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Solid Rocket Propulsion by Steven Stratton
Designing and Building a Small Scale Rocket Engine
The Rocket Equation
The Next Steps
Amateur Experimental Rocketry, unlike “Model Rocketry” is a pursuit in which the propulsion system is designed and built from scratch rather than purchased in a kit. The goal is to design, build, and launch rockets.
The most difficult aspect, the one that sets an Engineer apart from the average enthusiast, is the ability to predict performance. The ability to take the designed motor and predict thrust, acceleration, and altitude is what makes this activity what is colloquially known as “Rocket Science”.
The “Sugar” Rocket
The name “Sugar Rocket” comes from the chemical composition of the fuel. There are three main types of sugar rocket.
These fuels are mixed with potassium nitrate () which acts as the oxidizer.
The choice of this fuel is due to it’s ease of preparation and it’s overall stability.
Measure of Performance
Total Impulse is exactly what it sounds like. It is the total impulse delivered by the engine during burn.
Specific Impulse is the most popular way to measure the performance of a rocket or jet engine. It is commonly abbreviated as . By definition, it is the impulse delivered per unit of propellant consumed.
The total impulse is found by taking the area under the Thrust curve
Specific impulse is the total impulse divided by the mass of the fuel grain
While the most common method of comparing performance is specific impulse, rocket motors are classified based on their total impulse
The higher the impulse, the higher the letter classification.
The motor analyzed in this presentation is a class I.
Mass Flow Rate
= The Throat Area
= Chamber Pressure (also known as Total pressure)
= Combustion Temperature (also known as Total temperature) Combustion temperature is determined by doing a chemical analysis on the chemicals in the fuel grain
= Specific Gas Constant
= Ratio of Specific Heats (of combustion products)
= Volume of Empty Chamber
= Area of Fuel (changes with respect to time)
= Burn Rate of Fuel (this is determined experimentally)
= Density of Fuel Grain
Fuel Grain Area (Burning Area)
The Fuel Grain will be inhibited on the outside edge, thus it will burn on the inside cylinder, and at both ends. This leads to what is known as a “Progressive” thrust curve.
The total surface burning surface area will change as a function of time.
Progressive Thrust Curve
Produced by a cylindrical fuel grain inhibited on the outside edge.
Thrust curve from Simulink model
Fuel Burn Rate
Saint-Robert’s Burn Rate Law
= burn rate of fuel
= The burn rate coefficient
= The pressure exponent
= Chamber pressure
The burn rate coefficient and the pressure exponent are determine through experimentation. It is impossible to determine them theoretically.
Gas Exit Velocity
= Combustion Temperature
= Specific Gas Constant (of combustion products)
= Pressure at the nozzle exit
= Chamber Pressure
The goal when designing the nozzle is to make the exit pressure as close to atmospheric as possible. This results in the highest exit velocity of the gas.
= The Mach number at exit
Pressure at the nozzle exit is determined by the Mach number at exit.
Determining the Mach Number
The relationship between throat area and Mach number is given by
is the throat of the nozzle here.
is the exit area
*note: M is implicit in the equation. It must be solved for numerically.
Design of the nozzle
The most important governing principal of nozzle design is what is known as the area expansion ratio. It is the area of the nozzle exit point over the area of the throat .
Throat area :
Nozzle exit area
Detailed Drawing of the Rocket Nozzle in This Project
Motor Casing and Bulkhead
Maximum internal pressure of motor casing before permanent deformation occurs
Note: this is calculated assuming the motor casing is 1018 steel
Apply a safety factor of 1.5
This is acceptable since the internal pressure predicted by the simulation is 9.5 MPa.
Bulkhead mounting holes
Calculate the size of the shear pin needed
Calculate force acting against the bulkhead
6 shear pins acting in double shear divides the force by 6
(force acting on each shear pin)
Calculate size of shear pin needed to shear at 981 lb
Shear Strength of yellow brass: 34100 psi = 235 MPa
Diameter of shear pin =
Physical properties of brass
Brass shear pins in motor casing will shear long before the casing fails
Motor Casing and Bulkhead Drawings
Fuel Grain (Sorbitol)
The chosen fuel for this project is Sorbitol. It has a specific impulse nearly equal to Sucrose and Dextrose, yet it is much easier to cast in a mold. It is also much more pliable after it has cooled. The other fuels are brittle and run a risk of cracking before launch.
O.D. = 1.562”
Length = 8”
I.D. = 0.625”
The geometry of the fuel grain (i.e. the fact that it is a hollow cylinder) will produce what is known as a “progressive” thrust curve. The thrust will continually increase until the fuel is consumed.
The aspect of Rocketry that sets the engineer apart from the average enthusiast, is the ability to predict how the system will behave prior to testing.
Modeling the performance dynamics of a solid rocket motor is a complex undertaking. To do it properly, it requires that many systems update and work in unison.
For my project, I decided to use Simulink for the prediction model. In Simulink, I was able to build the main system comprised of a number of smaller subsystems.
Simulink Model Demonstration
Results (from Simulink model)
Total Acceleration Time
Plots of Acceleration and Thrust
Velocity and Altitude Results
1560 meters = 5118.1 feet = 0.97 miles
Mass Flow Rate and Chamber Pressure
Max Pressure = 9.5 MPa
(equal to: 1378 psi)
Total Impulse =
Specific Impulse =
Average Thrust =
Another popular way of comparing performance is to divide the Specific Impulse by the acceleration due to gravity. This leaves seconds as the units
Seconds = =
The next step in this project is to complete several “burns” of this motor in order to verify the prediction model. This is accomplished by firing the motor in a test stand built specifically for this type of test.
These tests will provide real thrust and pressure data that can then be compared with the predictions.
Launching The Rocket
Once the testing has been completed, the motor will be installed into the main body of the rocket along with the electronics that control the recovery system (i.e. launch the chute).
The plan is to record acceleration and altitude data while the rocket is in flight. If all goes well, this will be accomplished over the summer of 2015.
Carter, Slader. "Rocket Propulsion Systems." Personal interview. 20 Mar. 2015.
Lee, Shane B. "Matlab Simulation." Personal interview. 5 Apr. 2015.
Flandro, Gary A., Dr. "Rocket Dynamics." Southern Utah University, Cedar City. 18 Oct. 2014. Lecture.
Yunus A. Cengel, J. M. (2006). Fluid Mechanics, Fundamentals and Applications. New York: McGraw-Hill.
"Richard Nakka's Experimental Rocketry Site." Richard Nakka's Experimental Rocketry Site. N.p., n.d. Web. 29 Apr. 2015. <http://www.nakka-rocketry.net/>.
"Rocket Thrust Equations." Rocket Thrust Equations. N.p., n.d. Web. 29 Apr. 2015. <http://exploration.grc.nasa.gov/education/rocket/rktthsum.html>.most important governing principal of nozzle design is what is known as the area expansion ratio. It is the area of the nozzle exit point over the area of the throat .
"Richard Nakka's Experimental Rocketry Site." Richard Nakka's Experimental Rocketry Site. N.p., n.