# Aerodynamics stuff

Yeah, i dunno the best language to use really; it's a complicated thing to describe.

So let's say this. My contention is that:

For a hyzerflip, that turns over and then fades back at the end, the disc will be flat - wings-level, i mean - twice. I think that the front to back attitude, relative to the ground, will NOT be the same at those two times. After the turn, the nose will be lower than before.

It would be most pronounced in a strong crosswind, but the effect should exist whenever the disc moves sideways.

I think I understand what you are suggesting, but I'm not sure I have seen that type of behavior in a throw. Do you have an example from disc golf coverage or something? I tried looking at some distance competations now, and the throws look very much like what I get from the simulator.

One thing to be aware of is that when I talk about nose angle, it's always in relation to the disc's coordinate system as it flies through the air. It will look different viewed from the thrower's perspective. And when you bring strong wind into the picture, it could definitely alter the axis that the disc turns about, and gusts and turbulence can obviously make the disc do weird things.

Lissaman and Hubbard show a flare-out in their paper.

This looks to me more like the shape of throw I'd expect in real life, often landing gently rather than dropping steeply at the end. I'll keep an eye out for video of a real throw i guess.

I guess for clarity, since there's more than one discussion going on:

I think the attitude of the disc does change in a meaningful way (disagreeing somewhat with sw22).

And i think the height graph of a disc in flight often looks more like the one in Lissaman than the ones from Eric's simulator (and also, i think the reason for that is possibly that the simulator ignores the changes in attitude).

Does that make sense?

Lissaman and Hubbard show a flare-out in their paper.
View attachment 338894
This looks to me more like the shape of throw I'd expect in real life, often landing gently rather than dropping steeply at the end. I'll keep an eye out for video of a real throw i guess.

Is the range in the above the distance travelled by the disc (horizontal line length), or displacement from the thrower?

The above is not necessarily in disagreement with Eric's simulations if they reduced the horizontal coordinate to line length (i.e. x,y-> s). If you view a disc thrown from the side, its projection is going to look like a steeper descent as it fades when it stops pushing forward.

Is the range in the above the distance travelled by the disc (horizontal line length), or displacement from the thrower?

The above is not necessarily in disagreement with Eric's simulations if they reduced the horizontal coordinate to line length (i.e. x,y-> s). If you view a disc thrown from the side, its projection is going to look like a steeper descent as it fades when it stops pushing forward.
That's a very good point. That might be part if it.

I still feel that Eric's looks odd, though, with peak height happening in the second half of the throw. Whether measured by time, distance or displacement, I'd expect maximum height earlier than that and then a controlled glide down (more like Lissaman shape).

That's a very good point. That might be part if it.

I still feel that Eric's looks odd, though, with peak height happening in the second half of the throw. Whether measured by time, distance or displacement, I'd expect maximum height earlier than that and then a controlled glide down (more like Lissaman shape).

First of all, thanks for questioning my results, it helps to think about things from different perspectives, and maybe we can discover some new things.

You have to be careful with that Lissaman paper, though, what they do there is look at what an idealized lift input would give. In the third figure, shown below, you see that they manually adjust the lift coefficient, more than doubling it at the end of the flight. This was to give an upper bound for distance, but it ignores how the disc would actually behave. They also ignore turn/fade here. A flare-out like that is not realistic, I think. The disc will slow down and start to fade towards the end of the throw. This is somewhat mitigated by the fact that the angle of attack also increases, which increases the lift, as you see in my graph for the max distance throw, but not as much as in the paper by Lissaman and Hubbard.

Thanks - that's helpful. I assumed they were saying just that the magnitude of the lift increased at the end, rather than the lift coefficient. I can see how that would be unrealistic if that's what they did.

I do still think though that their graph better matches my intuitive feeling about a full-flight throw, where lift starts low, rises, plateaus as the disc glides down, and then increases again as the disc stalls out.

It's hard to find a perfect example on video. This is probably close - getting to peak height relatively early, a loooong glide down, and a flare out at the end. The flare isn't especially pronounced, i suppose, but overall this is more the shape i would expect of an optimised full-flight distance shot, rather than the later, steeper fall shown in your graph.

What do you think?

Thanks - that's helpful. I assumed they were saying just that the magnitude of the lift increased at the end, rather than the lift coefficient. I can see how that would be unrealistic if that's what they did.

I do still think though that their graph better matches my intuitive feeling about a full-flight throw, where lift starts low, rises, plateaus as the disc glides down, and then increases again as the disc stalls out.

It's hard to find a perfect example on video. This is probably close - getting to peak height relatively early, a loooong glide down, and a flare out at the end. The flare isn't especially pronounced, i suppose, but overall this is more the shape i would expect of an optimised full-flight distance shot, rather than the later, steeper fall shown in your graph.

What do you think?

It's hard to tell from these video angles, and it's also downhill, but I think the trajectory is actually flatter than it seems towards the end, it doesn't really flare out. Here's another example from a distance competition, that seems to match my result:

The apex of the flight is roughly at the halfway mark, then it travels to the right before more or less dumping out during the fade.

Yeah - i definitely think that a lot of throws match pretty well with your data, including some pretty big throws like eliezra's. But I'm surprised that an optimised throw looks like that.

Looking at your drift and height graphs side by side, the disc is moving a long way right before it reaches peak height, and my experience is that the very longest throws flip over pretty much at the peak height and then glide down to the right. It might be an illusion, but that is how it looks to me.

Getting that glide angle to be stable is very very touchy indeed - normally it will hyzer out or turn too much - but if we're looking at a mathematically optimised throw I'd expect a very long glide phase (and perhaps with a bit of a flare-out to use the last of the vertical momentum before hitting the ground).

