These threads always enter that twilight zone where the discussion is either above my head or totally outside the realm of relevance. I'm inclined to believe it's the latter, but I'm not above admitting that my understanding of fluid mechanics and solid body dynamics isn't all that good. Good for DGCR? Maybe. But I'll leave it at maybe.
I don't understand what makes you say this. You might even be right in SOME cases, but I think it's far more likely that lift is pointing toward the "top" of the disc. At some point, if the disc's angular momentum changes direction (i.e. banks/rolls/rotates), doesn't that mean that there's some force acting through the disc but not through the center of mass? If that's not lift or drag, what else could it be?
I may have been unclear, so I'll go into more detail. Let's draw some vector axes on the disc: X is the vector pointing through the back of the disc to the front. Y is the vector pointing from left to right across the disc, and Z is the vector pointing straight up from the center of the disc and straight down from the bottom. Lift by definition always points through the Z vector, and drag always points through the X vector. In actuality there are a bunch of forces in a lot of different directions who's net value is pointing in some direction between X and Z. The X portion is called drag, and the Z portion called lift. The point where are all of these forces summed up produce a zero moment (or zero torque) on the disc is the center of pressure. You are correct that this point is very rarely the center of mass. Just because lift points up in the Z direction, does not mean that it's pushing up from the center of the disc.
The lift is always pointing in the Z axis, even if the disc is tilted. This is essentially why a hyzer goes left. Gravity is pointing down, and lift is pointing both up and to the left. If a disc is at a 45 degree angle the lift vector is pointing at a 45 degree angle to the ground. If a disc is vertical the lift vector is pointing parallel to the ground.
I don't understand what the gravity vector has to do with this. I do think gravity is very important in the flight path of tomahawks and thumbers, but I think it's because of how much the y-direction velocity changes (more than with standard backhand or forehand throws). This, in turn, causes the angle of attack and lift/drag forces to change dramatically from beginning to end of an overhand throw.
Gravity is always important because it's a significant force on any throw. The big reason why it's important is that it's counteracting lift.
Let's take 3 throws for example, one by Simon Lizotte, one by me, and one by my mom. All these throws are going to be released at a shallow angle of attack, let's just call it 5 degrees.
Simon throws fast so his disc at 5 degrees is generating lift > gravity.
I throw pretty slow so my disc at 5 degrees is generating lift = gravity.
My mom has a noodle arm so her disc at 5 degrees is generating lift < gravity.
What's going to happen to these throws. Simon's throw is going to have a net upward acceleration (because lift is greater than gravity), so his disc maybe after a few seconds will reach an angle of attack of 1 or 2 degrees where lift = gravity.
My throw is going to continue on it's trajectory shortly after release because lift = gravity.
My mom's throw is going to gain downward velocity (because gravity > lift), such that her disc will be at a higher angle of attack shortly after release.
Eventually they will all reach a point where the lift force is nearly equal to the force of gravity. For Simon his disc will be at a low angle of attack and ascending, for me, it'll be flying at a higher angle of attack neither ascending or descending, and my mom's will be falling out of the sky at a steep angle of attack.
Now tilt these all of these discs to vertical so that the gravity vector is perpendicular to the lift vector. Now gravity is no longer pulling down against lift, the only force acting on the disc along the Z vector is lift. Eventually all these throws trajectories will change until the angle of attack reaches the zero lift point, because there is no gravity fighting it.
In an earlier post I mentioned a very simple thumber example, thrown vertically. It was just for illustration, as I don't think any decent overhander would ever throw like this. Dang, I just wish I had the time and equipment to study this stuff, cuz I really do think these things are interesting. What I'd really love to see (at least while reading this forum) is a video showing a tomahawk or thumber with lift, drag, velocity, and angular momentum vectors at all points during flight from release to landing. One can always dream...
I'm leaving the rest of the quote below, for completeness, but I think the premise is wrong. Also, the more I read it, the more confused I get. Earlier in your post you had mentioned that aerodynamic center doesn't relate to disc golf. That sounds possible to me. But I think what you're talking about below is the center of pressure, right? And the lift/drag forces that act through that center of pressure should be the ONLY forces causing a torque on the disc, right? If I'm wrong, I'd love to be corrected. Am I missing something?
You are correct, I'm talking about the center of pressure.
I'll explain the aerodynamic center as well so you can understand why it's not really important in disc golf:
As you increase the angle of attack of a wing the lift coefficient increases, so basically a wing flying really fast at a low angle of attack is generating the same amount of lift as a wing flying slow at a very high angle of attack. For a cambered wing, at a low angle of attack the center of pressure is towards the rear of the wing. As the angle of attack increases it moves forward toward a point about half way between the center and the front of the wing.
Let's now imagine our wing is a wrench and this point half way between the center and the front is a nut. If we push up slightly on the back of the wrench, we generate a certain amount of torque. We have a long lever, and a little bit of force. If we move close to the nut and push really hard, we end up with same torque, because we have a much shorter lever, but are compensating with increased force. This is essentially what is happening at the aerodynamic center, force increases as we move center of pressure closer, but the distance decreases so you end up with the same torque.
Now this is useful if you're designing an aircraft to simplify this one torque that is affecting it, since the wing is fastened to a larger craft. You can essentially measure the torque at the aerodynamic center and not worry about the changing lift coefficient. With a flying disc, the disc is the aircraft, so it's pretty much irrelevant. The only torque we are worried about is the torque around the center of the mass, since this is what will cause precession, not the torque as calculated at some point towards the front of the disc.
The torque around the center of mass is what causes the disc to precess. A nose down torque will cause the disc to turn over, and a nose up torque will cause it to fade. You can measure all of the forces around the disc and find a point where there is zero torque, this is what is called the center of pressure. You can visualize it as a line through the disc pointing in the direction of the net lift and drag force. If it is in front of the center of mass, it will cause the disc to nose up, and if it's behind it will cause it to nose down.
Now if you put the disc at an angle where lift equals zero, and all you have is drag, what is the net torque around the center of mass? As sidewinder pointed out for a symmetric disc, it would be zero. This is because the aerodynamic pressures pushing the disc down are exactly equal and opposite the pressures pushing up, because the surfaces are identical. For a cambered wing this isn't the case. The top and bottom are totally different, so while the total force pushing up is equal to the total force pushing down, they are not pushing in the same places. For a cambered wing this results in a nose down torque around the center of mass. So a cambered wing at the zero lift angle of attack is always going to have a nosedown torque. Hence a thumber pans right and a tomahawk pans left.