Hybrid Rocket Motor Final Report

Design and Testing of a Hybrid Rocket Motor

Mech581a4 Final Project Spring 2015

Group 1: James Duvall, Patrick Harvey, Ian May, Kevin Westhoff

1. Background and Literature Review

1.1. Introduction to Hybrid Rocket Motors A rocket engine is most simply described as a propulsion device which ejects stored mass to

generate thrust—capitalizing on the conservation of momentum described by Newton’s Third

Law. Most rockets seek to add as much stored energy as possible in the propellants in order to

increase the effective exhaust velocity and thus improve performance. There are many different

energy addition mechanisms which can be used, but by far the most common is chemical

combustion. Chemical rockets utilize an oxidizer and a fuel to generate a large amount of thermal

energy which is then converted to kinetic energy through a nozzle to generate thrust.

Chemical rocket motors can be divided into three main categories: liquid, solid and hybrid. Liquid

motors, as the name would suggest, uses both a liquid oxidizer and fuel (or just a liquid fuel for

monopropellant systems). Liquid motors can be throttled, shut down, and reignited and have the

best overall specific impulse performance, but they often require significant infrastructure to

manage the liquid propellants. This often includes heavy turbo pumps to supply the required mass

flow rates of the propellants and large, insulated storage tanks to store the propellants which are

often cryogenic. Conversely, solid rocket motors are extremely simple and require none of the

infrastructure of liquid motors. The oxidizer and fuel are mixed into a single propellant grain

which, once ignited, provide the required thrust. Solid motors are also storable—another advantage

cryogenic liquid propellants cannot compete with. However, solid motors cannot be throttled or

shut off and because the oxidant is already present in the fuel grain, it can be unintentionally

ignited.

Hybrid rocket motors are exactly what the name suggests: a combination of liquid and solid rocket

motors. Hybrid motors combine a solid fuel grain with a liquid or gaseous oxidizer. The flow rate

of the oxidizer can be controlled allowing a hybrid motor to be throttled, shut down and even

reignited. The use of a solid fuel grain simplifies the infrastructure by eliminating any need for

turbo pumps and valves for the fuel. However, the solid fuel grain typically complicates the fuel-

oxidizer mixing process. For large hybrid motors, this necessitates careful design of the oxidizer

injector geometry and the shape of the port casted in the fuel grain where oxidizer flows. Proper

injector and port shape designs ensure uniform regression of the fuel grain during burn and

predictable performance. The fuel grain for hybrid motors is also significantly safer than solid

motors because the oxidizer is not stored within the fuel, meaning that it cannot unintentionally

ignite.

Mech581a4 Final Project Spring 2015 Group 1

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1.2. Recent Uses of Hybrids While the military primarily uses solid rocket motors because of their simplicity and storability

and NASA uses liquid rocket motors because of their high performance, hybrid rocket motors are

favored by universities, private companies, and rocket enthusiasts because of their safety and low

costs. The use of hybrid rocket motors has increased dramatically in the past decade driven

primarily by the growth in private space companies. Before 2004, there was only one flight-

production use of a hybrid motor in a supersonic target drone for the military [2]. Today, hybrids

are seeing a much wider range of uses.

To date, three different companies have tried to develop a hybrid-powered manned space vehicle:

Copenhagen Suborbital, The Spaceship Company (on behalf of Virgin Galactic), and Sierra

Nevada. Copenhagen Suborbital, a non-profit Danish company, developed a nitrous oxide/

polyurethane hybrid engine that produced 15,000 lbf of thrust [3]. The Spaceship Company is

currently developing the suborbital space plane SpaceShipTwo, the successor to the X-Prize-

winning SpaceShipOne. The motor powering it (dubbed RocketMotorTwo) uses nitrous

oxide/Hydroxyl-terminated Polybutadiene (HTPB) to generate up to 60,000 lbf of thrust which

can propel the spacecraft to speeds of up to Mach 3.5 and an altitude of over 60 miles [4]. Finally,

the Dream Chaser developed by Sierra Nevada as a replacement to the Space Shuttle, used two

hybrid engines (nitrous oxide/HTPB) to generate over 100,000 lbf of thrust and carry the spacecraft

into orbit [5]. However, both Copenhagen Suborbital and Sierra Nevada have since switched to

liquid motors because of some unsolved combustion stability issues and the need to simplify the

refueling process.

Hybrid motors are also finding their way into automotive applications. The team behind the

Bloodhound rocket car is using a HTP/HTPB hybrid engine to generate over 27,500 lbf of thrust.

An internal combustion engine and jet engine will drive the car at lower speeds, but the rocket

engine will be used to push the car to speeds over 1000 mph [6].

Hybrid rocket motors are still in the early stages of their development. Many hybrid motors have

been replaced with liquid motors, but this merely reflects a reluctance to invest the time and energy

needed to better understand and perfect the performance of hybrid engines. The American Rocket

Company has successfully tested a 250,000 lbf thrust liquid oxygen/polybutadiene hybrid engine,

the most powerful ever produced [2]. They found that the primary issue with large scale hybrid

engines is maintaining combustion stability within the fuel grain, which is signified by large

Figure 1: A schematic of a hybrid rocket engine with a tank of either liquid or gaseous oxidizer which is injected

into the fuel grain to sustain combustion. The flow rate of oxidizer can be controlled allowing the engine to be

throttled or shut off completely at any time. [1]


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oscillating spikes in thrust. Already some countermeasures and redesigned components have

proven effective and work continues to improve our understanding of hybrid engines. As the

success of SpaceShipOne shows, the benefits of hybrid rockets should not be overlooked and as

long as the research into understanding and optimizing hybrid engines continue, they will likely

play a sizeable role in the future of commercialized space travel.

1.3. Bench-Scale Motor Testing Like solid motors, hybrid propellant combinations must be experimentally tested to determine the

fit parameters for the empirical expression that describes the fuel regression rate. Conventionally

the correlations have the form shown in equation (1), where �̇� is the instantaneous and spatially

averaged fuel surface regression rate and �̇�𝑂𝑥 is the measured oxidizer mass flux. Temperature

coefficient 𝑎 and pressure exponent 𝑛 are derived for a given fuel/oxidizer combination from test

results.

