Jet Vehicle Design Portfolio
Objectives
The objective is to design and construct a vehicle capable of efficiently transporting a payload in the form of marbles over a distance of at least 92 inches and no more than 172 inches, powered only by the jet expelled from the provided balloon and adhering to design limitations imposed by competition rules (size, material, etc). Additionally, the vehicle’s speed should be optimized to achieve a fast traversal of a 75-inch distance within the competition track.
Jet Exhaust and Thrust
Thrust equation: F=ṁVe+(pe-p0)Ae Where:
- F is thrust in N
- m is mass flow rate in kg/s
- Ve is exhaust velocity in m/s
- pe is exit pressure in Pa
- p0 is atmospheric pressure in Pa
- Ae is the exit area in m^2
The mass flow rate describes the rate at which air is expelled from the balloon. When we inflated the balloon to a circumference of 25 inches (63.5cm), it took approximately 1.6 seconds to fully deflate. According to our data from the manometer lab, for a balloon circumference of 25 inches (63.5 cm), the propellant mass is .009201 kg (9.201g). The mass flow rate can be determined by dividing the propellant mass by the time (in seconds) it takes for all the fluid to exit the balloon. This gives us a mass flow rate of .00575 kg/s.
ṁ=.009201 kg / 1.6 s = 0.00575 kg/s
To calculate the Ae (exit area of the nozzle), where the radius is .85 cm (17mm diameter):
Ae = pi r^2 = 2.27 cm2 = 0.0227 m^2
Because our exhaust flow will be subsonic, the flow exit pressure (pe) will be the same as the atmospheric pressure (p0). Therefore, we can use the following equation to calculate thrust.
F=ṁVe
And, to calculate the exit velocity:
Ve =m/(Ae)
Given that =1.204kg/m3, the density of air at room temperature, we can solve for velocity and find the thrust.
Ve =.00575 kg/s (.0227m2*1.204 kg/m3) = 0.21 m/s F = .00575 kg/s * .21 m/s =0.0012 N
Based on these calculations, the exit velocity of the propellant is estimated to be .21 m/s, and the thrust produced is estimated to be about .0012 N.
Brainstorming & Evaluation of Ideas
Vehicle Body
Considering that low-mass vehicles are at a distinct advantage, we considered various materials and geometries the body might take. For materials options included 3d printed plastic, laser cut wood (3mm thick), or laser cut acrylic (3mm thick). We reasoned that it would be optimal for the vehicle to be as short as possible to reduce weight of material used in the construction, while also keeping in mind that the walls should be at least 2 centimeters tall in order to effectively contain marbles.
A 3D-printed body would most likely be the lightest because it would be possible to reduce the infill and achieve the same wall thickness with less density. However, printing the body in one piece, with slots for the axles on the bottom, would require a substantial amount of material in supports and take significantly longer to fabricate. Between wood and acrylic, wood would be lighter as it is less dense. Laser cutting 5 pieces for the body would take less than 10 minutes, so we would be able to fabricate prototypes and make changes more rapidly. In the interest of time and material, constructing the body out of laser cut wood pieces would be ideal.
Sleds vs Wheels
To carry the vehicle body, we considered using 2 parallel sleds versus 4 wheels.
We decided to use wheels instead of sleds. Because the track surface is smooth and flat, wheels make less contact with the surface, thereby reducing energy lost to frictional forces. With sleds, there is a greater contact area with the ground, so initial force required to set the vehicle in motion would be higher to overcome inertia. We plan to fabricate the wheels on the laser machine.
Nozzle
When researching designs for the nozzle, we narrowed it down to three different geometries– a converging nozzle, a diverging nozzle, or a converging-diverging nozzle. The C-D (converging-diverging) nozzle design is commonly used for fluids traveling at supersonic speeds. The idea is that it first compresses the fluid down in the throat to accelerate it to supersonic velocities. The diverging nozzle reduces the pressure of the airflow at the exit. The converging nozzle narrows down the flow area, which increases the velocity of the fluid as it passes through.
The converging-diverging nozzle would be unnecessary for the low-pressure, low-velocity fluid generated by a balloon. The diverging nozzle reduces the pressure of the air at the exit, but doesn’t accelerate the airflow due to the lack of a converging section. Therefore, we decided to go with the converging nozzle which effectively narrows down the flow area to increase the velocity of the fluid as it passes through.
Valve
We explored the possibility of adding a valve in the pipe connecting the balloon to the nozzle. The intention of this valve would be to control the flow of the air, and consequently, the propulsion of the vehicle. With a valve, we would be able to regulate the airflow to precisely control the amount of thrust generated by the balloon, allowing for better control of the speed.
Introducing a valve adds complexity to the pipe and could potentially introduce additional problems to the propulsion system. Because 3D printing is not incredibly precise, it is possible that air leakage might occur. Additionally, it may take several tries to design a working print-in-place mechanism for the valve which would add several hours to our prototyping process. For these reasons, adding a valve is not in the scope of our initial design.
Bill of Materials
- 3mm baltic birch plywood
- 4x wheels
- 5 pieces for body
- 2x axles
- 3D printed parts
- 1x nozzle / chamber
- Wood glue
- To assemble pieces of vehicle body
- Hot glue
- To secure wheels to axles
- Balloon (propellant)