Goal: Decide on a source of thrust for rocket landing.
Why?: Thrust is the most important part of a rocket. This choice will dictate the rest of the rocket design. There are many options to decelerate the rocket, but we need to find a thrust source that is controllable and light enough for takeoff.
Results: Solid-fuel hobby rocket motors.
Next steps: Determine which motors to use, measure accurate thrust curves, and measure ignition delay time.
We started here because we can’t design any of the components or controllers until we choose a source of thrust.
The main design considerations are thrust-to-weight ratio, controllability, and price. The rocket has to be light enough for takeoff, strong enough to decelerate for landing, and we have to be able to control the thrust for orientation and altitude control. Price is the obvious limiter because we are college students.
The options we looked at for propulsion were:
- Liquid-fuel rocket engine
- Compressed air
- Rotor blades
- Solid-fuel hobby rocket motors
Liquid-propellant Rocket Engine
We could build a scaled-down version of the rocket engines used today that use liquid propellants, typically liquid oxygen combined with liquid hydrogen or a hydrocarbon like RP-1.
- Combustion usually gives a high thrust-to-weight ratio.
- We would be able to control the magnitude of the thrust by controlling the flow of the fuel.
- Price. This design requires many components including valves, pumps or high pressure tanks, nozzles, pipes, etc. And all of these components need to withstand very high temperatures and pressures.
- These are also relatively dangerous, and we would need a place to safely (and legally) build and test.
This design would also be very complex. This is a negative in that it would there is more that can go wrong and would require a lot of time to design and build. But complexity is also a positive in that we would have to learn a ton about thermodynamics and fluid dynamics in order to pull it off.
However, with our limitations in price and ability to test, the liquid-fuel rocket engine option was eliminated.
Compressed Air Tank
Option 2 is a compressed air tank with a valve to control flow.
- No danger of combustion
- Can control thrust via a valve
- Materials don’t need to withstand high temperatures
- Small air tanks are inexpensive and available off-the-shelf, and CO2 refills can be done cheaply at most sporting goods stores
- We may not be able to get enough impulse
- Hardware to control high pressure air is bulky and heavy
This seemed like a potential candidate to use for our rocket, so we needed to figure out if there was hardware available that was capable of providing enough thrust. This required us to find the fluid dynamics equations for flow exiting a pressurized tank.
We didn’t find these equations in our textbooks or online, so we derived them. Our undergrad fluids course always assumed incompressible flow, which is not a valid assumption for this system, so we had to research compressible fluids to develop our model. The governing equations are derived below, with the variables defined as follows:
We assume heat transfer is negligible, and therefore we use the isentropic flow relation.
Then we used Bernoulli’s equation for compressible flow.
Next we assume the fluid is ideal and use the ideal gas law.
Using the above equations, we were able to find the velocity of the air leaving the tank. Later, while looking into the equations for choked flow, we ended up finding an equation relating internal and external pressure to exhaust velocity, and we confirmed that our derivation was correct.
Above a critical value for P1, the flow becomes choked, meaning the velocity at the exit saturates to a constant value.
Next we use equation for mass flow rate out of the tank and the previous equation for velocity to find the thrust out of the tank.
Once we found the governing equations of the system, we plugged in the values of available hardware that we could potentially use and see if it would provide enough thrust. 800 psi CO2 paintball tanks were readily available, so this is what we decided to test in our model. We also decided we would use a solenoid valve to control the flow, which has an exit orifice diameter of 2.5mm. The solenoid valve must receive a regulated air pressure of 140 psi, but this still indicates choked flow out of the tank.
These numbers indicate a maximum thrust of 0.26 N, far below enough to counteract the weight of the components. This ruled out compressed air as a source of thrust.
The next option is to make a rotorcraft like a helicopter or quadcopter. While it would be cool to learn the complex dynamics of these vehicles, it isn’t technically a rocket.
Hobby Rocket Engines
The normal model rockets launched by hobbyists use solid-fuel engines.
- High thrust-to-weight ratio
- They are ready to use off-the-shelf for a low price.
- Once ignited, there is no thrust control
- Short burn time (1-3 seconds), meaning we will have no control of acceleration or orientation during most of the rocket’s descent
- There is an unknown delay time between sending the signal to ignite the motor and actual motor ignition
- According to the National Association of Rocketry (NAR), the thrust vs. time curves of these motors are highly non-linear [http://www.nar.org/standards-and-testing-committee/nar-certified-motors/]
Despite the nonlinear thrust curves and limited control time, these motors’ availability and thrust-to-weight ratio make them the best choice for our rocket.
Now that we have chosen our method of propulsion, we need to determine which motors to use since hobby rocket engines vary in total impulse and thrust duration. We also need to figure out the variance in ignition delay time and confirm the accuracy of NAR thrust curves. These thrust curves will be critical to developing the rocket control systems.