I imagine that the momentum would be conserved. So if the rifle normally shot a 30 gram ball at 300 meters per second, it would shoot a 5 kilogram ball at around 23 meters per second.
The larger size and lower speed of the cannon ball would likely reduce the range.
The larger size of the projectile would spread out the impact causing reduced damage.
The ballistics would be significantly different making it far harder to hit with.
This is how I would do it in my game:
Reduce the damage from 1d12 to 1d10
Change piercing type to bludgeoning
Reduce range from 40/120 to something like 20/60
Add knockback of 5 ft to medium targets or 10 for small
The really neat thing would be shooting non standard rounds that wouldn’t be possible from a musket like incendiary or smoke rounds.
This exact mechanic is present in the Mistborn book series. I don’t want to give spoilers because I recommend the books so highly, but I love the hard science nature of the way the magic system interacts with physics.
the books are the mistborn trilogy by Brandon Sanderson, and it’s second trilogy; wax and wayne.
the physics bit is central to both, but it’s a bigger focus in the second trilogy.
highly recommend all of them!
and for more wacky ideas…well, the entire rest of the cosmere series! especially tress of the emerald sea, which is largely standalone, but contains quite a bit of in-universe lore…
Ah, I wondered if it might have been a typo since “mistborn” seems like a more plausible word. I’ve been meaning to get around to Sanderson since forever, but I didn’t do any reading for the longest time, and I’ve been on a big sci-fi kick since starting up again because I’m mostly interested in stories that use novel premises to examine issues like human rights and the nature of consciousness/life, etc. I’ve felt like fantasy is too meaningless adventure-y? Not enough induction of personal growth. But I’m in the middle of The Magicians right now, and that’s really proving me wrong, and also there was Tehanu. That was a hard book to read because it was so real.
the cosmere series as a whole (of which the mistborn saga is a part) reeeeaaaally straddles the line between sci-fi and fantasy;
it’s all a kind of “hard fantasy”, where all of the powers that people use are strictly limited by a certain energy source (don’t want to spoil anything here, even though it’s a kind of unimportant detail overall).
so, in the mistborn saga for example, people swallow certain metals and use those metals to power certain abilities, depending on the metal, which uses up said metal. if it runs out, there’s no way to power those abilities anymore. and it DOES run out, it’s very much finite.
so if you like sci-fi, especially more on the hard sci-fi side, and have been enjoying some fantasy lately, i think it might be right up your alley! ;)
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.
I think damage reduction would be even more than that. The damage a projectile does to a target is directly related to its kinetic energy which is calculated as e = ½mv². So when you increase mass but reduce velocity you also reduce the damage by the square of the difference in velocity (I think). As long as the damage just relies on the physics of the projectile and not magic, that is.
I was assuming that the total energy would be maintained (In this case 1350 joules) and thus the damage should be the same if weren’t spread out. It has been 20+ years since I has to do any of that math so I could be wrong about any of that. And since the only paper that was handy happened to be an envelope I guess it was technically back of the envelope math. :)
I imagine that the momentum would be conserved. So if the rifle normally shot a 30 gram ball at 300 meters per second, it would shoot a 5 kilogram ball at around 23 meters per second.
This is how I would do it in my game:
The really neat thing would be shooting non standard rounds that wouldn’t be possible from a musket like incendiary or smoke rounds.
This exact mechanic is present in the Mistborn book series. I don’t want to give spoilers because I recommend the books so highly, but I love the hard science nature of the way the magic system interacts with physics.
They are in fact awesome books.
Searching Misborn gives me too many different results. Which one?
the books are the mistborn trilogy by Brandon Sanderson, and it’s second trilogy; wax and wayne.
the physics bit is central to both, but it’s a bigger focus in the second trilogy.
highly recommend all of them!
and for more wacky ideas…well, the entire rest of the cosmere series! especially tress of the emerald sea, which is largely standalone, but contains quite a bit of in-universe lore…
Ah, I wondered if it might have been a typo since “mistborn” seems like a more plausible word. I’ve been meaning to get around to Sanderson since forever, but I didn’t do any reading for the longest time, and I’ve been on a big sci-fi kick since starting up again because I’m mostly interested in stories that use novel premises to examine issues like human rights and the nature of consciousness/life, etc. I’ve felt like fantasy is too meaningless adventure-y? Not enough induction of personal growth. But I’m in the middle of The Magicians right now, and that’s really proving me wrong, and also there was Tehanu. That was a hard book to read because it was so real.
Anyhow, thanks to you both.
the cosmere series as a whole (of which the mistborn saga is a part) reeeeaaaally straddles the line between sci-fi and fantasy;
it’s all a kind of “hard fantasy”, where all of the powers that people use are strictly limited by a certain energy source (don’t want to spoil anything here, even though it’s a kind of unimportant detail overall).
so, in the mistborn saga for example, people swallow certain metals and use those metals to power certain abilities, depending on the metal, which uses up said metal. if it runs out, there’s no way to power those abilities anymore. and it DOES run out, it’s very much finite.
so if you like sci-fi, especially more on the hard sci-fi side, and have been enjoying some fantasy lately, i think it might be right up your alley! ;)
Love his magic systems. How’d you like stormlight 5? I balled.
I did as well.
not done yet with stormlight 5, but 4 was already…heavy…
You’re in for a ride. It’s good though. Enjoy :) Life before death
Have you been through the 3 body problem series by Cixin Liu? Soooo good. Loads of the stuff you mentioned.
I’m on the waiting list for it at the moment. :)
It’s great in audio too
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).
I think damage reduction would be even more than that. The damage a projectile does to a target is directly related to its kinetic energy which is calculated as e = ½mv². So when you increase mass but reduce velocity you also reduce the damage by the square of the difference in velocity (I think). As long as the damage just relies on the physics of the projectile and not magic, that is.
I was assuming that the total energy would be maintained (In this case 1350 joules) and thus the damage should be the same if weren’t spread out. It has been 20+ years since I has to do any of that math so I could be wrong about any of that. And since the only paper that was handy happened to be an envelope I guess it was technically back of the envelope math. :)