The physics of flight paths

In my ongoing experiment to see how technical I can make these posts without people getting annoyed, this is a new frontier. Not for the faint-hearted today!

When you throw a long disc, with a lot of pace, you need to start it more inside-out than a shorter throw. (You doubtless know that already.) At high speeds, the disc tries to flip towards an outside-in angle, so you need to start the disc with more I/O – sometimes nearly vertical for really big throws.

And yet, at the end of the flight, that same throw will die off to the left (for a right handed backhand) – exactly the opposite behaviour. It turns one way at high speed, and the other way at low speed. This is very odd.

And much more difficult to explain than you might think. Fortunately, I know you all love a bit of physics…

It’s not easy to come up with possible explanations – even wrong ones. It’s pretty counter-intuitive when you think about it that a disc should turn different ways at different speeds.

Obviously the disc is symmetric, so that doesn’t help us. There IS an asymmetry in its movement – one side is spinning towards where it’s going and one side is spinning away – so perhaps this means there’s more lift on one side than the other. But why would that swap over at low speed? We might be able to explain the disc tipping one way, but there’s no way that idea can explain it tilting back the other way later on. Whatever made it turn over is surely still happening. It might be happening a bit less strongly as the disc slows, but it should surely still be pushing in the same direction.

Fortunately, Bill Nye to the rescue, demonstrating a key concept we’ll need:

There are three concepts involved in our overall explanation. First is the reaction-at-a-right-angle thing that is demonstrated in the video. Second, we need to think about the lift on the disc. And third, we need to think about the angle of attack of the disc to the air it travels through.

The angle of attack is how much the front edge of the disc is raised – how much ‘stall’ is on the disc. A completely flat disc has a zero angle of attack. A disc with the front edge up, with a bit of touch and stall on it, will have a positive angle of attack – somewhere from 0-20° probably.

But that’s the angle relative to the ground – not to the air. A disc that is horizontal may well start with a 0° angle of attack to the air, but at the end, as it slows and falls, this will have changed. Even if it’s still flat in relation to the ground, it is now travelling downwards, and so its angle of attack to the air has gone way up. A disc that loses all its forward speed and ends up dropping straight down at the end would have as much as a 90° angle of attack – it’s hitting the air with the full flat underside of the disc even though it’s still horizontal (to the ground).

So the angle of attack is almost always low at the start of the flight¹ and much, much higher at the end as the disc starts to fall to earth.

Why does any of that matter? Well, it turns out that the lift force on the disc – the force that keeps it in the air longer than a brick – does not always act in the centre of the disc but toward the front or back. And it further turns out that the determining factor for where that force acts is the angle of attack². When the angle of attack is less than 9°, the lift acts behind the middle of the disc – toward the back.

Let’s think through the consequences of that. Gravity can be assumed to act at the centre of mass of the disc – which for a symmetric single-material object is going to be in the dead centre. So the centre of the disc is being pulled down – but somewhere towards the back of the disc, the lift is pushing up.

If we push down in one place and up in another, the disc should twist – that’s obvious. If we push the back of the disc up while the middle is pulled down, then the front of the disc should tip down. It should nosedive (and actually, it does, when there’s no spin on it.).

But spin changes everything, just like Bill was telling us. The spinning object makes the force act at 90° to where it normally would, and so instead of twisting from front to back as you might expect, the disc twists left to right. What started I/O will straighten; what started flat will flip over³.

And when the angle of attack is more than 9° – either because it’s thrown with a lot of stall, or because it has started to fall to earth – the lift force acts towards the front of the disc. By the same logic as before, the throw will now die off in the opposite direction. The angle of attack late in the flight is almost always much higher than 9°, as the disc loses forward momentum and drops down to the ground, and so it will die off⁴.

So – now you know. It isn’t actually the speed of the disc that influences which way it tilts in flight, but the angle of attack. This information seems close to useless (although fun) – but it does have some implications for gameplay. It means that the more stall you put on a throw, the less I/O you will need.

Your high hucks will die left; your low hucks will flip right. It doesn’t mean you threw it with too much or too little I/O – it means you threw it with too much or too little for the amount of stall you put on it. The height of a huck affects how much it will turn, and you need to compensate with the right amount of I/O to deal with that.

And now you know why those very short passes need to start outside-in. If you throw it so gently that it immediately starts to fall to earth, then it will never have a ‘flipping’ phase; it will only die off. It will start with a steep angle of attack, and you need to allow for that in the throw you make.

I don’t imagine many people will learn anything from this which changes how they play or coach – but I don’t care. I love this stuff… 🙂

1 Even a disc thrown upwards with the front edge raised will have a low angle of attack early on – it’s angled up, but it’s also travelling up early in the throw so the angle of attack to the air is low. Only air-bounce throws have a really sizeable angle of attack early in the throw (or very soft throws – meaning very little lift – which immediately start falling to earth).

2 This is really complicated! You can if you like just accept it as fact. It may just be a complex result of the way the airflow travels over the disc – some nasty equations in fluid dynamics that we really don’t want to get into.

But one thing I like to think about is that there are two types of lift on the disc – one caused by the ‘wing’ shape of the disc (i.e. the air has further to travel over the curved top than the flat bottom, meaning lower air pressure above the disc and thus some lift via the Bernoulli effect) and one caused just by the angle of attack (e.g. if you hold your hand out of a car window and angle it to the wind, it will feel lift just because it hits the air at an angle – nothing to do with wing shapes!).

With a flat disc – a 0° angle of attack – there’s none of that car-window lift at all, so all the lift is from the disc acting like a wing. Let’s assume that acts toward the back of the disc. If we assume that the car-window effect acts towards the front of the disc, and increases with the angle of attack, then at some point (which turns out to be above 9° for an Ultrastar) that lift will be larger than the Bernoulli lift, and the average position of the lift force will be towards the front of the disc.

That’s a possible explanation – no idea if it would be right though!

3 At higher speeds, there’s more lift and hence there’s a stronger force trying to twist the disc. Longer, faster throws will flip more than shorter, softer ones with the same angle of attack – which is why you need to start your hucks inside out.

You can fight it to some extent though – having more spin makes it harder for the disc to be twisted (due to the angular momentum), so more spin means the disc will hold its line better, both against the flipping force early on and the dying off force at the end. Discs with faster rotation fly straighter for longer.

4 The only way to prevent the angle of attack rising during the throw (and hence the disc trying to die off left) is to throw the disc downwards – front edge down – so that the throw never loses forward momentum (since gravity helps to accelerate it and fight the drag). This is a pretty useless option in Ultimate as the ground tends to get in the way – though it can be done on a downhill disc-golf hole. It’s possible to approximate what frisbee-scientists would call a ‘downward steady glide’ – a straight and unchanging flight. Like I say though, that can’t be done in Ultimate… your throws will all change orientation at some point.