# Tilted Axes, Spirals, and Dynamic Balance

I would think the wobble sign would denote a positive or negative rotation axis no? i.e. clockwise as opposed to counter-clockwise precession. In that case the underside / topside of the disc would be exposed from a different side of the disc so to speak as viewed from the front while wobbling. It's still not entirely clear to me how that exactly breaks the flight symmetry however.
I'm not sure i follow, but that might be me.

For a free disc, the wobble has to go around the disc at double the spin rate, i believe. So i don't think it could go the other way?

Hmm, that might be a bad link, Feynman said it was half the spin rate. Anyway, the spin and wobble are tied i think.

I'm not sure i follow, but that might be me.

For a free disc, the wobble has to go around the disc at double the spin rate, i believe. So i don't think it could go the other way?

It's largely in regards to sign conventions and a coordinate axis. Angular velocity has a (pseudo) vector direction associated with it (right hand rules and what not).

When we're usually talking about spin we're usually just discussing magnitudes (rpms), and not in a vector sense. A backhand throw from a lefty and righty rotate opposite of each other, and consequently have vectors that point opposite of each other, so they have the opposite sign in a coordinate sense.

Disc wobble is another type of rotation and consequently has its own angular velocity (directionality) associated with it. As such if the precession about the spin axis is in different directions (clockwise vs counter-clock wise as viewed from the top) they will have the opposite sign in a vector sense. Which is what I'm wondering the TechDisc software is doing with the plus and minus shenanigans.

It's largely in regards to sign conventions and a coordinate axis. Angular velocity has a (pseudo) vector direction associated with it (right hand rules and what not).

When we're usually talking about spin we're usually just discussing magnitudes (rpms), and not in a vector sense. A backhand throw from a lefty and righty rotate opposite of each other, and consequently have vectors that point opposite of each other, so they have the opposite sign in a coordinate sense.

Disc wobble is another type of rotation and consequently has its own angular velocity (directionality) associated with it. As such if the precession about the spin axis is in different directions (clockwise vs counter-clock wise as viewed from the top) they will have the opposite sign in a vector sense. Which is what I'm wondering the TechDisc software is doing with the plus and minus shenanigans.

Maybe it's that, or they accommodate right and left hand throwers by recording a +/- data point.

Hmm, that might be a bad link, Feynman said it was half the spin rate. Anyway, the spin and wobble are tied i think.

I'm not sure i follow, but that might be me.

For a free disc, the wobble has to go around the disc at double the spin rate, i believe. So i don't think it could go the other way?

IIRC the wobble rate is 2x the spin rate, but IDK that dampening the magnitude affects the spin rate or how it affects. I also read somewhere that drag doesn't really slow spin rate much, not sure if true or how true.
Feynman said it backwards when he told the story about the plates and was quoted. His math was the correct 2x.

I think this vid is saying the wobble direction is opposite to the direction of precession.

I didn't know where else to put this but thought it was interesting in context of weird tilted axis & body balance & countering effects. Bit of body learning value in there.

Tilted axis super spiral:

I haven't looked at the wobble part of the dynamics yet, but it's a really interesting question. The wobble definitely means that angular momentum is transferred between the axes, but not sure if you can say that you need to take momentum from the spin to damp the wobble. But the off-axis torque could initially have been used to give the disc more spin instead, so you definitely lose something there.

I am trying to set up a simulation now of how the wobble affects the aerodynamics, so should have some data there soon. My guess would be that the wobble doesn't create extra turn, and that it has more to do with release angle being thrown off, but we will see.

Alright, so I did some pretty complex computational fluid dynamics calculations including wobble, and the results are very interesting! It seems my hypothesis that wobble doesn't create extra turn was wrong.

First off, here is a visualization of the simulation with wobble, where red color is high velocity and blue color is low velocity. The disc is travelling from right to left here. Note that I've fixed the wobble angle (10 degrees) and frequency here, so there is no damping or anything, it's just to see the effect the wobble has on the aerodynamics.

And here is the drag coefficient and moment coefficient. I start the wobbling around the 1 second mark, so we can see how the coefficients change compared to a throw without any wobble. The drag increases as expected, and the moment oscillates around the static value as the nose dips up and down. Remember that negative moment means turn and positive moment means fade. But we clearly see that the oscillation is not symmetric, the moment drops more when the nose is down compared to how much it increases when the nose is high during the wobble. This means that the net effect will be increased turn compared to no wobble. This comes in addition to the fact that off-axis torque will reduce the spin rate, which also lowers the stability of the disc and makes it turn more. I could go more in-depth on the reason this happens, but to keep it short it is because the air flow going under the disc changes more due to the dynamic wobbling (the wake becomes smaller compared to a static disc) compared to the flow over the disc.

