[Help] Comprehensive Explanation of Disc Golf Physics

[IronIceandFire]

Warning: it's about to get technical.

I've been looking around for a comprehensive and technical explanation of why discs fly the way they do and everything I've found has been either outright incorrect or not as technical as I wanted. Even if there is another good explanation out there, I want to make a good explanation easier to find on Google.

Therefore, I've compiled an explanation that to my knowledge shows technically how discs work. If any physicists out there catch any errors, please let me know, the last thing I want to do is look like a buffoon claiming that my wrong answer is right.

I should note that there is another post on this website about this topic, but 1) I want to use slightly more technical language and 2) I'm not confident that the effects it describes are entirely responsible for disc flight.

Part A: Rotational physics.

Here's a quick refresher on the physics of precession. Let's say you have a totally flat disc floating in space. When you spin the edge counter-clockwise, you are imparting a force F at a radius r. This creates a torque, T:

T = r x F

Using the right hand rule, point your four fingers along the radius of the disc and curl them towards the direction of force: your thumb points towards the torque vector. See Figure 1.

Figure 1.

Say the disc continues rotating counter-clockwise, and also has mass m. In this case, there is a velocity vector tangent to the disc at radius r. This creates an angular momentum, L:

L = m(r x v)

Similarly, point your four fingers on your right hand along the radius and curl towards the velocity: your thumb points towards the angular momentum vector. See Figure 2.

Figure 2.

Now, what happens if you put a force downward on the edge of the disc while it is spinning? First, we can establish that before you apply force, this disc has the same angular momentum of L. Then, our force at a radius creates a torque. This time, however, using the right hand rule we find that the torque, T, is along the radius of the disc. See Figure 3. In order to find the new angular momentum, we add the torque vector T and the previous angular momentum vector L (this is a simplification I think, but it works with the unit vectors and gives us the right idea). In Figure 3, this new angular momentum is Lnew.

Figure 3.

This means that while force is being applied downwards on the right edge of a disc spinning counter-clockwise, it will pitch away from the viewer. If you don't believe me, try it! Spin a disc on your finger in that manner. If you tap the right edge of it while spinning, it will fall away from you.

Likewise, if that force is upwards, the disc will pitch towards the viewer.

Part B: Application to straight-flying discs.

In this section, assume that the disc is released with a velocity parallel to the ground and with its center axis orthogonal to the ground.

How does this affect disc flight? This is where parting line height (PLH) comes in. For our purposes, the parting line height will be the height at which the side of the disc begins to curve back towards the disc.

Figure 4 shows two extremes of PLH. Disc 1 has a PLH all the way at the top of the disc, and disc 2 has a PLH all the way at the bottom. Imagine both discs are released so that air is coming straight at them, as the figure shows.

Figure 4.

Zooming in, imagine that air is made up of little individual frictionless balls, each of which behave about the same way (this is a valid assumption). Each ball has a velocity, Fair (mistakenly thought it was a force initially, bear with me). When it contacts the disc, it imparts a resultant force, Fr, which is perpendicular to the surface of the disc because there is no friction. See Figure 5.

Figure 5.

Let's break down Fr for both disc shapes. For disc 1, there is a force upward, F1, and a force to the left, which is just drag. For disc 2, there is a force downward, F2, and drag. See Figure 5.

Remember what happens with a downward/upward force on the edge of a disc: it pitches forward or backward.

In this case, as a result of the forces applied to them from air, disc 1 will pitch towards from the viewer, and disc 2 will pitch away from the viewer. Disc 1 is OVERSTABLE, disc 2 is UNDERSTABLE.

This is why discs with a high PLH are overstable, and discs with a low PLH are understable.

Part C: Application to falling discs.

You may have seen a glaring omission in the previous section: if air causes (RHBH) understable discs to pitch right, how is it they can "recover" and fade left?

In this example, imagine that the disc is not traveling parallel to the ground, but rather is falling as it is traveling forwards, still orthogonal to the ground. In this case, air would not come straight at the side of the disc, but would come up at it. See Figure 6.

Figure 6.

The resultant force on disc 1 looks very similar to the previous example. However, the resultant force on disc 2 looks very different: again, the force on the disc is parallel to its surface because there is no friction. This time, however, that force is directly upwards because of the different angle of the disc's surface.

Let's break down Fr again. For disc 1, there is again a force upward, F1a, and drag. For disc 2, since the bottom of the disc was parallel to the ground, there is no drag, only an upward force. See Figure 6.

This time, both discs experience an upward force on their right edge while spinning counter-clockwise. This causes both discs to pitch towards the viewer.

