Measuring Beyblade Moment of Inertia

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Measuring Beyblade Moment of Inertia - vandergus - May. 02, 2020

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.

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.

For the platform, I needed something really light but also a way to align parts with the center. In order to get an accurate measurement, the axis of rotations of the part and the pendulum need to be lined up. I didn't see an easy way to get both of these things from my current household supplies so I decided to have it 3D printed. I could get something that weighed just a few grams as well as create custom alignment features for different Beyblade parts. I ended up using little adapter pieces that could be swapped out depending on what type of part I was measuring. I have to make some corrections to my current model (drivers don't fit) but I can make it available if anyone is interested.

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.

(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!

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)

RE: Measuring Beyblade Moment of Inertia - Cake - May. 02, 2020

This is awesome - I need to make my own testing setup to measure the MOI on my MFB collection...

RE: Measuring Beyblade Moment of Inertia - DeceasedCrab - May. 02, 2020

This is fascinating. I've always wondered what would happen if a serious physicist or mechanical engineer went nuts on the actual testing. Kudos to you for actually investigating the science.

I would ask, if possible, because many of us are 12 or younger, could you give us a brief explanation of the numbers on MOI. Does higher MOI mean it sounds longer before inertia kicks in? What's the significance of the MOI over mass number? I'm sorry if you already explained it, but I got lost in the details a little bit.

So over the years, bladers have been obsessed with easier to measure features. Mass, shape, precession, life after death (LAD) which is how long it continues to spin on the beystadium after it's tipped, Outward Weight Distribution (OWD) and Center Weight Distribution (CWD).

It's cool to learn about other features that affect beys.

RE: Measuring Beyblade Moment of Inertia - vandergus - May. 02, 2020

(May. 02, 2020 2:16 AM)DeceasedCrab Wrote: This is fascinating. I've always wondered what would happen if a serious physicist or mechanical engineer went nuts on the actual testing. Kudos to you for actually investigating the science.

I would ask, if possible, because many of us are 12 or younger, could you give us a brief explanation of the numbers on MOI. Does higher MOI mean it sounds longer before inertia kicks in? What's the significance of the MOI over mass number? I'm sorry if you already explained it, but I got lost in the details a little bit.

So over the years, bladers have been obsessed with easier to measure features. Mass, shape, precession, life after death (LAD) which is how long it continues to spin on the beystadium after it's tipped, Outward Weight Distribution (OWD) and Center Weight Distribution (CWD).

It's cool to learn about other features that affect beys.

I'll give it a shot.

If you have two beyblades spinning at the same speed, and they have the same weight, but one has a higher moment of inertia it means it has more total energy. If they both have the same driver (same friction against the stadium) then the one with a higher moment of inertia will spin for longer. It has more energy to start so it takes longer to use it all up.

Moment of Inertia itself is influenced by two things, a part's mass (weight) and a part's shape. If two parts have the same shape but one weighs more, it will have a higher MOI. If two parts have the same weight but one has more Outward Weight Distribution, it will have higher moment of inertia. In this way, Outward Weight Distribution is basically focusing on the shape part of MOI. If you look at the equations of MOI for simple shapes, they always consist of a mass term and a term related to its geometry. Like its length or diameter or something. The OWD is basically the geometry term.

Hopefully that helps. I don't talk to a lot of 12 year olds :). My boys are still too young for this stuff.

Edit: You can actually isolate the OWD from this data if you wanted to. Take the MOI and divide it by the mass. Some people call this the MOI to mass ratio. If you plot these numbers for the disks, they are all very similar, since all the disks are basically the same shape.

RE: Measuring Beyblade Moment of Inertia - BuilderROB - May. 02, 2020

(May. 02, 2020 2:43 AM)vandergus Wrote: Edit: You can actually isolate the OWD from this data if you wanted to. Take the MOI and divide it by the mass. Some people call this the MOI to mass ratio. If you plot these numbers for the disks, they are all very similar, since all the disks are basically the same shape.

