This is my analysis of how a dart flies. I'm a pilot, so, I want to learn how to think about this!
I'm still thinking about this, so this is very much a work in progress until I come up with a beautifully simple easy to understand and remember model. Until then, its just ramblings going about how to explain it all and consider everything!
I'm also a flight instructor, so I'm sorta lying through my teeth about some of this stuff? Why -- the purpose is to share knowledge to everyone so they can understand how things happen without being a physicist!
And my disource wanders into trying to figure out how to throw good darts since I am not ... and that should probably head to a new web page!
The dart has a center of gravity, the point at which the balance of the dart is centered. If that happened it would be just like throwing a ball bearing of the same mass of the dart. If we were throwing in a vacuum, that's all that we would need to throw -- there is no aerodynamic correction involved in the flight of the dart.
If we were throwing ball bearings at a dartboard that CoG will move in a ballistic trajectory on its way to the dartboard. A slowly thrown ball bearing will arc up and down more to reach the same target compared to a bearing thrown faster, which will have a flatter flight path. This is because gravitational acceleration has less time to effect the faster dart and it will drop less as a result during its flight.
The weight of the ball bearing doesn't matter as far as gravity is concerned -- gravity's downward acceleration is the same for a light and a heavy object. What does matter weight-wise are some other factors:
Take a look at a dart flight path -- It's ballistic! That means that a dart should always be landing in the dartboard nose down. At the best it will be landing level -- and that is for a really fast thrown dart -- it's going to stick in the board hard. If a dart is landing tail-down, something is going wrong with our throwing -- the dart is still trying to correct it's trajectory when it hits the board. Same thing is true for horizontal tails -- they should be pointing back at the thrower, not out in weird directions.
Back to that Center of Gravity: When it is flying all rotation of the dart will occur around the center of gravity. What causes rotation? Really the flights are the big thing that applies force, and that is due to the relative Wind hitting the flights:
How much drag and correcting force is there? It depends on a few things:
A large flight and a long shaft provide the most force to rotates the dart about its CoG. A small flight and a short shaft provide the least correcting force.
Flights stabilize the dart. If a dart is released off-center from the direction of throw, the flights correct the dart back toward its intendeded direction of flight.
The problem is that the corrections cause the dart to swerve one way and another around its intended course. For example if a dart is released pointed left of its throw, the flights will make an over-correction to be pointed in the direction of the throw, and will be pointed to the right of its throw. While this is happening the dart has moved to the left of its original flight path.
But wait, now the dart is left of its path, and pointed right ... so the dart corrects left and goes right of its prior flight path.
The big deal to get out of this is that the dart sorta hunts along its flight path in a bunch of "S turns". The mass of the dart, the length of the shaft, and the shape of the flight control how this happens. The same thing happens in a vertical plane, only it is more complex because the course isn't straight -- it is in a ballistic trajectory and it is changing all the time.
Why does all this matter?
The corrective force applied by the shaft & flights is independent upon the mass of the dart. It depends on the flight shape and the shaft length.
A shorter shaft will allow higher rates of correction, as the time it takes for the flights to weathervane from one extreme to another is reduced. This is due to a lower angular momentum with a short shaft. In other words, a Higher frequency range of corrections. However, it will also introduce more drag, as this allows more flight area to be seen more often by the relative wind.
A longer shaft will have a lower rate of corrections, and also will have lower drag because the flights will have more time to respond to the relative wind and generate corrections. That lower rate might mean more off-travel motion of the dart due to the s-turn flight path.
Lighter darts are affected more by shaft & flight choices than heavier darts since those components represent more of the mass and angular momentum of the dart when the barrel is light.
A heavier dart has more momentum. It will resist the side to side and up/down motions that the corrective force applies to the dart. In other words, the heavier dart will fly closer to its intended flight path with a given set of corrections by the tail.
So how the heck do you throw good darts?
We need to release a dart perfectly along a ballistic flight path towards its target. When this happens the flights add some drag, but compensate for it by keeping the dart tip pointed towards the dartboard. That's great for us -- the dart will stick when it hits instead of bouncing off.
If we don't do the above, the flights do us a favor by re-orienting the dart so it is aimed along its flight path. This has two costs: extra drag, the dart will be slowed from what we intended, so it's probably going to drop some due the dart slowing. Secondly, the dart is going to move away from the trajectory we are throwing it on, both horizontally and vertically, so it won't go exactly where we wanted it to.
So, to throw great we need to be able to throw a dart on a whole bunch of ballistic trajectories (due to the height of the target) and keep the dart perfectly aligned with those trajectories! Simple, Huh?!
There is a bunch of good literature on how to throw good darts, and our body does a great job of doing it automatically. As dart throwers we can just help out our bodies natural inclinations to throw darts properly.
There are two primary sources of error in throwing darts. Horizontal errors and vertical errors. If both errors can be eliminated we can throw Awesome Darts! From the above, we know that throwing perfect ballistic trajectories to different heights will get us on-target. The Horizontal part is done by train and aim.
So sources of innaccuracy:
Given that our body wants to throw great to start with, its mechanics issues that mess with that.
I think what causes inaccuracy in dart throwing is a bad release. Perhaps with a little bit from a poor throw thrown :-) in. Think of it this way -- your body is trying to throw good darts all by itself, yet elements of our technique screw it up and make the darts fly badly.
The following paragraphs assume that you are always throwing at the same target and not trying to "retarget" when you are off, which usually leads to over-compensation.
When you are aiming at T20 and get darts ranging in beautiful dead-nuts-on vertical lineup from D20 to Bull to 3s, you know that your horizontal aim and release is superb. What is varying is the ballistic trajectory, vertical release, and arm speed and elbow drop. Perhaps even a little thing as a jump or something might affect the release point considerably. It's important to release the dart on the upward arc of the ballistic trajectory, and the timing is critical.
When you are going for T20 and the darts keep on landing T1 and T5, you know that your ballistic trajectory is going perfectly. You are getting release after release with just the right timing, and the trajectory is spot on. What is going wrong is the horizontal action. This is most likely due to the motion of the arm just not being perfectly in-line with the throw. The body is trying to "muscle" the arm into the throwing line and over-controlling it.
When you get two darts dead on and the third is somewere totally else -- you probably had a vertical or horizontal release error, the dart is trying to correct, and wiggled itself to another part of the board.
Darts all over the place? I'm guessing its a grip issue. Every dart is getting released goofy and just turning-and-burning themselves to a different target. Or, you could just be totally aimed wrong and your body is trying to hard to correct from everything being off-axis for the throw that it just isn't going to work.
The description of the flight types is cobbled together from a couple of sites.