Actually I'm not sure. Today we make arrows out of carbon fibers and whatnot, making them lighter and thinner, to achieve better flight. The thing is that an adamantine arrow is not a nerf dart. While similar weight, your arrow will be non-porous, very thin, and very fast. Any wind is negligible, and a proper adamantine arrow wouldn't have an arrowhead, it would just have a point (with perhaps a groove to encourage bleeding). It would more resemble a needle than an actual arrow. That considered, it would slice through the air amazingly well.
The issue then, is energy. We know that a bow will contain a certain amount of energy when fired. If it's firing a wooden rod, then it will fire the rod. If it's firing a metal rod that's 2x the weight of wood, then it will take 2x the energy to achieve momentum and thus fly like half as fast. By contrast, if you make a carbon fiber arrow, then it might be 1/2 the weight, requiring 1/2 the energy to move and flying 2x as fast. Of course in practice it's not so clean cut, but the idea is solid. A given force upon a lighter object will propel the object further and faster.
In effect, an adamantine arrow would act more like the crossbow from Half-Life 2, it'll penetrate just about anything because it will fly at ridiculous speeds. It would need a needle point and a VERY slow taper to penetrate, because it would have rather poor "punch" but an amazing edge. If any of its penetrative power were converted into blunt contact, it would drain its energy pretty fast, but as long as it's achieving clean punctures then not much would be able to stop it.
"The flying ☼Adamantine Bolt☼ strikes the goblin in the head, shattering the skull and ripping the brain, passing clear through the other side!"
Of course in DF, projectiles are blunt damage, so none of this matters in gameplay.
Your adamantine needle is still made of a material that weighs 200g/m
3, so it will weigh almost nothing, and wind drag will still stop it very quickly. The faster something moves, the more drag it has pushing back against it. So a very light projectile just doesn't go very far, regardless of what it's made of. Nor will it hit very hard. That's why they use depleted uranium instead of aluminum in anti-tank rounds.
And you can't make a projectile from a bow (or crossbow) go any faster than you can make the bowstring move, no matter how light the projectile is. So halving the weight won't really double the speed. It's asymptotic, where the limit is the speed of the string with no projectile.
A needle-like arrow wouldn't be that great for doing damage. Oh, a headshot might be effective, but the main killing method of a projectile, whether an arrow or a bullet, is blood loss. That's why large caliber hollow point bullets are far more effective than small caliber solid rounds. Sure, James Bond could get by with a purse gun like a Beretta 418 with a 6.35mm round. He always hit
exactly where he wanted to. But mere mortals are better off with a 10mm that will open a nice big wound channel and make the target bleed out, even from a hit in a non-vital area. A high speed knitting needle would just make a little puncture that would seal itself right up if it didn't puncture anything critical. Even a headshot wouldn't be a sure thing with a needle. There are lots of documented cases of people surviving having rod-like objects punch through their brains, such as
Phineas Gage. If your arrow is going to drive the skull through the brain, it's going to have to transmit significant momentum into the skull, and a cork knitting needle (no matter how rigid) wouldn't have enough momentum.
Even a very slow taper requires splitting the skull apart, which requires applying force, which an adamantine projectile just won't be able to do.