I wanted to share a project that I've been working on recently. I'm not super into Beyblades (yet) but my boys just got their first set and I naturally had to figure out how they worked. Obviously there are tons of factors that go into making a good Beyblade, but the one that I focused on first was the moment of inertia (MOI). The MOI is the physical property of an object that describes its resistance to rotation, or its ability to keep rotating. It also determines how much energy an object has while spinning. Players often use mass as a stand in for MOI because it is easier to measure, but it doesn't tell the whole story. The total mass along with the distribution of the mass determine the MOI of an object. As a result, it's possible that a lighter Beyblade could have more rotational energy if its mass is properly distributed. So I decided to figure out how to measure it.
Experimental Setup
The short version is that I measured the period a rotating pendulum using a Beyblade as the mass. With that, I could calculate the moment of inertia. The rest of the section is only necessary if you want to do your own tests or you just like sciency stuff. Skip to "Results" if you like.
In all of my schooling (I'm a mechanical engineer), MOI was always calculated by measuring the geometry of an object. For example, the MOI of a disk-shaped object is 1/2*its mass*(its radius)^2. But calculating the MOI of an irregular object is difficult because they're not always easy to break down into simple geometric shapes. Fortunately, there is still a way to measure their MOI. It involves a weird looking thing called a trifilar pendulum.
A trifilar pendulum is essentially a pendulum that twists instead of swings. It has a small platform suspended by three long strings. You place an object on the platform, give it a small twist and watch as it spins back and forth. The period of the oscillation (how fast is goes back and forth) is related to the MOI. The slower it spins (for a given mass), the higher the moment of inertia.
I won't derive the equations for you (you can get that here), but there were quite a few details I had to pay attention to in order to get the setup right. If you don't build the pendulum correctly, the part's MOI will be overwhelmed by other effects in the system. Mainly, you want to design it such that the oscillations are as slow as possible and that they don't decay too quickly. I was using a stop watch to measure the period, so I had to make sure that inexact starting and stopping errors were small compared to the total measured time. Here are some good practices for building and using your trifilar pendulum.
![[Image: pn1Qbtn.jpg?1]](https://i.imgur.com/pn1Qbtn.jpg?1)
After constructing the pendulum I tried it out using a couple objects with simple geometries; a small wooden block and a stack of metal washers. I compared the MOI's calculated from dimensional measurements to the MOI's calculated from the pendulum and was consistently within +/-1%.
Results
I tested all of the Beyblades that I have, which include four from Hasbro's Burst Evolution series and eight from the Burst Rise series. Sorry, no Takara Tomy beys. I'm sure they're more interesting since there's more variation between Beyblades, but there's still some cool stuff going on here.
![[Image: iHlRmDR.png]](https://imgur.com/iHlRmDR.png)
(Interactive version here, with mouse over data and stuff)
The first thing to look at is a chart of MOI vs Mass. I expected a strong correlation because a higher mass means a higher MOI but I would also expect some variation around the trends. There could be some heavier parts that have a lower MOI because of their shape. Within each part type, the correlation with mass is pretty strong, with just a couple outliers. For example, Xcalius X3 is a beefy layer from the Evolution series, but it has a lower MOI than several of the Rise layers, even when those layers are lighter. The Rise layers have a larger diameter, giving them better mass distribution than the smaller Evolution layers. The disk MOI's stay closer to the trend line since there isn't much variation in their shape within Hasbro's Burst system. Comparing layers to disks, however, really shows the effect of shape on a part's MOI. While disks have a higher MOI on average, there are some layers that surpass disks, even with less weight. They don't have as much mass but they get it further from the axis of rotation, which means they would supply more energy while spinning.
Another chart I found helpful shows the breakdown of a Beyblade's total MOI by part so you can see which parts play the biggest role. In most cases, the disk is the highest contributing factor, but it some the layer is. I wasn't expecting that!
![[Image: eaMoiOf.png]](https://imgur.com/eaMoiOf.png)
So what do people think of this data? Is it useful? Would it help you build better combos if you had MOI for all your parts? Is weighing parts close enough? Are other aspects of the Beyblade just way more important than MOI? Like I said, I pretty new to battling and have zero competitive experience so I'm interested to hear feedback from the community.
Cheers.
Google Sheets Links Edit: After some of the discussion in the thread, I decided to make another chart that uses concepts more familiar to bladers. It plots each part's mass and Outer Weight Distribution (OWD) on separate axes. This makes it easier to see how the two aspects of moment of inertia (mass and shape) each contribute. Is MOI high because a part has a lot of weight or because it has well distributed mass. The chart illustrates a part's MOI by where it sits in the quadrant. The further up and to the right, the higher the MOI. The lines show the different levels of MOI as you move closer to the upper right corner. (Interactive Chart)
![[Image: lvNb9Xq.png]](https://imgur.com/lvNb9Xq.png)
Experimental Setup
The short version is that I measured the period a rotating pendulum using a Beyblade as the mass. With that, I could calculate the moment of inertia. The rest of the section is only necessary if you want to do your own tests or you just like sciency stuff. Skip to "Results" if you like.