Does that make sense? I think a lot of real world throws match your data very well, but i feel like an idealised, optimised distance throw (very much NOT a golf line) would peak earlier and glide steadily down for a long time, which suggests to me that (only right at the margins, admittedly) there is something missing in the model.

The apex of the flight is roughly at the halfway mark, then it travels to the right before more or less dumping out during the fade.
The apices of most of David's throws are closer to the first third of the flight, depending on amount of flip to ani.

The apices of most of David's throws are closer to the first third of the flight, depending on amount of flip to ani.
That's how i see it too.

I'm still thinking about this stuff. Here's a thought - have you ever tried MTA (with an ultimate disc or some other glidey thing, probably a glitch would work)?

Generally you'd throw into the wind, on hyzer but with the nose significantly up, and have it flip up to wings-level-ish and then stall back to you. But if you throw these a lot you'll start to notice a big difference between discs that stall/peak on slight hyzer and those that have a little turn at the peak (not too much turn, else it simply won't come back to the thrower at all!).

The hyzer stall will come back at you like a rocket and be very hard to catch. It was nose up, and is now coming backwards so it's very nose down. But the throw with fractional turn at the peak will often flatten out (in the nose to tail direction) and float back down to you quite gently.

There's a very very clear change in front-to-back orientation when you get it right - you throw it up at 45 degrees and it comes back nearly flat.

You'll see in that video how some of the throws drift down incredibly slowly, and halfway through the video there's a side angle slow motion showing just how steeply the nose is up at release. There's no doubt in my mind that the orientation changes very significantly.

I'm not claiming that the effect is anything like as large in a real golf throw, but i can't see any reason the effect wouldn't exist. And i think for the edge-cases it can matter a great deal.

The apices of most of David's throws are closer to the first third of the flight, depending on amount of flip to ani.

That's how i see it too.

Thanks for adding to the discussion, Chris! It would be really cool to have 3D tracking of the throws, with something like a TechDisc in an open field.

Benji, just to clarify one thing regarding the plots. You say the disc is moving right for a long time before hitting the apex, but it actually hits the apex just as it's starting to move right.

Regarding how early in the flight it hits the apex, I think this is due to the wind. It's important to note that the wind increases with height, so with wind you suddenly also want to get the disc high to get the most benefit from it, introducing another factor into the equation. Here is a comparison where I compare a throw in zero wind with a throw that has a significant left to right tailwind. I also scaled the axes equally for the x- and y-axes so that you don't get tricked by that scaling. Maybe this is more what you are thinking about? The apex is roughly at 1/3 with the wind, and you also get more of a glide/flare-out in the latter phase of the flight.

That's brilliant, thank you. And it's amazing that you get that sudden increase in lift at the end, flaring out, just because of the tail cross wind. Very interesting.

I still think that aerodynamically-induced changes in pitch would have an effect, particularly at the margins. What did you think of the mta examples? Obviously that throw shape is very different, thrown into a 30mph headwind, but that shouldn't really be so different to something thrown 30mph harder on a still day. I still think it's possible for an initial high pitch angle to decrease in flight, and i think the mta stuff is a reasonable demonstration of it happening. Do you see it differently?

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

That's brilliant, thank you. And it's amazing that you get that sudden increase in lift at the end, flaring out, just because of the tail cross wind. Very interesting.

I still think that aerodynamically-induced changes in pitch would have an effect, particularly at the margins. What did you think of the mta examples? Obviously that throw shape is very different, thrown into a 30mph headwind, but that shouldn't really be so different to something thrown 30mph harder on a still day. I still think it's possible for an initial high pitch angle to decrease in flight, and i think the mta stuff is a reasonable demonstration of it happening. Do you see it differently?
I forgot to reply to this. Yes, the MTA stuff is pretty cool. I think it's a different situation, though, as in such a shot the disc slows down all the way to zero at the peak. Then can flip around many different axes depending on where it goes after that point.

I forgot to reply to this. Yes, the MTA stuff is pretty cool. I think it's a different situation, though, as in such a shot the disc slows down all the way to zero at the peak. Then can flip around many different axes depending on where it goes after that point.
I dunno... Funny things definitely happen due to any wind gusts later in the throw, when the disc really has slowed to around zero airspeed - but at the peak, where ground speed is zero, the airspeed is probably at least 20-30 mph because of the wind. You wouldn't want to try and set mta records on a still day.

The flattening out at or around the peak is actually very reproducible in my experience.

Sorry, I didn't mean the shot was unpredictable and due to wind gusts, just that it's different since the disc is transitioning through zero speed at one point. I don't think you can convince me that there are other ways the disc can change its attitude other than gyroscopic precession, though

Sorry, I didn't mean the shot was unpredictable and due to wind gusts, just that it's different since the disc is transitioning through zero speed at one point. I don't think you can convince me that there are other ways the disc can change its attitude other than gyroscopic precession, though
I'm sorry too, i didn't mean to suggest there's anything other than precession happening.

I'm still just imagining that as the nose moves around the disc - and the axis for the precession changes - some interesting things might happen that would have an effect on the edge-cases when you're optimising a simulated throw. The mta is a rather extreme example, i grant you!

Imagine a disc on hyzer travelled an s-curve but without changing attitude at all (so no turn or fade). This is obviously impossible, but just let's imagine it for a thought experiment. The height of the nose would be different when it's traveling left than when it's traveling right, obviously.

Of course, in real life, it does turn and fade, and this is linked to its rightward or leftward movement, and perhaps in just such a way that the nose doesn't actually get higher or lower in the left-moving or right-moving parts of the throw. But it's not obvious to me that that would be the case - it seems intuitively at least possible that the nose actually could move up and down as the turn and fade interact with the curve of the flight path.

I'm probably very wrong, but hopefully I've explained my thinking in a way that let's you see where I'm wrong!

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