True. However, discs have different types of distribution. Some discs have more weight shifted towards the center, while some have the weight shifted towards the outer part. That and the weight determine the usefulness of a disc competitively.

RE: Measuring Beyblade Moment of Inertia - RustyWheelz - May. 02, 2020

That's really cool Vandergus. I'd be happy to read more if you continue to experiment. Like yourself, I'm a dad who took up blading to have a fun topic my boys and I could share. These seem like they'd make a great basis for science lessons. '0' is a great disc as you've found, heavy and well balanced. 0, 10 & 00 are also heavy and popular.

If you felt so inclined, I'd be curious if the layer/disc combos were always close to the sum total of the MOI of it's parts, or if due to the imbalanced nature of some parts and combos, if you'd find any that deviate meaningfully through harmonious or detrimental pairings?

Something else to consider in determining competitive beys are the various types and their strategies. 'Attack' type parts and beys for example are designed to instigate and benefit from violent collisions causing less aggressive beys solely focused on preserving spin to fail (or burst), so some designs analyzed one way might not capture it's intended value.

RE: Measuring Beyblade Moment of Inertia - Me-has-Bro - May. 02, 2020

vandergus, keep up the great work.

Your charts confirm what most players here have found out doing hundreds of test rounds, for example that R3 and O5 are not the best layers, and that vD5.0C.Fl would probably be the best combo You could build with Your parts (and thus resulting in the highest bar on your bar chart).

Maybe some players don't want to dive into your science, but the results (in form of charts) are very helpful, I think.

So please buy tons of beys (or simply ask kjrules17 if he lends You his collection) and examine on :-)

(sorry for my bad english - I live in Germany).

RE: Measuring Beyblade Moment of Inertia - vandergus - May. 02, 2020

(May. 02, 2020 3:29 AM)BuilderROB Wrote:
(May. 02, 2020 2:43 AM)vandergus Wrote: Edit: You can actually isolate the OWD from this data if you wanted to. Take the MOI and divide it by the mass. Some people call this the MOI to mass ratio. If you plot these numbers for the disks, they are all very similar, since all the disks are basically the same shape.
True. However, discs have different types of distribution. Some discs have more weight shifted towards the center, while some have the weight shifted towards the outer part. That and the weight determine the usefulness of a disc competitively.

Right! If you take MOI/mass, you get a number for each part that represents its OWD. The higher the number the greater the OWD. The lower the number the greater the CWD. It would let you compare OWD between parts more accurately. The combination of the weight and the weight distribution is in fact the moment of inertia.

(May. 02, 2020 7:36 AM)RustyWheelz Wrote: If you felt so inclined, I'd be curious if the layer/disc combos were always close to the sum total of the MOI of it's parts, or if due to the imbalanced nature of some parts and combos, if you'd find any that deviate meaningfully through harmonious or detrimental pairings?

Something else to consider in determining competitive beys are the various types and their strategies. 'Attack' type parts and beys for example are designed to instigate and benefit from violent collisions causing less aggressive beys solely focused on preserving spin to fail (or burst), so some designs analyzed one way might not capture it's intended value.

If all the parts are balanced (center of mass is on the axis of rotation) you're right, you can sum the part MOI's to get the total MOI. Imbalanced parts create a lot of problems with simple addition and even basic pendulum measurements.

I mentioned that you have to have the part's center lined up with the rotation of the pendulum. But for imbalanced parts, I don't always know where the center is. Even if you get an accurate measure of a single part, when you assemble it with a balanced part, its axis of rotation changes, meaning the MOI changes too.

It could be that all these effects are too small to notice. Xcalius X3 and Disk 1 are the only parts I have that is supposed to have some imbalance but I don't think it's very much. I just treat them as balanced parts. But until that is better understood, players should be assume there is more error in MOI measurements for unbalanced parts and beys.

Isn't there a Takara Tomy bey that has a balanced mode and an unbalanced (attack) mode. That would be an interesting beyblade to test, to see if the effect is noticeable.