Alright, so I did some pretty complex computational fluid dynamics calculations including wobble, and the results are very interesting! It seems my hypothesis that wobble doesn't create extra turn was wrong.
Thank you for this awesome fluid dynamic stuff! Yeah I was thinking the increased drag reduces both speed and spin, would reduce distance, and makes the disc turn more. At least at first. I know there's some sort of stabilization going on due to gyroscopic forces, so the wobble reduces fairly quickly in flight. But the damage is done on the front end of the flight, where wobble is greatest. Also there may be some trace of wobble that continues for quite awhile, if reduced. I've had years to study my own relatively high wobble (I've edited literally hundreds of hours of video of this) so I've spent a lot of time thinking about it despite no significant training or knowledge of the physics involved.

That said, let's talk about distance. In the simulations, distance actually increased due to more wobble. It appears to me that the added turn allowed the disc to flip up more and the flight path it was on was altered in order to make the disc fly farther. This was not expected by me. I figured the added drag from more wobble would cause the flight plate becoming more visible to wind forces, therefore slowing it down. But that doesn't necessarily mean reduced distance if the flight path ends up better for traveling farther. That said, if you could somehow get the same flight path with less wobble, I think there would be more distance.

So I think there's still some more experimentation that would need to be done on that front, by people with more knowledge, experience, and training.

Thank you for this awesome fluid dynamic stuff! Yeah I was thinking the increased drag reduces both speed and spin, would reduce distance, and makes the disc turn more. At least at first. I know there's some sort of stabilization going on due to gyroscopic forces, so the wobble reduces fairly quickly in flight. But the damage is done on the front end of the flight, where wobble is greatest. Also there may be some trace of wobble that continues for quite awhile, if reduced. I've had years to study my own relatively high wobble (I've edited literally hundreds of hours of video of this) so I've spent a lot of time thinking about it despite no significant training or knowledge of the physics involved.

That said, let's talk about distance. In the simulations, distance actually increased due to more wobble. It appears to me that the added turn allowed the disc to flip up more and the flight path it was on was altered in order to make the disc fly farther. This was not expected by me. I figured the added drag from more wobble would cause the flight plate becoming more visible to wind forces, therefore slowing it down. But that doesn't necessarily mean reduced distance if the flight path ends up better for traveling farther. That said, if you could somehow get the same flight path with less wobble, I think there would be more distance.

So I think there's still some more experimentation that would need to be done on that front, by people with more knowledge, experience, and training.

Yes, I guess the increased turn can give more distance in some cases. But like you point out, then there would be another line, or another disc, that would give you even more distance.

And like I said before, I have some concerns on how the TechDisc simulator handles this. I doubt they have gone to the level of detail of these types of fluid simulations or experiments. Don't get me wrong, I love my TechDisc (it has quantitatively proven that I throw just as bad as I thought I did…), it's just the healthy skepticism that comes with being a scientist.

Alright, so I did some pretty complex computational fluid dynamics calculations including wobble, and the results are very interesting! It seems my hypothesis that wobble doesn't create extra turn was wrong.

First off, here is a visualization of the simulation with wobble, where red color is high velocity and blue color is low velocity. The disc is travelling from right to left here. Note that I've fixed the wobble angle (10 degrees) and frequency here, so there is no damping or anything, it's just to see the effect the wobble has on the aerodynamics.

View attachment 339754

And here is the drag coefficient and moment coefficient. I start the wobbling around the 1 second mark, so we can see how the coefficients change compared to a throw without any wobble. The drag increases as expected, and the moment oscillates around the static value as the nose dips up and down. Remember that negative moment means turn and positive moment means fade. But we clearly see that the oscillation is not symmetric, the moment drops more when the nose is down compared to how much it increases when the nose is high during the wobble. This means that the net effect will be increased turn compared to no wobble. This comes in addition to the fact that off-axis torque will reduce the spin rate, which also lowers the stability of the disc and makes it turn more. I could go more in-depth on the reason this happens, but to keep it short it is because the air flow going under the disc changes more due to the dynamic wobbling (the wake becomes smaller compared to a static disc) compared to the flow over the disc.

View attachment 339755
I don't have an awful lot to add to the conversation just now, but i couldn't let this pass without saying how completely incredible it is that you're doing this. Thank you!

This is surely publishable research if you wanted to, right? I've never seen wobble dealt with properly in the literature.

I don't have an awful lot to add to the conversation just now, but i couldn't let this pass without saying how completely incredible it is that you're doing this. Thank you!

This is surely publishable research if you wanted to, right? I've never seen wobble dealt with properly in the literature.
I lied, i actually do have a question, now that i think about it.

We've talked a bit (not sure if in this thread or another) about the beating-in of a disc and what it is that might make it turn more. I wonder if this result impacts that discussion?