In all of my schooling (I'm a mechanical engineer), MOI was always calculated by measuring the geometry of an object. For example, the MOI of a disk-shaped object is 1/2*its mass*(its radius)^2. But calculating the MOI of an irregular object is difficult because they're not always easy to break down into simple geometric shapes. Fortunately, there is still a way to measure their MOI. It involves a weird looking thing called a trifilar pendulum.
A trifilar pendulum is essentially a pendulum that twists instead of swings. It has a small platform suspended by three long strings. You place an object on the platform, give it a small twist and watch as it spins back and forth. The period of the oscillation (how fast is goes back and forth) is related to the MOI. The slower it spins (for a given mass), the higher the moment of inertia.
I won't derive the equations for you (you can get that here), but there were quite a few details I had to pay attention to in order to get the setup right. If you don't build the pendulum correctly, the part's MOI will be overwhelmed by other effects in the system. Mainly, you want to design it such that the oscillations are as slow as possible and that they don't decay too quickly. I was using a stop watch to measure the period, so I had to make sure that inexact starting and stopping errors were small compared to the total measured time. Here are some good practices for building and using your trifilar pendulum.
- Long, thin strings: Mine are 850 mm. I can hang it from a kitchen counter top and it almost reaches the ground. The longer the strings, the slower the oscillations. I used sewing thread to keep the strings as light as possible.
- Small, lightweight platform: The pendulum technically measures the MOI of the platform + the object on it. You want to minimize the MOI of the platform so the part is the biggest factor to the behavior of the pendulum. (more on the platform design later)
- Measure multiple oscillations: I usually measure the duration of 50 oscillations, then take the average to find the length of a single period.
- Use small oscillations: The equations derived for the pendulum motion are only accurate for small angles of rotation. I goofed this up the first time I used the pendulum and had to do a lot of digging to find out why my measurements were so far off.
After constructing the pendulum I tried it out using a couple objects with simple geometries; a small wooden block and a stack of metal washers. I compared the MOI's calculated from dimensional measurements to the MOI's calculated from the pendulum and was consistently within +/-1%.
Results
I tested all of the Beyblades that I have, which include four from Hasbro's Burst Evolution series and eight from the Burst Rise series. Sorry, no Takara Tomy beys. I'm sure they're more interesting since there's more variation between Beyblades, but there's still some cool stuff going on here.
The first thing to look at is a chart of MOI vs Mass. I expected a strong correlation because a higher mass means a higher MOI but I would also expect some variation around the trends. There could be some heavier parts that have a lower MOI because of their shape. Within each part type, the correlation with mass is pretty strong, with just a couple outliers. For example, Xcalius X3 is a beefy layer from the Evolution series, but it has a lower MOI than several of the Rise layers, even when those layers are lighter. The Rise layers have a larger diameter, giving them better mass distribution than the smaller Evolution layers. The disk MOI's stay closer to the trend line since there isn't much variation in their shape within Hasbro's Burst system. Comparing layers to disks, however, really shows the effect of shape on a part's MOI. While disks have a higher MOI on average, there are some layers that surpass disks, even with less weight. They don't have as much mass but they get it further from the axis of rotation, which means they would supply more energy while spinning.
Another chart I found helpful shows the breakdown of a Beyblade's total MOI by part so you can see which parts play the biggest role. In most cases, the disk is the highest contributing factor, but it some the layer is. I wasn't expecting that!
So what do people think of this data? Is it useful? Would it help you build better combos if you had MOI for all your parts? Is weighing parts close enough? Are other aspects of the Beyblade just way more important than MOI? Like I said, I pretty new to battling and have zero competitive experience so I'm interested to hear feedback from the community.
Cheers.
Google Sheets Links Edit: After some of the discussion in the thread, I decided to make another chart that uses concepts more familiar to bladers. It plots each part's mass and Outer Weight Distribution (OWD) on separate axes. This makes it easier to see how the two aspects of moment of inertia (mass and shape) each contribute. Is MOI high because a part has a lot of weight or because it has well distributed mass. The chart illustrates a part's MOI by where it sits in the quadrant. The further up and to the right, the higher the MOI. The lines show the different levels of MOI as you move closer to the upper right corner. (Interactive Chart)
![[Image: 88-E6-FCCC-E8-AF-48-FB-A3-F2-32-E31-D8-DDA09.jpg]](https://i.postimg.cc/q7DDdNkV/88-E6-FCCC-E8-AF-48-FB-A3-F2-32-E31-D8-DDA09.jpg)
![[Image: 84-CB9286-C306-4-D2-D-B3-E2-CD380-EA5-E132.jpg]](https://i.postimg.cc/sgfQnGSM/84-CB9286-C306-4-D2-D-B3-E2-CD380-EA5-E132.jpg)
