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In my story magic allows for the creation of accelerators that can multiply the speed of any object that passes through them. These accelerators allow for modified conventional weapons to fire at rail gun velocity and beyond. My question is how fast would a tungsten .50 BMG bullet need to be found in order for it to melt from air resistance?

Currently I’m running on the assumption that anything past 50,000 fps will melt the tungsten well before getting to any target.

Notes:

The accelerators do not touch the objects they accelerate and ignore Newton’s third law of motion, meaning that while they magically accelerate an object to a multiple of their current speed they do not physically interact with the projectile. The world has earth-like gravity, air etc. The projectile weighs 1218 grains and has a ballistic coefficient of 1.088.

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  • $\begingroup$ Atmosphere is close enough to earth same with gravity. The magic bends or in some cases allows for the complete avoidance of some fundamental laws to an extent, however this is isolated to the magic and the objects created with it. Thanks for the tips $\endgroup$ – Mock 10 Oct 26 '19 at 22:08
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    $\begingroup$ It is only the accelerators that ignore the third law of motion since they increase the speed of objects without physically touching them meaning you have the same recoil as a conventional weapon that uses the same round. The accelerators are effectively enchanted rings mounted in a frame so that the projectile passes through them. $\endgroup$ – Mock 10 Oct 26 '19 at 22:15
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    $\begingroup$ "Increase the speed of objects without touching them" describes a coilgun, specifically one that magnetically levitates the projectile away from the coils. This isn't in violation of Newton's Third Law; the rings will recoil as they impart force on the projectile, but there will be no conduction of heat. $\endgroup$ – Cadence Oct 26 '19 at 23:55
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    $\begingroup$ Practically speaking, how the bullet gets to melting speeds is completely irrelevant. The question, simplified, is "How fast can a tungsten bullet go without melting from air friction?" - Which, sadly, I have no idea how to calculate. $\endgroup$ – Andon Oct 27 '19 at 0:23
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    $\begingroup$ @Andon incidentally, the major source of heating will not be friction, but compression of air in front of the projectile. A magical frictionless supersonic projectile would still be subject to compression heating, because the air in front of it simply can't get out of the way fast enough. $\endgroup$ – Starfish Prime Oct 27 '19 at 10:14
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Computation of stagnation temperature behind the shockwave in front of a hypersonic projectile is Really, Really Hard, so I'm not going to attempt to do that right now.

Various Space Gun projects have arisen over the years, and the general consensus seems to be that a gun shooting at escape velocity (>11km/s) at low altitude is basically impractical, though I haven't found anyone who has shown their work here. Your 50000fps estimate is equivalent to about 17km/s, and is therefore almost certainly too high.

The SHARP light gas gun was intended to reach muzzle velocities in the region of 8km/s. I assume that the project scientists and engineers believed this to be practical, but the project was more or less discontinued. The Quicklaunch light gas gun was intended to fire somewhat larger projectiles at more like 6km/s. The StarTram maglev accelerator had muzzle velocities in excess of 8km/s, but the muzzle needed to be at least 4000m above sea level to get out of the thickest part of the atmosphere to reduce drag and heating. In any of these designs, the final product (a space launch vehicle) could have carried its own active cooling systems and ablative heat shield, increasing its survivability compared to your dumb projectile.

The Sprint missile only reached about 3.5km/s using an ablative heat shield (which reached temperature hot enough to melt tungsten) but was comparatively chunky as it has to carry much more stuff (multistage rocket, nuclear warhead, guidance equipment, etc) than a simple dumb projectile and it actively accelerated whilst in the thick atmosphere, so I suspect your bullet will be able to go a little faster than this.

Modern railguns can readily achieve muzzle velocities of 2.5km/s at very low altitude. The true answer therefore lies somewhere between about 3.5 and 9km/s, but its precise computation is left as an exercise to the reader.

There are additional issues, like initial heating being sufficient to cause melting, but drag then slowing the projectile below the critical velocity, and so on and so forth. Rocket science is hard, so you'll have to make do.

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