�̇� = 𝑎 �̇�𝑂𝑥𝑛

(1)

In general, results from small scale hybrid motorss show good agreement with those from larger

scale hybrids and so the majority of fuel regression tests are performed on smaller test bench scale

engines because they are both safer and cheaper. As such, a number of bench top test firings have

been conducted. These tests usually result in computation of 𝑎 and 𝑛 for the fuel combination used

and a reporting of the chamber pressure and thrust observed. This data is useful in providing initial

boundary conditions for designing a hybrid rocket motor.

The regression rate values for HTPB were found by Shanks and Hudson [7]. During their study, a

maximum chamber pressure of 500 psia with an oxidizer flow rate between 2.5 and 10 lb min-1

were observed. From 24 firings, the regression rate temperature coefficient and pressure exponent

were found to be 𝑎=0.131and 𝑛=0.674. These values can be used in equation (1) to predict the

fuel regression rate for any HTBP hybrid geometry given an oxidizer flow rate.

Greiner and Frederick [8] tested HTPB with gaseous oxygen to analyze combustion stability. The

tests were run at an oxidizer mass flux rates of 0.378 lbm sec-1 in-2 for HTPB with a mean chamber

pressure of 460 psia. However, the chamber pressure was observed to oscillate with a peak to peak

amplitude of up to 100 psi. It was found that longer mixing chambers resulted in much smaller

pressure oscillations. They believed that the pressure oscillations were from vortex shedding of

the boundary layer on the fuel grain in the area between the fuel grain and the nozzle. They

recommended that the end of the fuel grain be butted up against the nozzle so as to eliminate this

effect.

2. Objectives The primary objective of this project is to apply existing hybrid rocket theory to design, build and

test a hybrid rocket motor. A fuel is selected and thermodynamically characterized in order to

develop an analytical model which predicts the performance of the rocket motor and provides

means to optimize the fuel grain and nozzle geometry. The motor is then manufactured and tested


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from supplied materials. Data collected from the testing allows for comparison of observed

performance to that predicted by the analytical model.

3. Constraints The design constraints for the problem are as follows:

Oxidizer: Gaseous Oxygen (GOx)

Maximum Chamber Pressure: 165 psia

Maximum GOx Flow Rate: 500 SLPM

Minimum Initial Thrust: 8 lbf

Fuel Grain Outer Diameter: 1.175 in

Maximum Fuel Grain Length: 12 in

Nozzle Exit Pressure: Optimized for ambient pressure (12.27 psi in Fort Collins)

The majority of these constraints are determined based on the performance limitations of the test

stand and the safety of the participants. The minimum thrust of 8 lbf is selected so that some design

and optimization work would be required in order to get a satisfactory hybrid rocket motor design.

4. Propellant Choice The following four propellants were selected for investigation:

HTPB

85% HTPB, 15% Aluminum by Weight %

Paraffin

50% HTPB, 50% Paraffin by Weight %

HTPB is a very common hybrid fuel and there is a lot of data available on its regression rate.

Aluminum particles can be added in order to increase the energy density of the fuel. Several recent

studies have looked at paraffin as a fuel for hybrids in order to try to produce higher thrusts. A

50/50 HTPB/paraffin combination was also considered in order to try to reduce paraffin’s burn

rate so as to get a longer burn time. All of these fuels were analyzed (as presented in sections 5

and 6) and compared in order to determine which fuel would give the overall best performance.

Ultimately 85% HTPB 15% Aluminum fuel was selected due to high predicted performance and

availability of correlations in the literature.

5. Thermodynamic Calculations Thermodynamic calculations were critical for evaluating the performance of each investigated

propellant combination. As a hybrid rocket burns, the surface area of the fuel grain changes. For

an assumed constant oxidizer flow rate, the oxidizer to fuel ratio changes throughout the duration

of the burn. Therefore, the chamber combustion temperature, ratio of specific heats (𝛾), molecular

weight of the exhaust products, and the characteristic exhaust velocity (C*) were all calculated

over a range of oxidizer to fuel ratios. This information was then used in the design calculations

in section 6.


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The properties of each of the four propellant choices were calculated using the NASA Chemical

Equilibrium with Applications (CEA) program. The following figures illustrate the

thermodynamic performance predictions for HTPB:Al (85:15 by wt%). The input file for the CEA

program used to produce these figures is shown below:

problem rocket equilibrium o/f=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.95,1.0,1.05, 1.1,1.15,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0 p,psia=165.00 supar=2.75 reactants fuel HTPB C 7.337 H 10.982 O .058 wt%=85 h,cal=-2970.00 t(k)=298.15 fuel = AL wt%=15 t(k)=298.15 oxid = O2 wt% 100. t(k)=298.15 output siunits end

Figure 2 shows plots various thermodynamic and performance properties of the fuel combination.

The ratio of specific heats and molecular weight of the equilibrium products are taken at the nozzle

throat. Figure shows the equilibrium species present.

Figure 2: Plots of the Weight of Chamber Products (top left), Ratio of Specific Heats of Exhaust Products (top right),

Adiabatic Chamber Temperature (bottom left) and the Characteristic Exhaust Velocity, C* (bottom right) for HTPB:Al (85:15 by wt. %) with GOx


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Figure 3: Mole Fractions of All Equilibrium Species for HTPB:Al (85:15 by wt.%) with GOx

The adiabatic chamber temperature increases with increasing O/F ratio. The rate of increase

appears to taper significantly at an O/F ratio of 1.75. The ratio of specific heats has a significant

spike in the O/F range of 1.0-1.1. Once the O/F ratio is 1.6, the ratio of specific heats is relatively

constant. The molecular weight of the equilibrium products first decreases linearly in the O/F range

0.1-1.0, then increases linearly in the O/F range 1.0-2.0. The effective exhaust velocity is parabolic

with O/F ratio in two regimes, reaching a maximum at an O/F ratio of 1.4. The equilibrium species

are composed primarily of H2 and CO when the O/F is in the range of 1-1.1. As O/F is increased

past 1.1 to 2, CO2, H2O, OH-, H+, and Al2O3 are seen with significant mole fractions in addition to

that of H2 and CO in the predicted equilibrium species.

