length: %.4f cm\n', x_expand_max ...
* 100); % Expansion section
Expanding Section Length: 1.4901 cm
% length [cm]
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fprintf('Straightening Section Length: %.4f cm\n', x_straight_max ...
* 100); % Straightening
Straightening Section Length: 8.4708 cm
% section length [cm]
fprintf('Total Diverging Section Length: %.4f cm\n', x_div_total ...
* 100); % Diverging section
Total Diverging Section Length: 9.9610 cm
% length [cm]
fprintf('Total Nozzle Length: %.4f cm\n', x_total ...
* 100); % Total nozzle length [cm]
Total Nozzle Length: 11.5002 cm
Plot results
% Mach Number Along Nozzle
figure;
plot([x_conv'*100, (100*x_conv(end) + x_plot*100)], [M_conv' M_expand
M_straight]);
xlabel('Length Along Nozzle (x) [cm]');
ylabel('Mach # [-]');
title('Mach Number Along Nozzle');
grid on;
% Pressure Ratio along Nozzle
figure;
plot([x_conv'*100, (100*x_conv(end) + x_plot*100)], P_x/P_atm);
xlabel('Length Along Nozzle (x) [cm]');
ylabel('Pressure Ratio (P_{exit}/P_{atm}) [-]');
title('Pressure Ratio Along Nozzle');
Final Project Report Custom Rocket Motor
May 7, 2025 Page 59 of 70
grid on;
% Nozzle Contour
figure;
hold on;
plot([100*x_conv' x_plot*100+100*x_conv(end)],100*[d_conv'/2 d_expand/2 ...
d_straight/2], 'b');
plot([100*x_conv' x_plot*100+100*x_conv(end)],-100*[d_conv'/2 d_expand/2 ...
d_straight/2], 'b');
xlabel('Length Along Nozzle (x) [cm]');
ylabel('Nozzle Radius [cm]');
title('Nozzle Contour');
grid on;
Final Project Report Custom Rocket Motor
May 7, 2025 Page 60 of 70
Appendix 1E. Procedure for Hydrostatic Pressure Testing of the Rocket
Motor Pressure Vessel
Objective: To safely perform a pressure test on a pressure vessel using water and compressed nitrogen
gas to ensure its integrity and functionality at its rated pressure of 1200 psi.
Materials and Equipment:
1. Pressure vessel to be tested
2. Water supply (3 liters for filling the vessel)
3. High-pressure nitrogen cylinder (min. 2000 psi)
4. High-pressure nitrogen regulator (up to 1800 psi)
5. Gas line and valve for connecting nitrogen to the vessel
6. Pressure relief valve (for overpressure protection at 2000 psi)
7. Bleed valve (for controlled pressure release)
8. Leak detection solution or soap solution (for low-pressure leak checks)
9. Personal protective equipment (PPE) – ANSI goggles, hearing protection
1. Pre-Test Preparation
Inspect all equipment to verify that it is in good working condition and rated for the required test
pressures with some safety factor.
Verify the Makerspace is empty, locked, and sign posted on the door.
Ensure test cell is clear of debris and test area is in clear view through the windows
Ensure appropriate PPE.
Review test specifications to verify the required test pressure (1.5 times the vessel's design
pressure of 1200 psi).
2. Fill the Pressure Vessel
Install forward closure and nozzle assembly (with throat blocker) on the vessel’s inlets and outlets
to ensure no water or gas can escape.
Fill the vessel completely with water through the hole for the gas fill inlet valve, ensuring that
there are no air pockets trapped inside.
Check for leaks during the filling process by inspecting vessel seams and fittings at atmospheric
pressure. If any leaks are found, resolve before proceeding.
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3. Install the Nitrogen Connection
Install the gas inlet valve into forward closure
Install a nitrogen gas line on the vessel’s gas inlet valve. Ensure all connections are secure.
Attach the high-pressure nitrogen regulator to the nitrogen cylinder and ensure it is set to reduce
pressure to the desired test pressure.
Check for leaks by applying a leak detection solution to all fittings and connections. Tighten or
replace components if necessary.
4. Hydrostatic Test
*Note: If leaks occur while pressurizing, quickly depressurize the vessel.*
Open the nitrogen regulator valve slowly to introduce nitrogen gas into the vessel. Gradually
increase pressure.
Stop the rise in pressure at approximately 100 psi, and call out when pressure is reached
Visually inspect the pressure vessel to ensure that no leaks are present, document seal locations
Continue opening the nitrogen regulator once the test cell is vacated. Call out every 100 psi
increment
Closure regulator when 1800psi is reached.
Maintain the target pressure for at least 30 seconds.
Monitor the vessel for signs of leaks or failure during this period without entering the test cell
Gradually open the bleed valve to release the nitrogen pressure, ensuring no residual pressure
remains in the system.