This is why all discs act overstable at the end of their flight.

Part D: Application to rising discs.

How do discs glide any distance through the air? This is a result of Bernoulli's principle. This principle states that a high-velocity region of fluid will have a lower pressure than a low-velocity region of fluid.

When air flows over a disc, it has further to go when it passes under the disc than when it passes over a disc. As a result, the air is slowed down underneath the disc. Bernoulli's principle states that this slow air will have a higher pressure than the fast air over the disc. As a result, the disc will feel a net force directly upward along its axis of rotation. See Figure 7. While this force is stronger than gravity, the disc will experience an upwards acceleration. The faster a disc is moving, the more lift it will experience.

Figure 7.

Notably, this rising motion has the opposite effect of a falling motion, causing a disc to act more understable.

If discs never rose, they would immediately start falling, acting overstable. Because they experience lift, they not only can stay in the air longer, but also have time to act understable.

Discs act more understable when thrown faster because a) they experience more lift, making them act understable, and b) they don't fall as soon, giving them more time to act understable.

Discs act more understable when they are beaten in and when they are bent like a saddle because both phenomena force the PLH down, exposing more of the top of the disc.

Part E: What determines the fade of a disc.

So far, we have been talking about the shapes of different drivers, though the same principles can be applied to any disc shape (or any spinning object, for that matter). However, why are putters so different than drivers?

At the short ranges involved with putting, it is easiest to aim if the disc flies exactly the direction in which you threw it, and does not substantially fade to either side. What does this mean? It means that the same upward force on the edge of the disc has less effect on the angular momentum vector. In order to resist that force, the disc must have a higher moment of inertia. This is a measure of how hard an object is to spin. An ice skater with arms outstretched has a high moment of inertia, and because it is reduced when she brings her arms in, she is easier to spin, and spins faster.

How can a disc have "its arms outstretched"? This is the same question as "how can a disc have its weight further from its center axis"?

This is achieved by changing the shape of the edge of the disc. In Figure 8, assume the discs have the same weight, and assume that the weight of the edge in the red circle is the same for both. If we approximate the center of mass (com) of the weight in the red circle, we find that the com of the driver is closer to the center axis than the com of the putter. That is, rd is shorter than rp.

Figure 8.

As a result, the moment of inertia for a given driver is lower than that of a putter. Therefore, the putter will resist pitching from the forces of air more than the driver.

That is why putters fade less than drivers.

Conclusion

In case the photos don't show up in the post, here is a link to all of them: https://imgur.com/a/2CedRdV

There are a few things here I haven't mentioned. First, what determines the speed of a disc. I imagine this is simply a measure of its wind resistance, but I don't know.

Second, what determines the glide of a disc and why the bottom rim of some discs is curved. I imagine this is something to do with fluid dynamics, which I know very little about.

Third, the other post about physics on this website. Frankly, I didn't follow it very well because I couldn't see the figures. However, the parts I did understand were more or less based in good science, but would not create enough force to significantly affect the flight of a disc.

 

[OveHalseth]

Great explanation!

Do you have any thoughts/explanation of how more/less spin on a disc would affect it's flight?

 

[Meillo]

I'd say that the fade at the end of the flight is caused mainly be slowing down (thus acting more overstable) than by falling (having different wind angle and thus higher PLH). Think of stall-out shots as an extreme example.


I'd love to get a physical view on the beating in to fly more understable topic. There's still the myth (IMO) out there that hitting stuff would bend the wing down to result in a lower PLH. I think that this makes no sense. E.g. kipping off the ground removes parts of the lower wing, thus making the PLH higher. Most people would hit trees and rocks rather with the underside of the wing than with the upperside, because a disc falls down on them and rather flies nose-up than nose-down when hitting anything. The increasing understability probably comes from roughed disc surface and thus more air friction. Could you get on that topic with physics?

(You'd be king, if you could explain the different flights and the different seasoning schemes of Teebird and Eagle in comparison. Why does the Eagle have more turn and more fade? Why does the Teebird lose fade first, but the Eagle develop turn first? The molds are very similiar, but with a flatter outer part of the upper wing on the Eagle, and more thicknes there on the Teebird.)

 

[txmxer]

L + T =/= Lnew

 

[oldmandiscer]

I'd say that the fade at the end of the flight is caused mainly be slowing down (thus acting more overstable) than by falling (having different wind angle and thus higher PLH). Think of stall-out shots as an extreme example.