A common theory is that the lip gets bent down when a disc hits things, and/or that the bottom of the disc is scraped off - both of which lower the effective parting line height. As i said before, i personally think the rim would be bent both up AND down when the disc hits things - and if that were the case, could this asymmetry you've found in the effect on the moment explain the fairly slight additional turn we see?

I lied, i actually do have a question, now that i think about it.

We've talked a bit (not sure if in this thread or another) about the beating-in of a disc and what it is that might make it turn more. I wonder if this result impacts that discussion?

A common theory is that the lip gets bent down when a disc hits things, and/or that the bottom of the disc is scraped off - both of which lower the effective parting line height. As i said before, i personally think the rim would be bent both up AND down when the disc hits things - and if that were the case, could this asymmetry you've found in the effect on the moment explain the fairly slight additional turn we see?
Also when I raised the "dimple tech" idea there was an interesting interaction in this thread I am not qualified to comment on:

Also when I raised the "dimple tech" idea there was an interesting interaction in this thread I am not qualified to comment on:
Yeah - it's all fun stuff.

I'm fairly convinced by the argument that dimples on the flat of the disc (like the raketen had) won't help a golf disc like they do a golf ball, because a disc is already so much more aerodynamic.

But Eric's numbers here raise the possibility of a different kind of dimple - deliberate tiny nicks in the very edge of the rim. I think honestly that Eric needs to get that idea patented quick and then get one of the disc companies to pay him a lot of money to research it. It might well offer up new combinations of glide/turn/fade that are otherwise very hard to achieve out-of-the-box.

And like I said before, I have some concerns on how the TechDisc simulator handles this. I doubt they have gone to the level of detail of these types of fluid simulations or experiments.
Eric, thanks, is the perceived increased distance coming from the TechDidc simulator or is there any science behind it? In my experience, the increased drag caused by the wobble (during the initial part of the flight, where drag is already higher and until gyroscopic dampens it) reduces air speed significantly.

Eric, thanks, is the perceived increased distance coming from the TechDidc simulator or is there any science behind it? In my experience, the increased drag caused by the wobble (during the initial part of the flight, where drag is already higher and until gyroscopic dampens it) reduces air speed significantly.
I think Eric is saying that the examples of increased distance are simply because the wobble adds turn to a disc that otherwise wouldn't achieve a full flight - wobble might add distance for a given stability/hyzer angle/nose angle, but couldn't add extra maximum distance potential to an 'optimised' throw.

I think Eric is saying that the examples of increased distance are simply because the wobble adds turn to a disc that otherwise wouldn't achieve a full flight - wobble might add distance for a given stability/hyzer angle/nose angle, but couldn't add extra maximum distance potential to an 'optimised' throw.
This is what I was taking away so far, but interested if I'm off my rocker.

This is what I was taking away so far, but interested if I'm off my rocker.
You may be, more generally, i couldn't say. But it's a safe bet that you're right on this one. There's no way that wobble, with additional drag, can add distance potential, unless perhaps the lift associated with wobble-drag was somehow way stronger than ordinary smooth-flight lift. Which seems highly unlikely, to say the least.

I think Eric is saying that the examples of increased distance are simply because the wobble adds turn to a disc that otherwise wouldn't achieve a full flight - wobble might add distance for a given stability/hyzer angle/nose angle, but couldn't add extra maximum distance potential to an 'optimised' throw.
Yes, but where is the perceived distance increase conversation coming from, (Tech Disc or science)? Real world examples of more turn caused by wobble are nearly imperceptible because BH wobble is typically dampened before you can see any effect on turn and significant FH wobble seems to quickly increase fade.

Yeah there is a difference between speed and distance, basically. Distance might increase with wobble - but only if the increased turn produces a better flight line. But no doubt the disc slows down in flight to some extent because of the drag. But as Chris says above, I think the amount of wobble diminishes pretty quickly in the flight, so the change in turn might be more dramatic than the change in speed.

Yes, but where is the perceived distance increase conversation coming from, (Tech Disc or science)? Real world examples of more turn caused by wobble are nearly imperceptible because BH wobble is typically dampened before you can see any effect on turn and significant FH wobble seems to quickly increase fade.
Perceived distance increase was noted by Nick, from the simulator. Eric just agreed that it is possible for a particular throw to get more distance, if it previously didn't have optimal turn - but also made clear that he didn't have total faith in the simulator anyway.

Personally, I'm convinced that wobble has a measurable effect on real-world turn. It's especially clear in a headwind. Based on slow motion footage, I'd say the disc can definitely wobble for the first 10 yards or more out of the hand before damping is complete, which surely must have an effect given the size of the asymmetry Eric found.

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