Your second question is where I was hoping to get more opinions from the community. I know that MOI isn't everything to a Beyblade's performance and certain types may care more about it than others. For example, attacks types still care about raw mass because they want high linear momentum for attacks. Linear momentum, the momentum you have while traveling in a line, only cares about an objects mass, not its MOI. Stamina types, on the other hand, care mostly about rotational momentum. There are also questions about MOI on the top of the bey vs the bottom. If you have high MOI in the disk, it makes you more prone to bursting (I think). Lot's of stuff to dig into!

RE: Measuring Beyblade Moment of Inertia - Cake - May. 02, 2020

(May. 02, 2020 12:43 PM)vandergus Wrote: Your second question is where I was hoping to get more opinions from the community. I know that MOI isn't everything to a Beyblade's performance and certain types may care more about it than others. For example, attacks types still care about raw mass because they want high linear momentum for attacks. Linear momentum, the momentum you have while traveling in a line, only cares about an objects mass, not its MOI. Stamina types, on the other hand, care mostly about rotational momentum. There are also questions about MOI on the top of the bey vs the bottom. If you have high MOI in the disk, it makes you more prone to bursting (I think). Lot's of stuff to dig into!

Burst has some particularly interesting interactions with moment of inertia thanks to the Burst gimmick. Since Bursting is driven by the angular momentum of the Disk/Driver section of the Beyblade as the lower half keeps moving while the Layer takes the force of an impact, you can potentially increase Burst resistance by using a Disk/Driver setup with lower moment of inertia that's less likely to slip relative to the Layer, and/or by using a Layer with greater moment of inertia that will be slowed less by an impact.

Otherwise, greater moment of inertia (all other things being equal) is very desirable for a Beyblade. But, of course, we don't have the luxury of tampering with the Beyblade's mass and mass distribution completely independently of other factors; the shape of a part is also essential for determining its properties in a collision, since every collision between Beyblades is an opportunity to favorably trade angular momentum for linear motion on the opponent (for Attack) or for a greater loss in momentum for the opponent (for Defense and Stamina). Even for parts that won't generally contact opponents, shape can be important for Life After Death, a community term for a Beyblade's ability to keep spinning smoothly with minimal energy loss even when it's precessing far enough to start touching the floor at 2 or more points.

RE: Measuring Beyblade Moment of Inertia - Me-has-Bro - May. 02, 2020

vandergus: The beyblade that can be switched between balanced mode and unbalanced mode is called Alter Chronos. There's a Hasbro Variant of it called Cognite C3 (SwitchStrike series).

Some people (and me) say they dont notice any differences switching between modes of aC3. Maybe one could find a change in MOI with Your experiment...

RE: Measuring Beyblade Moment of Inertia - superrobotking - May. 02, 2020

I would love to see if the MOI correlates with same disc but diffrent number of stars under them

RE: Measuring Beyblade Moment of Inertia - Nitrogenic - May. 02, 2020

(May. 02, 2020 6:55 PM)superrobotking Wrote: I would love to see if the MOI correlates with same disc but diffrent number of stars under them

I think more stars means mroe weight and a better mold.

RE: Measuring Beyblade Moment of Inertia - vandergus - May. 02, 2020

(May. 02, 2020 6:55 PM)superrobotking Wrote: I would love to see if the MOI correlates with same disc but diffrent number of stars under them

I have three Sting disks, a 2 star, a 3 star and a 4 star. Their weights are 19.0 g, 19.0 g, and 18.8 g respectively. The 3 star Sting has an MOI of 4,740 g-mm2 and the 4 star has an MOI of 4,677. I haven't measured the 2 star since it was the same weight as the 3 star.

I added another chart to the original post.

RE: Measuring Beyblade Moment of Inertia - superrobotking - May. 02, 2020

(May. 02, 2020 8:39 PM)Nitrogenic Wrote:
(May. 02, 2020 6:55 PM)superrobotking Wrote: I would love to see if the MOI correlates with same disc but diffrent number of stars under them

I think more stars means mroe weight and a better mold.

