The Pinewood Derby Project

About the Project

With this project we wanted to observe the physics that go into a pinewood derby car, and use that knowledge to try and make an ultra fast concept to beat previous models we had from cub scouts and other events. This project was broken into three parts: the initial physics analysis, the car design and assembly, and an analysis of the results in the end.

Here are the ground rules:

The car cannot exceed 7 inches in length and 2.25 inches in width
The car cannot exceed 5 ounces
No liquid lubricants
I'm leaving all other rules up for modification to allow the most creative freedom with this project- This includes wheel shape/size, wheelbase length, and wheel mounting modification (polished/bent axles).

Forces acting on the car

Understanding the track is crucial to understanding the motion of the car. For now I will be analyzing the tracks with two more distinct sections, rather than the tracks with one large swooping curve. Using our physics knowledge we will be able to determine some of the characteristics of our car

Track Part 1:

This is the part of the track where the car accelerates. Here the car will have a large amount potential energy while being held at the top of the track, that will all be released into kinetic energy as soon as the race begins.

KE initial + PE initial = KE final + PE final

PE initial = KE final

mgh = (1/2)mv^2

gh = (1/2)v^2

v = root(2gh)

This means that for the first leg of the race, the mass of the car doesn't matter. Because gravity is a constant, the only part on the block we can modify to change the velocity of the car is the height, which will be the height of the center of mass of the car off of the ground.

Track Part 2:

This is the flat part of the track where the car rolls to the finish line. In this section the car will enter the straightaway with some initial velocity determined by part one, and gradually slow down due to friction and air resistance.

Translational Inertia = mass * acceleration

Assuming acceleration is the same for two cars and inertia is what will keep the cars rolling on the straight part of the track, mass will be the only determining factor on the final stretch. More mass will lead to more inertia, and the car will hold its speed for longer.

In all parts of the track friction will have an impact on the car's speed, slowing it down the more there is. thus, friction must be minimized to maximize speed.

Wheel Rotation

Our Design

Design PArt 1

As we learned while analyzing the track, the weight of the car will need to be maximized
We also learned that we need to maximize the height of the center of mass of the car off the ground (below the track)
- Therefore, weight should be concentrated near the rear of the car, as that point will be higher at the start line.
- We need to make sure that the car doesn't do a wheelie though, so the weight should probably be in front of the rear axle
It will also be important to minimize friction on the car
- Friction between the wheels and the ground
  - The wheels should touch the ground as little as possible
- Friction between the wheels and the axles
The wheel design is also important.
- Make as light as possible and minimize the rotational inertia

Design PArt 2

Weight should be concentrated near the rear of the car, but in front of the rear axle
The car needs to be as low profile as possible to reduce drag
Ideally only three wheels need to touch the ground
Ideally only one edge of the wheel needs to touch the ground (not the entire tire)
Axles should be polished to reduce friction between axles and wheels
Lubricant should be added to reduce friction between axles and wheels
Wheels should have thinner tires to concentrate mass at the center of the wheel
Wheels could even be like washers (no tire)

Our design was made to minimize the weight at the front of the car while maintaining nice aesthetics.

Final Design

The final design for our pine car turned out pretty well, although it could have used more time with the final touches. As the wheels were attached, the axles were greased with graphite to reduce friction, and the car weight was calibrated using a small hole on the bottom with some putty. Additionally, only three of the cars wheels make complete contact with the ground to further reduce friction.

Rotational Inertia Calculations

These calculations prove that wheel mass distribution greatly affects rotational inertia.

Control car

We also designed a simple car to use as a control subject.

A higher rotational inertia means more torque is required to rotate the object. Hence a lower rotational inertia leads to less torque needed to rotate the object faster.

Fluid Dynamics

Drag is another factor that affects the velocity of the car. We attempted to use solid works fluid simulations to calculate the drag coefficient.

Results

After trying the car for the first time, I noticed that it was far slower than any of the other models, even the baseline "brick" on wheels. It turned out that one of the wheels had a tiny imperfection that was preventing it from turning all the way around. This shows how even the smallest of detail can have a huge impact on performance. After that, however, I set up a race between this car and the Brick to see how much our physics knowledge had allowed us to improve upon the original format. Despite the lack of a proper track it was clear that the new car accelerated faster on the downhills, and could travel farther and faster on the straightaways. Clearly some of our changes had been effective.

To better understand which changes in particular had worked, we put the new car against some other older cars that were correctly weighted. The new one continued to win, suggesting that one of the primary reasons for it's success came from the newly greased axles that reduced friction. Upon adding lubrication to some of the other car's axles, we noticed that the races got much closer, with the new car even losing a few. This was probably because many of the other cars also were well weighted and had polished axles, but also had thinner wheels, giving them an advantage in acceleration.

Conclusion

Ultimately, we believe that our research into pinewood derby cars was a success, as it allowed us to create a much more competitive model than the generic builds that most might come up with, only by making a few strategic decisions. Proper weight distribution (in wheels and body) and friction seemed to have the biggest impact on performance, with little changed by air resistance or overall weight. Hopefully you all found this project interesting, and maybe it'll come in handy if you ever find yourself competing in a pinewood derby race!

Tensegrity Sculpture Analysis

About the Project

Due to the limitations of COVID19, not everyone had the materials to help with the process of building the physical pinewood derby car. So the team decided that to fill the time waiting for the physical models, we would analyze the physics of those nifty physics sculptures to left built using a tensegrity principles.

What is Tensegrity?

Tensegrity is a structural principle that focuses on using continuous tension to create stable structures. It stands for "tensional integrity".

You will most likely see this principle in physics sculptures but you can find it in large scale architecture as well!

Initial Process

Most of the research part of this project went into Chapter 12 of our physics textbook, which dissect topics such as equilibrium, indeterminate structures, as well as elasticity; those three concepts are integral to understanding tensegrity.

Technical notes could be found in our OneNote page, I'm not going to post them here because I don't think it would be very interesting to look at.

The right is a lego tensegrity sculpture that Harrison built for this.

As we continued research on analyzing the tensegrity structure to the left, we started to realize that it's too complicated and we don't have the tools to analyze a three dimensional object like that yet, so we decided to analyze an easier and more common model, the 3 strut prism.

Analysis of the 3 strut Prism

The 3 strut prism is one of the simplest examples of a tensegrity sculpture and can be extended into 4 struts, 5 struts, and so on. There are a lot of analysis on this structure so we picked this one as we have more resources to look at.

The Problem

One of the hardest part in building a 3 strut t prism is calibrating the right length for the tendons, if they are either too long or too short, you'll end up with a pile of strings and rods, and not a stable prism. So our problem here is to calculate the tendon length using given constants.

The Calculation

Starting out as a simple (but unstable) triangular prism, we are given the constants for rod length and the end tendon (the strings that forms the triangles at the end of the rods) length. But we the main tendons that makes the structure stable.

As you can see in the explanation above, you have to twist the triangular prism and attach the main tendon to make the structure stable, and the length of that tendon has a very specific value because it wouldn't work if it doesn't apply enough tension to the structure.

That is the length we are trying to find.

Here we put the 3 strut prism (w/o main tendons) on a 3 dimensional polar graph. We define the different variables and establish the twist angle from a top down view.

Here, we evaluate our givens and variables and form a question. With the question we move forward with a basic formula and plug in the appropriate constants and variables that applies for us.

Here we use take the derivative of the equations we formed above and find the minimum critical point for the minimum length of the tendon and solve for the rest.

With our givens, our main tendons came out to be around 6.21 inches.

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