I'd love to get a physical view on the beating in to fly more understable topic. There's still the myth (IMO) out there that hitting stuff would bend the wing down to result in a lower PLH. I think that this makes no sense. E.g. kipping off the ground removes parts of the lower wing, thus making the PLH higher. Most people would hit trees and rocks rather with the underside of the wing than with the upperside, because a disc falls down on them and rather flies nose-up than nose-down when hitting anything. The increasing understability probably comes from roughed disc surface and thus more air friction. Could you get on that topic with physics?

(You'd be king, if you could explain the different flights and the different seasoning schemes of Teebird and Eagle in comparison. Why does the Eagle have more turn and more fade? Why does the Teebird lose fade first, but the Eagle develop turn first? The molds are very similiar, but with a flatter outer part of the upper wing on the Eagle, and more thicknes there on the Teebird.)

PLH gets lower when you skip off stuff. The wing gets lower to the table or whatever you measure it on. Yes discs bend when you hit trees and the wing gets bent down lowering the PLH. This is easily seen with a DX Teebird or similar.

 

[seedlings]

Great thread!

PLH gets lower when you skip off stuff. The wing gets lower to the table or whatever you measure it on. Yes discs bend when you hit trees and the wing gets bent down lowering the PLH. This is easily seen with a DX Teebird or similar.

There are also pock mark ding irregularities (dimples) that develop, which change the surface (golf ball).

 

[RFrance]

Here are some published works on Flying Discs or Frisbees.

Dynamics and Performance of Flying Discs, UoM administered thesis: Phd, Noorfazreena Kamaruddin
https://www.research.manchester.ac.uk/portal/files/54511821/FULL_TEXT.PDF

Flight and attitude dynamics measurements of an instrumented Frisbee, Ralph D Lorenz
INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY Meas. Sci. Technol. 16 (2005) 738–748
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=EE7165129C26E24FD49F07C30576F2C6?doi=10.1.1.73.4451&rep=rep1&type=pdf

 

[kevdiv48]

Here is another really good one that has been linked on this site before

Frisbee Flight Simulation and Throw Biomechanics
Thesis for Mater of Science in Mechanical Engineering at the University of California Davis
Sarah Hummel 2003

 

[PMantle]

There's still the myth (IMO) out there that hitting stuff would bend the wing down to result in a lower PLH. I think that this makes no sense. E.g. kipping off the ground removes parts of the lower wing, thus making the PLH higher. Most people would hit trees and rocks rather with the underside of the wing than with the upperside, because a disc falls down on them and rather flies nose-up than nose-down when hitting anything. The increasing understability probably comes from roughed disc surface and thus more air friction. Could you get on that topic with physics?

I think all of this is wrong. I know it is about the PLH because I have cycled drivers enough to see the fact that the PLH lowers. Also, removing parts of the lower wing would lower PLH.

 

[IronIceandFire]

Great explanation!

Do you have any thoughts/explanation of how more/less spin on a disc would affect it's flight?

A higher spin would also increase the moment of inertia, making the disc resist pitching. This is why generally it's recommended to putt with spin: the disc will fade less.

 

[IronIceandFire]

I'd say that the fade at the end of the flight is caused mainly be slowing down (thus acting more overstable) than by falling (having different wind angle and thus higher PLH). Think of stall-out shots as an extreme example.


I'd love to get a physical view on the beating in to fly more understable topic. There's still the myth (IMO) out there that hitting stuff would bend the wing down to result in a lower PLH. I think that this makes no sense. E.g. kipping off the ground removes parts of the lower wing, thus making the PLH higher. Most people would hit trees and rocks rather with the underside of the wing than with the upperside, because a disc falls down on them and rather flies nose-up than nose-down when hitting anything. The increasing understability probably comes from roughed disc surface and thus more air friction. Could you get on that topic with physics?

(You'd be king, if you could explain the different flights and the different seasoning schemes of Teebird and Eagle in comparison. Why does the Eagle have more turn and more fade? Why does the Teebird lose fade first, but the Eagle develop turn first? The molds are very similiar, but with a flatter outer part of the upper wing on the Eagle, and more thicknes there on the Teebird.)

I think that once the roughness reaches a certain point, it does start to affect the disc, making it more understable, though I'm not sure exactly why.

I've attached a picture of the side profile of the (champion) Eagle and the (star) TeeBird here:

I've never thrown the Eagle, but in my experience the TeeBird was on the understable side. Based on the lines I've seen Heimburg throw, the Eagle looks similar to the Thunderbird in terms of stability. If it is in fact less stable than the TeeBird, I have no idea why. My only guess would be the effect of the domed top, which involves fluid dynamics I don't know about. I know I'm not really answering your question well, I apologize! I just don't really know about the intricacies of each flight.

