Ballistic accuracy tests

5.45 million. It is expensive and very heavy, I'll probably look for some kind of ballance between the beryllium copper and the osmium one. Probably vanadium steel? I'm not sure its that conductive but I'll try. It sure looks like two separate materials for the barrel bracing and the barrel itself will bring a lot of interesting options to the table.

All tests are at 1000km.

Here is the gun:

No problem.
this is firing at a redesigned gunship at around 700kms



you can see that even the ricochets are in one stream.... 

Sorry to say it but your optimization ruins the accuracy. Additional barrel bracing is what i makes you ultra accurate ... I've gone a bit different way with the optimization - less speed... :



Edit: The new gun has even tighter grouping, I guess because of the shorter barrel.
You can clearly see that below the particles the impacts are a thin line... at 1000 km.

I sure hope its a bug in the designer not in the accuracy

One way to examine dispersion without testing in combat is to hover your mouse over the bottom-left corner of the range graph, to show the tooltip on the very first data point.  For example, you can see the range against targets with a cross sectional area of 0.0712 m².  You can resize the sidebar to make the graph wider and check the range against even smaller targets.  If increasing the thickness of the barrel armor improves the range against a target, you're dispersion-limited at that cross-section.  If it doesn't, you're velocity-limited.

The relevant material properties here are Young's modulus and density. Young's modulus is a measure of how much force it takes to stretch the material by a particular amount. Density is actually bad, because material farther from the bore stretches more when the barrel bends, and so you want the barrel as girthy as possible.  Lower density means you can do that with less mass.

Osmium has very high Young's modulus, but its density is also huge.  Hafnium carbide is usually superior.  It has nearly half the density, but the elastic modulus is only a little bit lower, and it's twice as conductive.  Kind of weak, though, and more expensive.

Beryllium is extremely good, but expensive. Also its yield strength sucks, so you may end up yield-limited rather than stiffness-limited.

You can also just stick with aluminum copper lithium and pile the barrel armor on thick. (Aluminum zinc magnesium has an extra zero in the Young's modulus, so only use it if you don't care about realism.)

Amorphous carbon is incredibly good on elastic modulus and density, but it's not conductive enough for rail guns.  You can use it for coil guns though, but until capacitor voltage can be set per-stage, or somebody figures out how to get decent efficiency out of what we've got, they have to have very few stages (<3) or be line-powered.  The 1 GW limit means line-powered coil guns can only achieve high velocities with super-light projectiles, and have to have very long barrels.  That works against the stiffness of amorphous carbon, but they can still be made with very low dispersion. Example.