Alternative Energy Vehicle

The goal of this project was to build a vehicle capable of carrying two "passengers" (rolls of pennies) exactly 5 meters. You could use whatever materials to build your vehicle, and the vehicle could be of any type — however, you could not use gasoline, stored electricity (batteries) or nuclear power to derive your energy. Once a working prototype was completed, you would present your vehicle design to Hyundai and it would be judged based on how close to 5m it got and how useful the energy source was.

For this project, our group decided to use the basic structure of a gondola along a string. However, each individual built their own model which used different energy sources. I went through several iterations of my model — they all were feasible on a real scale, but with the level of manufacturing and materials I have at home I was not able to make most of them work.

Prototype 1: Tesla Coil (Wireless Power)

The idea of this model was to use a tesla coil to wirelessly transmit power to the vehicle. A tesla coil is essentially a resonant coil — by constructing a similar coil system and placing it near the tesla coil, the magnetic flux will cause the coil to resonate at the same frequency as the tesla coil, meaning that alternating current can be obtained from the terminals of the coil. This is inductive power transfer. In my machine, I was able to get this system working. However, I was not able to get enough current transferred to power a motor, since my tesla coil is just a desktop hobby model and not very powerful.

Prototype 2: Electromagnetic Drive

This system used an arrangement of magnets and an electromagnetic coil to propel the vehicle. (For a diagram, see the slideshow below.) Power would be applied directly beneath the vehicle to a long coil (running the 5m which the vehicle would travel). This results in all the forces pushing the two magnets mounted on the vehicle forward (see right panel in slideshow). While this system did work, it was not powerful enough to move the whole gondola assembly because I do not have the precision tools needed to make the coil as efficient as possible.

Prototype 3: Thermoelectric Power

Using a peltier module, one can generate electricity from a heat source and a source of cold. This phenomenon is known as the Seebeck Effect, and it is how many of NASA's spacecraft get their power from hot nuclear materials. My source of heat was a camp burner, and my source of cold was ice. Once again, this system worked — though unfortunately it was not capable of pulling the weights (passengers) because I do not have the kind of precision burners and radiators I would need to make it most effective.

Prototype 4: Hydropower

This final prototype worked perfectly. By spraying pressurized water at a waterwheel assembly, and driving a winch-like system with that waterwheel, I was able to move my gondola (passengers included) the 5m distance. This design is covered in-detail on the slideshow.

Core Concepts

Kinetic Energy

Kinetic energy is the energy of motion. For more about this, see the Rube Goldberg Machine page.

Gravitational Potential Energy

Gravitational potential energy is potential energy due to gravity ("stored gravity energy"). It is equal to the mass of the object times its height above the ground times the acceleration due to gravity (roughly 9.8m/s²). The unit for this energy (as with all energy) is Joules, abbreviated "J". In the second spreadsheet above, you can see the measurements of gravitational potential energy at each time interval. Because my teammates' vehicles were gravity-powered, this potential energy represents all the energy the gondola "had left". When it got to the end of the run (hitting the ground), it had no stored gravitational energy left — at the start (when it was up high), it had quite a bit. Notice how most of the potential energy converts into kinetic energy: most of the gravitational energy gets "used up" by moving the vehicle, which is its kinetic energy.

Total Energy

The total energy is the sum of all energies in the system (potential, kinetic, thermal). For systems which do not have any external input ("closed-box" systems) like my teammates' gravity cars, the total energy is simply the potential energy of the system at the start of its evolution. In their cars, this was the gravitational potential energy at the start (~7.546J). In a "closed-box" situation, we know that the total energy must be constant, since the law of conservation of energy states that energy cannot be created or destroyed.

Thermal Energy

Thermal energy is energy lost to heat. The most common appearance is when friction occurs — friction creates heat, so a system involving lots of friction will have lots of thermal energy. Because of the law of conservation of energy, this means that the kinetic energy must drop (so that the total energy stays constant), which is why things slow down when they encounter friction. Thermal energy can be calculated as the total energy minus the potential and kinetic energy of the system. (Thermal energy is the "missing piece" in the "total energy pie" if you know the potential and kinetic energy.) In both spreadsheets, you can see the thermal energy increases as the vehicle goes along the cord (more and more friction has been encountered, so more and more energy has been lost).

Distance, Velocity, Acceleration and Jerk vs Time

It is often helpful to find a relation between a positional quantity and time. For instance, we may wish to see how the position of a car changes as time goes on, or we may wish to see how its acceleration varies. The most common way to visualize this relationship is a graph — we put time on the x (horizontal) axis, because it is the "thing which we vary" (we want to find a relationship between a given time and the position, not a given position and a time). This is called the independent variable. We put distance/velocity/etc on the y (vertical) axis, because it is the "thing which we output" (we want to get out, say, a distance for every time we put in). This is called the dependent variable. Now, for each time value that we plug in, we see what distance/velocity/etc we get out and then mark a point at (the time, the [quantity]). When you connect all the points, you get a nice smooth line graph showing what one aspect of your test object's motion is at each point in time. For examples of such graphs, see the slideshow/spreadsheets.