6. Design Calculations In order to model the performance of the hybrid engine, one dimensional flow is assumed in order

to simplify calculations. Wright et al. [9] observed pulsating and swirling flow fields in the

combustion chamber of their hybrid motor and so concluded that one dimensional flow was not a

valid assumption. However, when a similar scale rocket design project was conducted in the past,

one dimensional flow was assumed and the test data collected showed reasonable agreement with

the model [10]. Therefore, one dimensional flow is deemed sufficient for the design needs of this

project.

A discretized, time step model was developed, centering on use of correlations from the literature

in the form of equation (1). The values for a and n for each fuel are taken from previous


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experiments and are summarized in Table 1. Each correlation specified the units required for

oxidizer mass flux (�̇�𝑂𝑥) and reported for fuel surface regression rate (�̇�). The oxidizer mass flux

(�̇�𝑜𝑥) was calculated by dividing the known oxidizer flow rate of 500 SLPM by the port area of

the fuel, taking care to convert to the required units per the correlation under consideration. The

port area increases as the fuel is consumed, leading to a decreasing oxidizer mass flux as the burn

progresses.

Table 1: A summary of a and n values used for each fuel

Fuel (with GOx) a n source

HTPB

0.104 0.681

85% HTPB, 15% Al by Weight %

0.145 0.775 [11]

Paraffin

0.488 0.620 [12]

50% HTPB, 50% Paraffin by Weight %

0.1146 0.5036 [13]

First, the instantaneous fuel surface regression rate (�̇�) is calculated from equation (1). The mass

flow rate of the fuel is calculated from the fuel surface regression rate (�̇�) and the burn area (𝐴𝑏),

as shown in equation (2).

�̇�𝑓 = �̇�𝜌𝑓𝐴𝑏

(2)

The mass flow rate of the oxidizer was assumed to be constant and the oxidizer to fuel (O/F) ratio

was then calculated for each time step as �̇�𝑂𝑥/�̇�𝑓. The thermodynamic properties 𝛾 and 𝐶∗ were

calculated from polynomial fits to the output of the NASA CEA code, as functions of O/F. The

chamber pressure was then calculated using the characteristic exhaust velocity (𝐶∗), the total mass

flow rate, the area of the throat (𝐴𝑡), and the back pressure (𝑃𝑏), which is typically ambient

pressure.

𝑃𝑐 =𝐶∗(�̇�𝑓 + �̇�𝑂𝑥)

𝐴𝑡+ 𝑃𝑏

(3)

The addition of the back pressure is not specified in the equations presented in class, but was found

to be necessary during later exploration of a variable oxidizer flow rate model. When low flow

rates are encountered, equation (3) will predict values less than ambient, indicating that it actually

calculates a gage pressure, not an absolute pressure. The exit pressure (𝑃𝑒) is calculated from

equation (4) where 𝐴𝑒 is the exit area of the nozzle and 𝐴𝑡 is the throat area.


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𝐴𝑒

𝐴𝑡=

√𝛾 (2

𝛾 + 1)

𝛾+12(𝛾−1)

(𝑃𝑒

𝑃𝑐)

1𝛾

√2𝛾

𝛾 − 1[1 − (

𝑃𝑒

𝑃𝑐)

𝛾−1𝛾

]

(4)

The thrust coefficient (𝐶𝐹) could then be found from equation (5).

𝐶𝐹 = √𝛾 (2

𝛾 + 1)

𝛾+12(𝛾−1)

√2𝛾

𝛾 − 1[1 − (

𝑃𝑒

𝑃𝑐)

𝛾−1𝛾

] + (𝑃𝑒

𝑃𝑐−

𝑃𝑏

𝑃𝑐)

𝐴𝑒

𝐴𝑡

(5)

The predicted thrust (𝐹) and specific impulse (𝐼𝑠𝑝) for the rocket were calculated as follows

could then be calculated via equations

𝐹 = 𝐶∗(�̇�𝑓 + �̇�𝑂𝑥)𝐶𝐹

(6)

𝐼𝑠𝑝 =𝐶∗𝐶𝐹

𝑔0

(7)

The port area (𝐴𝑝) and burn area (𝐴𝑏) were then calculated from knowledge of the fuel surface

regression rate (�̇�) and the iteration continued. The nozzle and fuel grain geometry for each fuel

type was modified until the best performance was seen. The optimized design parameters and the

initial performance predictions for each propellant are summarized in Table 2 and Table 3. The

predicted performance over the total burn for each fuel type is summarized in

Figure 4.

Table 2: Optimized Design Parameters of Investigated Propellants with GOx

Table 3: Initial Performance Predictions of Investigated Propellants with GOx


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Figure 4: Plots of the Predicted Characteristic Exhaust Velocity, C*, (top left), Predicted Chamber Pressure (top right),

Predicted Oxidizer to Fuel Ratio (middle left), Predicted Thrust (middle right) and Predicted Specific Impulse (bottom left) of

the four investigated propellants with GOx


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It was found that while pure paraffin provided the highest thrust, it had both the fastest burn time

and the lowest specific impulse. HTPB showed reasonably good performance all around but the

HTPB-Paraffin combination provided only a small improvement in thrust at the cost of a large

drop in specific impulse. Overall, HTPB-Al was chosen as the optimal fuel. It showed the highest

predicted specific impulse while still maintaining a fairly large thrust and relatively long burn time.

7. Detailed Design Drawings The CAD design was done using SolidWorks. O-Ring grooves were dimensioned according to the

Parker Handbook for male static radial o-ring seals. The snap ring groove was dimensioned

according to the specifications provided by McMaster Carr. Figure 5 shows an exploded view of

the motor assembly, while Figure 6 shows a drawing for the motor casing and Figure 7 shows a

drawing for the nozzle.

