30 grams is a round number somewhere in the ballpark of a musket ball. I am also uncertain as to how you ended up with 19.2 km/s.
To the best of my recollection the energy should be conserved according to the formula: energy = mass * velocity squared
Mass is in kg and velocity is in m/s
So solving for v would give us around 2.3 km/s for a 0.5 g projectile. At that speed, the projectile would most likely detonate immedeately due to air resistance rendering it problematic as a firearm.
Your original comment specified a conservation of momentum, rather than energy, the formula for momentum is Mass * Velocity.
300m/s * 30 gram is the same as 19200km/s * 0.468 gram (I am told that enlarge reduce only does factors of eight so chose 1/64th the mass rather than 1/60th) The kenetic energy forumla is Half * Mass * Velocity squared, hence why lighter faster projectiles have increased energy for the same momentum.
As to Areodynamic heating, I think you are fine up to 3m, the grain of sand has a radius of 3.5mm (from volume of a sphere and density of quartz), using newtons impact formula D=L(A/B) L is the length of the penetrator (7mm) A is the density of quartz (2.64) B is the density of air (0.0012) the grain of sand should be able to travel ~15 m, even if it vapourises during that process. Though I wouldn’t be opposed to 2d4 fire “splashback” to the user and any surrounding persons.
30 grams is a round number somewhere in the ballpark of a musket ball. I am also uncertain as to how you ended up with 19.2 km/s.
To the best of my recollection the energy should be conserved according to the formula: energy = mass * velocity squared
Mass is in kg and velocity is in m/s
So solving for v would give us around 2.3 km/s for a 0.5 g projectile. At that speed, the projectile would most likely detonate immedeately due to air resistance rendering it problematic as a firearm.
Your original comment specified a conservation of momentum, rather than energy, the formula for momentum is Mass * Velocity. 300m/s * 30 gram is the same as 19200km/s * 0.468 gram (I am told that enlarge reduce only does factors of eight so chose 1/64th the mass rather than 1/60th) The kenetic energy forumla is Half * Mass * Velocity squared, hence why lighter faster projectiles have increased energy for the same momentum.
As to Areodynamic heating, I think you are fine up to 3m, the grain of sand has a radius of 3.5mm (from volume of a sphere and density of quartz), using newtons impact formula D=L(A/B) L is the length of the penetrator (7mm) A is the density of quartz (2.64) B is the density of air (0.0012) the grain of sand should be able to travel ~15 m, even if it vapourises during that process. Though I wouldn’t be opposed to 2d4 fire “splashback” to the user and any surrounding persons.