is a “30 gram ball” some kind of archeaic unit? 30/5000 = 1/166 != 23/300 = 1/13.
but anyway, I feel this ruling would open an even better exploit the other way. Shoot an enlarged half-gram grain of sand weighing 30 gram at 300 meters per second, when it travels through the ring it will reduce down to it’s original size increasing speed to 19.2 km/s, having a new kenetic energy of 92 megajoules or 22kg of tnt.
In dnd terms that’s maybe 6d6 fire damage, range 10/30.
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.
is a “30 gram ball” some kind of archeaic unit? 30/5000 = 1/166 != 23/300 = 1/13.
but anyway, I feel this ruling would open an even better exploit the other way. Shoot an enlarged half-gram grain of sand weighing 30 gram at 300 meters per second, when it travels through the ring it will reduce down to it’s original size increasing speed to 19.2 km/s, having a new kenetic energy of 92 megajoules or 22kg of tnt.
In dnd terms that’s maybe 6d6 fire damage, range 10/30.
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.
13*13=169, so the kinetic energy would be almost the same (but not momentum).