Figure 5: Exploded Rocket Motor Assembly


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Figure 6: Drawing of Motor Casing


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Figure 7: Drawing of Nozzle


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Figure 8: Picture 1: HTPB:Al Fuel Grain in Casting Tube; Picture 2: Motor Casing with Fuel Grain Inserted; Picture 3: Looking Down Motor Assembly from Bulkhead Side; Picture 4: Exhaust End of Motor Assembly; Picture 5: Nozzle with O-Rings

Figure 8 shows pictures taken of the machined components, casted fuel grain, as well as the rocket

motor assembly before the test was performed. The two O-rings seen in Picture 5 of Figure 8

provided adequate sealing of the combustion chamber. The snap ring seen in Picture 4 of Figure 8

kept the assembly in place within the motor casing during the burn.

8. Experimental Setup The hybrid rocket motor is instrumented to measure chamber pressure, oxidizer mass flow rate,

and thrust. This instrumentation and all control components is integrated onto a single rocket motor

test stand consisting of several critical components as detailed below and in Figure 9:

1. Motor

2. Pressurized oxygen and nitrogen bottles

3. GOx volumetric flow controller

4. Chamber pressure transducer

5. Thrust strain gauge

6. Bulkhead and igniter assembly

7. LabView data acquisition software

The rocket motor is threaded into the bulkhead and anchored to a linear track. The bulkhead serves

as the connection between the motor and the oxidizer supply, holds a tap for the pressure transducer

used to measure the chamber pressure, and finally contains the igniter assembly. The igniter uses

two automotive sparkplugs to generate a spark across a tuft of steel wool. The linear track holds

the motor fixed to the test stand while allowing motion in only one direction. The strain gauge is

affixed to one end of this track such that the thrust of the motor is only countered there for its

measurement. Upstream of the bulkhead lies the volumetric flow controller. The design constraints

include a maximum oxidizer flow rate of 500 SLPM. As such the mass flow controller intakes the

pressurized oxidizer supply, measures the obtained flow rate, and actuates a solenoidal gate valve

accordingly. For the duration of the burn LabView is utilized to record traces of the chamber

pressure, oxidizer flow rate, and strain of the linear track bumper assembly. These recorded values

are easily converted to the desired measurements of thrust [lbf], chamber pressure [psia], and


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oxidizer flow rate [SLPM]. Finally, the burn is terminated by cutting off the oxidizer supply and

forcing nitrogen through the piping system, bulkhead, and motor.

Figure 9: The rocket test stand with the seven major components labeled

9. Expected Experimental Results and Conclusions The measured quantities, instantaneous chamber pressure (measured in units of gauge pressure),

instantaneous oxygen mass flow rate, instantaneous thrust, and the total mass of fuel consumed,

are easily converted into the forms reported in the models for comparison. The chamber pressure

needs only to be shifted by the standard accepted atmospheric pressure in Fort Collins, and the

total mass of fuel burned divided by the burn time to yield an approximate fuel mass flow rate.

With these transformed quantities in hand, comparison to the model becomes simple as is

illustrated in section 11.

10. Experimental Results During the test there are two primary detriments to the achievable performance. The pressure of

the supplied oxidizer was limited to ~115 psia rather than the design value of 165 psia thereby

limiting the obtainable thrust. Secondarily, the mass flow rate peaked at 400 SLPM as compared

to the design criteria of 500 SLPM. This reduction in oxygen flow rate led to a substantially lower

fuel regression rate thus limiting the total mass flow rate, lowering the specific impulse, and further

reducing the thrust.


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Figure 10: Test Firing of HTPB:Al (85:15 by wt. %) Hybrid Rocket Motor with GOx

Figure 11: Plots of the Measured Chamber Pressure (Adjusted for 12.27 psi Atmosphere in Fort Collins) (top left), Measured

Oxygen Volumetric Flow Rate (top right) and the Measured Thrust (bottom)


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Additionally, photos were taken of the fuel grain after burn (Figure 12). Diametric measurements

were taken at both the bulkhead and exhaust sides of the spent fuel grain. There was no significant

difference between the amount of fuel grain remaining in the bulkhead side compared to the

exhaust side based off of the caliper measurements. This provides some validation to the

assumption that a constant fuel regression rate for the entire fuel grain is a decent approximation.

Figure 12: Remaining Fuel, Casting Tube, and Phenolic Tube after Burn (Bulkhead Side).

When the rocket motor was disassembled after burn, there appeared to be significant Al2O3

accumulation in the converging section of the nozzle (Figure 13). There also appeared to be erosion

that occurred at the throat as evidenced by grooves that were carved into the graphite. This induced

several immediate sources of error in the rocket motor test. First, the amount of Al2O3

accumulation indicates that two-phase flow was present in the nozzle. This is significant because

the solid Al2O3 particles do not move with the same effective velocity as the exhaust gases and

cause the performance of the rocket to decrease. Second, the throat area was not constant through

the burn. The throat area is a critical parameter in the model as it dictates the chamber pressure

and mass flow rate of the combusted fuel and oxidizer. The model assumes the throat area remains

constant; by inspection of the nozzle post burn, it appears erosion of the throat did occur.


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Figure 13: Al2O3 Accumulation and Erosion Observed in Converging Section of Nozzle after Burn


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11. Comparison of Experimental Results with Model Due to limitations in the experimental setup, the oxygen flow rate never reached 500 SLPM.

However, the GOx flow rate of 500 SLPM was used in all of the initial performance calculations

to inform the decision of propellant selection. Therefore, the model with a 500 SLPM GOx flow

rate over-predicted the performance compared to the performance measured during the test. To

account for the reduced GOx flow rate, the model was adjusted to have a constant GOx flow rate

of 350 SLPM, which is more consistent with the measured flow rate. Additionally, the NASA CEA

code was used assuming a chamber pressure of 118 psia to account for the lower chamber pressure

observed during the test. Coupling the lower oxygen flow rate and lower chamber pressure, the

following figures were generated.

Figure 14: Plots of the Measured and Predicted Chamber Pressure (top left), Thrust (top right) and Thrust Coefficient with a

Constant GOx Model

Comparing the results of the constant GOx flow rate model versus the experimental results shows

several discrepancies. Most notably, the transient portion of the chamber pressure, thrust, and

thrust coefficient is not captured in the model. This is due to the constant GOx flow rate that the

model assumes is present at time zero of the test. The predicted chamber pressure decreases slowly

with time; this phenomena is not seen in the measured data. The discrepancy seen in the model is


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due to the mass flow rate of the fuel slowing as the port area increases with burn time. This would

suggest that the a and n values for the fuel regression rate equation are not an exact fit for the

rocket size and oxygen mass flux seen in this experiment.

