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I will give you credit on the bowstring speed. You've got me there, the arrow won't fly faster than the string.
However, you keep comparing adamantine arrows to different projectiles, and it simply doesn't work like that. An anti-tank round is designed to bludgeon through armor, or to penetrate it slightly and then explode inside the armor. Anti-personnel rounds work because a person has negligible protection, you can penetrate a human with a powerful air rifle. Hollow points will expand and cause wide-area damage, but they get very little penetration when they hit something harder than a human. Don't see hollow-points being used against reinforced glass. Instead you see FMJ being used, the iron jacket turning the bullet rigid and allowing it to punch through things which are solid. An adamantine arrow would be comparable to a very small, overpacked FMJ - imagine that you used 2x or 3x the gunpowder on a small-caliber FMJ round, and that instead of iron it were made of titanium. It'd get amazing penetration, although it wouldn't penetrate a lot, it would just blow pin-holes through material. Ideally, an adamantine bolt would be able to sluice through material like a pneumatic needle or somesuch, and could be made with bleeder holes in case it were imbedded in a foe.
However, all of this is moot with arrows. You can't get enough speed with a bow to do that, so I concede the point. If we had explosively fired (ie, not spring loaded or thrown) harpoon shooters, then an adamantine harpoon would do a fantastic job.
Modern anti-tank rounds don't contain any explosive. They are pure
kinetic energy penetrators. A thin rod with fins, much like a big metal arrow. A typical one fired from a 120mm cannon is maybe 20mm or so thick and 50cm long. In the cannon it is surrounded by blocks of light material known as sabots (they were originally wood and looked somewhat like Dutch shoes, which are called sabots). The sabots fall off as soon as the round leaves the barrel, leaving the low-drag penetrator to fly onward. This allows a large powder charge to push on a small diameter rod, much like your suggestion. They don't need to explode because when they penetrate the armor they make a decent chunk of the interior of the armor spall off and act like shrapnel. But even without spalling, just having the penetrator pass through an enclosed space at high speed makes enough of a shockwave to kill the occupants. But this all depends on the density of the projectile so it can maintain its velocity and have enough kinetic energy to punch through the armor. That's why they use depleted uranium. It's the densest reasonably priced material.
In small arms, armor piercing rounds are much like a FMJ, with the usual copper jacket (iron would make too much wear in the barrel, I don't think I've ever heard of it being used for small arms) and lead filling, but with a dense rod (usually either tungsten or depleted uranium) in the center to do the penetration.
FMJ is really a fairly lousy round for just about any use except targets. They don't penetrate well through hard targets, and don't wound well. The later reason is why they are widely used, ironically. They are required by international law (I think it was one of the Hague conventions) for all military anti-personnel use because they are less lethal than expanding or exploding rounds. It's OK to lob big chunks of explosives onto troops, OK to run over them with large tracked vehicles, OK to set them on fire with napalm, but not OK to shoot them with bullets that will do a good job of killing them. Actually, I'm not sure napalm is OK for anti-personnel use. You may only be able to use it against equipment. Like the rifle the guy is carrying, or his uniform. That's OK. <shrug>
But anyway, density is absolutely required for a projectile that needs to penetrate a rigid material. A low density projectile will lose velocity too quickly to have any range. And even if it has the range, it still needs energy to punch a hole through anything. Even making a 1mm hole through steel armor requires displacing a 1mm cylindrical volume of steel, which takes energy no matter how sharp the point is. The steel has to be moved aside, and doesn't want to move. A thinner penetrator has less steel to move, but has less energy to do it with.
Cotton candy just wouldn't make a good projectile, regardless of how fast you launch it. At least not by itself. An adamantine bodkin on a wood arrow with be very nice for punching through plate or mail, though. And an adamantine broadhead on a wood arrow would slice through leather or flesh like a hot knife through butter. Would probably get through plate decently, too. Just like an adamantine axe blade with a lead weight to give some heft to the swing would be better than a pure admantine axe.
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Topic: Adamantine and Slade Science together with physics quirks (Read 207895 times)