Not true as I bought a huge lot of beyblades and weighed most of the disc and there's a difference

https://docs.google.com/spreadsheets/d/1Zqj3Ma6wpmqhtIb1obb2QXLv0NhP0-YelCPOd77dQG0/edit?usp=drivesdk

(May. 02, 2020 9:27 PM)vandergus Wrote:
(May. 02, 2020 6:55 PM)superrobotking Wrote: I would love to see if the MOI correlates with same disc but diffrent number of stars under them

I have three Sting disks, a 2 star, a 3 star and a 4 star. Their weights are 19.0 g, 19.0 g, and 18.8 g respectively. The 3 star Sting has an MOI of 4,740 g-mm2 and the 4 star has an MOI of 4,677. I haven't measured the 2 star since it was the same weight as the 3 star.

I added another chart to the original post.

Very cool! Yeah there has been debate what the stars ment if any.

There's a Corocoro Article by someone at takara tomy explaining it affect the center of gravity but people here are skeptical on this artical for some reason.

RE: Measuring Beyblade Moment of Inertia - Cake - May. 03, 2020

In theory the higher star molds could be marginally heavier, and the 4 star molds would theoretically have ideal weight and balance, but in practice the miniscule mass difference of the addition of a handful of tiny stars is usually drowned out by the effects of random variance in the manufacturing process. The peak quality 4-star Disk is probably better than the peak quality for a 3-star Disk, but any potential extra material from the little stars is no guarantee that the wheel doesn't have inconsistencies in density that negate those benefits.

Ideally, weighing and testing all your parts yourself is the best way to identify your strongest parts, since the random variation is mostly invisible. There have been plenty of rumors that "[X] part/mold/mold stamp/star number" is objectively the best (this goes for all generations, not just Burst), but the only way to confirm or invalidate it for your particular parts is to test it for yourself.

RE: Measuring Beyblade Moment of Inertia - RustyWheelz - May. 03, 2020

I have in hours of combining found that certain combos appear to create a sympathetic symmetry where slight imperfections in each part perhaps are righted in pairing. I'd like to be able to confirm if sometimes the combo receives a greater MOI than the sum of its parts? These lead me to wonder if some happy accidents are pre-planned by TT to be discovered.

Quote:Isn't there a Takara Tomy bey that has a balanced mode and an unbalanced (attack) mode. That would be an interesting beyblade to test, to see if the effect is noticeable.

Operate is one driver which does this with a switchable mode change causing the bey to throw itself around, adding some extra violence at the cost of stamina. Also with the GT system, the extremely unbalanced layer weight Go causes the same effect. Interestingly, by pairing these parts (and mounting them so they counter-balance) you can cancel out some of the effect of both (but at no competitive value).

Quote:Your second question is where I was hoping to get more opinions from the community. I know that MOI isn't everything to a Beyblade's performance and certain types may care more about it than others. For example, attacks types still care about raw mass because they want high linear momentum for attacks. Linear momentum, the momentum you have while traveling in a line, only cares about an objects mass, not its MOI. Stamina types, on the other hand, care mostly about rotational momentum. There are also questions about MOI on the top of the bey vs the bottom. If you have high MOI in the disk, it makes you more prone to bursting (I think). Lot's of stuff to dig into!

So much of the true fun my sons and I share in beyblades is coming to discover the value in parts and combinations of parts so as to be able to create and counter advantages in our family meta. Having more ways to see the value of parts expressed in useful terms would help to visualize how combos might work without the luxury of having every part to test.

Right now TT and Hasbro have simplified numerical expressions to give players an idea of how a bey or in TT's case, certain parts may perform, but they seem to reflect more on the idea of what the part was designed for than a literal reflection of performance and they change relative to new parts coming in, leaving a history of pointless numbers. Perhaps someday, TT or Hasbro might recognize the competitive and educational potential for having a more robust set of real world performance data on parts - but then, for the price, it would probably be pretty hard to reign in expectations vs sample variation.