5. Post-Test Inspection
Visually inspect the vessel for signs of any damage, including cracks, bulging, or other
deformation.
Drain the water from the vessel if required, making sure it is done safely and without causing
damage to the vessel or surrounding area.
Check for any remaining leaks after depressurization by inspecting the vessel and connections
again.
This procedure was based on this manual by the MIT Rocket Team:
https://wikis.mit.edu/confluence/pages/viewpage.action?pageId=177799272
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Appendix 1F. DAQ Setup Procedure
1. The wiring sequence from test stand to DAQ is load cell→ insulated wire→ amplifier→ Channel
1 on DAQ
a. Wire according to Figure 1 and the numbering scheme on the stickers attached to the
wires
Figure 1: Load cell wiring
2. The wiring sequence from test stand to DAQ is pressure transducer→ circuit box→insulated
wire→Channel 3 on DAQ
a. Wire according to the numbering scheme on stickers attached to wires. Note that the
same insulated wire is used for both the load cell and pressure transducer.
3. Plug in Dataq DI-1100 to computer
4. Launch WinDaq dashboard
5. Select DI-1100
6. Click “Start WinDaq Software”
7. Go to Edit >> Enable Channels
8. Unselect all but channel 1 (Load Cell) and 3 (Pressure Transducer) click “OK”
9. When ready, go to File>>Record. Set recording time to one hour.
a. *Note: Hit Record before flipping switches AND ensure that computer will not sleep
during test.
b. Once static fire is complete, go to File>>Close
c. Save file as “Static Fire Test #-”
10. Go to your saved file, open it, and click on File>>Export as Excel File
11. In Excel, plot curve, calculate impulse, etc…
a. The calibration factor for the load cell is 584.77 [N/V] (see load cell calibration test)
b. The calibration factor for the pressure transducer is 555.56 [psi/V]
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Appendix 1G. Procedure for Static Fire
Trinity University - Customized Rocket Motor
Procedure for Static Fire
1. Pre-Test Preparation
Test Site:
This test will be held in Pipe Creek, TX.
The test apparatus will be set up in a location that is clear of debris and dry grasses / other
organic matter in its immediate vicinity.
Safety Clearance:
Ensure a minimum personnel distance of 300 feet [1].
Throughout this test, the designated safety officer will:
Read the procedure aloud, ensuring all steps are being followed
Be in charge of maintaining the 300 feet keep-out zone
Equipment Checklist:
Ratchet straps w/ carabiners (x4)
Steel stakes with loops (x4)
Tape measure
Ruler
Coils of wire (x2, 300 ft ea.)
Ignition system
Ignitors
Distance Measurement Wheel
Multimeter
Motor
Nozzle
Various wrenches
DAQ computer
Load cell interface adapter
Pressure transducer
Load cell and mount
Allen keys
O-ring Grease
First aid kit
Temperature strips
Safety glasses (x15)
Gloves for integration
Masking Tape
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Sandpaper
Cameras (x2)
Tripods (x2)
Paper copy of procedure (x2)
SD cards (x2)
Flash drive
Backup AA Batteries (x3)
Backup 9V Batteries (x3)
ABC Fire extinguisher (x2)
Water bottles
Lenses for cameras
Wiring diagrams and procedures for the DAQ
Cap for nozzle
Motor transport cap
Wire cutters / stripper
Test stand
Bolts for motor
Umbrellas
2. Preliminary Test Setup [1]
All persons should put on their eye protection
Spread water around the test site to minimize fire risk - buckets will be filled with water from the
Law family house
Concurrently, set up tents provided by the Law family to cover the test area while the motor is
being set up
Set up an additional tent approximately 100 ft away from the test site to serve as a DAQ control
location
Ensure that pictures have been taken of all components before proceeding.
Forward closure with pressure transducer
Nozzle before installation
Case with forward closure bolts in primary focus of cameras
Exposed propellant surface below transport cap. To take this picture, remove cap, take
picture, then ensure cap is re-installed before continuing
Attach the temperature indicating labels at specified locations on the motor case
One on the forward closure, one on the retaining ring, two on the aluminum case above
the junctions between liner and nozzle/pressure transducer, one in the middle of the case
Take photographs of the case with these installed
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Set up DAQ control computer at the DAQ control location, and unspool DAQ connection wire to
the test site
Set up pressure transducer:
Connect wiring between pressure transducer and its DAQ according to the requisite
procedure
Procedure: DAQ Setup
Run DAQ program to ensure that connection is good with pressure transducer
Set up load cell:
Connect wiring between the load cell and its DAQ Procedure: DAQ Setup
Run DAQ program to ensure that connection is good
Using the wrench, tighten/untighten the bolts of the test stand if necessary.
Spool out two wires a distance of 300 ft parallel to each other to the test control location.