The predicted thrust of the constant GOx model is much greater than the strain gauge measured.

Again, this is due primarily to the assumption of a constant GOx flow rate. The measured thrust

did have a linearly decreasing trend once the chamber pressure transient settled which was readily

evident in the predicted thrust of the model.

The predicted thrust coefficient is much greater than what was determined from the measured data.

The nozzle was designed for very specific chamber and atmospheric conditions. Operating at the

expected conditions of 165 psia chamber pressure, the nozzle would have expanded the flow to

exactly atmospheric pressure. The expansion in the diverging section of the nozzle would

contribute an increase in the overall thrust of the motor. However, the chamber pressure was much

lower (~118 psia once the transient settled) meaning that for the same flow rate through the nozzle,

assuming choked flow at the throat for both 118 and 165 psia conditions, the flow was over-

expanded. This causes the nozzle correction factor (Δ𝐶𝐹) to be negative to account for the over-

expansion seen in the diverging portion of the nozzle. Although no oblique shockwaves were

observed during the test fire, the measured thrust coefficient data would suggest otherwise.

Table 4 contains the performance comparisons of the constant GOx model and the measured data.

For calculations that involved numerical integration, the Trapezoidal Rule was applied.

Table 4: Performance Comparisons Between Measured Data and Constant GOx Model

The low thrust coefficient efficiency is attributed primarily to the lower-than-expected chamber

pressure causing the nozzle to over-expand the flow. The total impulse of the model with constant

GOx is much higher than what was measured. This is due to the instantaneous and constant

oxidizer flow rate the model assumes which causes the thrust to immediately jump to 7 lbf and

decay minimally through the burn. The average measured specific impulse is much less than the

model predicts. This is due to constant oxidizer flow rate assumptions of the model, but is also due

to the inaccuracy of approximating the mass flow rate of the HTPB-Al fuel grain from the

measured data. The mass flow rate was determined by measuring the mass of the fuel grain before

and after the burn and dividing the difference by the total burn time. The issue with this approach

is that the burn time observed in the measured data (8.8 seconds) is less than the amount of burn

time seen in the videos of the rocket test (~10.5 seconds). This same source of error propagates to

the calculation of the average effective exhaust velocity which requires average mass flow rates of


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oxidizer and fuel. The error associated with the measurement technique implies that the mass flow

rate of the fuel during the burn was greater than it actually was which causes the average effective

exhaust velocity and average specific impulse to be lower.

12. Refined Theoretical Model The refined theoretical model uses a sixth-order polynomial fit to approximate the measured

oxidizer flow rate versus time. A plot of the measured GOx flow rate, the polynomial fit, and the

output from the refined theoretical model are shown in Figure 15. This shows that there is very

good agreement between the polynomial fit from the model and the experimentally measured data.

Additionally the time scale over which the data is considered is increased from 8.8 seconds to 9.4

seconds, with the additional time coming at the beginning of the burn. This time was ignored in

initial discussion of the experimental data due to erroneous strain gage data for the first 0.6

seconds. However the GOx flow rate and pressure data was non-zero during this time so it was

included here while the strain gage data was ignored as required.

Figure 15: As Measured and Refined Theoretical Model GOx Flow Rate

Similarly to the previous model, polynomial fits for the effective exhaust velocity and ratio of

specific heats versus oxidizer to fuel ratio were developed from the NASA CEA code for a

chamber pressure of 118 psia. Additionally a polynomial fit was applied to the exit pressure versus

oxidizer to fuel mass ratio reported by the NASA CEA code. The previous model did not account

for the changing pressure at the exit plane of the nozzle during the burn. This change was not

appreciable when the oxidizer mass flow rate was fixed but becomes important once a variable

GOx flow is included. The value reported by the NASA CEA code only applies when the flow is

choked through the nozzle. Logic was included in the model to check for this, with the condition

for choked flow as shown in equation (8), where 𝑃𝑐 is the chamber pressure and 𝑃𝑏 is the back

pressure. If this condition is not satisfied then the pressure at the exit plane of the nozzle in the

model is set equal to the back pressure, which is the ambient pressure in this case.


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𝑃𝑐 ≥ 𝑃𝑏 (2

𝛾 + 1)

𝛾𝛾−1

(8)

Figure 16 shows the chamber pressure versus time and Figure 17 shows the thrust versus time for

the refined theoretical model and measured data. There is better agreement between the

experimental data and refined, variable GOx flow rate theoretical model than between the

experimental data and initial, constant flow rate model. The general trends in chamber pressure

versus time between the two data sets are similar, as shown in Figure 16. There are generally three

regimes; a first regime characterized by very rapid increase in chamber pressure versus time, a

second regime with a lesser rate of pressure rise, and a third regime of near constant pressure.

These regimes can also be seen in Figure 15. The rate of pressure rise in the experimental data in

regime 1 is greater than that predicted by the model. The measured pressure and the predicted

pressure both transition from the first regime to the second at a pressure of around 70-80 psia but

at different times, with the model transitioning later by about one second. The rate of pressure

increases in the second regime is nearly identical in the two data sets. The experimental data also

reaches the third, constant pressure regime before the theoretical model. The steady state pressure

in the theoretical model is greater than that seen in the measured data. The experimental data

centers on approximately 118 psia, while the theoretical model centers on approximately 130 psia

in the constant pressure regime.

Figure 16: Refined Theoretical and Experimental Chamber

Pressure vs. Time

Figure 17: Refined Theoretical and Experimental Thrust vs.

Time

There are three analogous regimes in the experimental thrust and revised theoretical model as

shown in Figure 17. However the initial first regime of transient force data was not accurately

measured as previously mentioned and as such is not included. There is greater disparity between

the experimental data and the theoretical model when comparing thrust than when comparing

chamber pressure. There is a similar rate of increase in thrust during regime 2, but the measured

data falls off and transitions into regime three of constant thrust at an earlier time and lower thrust

than the model predicts. The theoretical model predicts constant thrust in regime 3 of around 8.3

lbf while the experimental results gave steady state thrust centering on approximately 5.5 lbf.


