Pitch and roll on curvy throws
The disc has two angles, not one
The following lesson is something that many experienced throwers already know, whether implicitly or explicitly, through experience. But I've found this lesson to be helpful in teaching newer players to throw inside-out and outside-in throws.
The common way to teach inside-out and outside-in throws ("curvy" throws) is to tell people to put the outside edge of the disc up (for outside-in) or down (for inside-out). From here on, I'll only discuss outside-in ("OI") for simplicity.
Many instructional videos or articles will discuss this angle—how much the 'outside edge' of the disc is up. For example, this YouTube video says: "the difference between [the OI] and the flat backhand is the angle at which you release the disc...you want to angle the outside edge of the disc upwards...". Or this one where she throws OIs at different angles and says "all I'm changing is the angle of the disc....". This old USA Ultimate video says: "changing the angle that you release the disc at will change the course of its flight. Discs released with the outside edge up are called outside-in throws..." (Rowan has a video called "How To Curve & Shape Your Forehand in Ultimate Frisbee", but he's discussing body position—torso, arm angle, etc—and not discussing the disc, so it's not relevant to the discussion here.)
Ultiworld's feature on the backhand makes a similar point:
Additionally, you can shape the flight of the disc with your angle of release. On a lower-power throw thrown on an inside-out (hyzer) angle, you can get the disc to bend through the air. You can do the same with an outside-in (anhyzer) angle, arcing away from the body and then back towards the middle of the field.
Where these lessons are lacking is that a thrown disc has two angles. Teaching this concept is simple enough, and, in my experience, this knowledge can help newer players more efficiently learn to throw with shape.
Pitch and Roll
In aerodynamics, a flying plane has three angles: pitch, roll, and yaw.
Let's get yaw out of the way first. Yaw is how much the nose (of the plane or disc) is pointing to the left or right. We don't need to talk about yaw when throwing a frisbee, because it's a symmetrical, spinning disc. That leaves us with the other two angles.
Roll is the angle a plane has when one of its wing tips is closer to the ground and the other is closer to the sky. On a frisbee throw, the roll is equivalent to the "OI angle" discussed above—it's how much you angle up the outside edge of the disc. Roll is "the angle" that they're talking about in the sources above when people say they're changing "the angle" of the disc.
Here's what roll angle looks like on a plane and a frisbee. The left (from our perspective) wing of the plane is lower than the right wing; the same is true for the disc:
Planes and frisbees also have a pitch angle. Pitch is how much the nose is pointing up or down. It's a little harder to visualize because you can't point the nose of the frisbee too far up (or down) and still have a useful throw—in the image below, the frisbee's pitch angle is maybe only 5 degrees. Many hucks are thrown with the nose pitched slightly up. This causes the disc to float nicely, as the air is pushing on the slightly exposed underside of the disc, causing it to hang in the air longer and slow down.
Pitch angle looks like this:
Pitch angle also influences a throw's shape
These two angles—pitch and roll—exist on every throw, whether curvy or flat. Changing the pitch angle (the nose up/nose down) angle on a curvy throw is what makes it either soft or blade-y. Adding a little roll angle to a flat, soft forehand gives you an OI throw that hangs in the air and curves slowly.
Understanding that pitch influences a throw's shape helps us resolve an issue that seems to be very common among beginners. When learning to throw an OI, they're told to "put the outside edge up". However, when they do that, they inadvertently put the nose of the disc up as well. They try to throw an outside-in, and the disc goes outside...but doesn't come back in. With the nose up, the disc floats and stalls in the air instead of curving back towards the receiver.
When we use the language of a disc only having one angle, "the angle", the only solution to a disc that goes outside-but-not-back-in is to tell our thrower: you need more angle. But this isn't right—often what they need isn't more (roll) angle on the outside edge. Instead, they need to change the pitch angle—they need to put the nose down so the disc bites back towards the ground and curves back "in", instead of floating and stalling.
If we teach players that there's only one angle to change to put shape on throws, they'll lack the knowledge they need to fix issues in their technique and develop a full complement of throws.
I find that this concept—these two angles—are easy enough to teach to most beginners (though, to be clear, I'm not coaching any young kids). Learning that they need to adjust the nose angle down can help a player master the OI more quickly than they otherwise would. In my experience it's almost always the case, at least for OIs, that they'll need to learn to put the nose down and not up.
Final thoughts
I hope a clearer understanding of pitch and roll can help us teach throws more efficiently. For more experienced players, perhaps it can help you to have a clearer mental image of your throws. Changing the pitch angle changes the flight path in ways that we might naively assume are due to the roll angle. Here are a few other quick examples:
When learning to pull, some of my IO backhands were turning over and turning into OIs. It wasn't because they "weren't IO enough", instead I had the nose of the disc up too much. Putting the nose down helped the throw maintain its shape for longer.
Thinking about nose up/nose down can help us understand our upside down throws. When a hammer "double helixes", it's often because we've put the nose too far up (as described well by Rowan in this video). You shouldn't just have "one" hammer—be able to change the nose angle to make it floaty or blade-y depending on what the situation calls for.
But control of the nose angle isn't just something we use to keep our hammers from double-helixing. It's a more generally useful concept—it's a core part of what determines the flight of every curving throw.