Hit stakes into the ground (one on each corner of the test stand, 6ft away from each corner) with a
sledge hammer, with welded circles pointing towards the test stand.
Attach ratchet straps to the test stand and stakes (don’t tighten yet).
Set up the cameras at the appropriate distance.
Remove the red nozzle transport cap and install the motor’s nozzle after ensuring the o-ring is
properly lubricated.
Take pictures of the fully assembled motor, focusing on bolts, the nozzle, and forward closure.
Record any general notes regarding the assembly process onto the back of the procedure
document.
Place the nozzle cap onto the end of the nozzle.
Place the motor in the test stand with the nozzle directed upward.
Tighten the bolts on the motor clamps as needed to secure the motor.
Tighten the ratchet straps until the stand is snugly in place.
Set the red ignition box a few feet (the full distance of the ignitor wire, plus 3 ft extra) from the
motor.
Start recording on the cameras and ensure that the DAQ control computer is set to never sleep.
Send all spectators to the control location along with one member of the design team, send
another team member to the DAQ control location, and leave 2 team members at the test site.
Before connecting the white box to the other ends of the long wires, flip both switches and ensure
that both LEDs light up.
On the control side, connect the grey wires from the white box to the long wires.
Flip both switches and verify that a click is heard from the relay in the red box.
Disconnect the grey wires from the white box on the control side.
After removing its red cap, install the ignitor into the motor:
The tip should be placed at the forward end of the motor, as far in as possible.
Tape the wire to the case, ensuring the ignitor can no longer move.
Reinstall the red nozzle cap onto the motor with the ignitor installed
Clip the brown wires from the ignition box to the ignitor wires, ensuring clips are not touching.
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Take a good “before” picture of the complete test setup, visually verifying that the
ignitor is still taped as before. Test setup should be configured as seen to the right:
The person at the DAQ control location should commence recording on the DAQ
system, ensuring that data is being recorded and that the computer is set to not go
to sleep.
Retreat all persons to the control side of the ignition system.
Reattach the ignition wires to the white control box on the control side.
Ensure that all persons are wearing their eye protection, fire extinguishers are
easily accessible, and the range is clear.
Alert all persons that the test is commencing shortly.
Flip the first switch and alert all persons that the test is live.
Count down from 10 seconds and then flip the section switch.
4. Post-Test Actions [2]
Do not approach the motor until all smoke has dissipated from the motor.
If the motor has not ignited, disconnect the grey wires and approach the motor.
If the motor has ignited catastrophically, proceed to the recommended actions indicated
on the Risk Management Plan
Once the motor has fired, wait two minutes before approaching the site to allow residual gas to
clear. Only team members and the designated safety officer should approach at this point.
Do not touch any components until sufficient time has elapsed; 5 minutes is sufficient.
Take a good “after” picture of the test
Begin collecting the test setup, including spooling the wire and saving the DAQ data.
Inspect the motor casing, nozzle, and ignitor for immediately visible signs of damage.
Save all relevant data to team google drive or place on redundant physical drive
Pressure and thrust data
Videos of exhaust plume
Pictures
Seal end of nozzle with masking tape for transport
Restore the test site to its original condition.
Rev. 4/28/2025
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Appendix 1H. Ignition Circuit Documentation
Figure H1. Diagram of ignition circuit
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Appendix 2. Parts List
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References (IEEE)
[1] Tripoli Rocketry Association, "Tripoli Safety Code," [Online]. Available:
https://www.tripoli.org/safetycode. [Accessed: 01 Apr, 2025].
[2] J. D. Schiavo and J. Benke, "Hydrostatic Test & Static Fires," MIT Rocket Team Wiki, Jun. 15, 2023.
[Online]. Available: https://wikis.mit.edu/confluence/pages/viewpage.action?pageId=177799272.
[Accessed: Feb. 2, 2025].
[3] Hamilton, R. Scott, et. al., “Solid propellant bonding agents and methods for their use,”
US9181140B1, Dec. 30, 1993. Available:
https://patents.google.com/patent/US9181140B1/en#:~:text=Tepanol%20also%20electrostatically%20coo
rdinates%20with,particles%20within%20the%20propellant%20matrix, [Accessed: May 04, 2025]
[4] Harry Amadeo, “Reliant Robin 54/1200 Firing #1 — J350,” YouTube, Mar. 12, 2020.
https://www.youtube.com/watch?v=smL0fXx0gtY&list=PLxOd_pKlpu5RuS-f4ZBsnsep276XuoSdV&in
dex=1 [Accessed May 05, 2025].
[5] Sennott, Ausin, “Half Cat Sim,” Half Cat Rocketry, 2019. https://www.halfcatrocketry.com/halfcatsim
Final Project Report Custom Rocket Motor
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