22

Figure 18: Refined Theoretical and Experimental Thrust Coefficient Versus Time

The thrust coefficient computed from the experimental data and that given from the variable GOx

model are plotted on the same set of axes in Figure 18. The general trend seen in the

experimentally calculated values is seen in the refined theoretical model and are approximately

analogous to the three regimes described for chamber pressure and thrust. The measured thrust

coefficient is less than that predicted by the model in a similar fashion to the thrust.

The total impulse, average specific impulse, effective exhaust velocity efficiency, and thrust

coefficient efficiency were computed for the new theoretical model. The results are summarized

in Table 5.

Table 5: Comparison of Experimental Result and Refined Theoretical Model

This shows that in general the actual rocket underperformed in comparison to the refined

theoretical model. The thrust coefficient efficiency of the refined theoretical model (74.90%) is

very similar to that of the initial, constant GOx flow theoretical model (72.26%). The total and

specific impulse comparison to the refined model and also very similar to the initial model. The

effective exhaust velocity efficiency increased from 85.61% with the initial model to 92.31% with

the theoretical model. The refined model more accurately captures the general trends than the

initial model but still over predicts performance. The reason for this likely lies in the addition of

the aluminum particles. It is likely that the predicted performance increase from their addition was

not realized in reality. This is apparent from the accumulation of aluminum oxide in the

converging section of the nozzle as shown in Figure 13.


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A method was developed to estimate the specific impulse of the experimental data on a point by

point basis to compare to the refined theoretical model. The scheme involves solving the general

expression for thrust, shown in equation (9), for the total mass flow rate by estimating the exit

pressure and exit velocity as functions of the chamber pressure while taking into account the real

performance of the rocket motor versus the theoretical model. The NASA CEA code was run at

varying chamber pressures and polynomial fits were made for the exit pressure and exhaust

velocity versus chamber pressure. These fits were applied to measured chamber pressure to

estimate the exhaust velocity 𝑉𝑒(𝑃𝑐,𝑒𝑥𝑝) and the exit pressure 𝑃𝑒(𝑃𝑐,𝑒𝑥𝑝). The exhaust velocity was

further refined by multiplication with the thrust coefficient efficiency 𝜂𝐶𝐹 and the effective exhaust

velocity efficiency 𝜂𝐶∗ to account for the real performance seen. This resulted in the expression

shown in equation (10) for the instantaneous total mass flow rate as a function of the

experimentally measured chamber pressure and thrust. Knowledge of the total mass flow rate for

a given chamber pressure and thrust allowed computation of the specific impulse on a point by

point basis.

𝐹 = 𝑚𝑡̇ 𝑉𝑒 + (𝑃𝑒 − 𝑃𝑏)𝐴𝑒

(9)

�̇�𝑡(𝐹𝑒𝑥𝑝, 𝑃𝑐,𝑒𝑥𝑝) =𝐹𝑒𝑥𝑝 + [𝑃𝑏 − 𝑃𝑒(𝑃𝑐,𝑒𝑥𝑝)]𝐴𝑒

𝜂𝐶𝐹 𝜂𝐶∗𝑉𝑒(𝑃𝑐,𝑒𝑥𝑝)

(10)

Figure 19 shows the experimentally estimated specific impulse and refined theoretical model

specific impulses versus time.

Figure 19: Experimentally Estimated and Theoretical Specific Impulse vs. Time

The initial transient in the experimentally estimated specific impulse is not captured due to the

strain gage malfunction discussed previously. The general trends in the two plots are similar

despite this, with similar three regime behavior seen in other comparison plots.

There are a few methods by which this scheme may be validated. First, the average specific

impulse from the point by point estimation may be calculated and compared against that calculated

earlier. The values agree almost exactly, with the previously calculated average specific impulse


24

being 144.98 s and the average specific impulse calculated by the scheme described here being

144.72 s. This is a difference of just 0.18% which is quite remarkable. Additionally, the

instantaneous fuel mass flow rate may be calculated from the instantaneous total mass flow rate

by subtracting the oxidizer mass flow rate at that point. The point by point fuel mass flow rate

may then be numerically integrated to yield the total fuel mass consumption. This value is also in

excellent agreement with that observed. The measured total fuel mass consumption was 77.25 g

and the total mass fuel consumption from this method is 76.70 g, a difference of just 0.71%.

13. Conclusions and Recommendations Herein, a 8 lbf thrust hybrid rocket motor was designed, manufactured, and tested. Many potential

fuels were considered and compared against one another by use of the model developed in section

6. The NASA Chemical Equilibrium Code was used to calculate C* and γ over a range of O/F

ratios. These predicted fuel characteristics were then used in a finite difference scheme to evolve

the chamber pressure, fuel mass flow rate, O/F ratio, thrust coefficient, thrust, and specific impulse.

From this, a rocket motor utilizing a 85 wt% HTPB, 15 wt% aluminum fuel grain with a nozzle

expansion ratio of 2.75 and a throat diameter of 0.252 inches was chosen as the optimal design.

An aluminum motor casing was turned to size and threaded to accept the bulkhead, the nozzle was

turned out of graphite to the appropriate shape, and the fuel grain was cast in a paperboard tube

coupled with a phenolic tube. Finally the motor was instrumented to measure the chamber

pressure, generated thrust, and oxidizer mass flow rate as functions of time throughout the burn.

The design, construction, and testing of a 8 lbf thrust hybrid rocket engine lies well within the

realm of an upper division undergraduate or early graduate course. The entire process contained

within this project is an invaluable method by which the course content becomes fully understood

and prerequisite knowledge reinforced.


25

Works Cited 1. Campbell-Knight, C., Hybrid Rocket Motor Overview., in Space Safety Magazine. 2014.

2. Large-Scale Hybrid Motor Testing, in Fundamentals of Hybrid Rocket Combustion and

Propulsion. 2007, American Institute of Aeronautics and Astronautics. p. 513-552.

