Did you know that circles aren't the only shapes that can roll? In fall 2021, I took a course called experimentation and measurement, where the final project asked us to conduct our own experiment using our choice from different types of lab equipment on campus. My team decided to use a rolling car ramp to measure the efficiency of non-circular rolling profiles.
Circles are one example of an infinitely large family of constant-diameter shapes. The most common non-circular constant diameter shape is called the Reuleaux Triangle. It's constructed from the intersection of three spheres whose centers are coincident on the edges of the other two. Any "diameter" slice taken through the shape will have the same diameter, which is equal to the radius of the shape.
I waterjet cut the main profiles out of 3/4in Aluminum plate, and then turned a shoulder out of them on the lathe. The size and depth of this shoulder was very precise. In our experiment, we would compare the triangular roller to a round wheel, so it was important that the two masses had near identical masses and moments of inertia about their rotating axes.
To better demonstrate how this shape has constant diameter, I 3D printed a solid with the same property, by intersecting four spheres:
For a more in-depth explanation of how this shape was constructed, check out this video:
After cutting out the raw blanks on the waterjet, I cleaned them up on a manual lathe and mill.
Inspection revealed that these parts were within 0.3% of the mass and 0.5% of the Moment of Inertia compared to the circular wheels we modeled them after.
Once I finished machining the triangles, I fixed them to a piece of threaded rod and set them rolling:
The wheels wobbled as expected, but now all that was left was to compare their performance to a regular round wheel and determine exactly how much energy was lost to friction and the eccentric rotation of these wheels:
In the end, we quantified exactly how much energy was lost when rolling a non-round wheel versus a regular round wheel. We found that a Reuleaux triangle wheel had less than 60% of the maximum kinetic energy that the round wheel exhibited in rotation.
In this experiment, my team verified our knowledge that a circle is indeed the optimal shape for a wheel. While the results of this experiment may seem unsurprising, none of the engineers in my group thought that the Reuleaux triangle would provide superior performance to a standard round wheel, and that was not the reason we conducted this experiment. Besides scholastic motivation (the project was required, after all), this project was a way to explore the dynamics of non-uniform rolling solids and quantify the expected drop in efficiency. The rolling method we demonstrated in this lab further did not utilize the constant-diameter property of these wheels.
This project was instrumental, however, in motivating me to continue making videos. To this day, the videos I made for this project are my most-viewed ever, with the series receiving over 10 million views as a whole. Thank you for reading, and feel free to check out my other projects!