 

[IronIceandFire]

L + T =/= Lnew

Ha ha, I knew someone would get me for that. You're right, it's not as simple as that. However, I sacrificed exact calculations here for intuitive understanding, and the effect I describe is still accurate and easily testable.

 

[IronIceandFire]

I'd say that the fade at the end of the flight is caused mainly be slowing down (thus acting more overstable) than by falling (having different wind angle and thus higher PLH). Think of stall-out shots as an extreme example.


I'd love to get a physical view on the beating in to fly more understable topic. There's still the myth (IMO) out there that hitting stuff would bend the wing down to result in a lower PLH. I think that this makes no sense. E.g. kipping off the ground removes parts of the lower wing, thus making the PLH higher. Most people would hit trees and rocks rather with the underside of the wing than with the upperside, because a disc falls down on them and rather flies nose-up than nose-down when hitting anything. The increasing understability probably comes from roughed disc surface and thus more air friction. Could you get on that topic with physics?

(You'd be king, if you could explain the different flights and the different seasoning schemes of Teebird and Eagle in comparison. Why does the Eagle have more turn and more fade? Why does the Teebird lose fade first, but the Eagle develop turn first? The molds are very similiar, but with a flatter outer part of the upper wing on the Eagle, and more thicknes there on the Teebird.)

I think that your idea about the disc slowing down is very much valid. I agree that it's probably a combination of both factors.

When I think of beating in a disc, I think of someone throwing their disc directly at a hard object, such that the disc contacts early in its flight. Early in a disc's flight, there is still enough lift such that the disc contacts the object while moving upward, which would function to bend the PLH down, increasing understability.

Regarding the Eagle and TeeBird, I'm afraid I'm fairly useless when it comes to specific flight characteristics. However, I can comment on stability. I've never thrown the Eagle, but I have thrown the TeeBird, and I found it to be fairly understable, such that I didn't have enough touch to throw it consistently forehand (why do discs act more understable FH? I might try that one later). Watching Heimburg throw the Eagle, it looks like its stability is close to the Thunderbird, though that's only speculation.

I've attached the side profile of the (champion) Eagle and the (star) TeeBird:

Looking at the side profiles, I would predict that the TeeBird would be more understable than the Eagle. However, I also believe your testimony. I think that if the effect in practice is opposite of predicted, it would be something to do with the domeyness of the TeeBird compared to the Eagle. However, the fluid dynamics associated with that is beyond me.

 

[IronIceandFire]

How do I delete this? lol I thought my other reply hadn't posted

 

[bsammons]

It just dies as a "need to be deleted" post haha.

There's a post out there that discusses the fluid dynamics of a disc when thrown. Someone better at searching than I should be able to find it, it discusses pretty much all the questions on here that you don't have the background to answer - would be a great thread to link to this one, to get an all-inclusive "pretty much every force that acts on a disc" thread.

 

[armiller]

Warning: it's about to get technical.

Just curious if you've looked through this one yet: https://www.dgcoursereview.com/forums/showthread.php?t=2250

It's a sticky in this Technique forum. As you mentioned and have noticed, there is a lot of misinformation out there and even in these better threads. But with a little sifting, it's not too hard to find the good info and more trustworthy sources. I guess that's the downside of having a discussion thread on an internet forum. No textbooks specifically on frisbee flight, as far as I can tell...

I'll try to take a look at your longer initial post later. I'm at work now.

 

[IronIceandFire]

Just curious if you've looked through this one yet: https://www.dgcoursereview.com/forums/showthread.php?t=2250

It's a sticky in this Technique forum. As you mentioned and have noticed, there is a lot of misinformation out there and even in these better threads. But with a little sifting, it's not too hard to find the good info and more trustworthy sources. I guess that's the downside of having a discussion thread on an internet forum. No textbooks specifically on frisbee flight, as far as I can tell...

I'll try to take a look at your longer initial post later. I'm at work now.

This is the post I reference in my original. I think that a lot of the effects it talks about are too minor to have significant effects on the flight of discs, and some effects are simply not accurate at all the way they are explained. I'd gladly listen to supporting evidence, though.

 

[Meillo]

PLH gets lower when you skip off stuff. The wing gets lower to the table or whatever you measure it on. Yes discs bend when you hit trees and the wing gets bent down lowering the PLH. This is easily seen with a DX Teebird or similar.

I think all of this is wrong. I know it is about the PLH because I have cycled drivers enough to see the fact that the PLH lowers. Also, removing parts of the lower wing would lower PLH.