3. Hybrid Rocket Engines - Copenhagen Suborbitals. Copenhagen Suborbitals [cited 2015

April 30, 2015]; Available from: http://copenhagensuborbitals.com/technology-2/hybrid-

rocket-engines/.

4. SpaceShipTwo. The Spaceship Company [cited 2015 APril 30, 2015]; Available from:

http://www.thespaceshipcompany.com/vehicles/view/ss2.

5. About Dream Chaser. Sierra Nevada Corporation [cited 2015 April 30, 2015]; Available

from: http://www.sncspace.com/ss_about_dreamchaser.php.

6. Rocket Engine. The Bloodhound Project [cited 2015 April 28, 2015]; Available from:

http://www.bloodhoundssc.com/project/car/engines/rocket-engine.

7. Shanks, R. and M.K. Hudson, A Labscale Hybrid Rocket Motor for Instrumentation

Studies. Journal of Pyrotechnics, 2000. 11: p. 1-10.

8. Greiner, B. and J. R. A. Frederick. Results of Labscale Hybrid Rocket Motor Investigation.

in AIAA/SAE/ASME/ASEE 28th Joint Propulsion Conference and Exhibit. 1992. Nashville,

TN.

9. Wright, A.B., et al., Optical Studies of Combustion Chamber Flame in a Hybrid Rocket

Motor. Journal of Pyrotechnics 2005. 21: p. 21-30.

10. Marchese, A.J. Work In Progress - This Is Rocket Science: Development and Testing of a

Hybrid Rocket Motor in a Rocket Propulsion Course. in ASEE/IEEE Frontiers in

Education Conference. 2006. San Diego, CA.

11. Zilliac, G. and M.A. Karabeyoglu, Hybrid Rocket Fuel Regression Rate Data and

Modeling, in 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 2006:

Sacramento, California.

12. Zilliac, G., et al., Scale-Up Tests of High Regression Rate Paraffin-Based Hybrid Rocket

Fuels. Journal of Propulsion and Power, 2004. 20(6).

13. Lee, T.-S. and H.-L. Tsai. Fuel Regression Rate in a Paraffin-HTPB Nitrous Oxide Hybrid

Rocket. in 7th Asia-Pacific Conference on Combustion. 2009. National Taiwan University,

Taipei, Taiwan.

http://copenhagensuborbitals.com/technology-2/hybrid-rocket-engines/

http://copenhagensuborbitals.com/technology-2/hybrid-rocket-engines/

http://www.thespaceshipcompany.com/vehicles/view/ss2

http://www.sncspace.com/ss_about_dreamchaser.php

http://www.bloodhoundssc.com/project/car/engines/rocket-engine


26

Appendix: Variable GOx Theoretical Model

This section presents the MATLAB code for the variable GOx theoretical model and associated

fucntions. The main code is presented first with the functions given after.

clear %Define unit conversion constants kg_to_lbm=2.2046226218488; %1kg = 1kgtolbm lbm in_to_m=0.0254; Pa_to_psi=0.000145037738; g0_SI=9.81; TotalFuelMass_SI=0; %Define atmospheric conditions P_SL_SI=101325; %Sea level ambient pressure, Pa P_SL_in=P_SL_SI*Pa_to_psi; %Sea level ambient pressure, psi P_CO_SI=84400; %Fort Collins ambient pressure, Pa P_CO_in=P_CO_SI*Pa_to_psi; %Fort Collins ambient pressure, psi

%Define constraints/constants %rhoFu_SI=1182.75; %Fuel Density, kg/m^3 rhoFu_SI=1022.6; %fuel density a=0.145; %Pre-exponential term n=0.775; %Exponent

Do_in=1.175; %Fuel grain outer diameter, in Dp_in_init=0.7; %Initial Port Diameter, in

%Define design parameters Dt_in=0.252; %Throat Diameter, in L_in=12; %Fuel grain length, in L_SI=L_in*in_to_m; AR=2.75; %Area ratio, Ae/At

Dt_SI=Dt_in*in_to_m; %Throad Diameter, m At_in=pi/4*Dt_in^2; %Throat area, in^2 At_SI=pi/4*Dt_SI^2; %Throat area, m^2

Tst=300; %Standard reference temperature, K Pst=101325; %Standard reference pressure, Pa MWOx=32; %Molecular weight, oxidizer, kg/kmol R=8314; %R, Gas constant, J/kmolK rhoOx_SI=(Pst*MWOx)/(R*Tst); %Oxidizer density, kg/m^3 TotalFuelMass_SI=0;

i=1;

%Define calculated quantites Dp_in(i)=Dp_in_init; Dp_SI(i)=Dp_in(i)*in_to_m; rp_in(i)=Dp_in_init/2; rp_SI(i)=rp_in(i)*in_to_m;


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%Define time variable and time step

deltat=0.1; burnTime=9.40; t=0:deltat:burnTime; stop=length(t);

while (i<=stop)

%Calculate port and burn areas

Ap_SI(i)=pi*rp_SI(i)^2; %Port area, m^2 Ap_in(i)=Ap_SI(i)/(in_to_m^2); %Port area, in^2 Ab_SI(i)=pi*Dp_SI(i)*L_SI; %Burn area, m^2 Ab_in(i)=Ab_SI(i)/(in_to_m^2); %Burn area, in^2

%Calculate mass fluxes, flow rates, and OF VdotOx_SLPM(i)=getGOx(t(i)); %Oxidizer vdot, SLPM MdotOx_SI(i)=VdotOx_SLPM(i)*rhoOx_SI*.001/60; %Oxidizer mdot, kg/s MdotOx_cgs(i)=MdotOx_SI(i)*.001; %Oxidizer mdot, g/s MdotOx_in(i)=MdotOx_SI(i)*kg_to_lbm; %Oxidizer mdot, lbm/s GOx_SI(i)=MdotOx_SI(i)/Ap_SI(i); %Oxidizer mass flux, kg/m^2s GOx_cgs(i)=GOx_SI(i)*0.1; %Oxidizer mass flux, g/cm^2s

rdot_SI(i)=0.001*a*GOx_cgs(i)^n; %fuel regression rate, m/s rdot_in(i)=rdot_SI(i)/in_to_m; %fuel regression rate, in/s;