But what exactly is velocity, or acceleration? There is a satisfying uniformity to this system which can be revealed in a simple way. Velocity is the change in position. Acceleration is the change in velocity. Jerk is the change in acceleration. Snap/Jounce is the change in jerk... and so on and so on. It is then simple to match the intuitive understanding with the logical definition: velocity is how fast you're going, acceleration is a measure of how much you're speeding up or slowing down, jerk is how fast you're speeding up / slowing down, etc etc. So if we graph acceleration, we are saying "how much are we speeding up or slowing down at each point in time?"

Of course, this leads to the natural conclusion: each element is the derivative of the previous. So velocity is d/dt position, acceleration is d/dt velocity, and so on. This causes a new question to arise: what happens if we go the other way, and integrate position instead of differentiate? The answer is that we get absement. Absement is a bit more difficult to explain; essentially, it is a measure of "how far away the object has moved from its initial position and for how long" at each point in time. For instance, if an object sits at its initial position the absement will stay at 0 — but if the object's position is given by t meters (where t is the time in seconds), then the absement will be t² / 2. (For every θ, 0 ≤ θ ≤ t, the object's position can be described as y = θ. It suffices to say we wish to find the area under this curve, as per the integral's definition; we are measuring the total "away-ness" of the object. Our curve is a triangle shape with base and height t — since we wish to find the area, we know that it is t² / 2.) Now, we can go even farther than absement (as far as we want really), but the meanings become more and more difficult to comprehend the farther we go. (Absity, the next integral, is the measure of "how long it has been how far away for how long". Confusing!)

Using the derivative and integral definitions, we can derive units for these quantities. We will let time be in seconds, and position in meters. Then the derivative of position (velocity) is meters per second (m/s), the derivative of velocity (acceleration) is meters per second squared (m/s²), etc etc. In the other direction, we have the integral of position (absement) is meter-seconds (m·s), the integral of absement (absity) is meter-seconds-squared (m·s²), etc etc. You can see the symmetry in these systems — because integration and differentiation are (almost) inverses, the units of each quantity are either multiplied or divided.

Rotational Inertia

Suppose you have two disks: one that is hollow and only has significant mass around the edges, and one that is solid. (The solid one is slightly heavier.) Which one will be easier to spin? Well, the measure of an object's resistance to rotational state is called its rotational inertia. Essentially, this means the rotational inertia is a measure of "lack of easy-spinny-ness". There are a few different ways to define this quantity, but for our purposes we will use the definition that rotational inertia is the product of the mass of the object and the square of the distance from its centroid to the axis of rotation. Note, importantly, that this assumes the mass is a point mass; so for more complex masses with varying density, we must simulate that by summing the total rotational inertia of infinitely many point masses distributed throughout the object at the appropriate density (in other words, take the integral of density times the squared distance to the axis).

So, returning to the question — the solid disc has fixed density, so we can say that its mass is evenly distributed relative to the axis of rotation. However, the hollow disk only has significant mass around its edge, so its mass is overall "farther out". This means that if we were to integrate the point masses of the hollow disk, they would have higher rotational inertia than the solid disk because they are much farther away from the axis of rotation. So even though the solid disk is slightly more massive, it would be easier to spin!

This is important when designing wheels or other spinning mechanisms which should be able to be spun as easily as possible: all mass should be as centralized as possible about the rotation axis. However, if one wishes to design a wheel which should keep spinning and not be stopped easily (i.e, a flywheel), all mass should be spread out on the edge as much as possible.

Reflection

Overall I think I did very well with this project and I was very satisfied in the end. I certainly stretched my critical thinking skills because I had to try so many different prototypes before one actually worked. It made me really think about what is feasible with what I have, not what what is feasible in general. Additionally, I had more critical thinking work when writing this document itself: there was a lot of calculus work that factored in to explaining the concepts in more intricate detail. Also, I feel that our group's communication was great: we had a professional-looking presentation which made our whole project very clear.

However, no project is perfect. I feel that our collaboration might have been a little lacking; while we did fine, we didn't really work with each other very much on the build/design process. Much of this is induced by the distanced-learning circumstances, but there still could've probably been a little more. This might have been an issue with my communication — I probably should've given the group more detailed updates on what I was doing (and the issues I was encountering) to facilitate more collaboration.

Despite these small flaws, I feel that this project was a great learning experience. It was a great exploration in a lot of different types of energy sources, conversions, and utilization techniques.