When I think of beating in a disc, I think of someone throwing their disc directly at a hard object, such that the disc contacts early in its flight. Early in a disc's flight, there is still enough lift such that the disc contacts the object while moving upward, which would function to bend the PLH down, increasing understability.

I could agree on the hitting a tree in the early part of the flight (when the velocity is greatest and thus the bending is strongest). But why do my discs start to fly understable as well despite I suffered severely from nose-up releases? ;-) I'm pretty sure my discs did not hit trees with the upper part of the wing.

If I have a disc with some dome, it's easier to follow the thought that it could bend down, but for a very OS disc, like maybe a Justice or a puddletop Zone, how could their wing bend down? Take a puddletop Zone ... that wing would rather bend up, because of the puddletop and because of the wing shape. But a beat-in Zone becomes more understable as well.

I'm still thinking that the wing bending down could be a factor on some discs, but not the general explanation for beat-in discs becoming more understable. I guess that the friction of the roughed-up surface might be the main reason.


Also, I cannot follow the statement, that removing a part of the lower edge of the wing, would lower the PLH. Removing the lower edge of the wing makes the wing definitely higher and thus the PLH higher.

The thing that could make a difference is the notch on Teebird and Eagle-X wings, that differs from Eagle-L wings. Eagle X and L both generally have the same PLH but the X has that notch at the outer end of the lower wing part. This notch makes it more overstable. You see it on many overstable discs. If skipshots remove this notch, it could make it more understable.

 

[Meillo]

Regarding the Eagle and TeeBird, I'm afraid I'm fairly useless when it comes to specific flight characteristics. However, I can comment on stability. I've never thrown the Eagle, but I have thrown the TeeBird, and I found it to be fairly understable, such that I didn't have enough touch to throw it consistently forehand (why do discs act more understable FH? I might try that one later). Watching Heimburg throw the Eagle, it looks like its stability is close to the Thunderbird, though that's only speculation.

I've attached the side profile of the (champion) Eagle and the (star) TeeBird:

Champion Eagles are typically very overstable, as you describe. But Star and DX Eagles are not. They do have turn, and fly according to the flight numbers (-1/3), which (newish) Champion Eagles do not. Teebirds vary in wing height and thus HSS quite a lot. You can have anything from -2/1 to 0/3 over runs and plastics. Dome on Teebirds and Eagles varies greatly as well. If you want to compare Teebird and Eagle-X wings, then you need to get two discs with the same PLH and dome. Then you find the difference on the upper wing within the first 10mm from the outside: the Teebird is more blunt and thicker there.

The HSS differences of new Teebirds is very much in direct relation to the PLH. Get a high-PLH Teebird (in premium plastic) and you'll discover the real Teebird flight, which resists turn well (unless into headwinds).

 

[oldmandiscer]

I could agree on the hitting a tree in the early part of the flight (when the velocity is greatest and thus the bending is strongest). But why do my discs start to fly understable as well despite I suffered severely from nose-up releases? ;-) I'm pretty sure my discs did not hit trees with the upper part of the wing.

If I have a disc with some dome, it's easier to follow the thought that it could bend down, but for a very OS disc, like maybe a Justice or a puddletop Zone, how could their wing bend down? Take a puddletop Zone ... that wing would rather bend up, because of the puddletop and because of the wing shape. But a beat-in Zone becomes more understable as well.

I'm still thinking that the wing bending down could be a factor on some discs, but not the general explanation for beat-in discs becoming more understable. I guess that the friction of the roughed-up surface might be the main reason.


Also, I cannot follow the statement, that removing a part of the lower edge of the wing, would lower the PLH. Removing the lower edge of the wing makes the wing definitely higher and thus the PLH higher.

The thing that could make a difference is the notch on Teebird and Eagle-X wings, that differs from Eagle-L wings. Eagle X and L both generally have the same PLH but the X has that notch at the outer end of the lower wing part. This notch makes it more overstable. You see it on many overstable discs. If skipshots remove this notch, it could make it more understable.

I think because of the flight plate on top is structural not allowing the disc to bend that way, so the weak point (bottom) is going to bend down. Think of the entire disc folding like a hard shell taco. It's going to fold at the point of least resistance so the flight plate is like the bottom outer shell of the taco.

Now the disc doesn't fold that much of course unless it;s supper floppy, but I think the flight plate is creating the impact downward into the wing.

Thinking about it too is the point that joins the flight plate and wing will act like a hinge, so it will bend down from the hinge point. The center of gravity for the wing even on a FB is lower then the hinge.