MdotFu_SI(i)=rhoFu_SI*Ab_SI(i)*rdot_SI(i); %Fuel mdot, kg/s TotalFuelMass_SI=TotalFuelMass_SI+(MdotFu_SI(i)*deltat); MdotFu_in(i)=MdotFu_SI(i)*kg_to_lbm; %Fuel mdot, lbm/s

OF(i)=MdotOx_SI(i)/MdotFu_SI(i); %O/F ratio

%Get Cstar and gamma CStar_SI(i)=getCStar(OF(i)); %Cstar, m/s CStar_in(i)=CStar_SI(i)/(12*in_to_m); %Cstar, ft/s gamma(i)=getGamma(OF(i)); %gamma

%Calculate chamber/exit pressure Pc_SI(i)=(CStar_SI(i)/At_SI)*(MdotOx_SI(i)+MdotFu_SI(i))+P_CO_SI;

%Chamber pressure, Pa Pc_in(i)=Pc_SI(i)*Pa_to_psi; %Chamber pressure, psi

%Check for choked flow chokeCond(i)=(2/(gamma(i)+1))^(gamma(i)/(gamma(i)-1)); if Pc_SI(i)/P_CO_SI >= chokeCond Pe_in(i)=getExitPressure(OF(i)); %Exit Pressure, psi else Pe_in(i)=P_CO_SI; end


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%Calculate CF0 gamma_expon(i)=(gamma(i)+1)/(2*(gamma(i)-1)); CF0_T1(i)=sqrt(gamma(i))*(((2/(gamma(i)+1))^gamma_expon(i))); CF0_T2(i)=(2*gamma(i)/(gamma(i)-1))*(1-((Pe_in(i)/Pc_in(i))^((gamma(i)-

1)/gamma(i)))); CF0(i)=CF0_T1(i)*sqrt(CF0_T2(i));

DeltaCF_CO(i)=((Pe_in(i)/Pc_in(i))-(P_CO_in/Pc_in(i)))*AR;

CF_CO(i)=CF0(i)+DeltaCF_CO(i);

%Calculate thrust and Isp F_CO_in(i)=CF_CO(i)*Pc_in(i)*At_in; Isp_CO(i)=CStar_SI(i)*CF_CO(i)/g0_SI;

i=i+1; rp_SI(i)=rp_SI(i-1)+(rdot_SI(i-1)*deltat); rp_in(i)=rp_SI(i)/in_to_m; Dp_SI(i)=2*rp_SI(i); Dp_in(i)=Dp_SI(i)/in_to_m; end

figure(1); subplot(2,2,1) plot(t,Isp_CO); title('Isp');

subplot(2,2,2) plot(t,Pc_in); title('Chamber Pressure')

subplot(2,2,3) plot(t,F_CO_in) title('Thrust (lb)');

subplot(2,2,4) plot(t,CF_CO); legend('Sea Level','Colorado'); title('CF');

figure(2); subplot(2,2,1); plotyy(t,OF,t,gamma); legend('OF','Gamma'); title('OF and Gamma');

subplot(2,2,2) plot(t, gamma); title('Gamma');

subplot(2,2,3) plot(t,CStar_SI) title('C*')


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t=transpose(t); rp_in=transpose(rp_in); rdot_in=transpose(rdot_in); MdotFu_in=transpose(MdotFu_in); OF=transpose(OF); CStar_in=transpose(CStar_in); CStar_SI=transpose(CStar_SI); gamma=transpose(gamma); Pc_in=transpose(Pc_in); Pe_in=transpose(Pe_in); CF0=transpose(CF0); DeltaCF_CO=transpose(DeltaCF_CO); CF_CO=transpose(CF_CO); F_CO_in=transpose(F_CO_in); Isp_CO=transpose(Isp_CO); MdotFu_SI=transpose(MdotFu_SI); MdotOx_SI=transpose(MdotOx_SI)

function [ X ] = getExitPressure( OF ) %Takes OF as an argument and returns exit pressure in psi x0=0; x1=0; x2=0; x3=0; x4=0; x5=0; x6=0; if (OF >= 0.1) && (OF < 1.05) x0=9.9831; x1=-0.7969; x2=3.1795; x3=-2.1785; elseif (OF >=1.05) && (OF <= 2.0) x0=739.47; x1=-2374.4; x2=3051.9; x3=-1941.4; x4=612.01; x5=-76.545; end

Val=(x6*OF^5)+(x5*OF^5)+(x4*OF^4)+(x3*OF^3)+(x2*OF^2)+(x1*OF)+x0; X=Val;

end

function [ X ] = getGamma( OF ) %Function takes OF ratio and returns gamma x0=0; x1=0; x2=0; x3=0;


30

x4=0; x5=0; x6=0; if (OF<1) x0=1.1667; x1=-0.899; x2=3.8667; x3=-7.5509; x4=6.8454; x5=-2.3202; elseif (OF>=1) && (OF<1.10) x0=-38.65; x1=75.18; x2=-35.42; elseif (OF>=1.10) && (OF<=2.0) x0=15.391; x1=-46.345; x2=60.149; x3=-38.798; x4=12.409; x5=-1.5732;

end

Val=(x6*OF^6)+(x5*OF^5)+(x4*OF^4)+(x3*OF^3)+(x2*OF^2)+(x1*OF)+x0; X=Val;

end

function [ X ] =getCStar( OF ) %Function takes the oxidizer to fuel mass ratio and returns Cstar in m/s x0=0; x1=0; x2=0; x3=0; x4=0; x5=0;

if (OF >= 0.1) && (OF < 1.1) x0=1121.08; x1=3196.87; x2=-11539.39; x3=22460.77; x4=-20781.25; x5=7221.11; elseif (OF >=1.1) && (OF <= 2.0) x0=-4661.31; x1=15934.41; x2=-14511.54; x3=5835.97; x4=-878.94; x5=0; end Val=(x5*OF^5)+(x4*OF^4)+(x3*OF^3)+(x2*OF^2)+(x1*OF)+x0; X=Val; end

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Hybrid Rocket Motor Final Report