I'm trying to imagine how a layer could be analyzed in a meaningful way to be able to denote the potential for and probable severity of contact, as well as MOI. Then you could weigh the trades offs when considering builds. That said, I think once experienced, players mostly find a lot of this knowledge becomes inherently understood. Perhaps not explainable, but understood. Additionally, Hasbros slopes and TT's 'teeth' affect the burst rate with TT granting some contact promoting 'attack' type drivers a stronger 'dash' spring to increase viability against high MOI focused parts. Leading to high and low MOI, if you were to open your investigation someday to Takara's new Sparking beys - some featuring a 'double' chassis which is locked to the ring (essentially the disc and layer are fused) - then it changes again how high and low MOI would function on bursting a bey.

RE: Measuring Beyblade Moment of Inertia - superrobotking - May. 17, 2020

vandergus

I just picked up a Digital Sword Launcher because it has a "Power" measuring reader on it. Not sure what "units" its in but I figured this would be fun to try and do some physics and get my brain jogging again with it.

I actually don't know what I can do with Mass, Time and Power. I haven't done physics in roughly 14 years.

But still it might be interesting to check out the Digital Sword launcher purely to have more units of measurements.

RE: Measuring Beyblade Moment of Inertia - ReekoBlader - May. 17, 2020

(May. 17, 2020 6:14 AM)superrobotking Wrote: vandergus

I just picked up a Digital Sword Launcher because it has a "Power" measuring reader on it. Not sure what "units" its in but I figured this would be fun to try and do some physics and get my brain jogging again with it.

I actually don't know what I can do with Mass, Time and Power. I haven't done physics in roughly 14 years.

But still it might be interesting to check out the Digital Sword launcher purely to have more units of measurements.

I’m pretty sure that the units are RPM

RE: Measuring Beyblade Moment of Inertia - vandergus - May. 22, 2020

(May. 17, 2020 6:46 AM)ReekoBlader Wrote:
(May. 17, 2020 6:14 AM)superrobotking Wrote: vandergus

I just picked up a Digital Sword Launcher because it has a "Power" measuring reader on it. Not sure what "units" its in but I figured this would be fun to try and do some physics and get my brain jogging again with it.

I actually don't know what I can do with Mass, Time and Power. I haven't done physics in roughly 14 years.

But still it might be interesting to check out the Digital Sword launcher purely to have more units of measurements.

I’m pretty sure that the units are RPM

I'm pretty sure they're not using real units. I looked into the digital sword launcher when I first started this project because I wanted a way to measure RPM but when I looked at videos of people using it, the numbers didn't look in line with typical RPM values for Beyblades.

If you could measure the launch RPM of a beyblade it would be super helpful, though. With the moment of inertia, and the rotational speed, you can calculate the total rotational energy of the beyblade.

RE: Measuring Beyblade Moment of Inertia - Cake - Jun. 01, 2020

All the needed infrastructure to read launcher RPM is there - the Beylogger almost certainly could spit out actual RPM numbers if it were programmed to do so
Burst launchers have a little window in the top, through which you can see a disk colored in alternating black and white segments. The Beylogger contains an optical rotary encoder - a sensor system that shines a light onto the alternating black and white patches to read the changes in reflectivity as the disk spins. This lets it know how fast the launcher prongs are spinning based on the time between black/white signals - I'm sure it would be possible to at the very least build your own Beylogger knockoff that gives RPM readings instead - I don't know what kind of electronics are in the Beylogger to say whether it's worth trying to retool it. (But it probably isn't.)

RE: Measuring Beyblade Moment of Inertia - MAANMOA - Mar. 25, 2021

Hey you mentioned that you can share the 3d printing blueprint if someone asks for it; can you please please please share it with me? I am doing a research essay on MOI in beyblades and I need to have that trifilar pendulum. Thank you so much in advance

RE: Measuring Beyblade Moment of Inertia - TheRogueBlader - Mar. 25, 2021

I did a project like this a couple months ago for my science fair and it was on Beyblades, but not nearly this advanced