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Goals for System Design
Goals for System Design
Create a system model of the rocket that can model the resistance forces of spinning
Code model in MATLAB to display transient response to spinning
Design the pneumatic system for cold gas thruster
Create a system model of system to use for nozzle design code
Design Analysis
To design a system that spin stabilizes an entire rocket, I first had to model the forces and torques on the body.
By using a summation of torques, I could find how much force the thrusters will have to produce.
Based on the free body diagram, I found that there were three main torques: skin drag, fin drag, and angular momentum. This can be modeled as a second order system to create a force function
Skin drag will be neglected since the rocket body is smooth, and spinning at a very low velocity and would be insignificant to the other forces
Free Body Diagram
Free Body Diagram
Side View
Side View
Free Body Diagram
Free Body Diagram
Cross Section
Cross Section
Drag Force
Drag Force
Drag Equation
Drag Equation
Drag can easily be calculated using this main drag equation. By replacing the velocity term with radius and angular velocity, the drag equation can be converted to cylindrical coordinates. Then by multiplying the radius of the center of pressure to the center axis of the rocket, I could calculate the torque that each fin produces.
Pressure drag on the fins will be a dynamic force since the velocity of the fins will affect the drag coefficient, due to laminar and turbulent regimes.
Rotational Inertia
Rotational Inertia
Torque Equation
Torque Equation
To accelerate a body of mass, a force must be produced, thus newtons second. since we are rotating the body, we will need to use inertia to find the torque required.
Definition of torque:
T = dL/dt
L = I*w = Rotational Inertia * Angular velocity
I can integrate the expression to get this equation. This will model the entire ship as a solid cylinder, which wont be entirely accurate, but it is a good enough approximation for our purposes.
System Model
System Model
Now that rocket has it own system model that can calculate the force the ship will experience during flight, its time to design a system that will be capable of producing enough force to spool up the system within a desired time.
This system utilizes a 4500 psi tank with a 300 psi pressure regulator that is stepped down to 200 psi regulator. The second regulator was used to make interfacing with the tank safer and more convenient to use.
The accumulator is designed to prevent an over drawing a flowrate from the regulator, which can cause the pressure to drop to zero. Since the system will be controlled by pwm bursts, the accumulator can allow the regulator to recharge the accumulator.
The solenoid will have to be capable of high frequency control, high flow and operate at high pressure. The discharge coefficient of the solenoid, Cv value, is an important factor in calculating the force of the in the thruster.
The thrusters can be designed using iterative design process coded in MATLAB that requires a model of the system described above using isentropic relationships to calculate the force the thrusters will produce.
Simulated System Performance
Simulated System Performance
Model Diagram
Model Diagram
Model Simulation
Model Simulation
This Model was used to visually see how a nozzle will preform, based on the thrust it was predicted to produce. This model takes into account the drag on the fins, and the inertial resistance. These force are then countered by a constant thruster force to produce these graphs of the simulated ship angular velocity.
This model also provided the ability to calculate the amount of gas that is lost during constant flight, which helped for sizing the air tank capacity
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