Yeah, I probably obsess too much about actual physics when looking at a video game - I get that. But I was trying to get a better sense of just how difficult it would be to use kinetic weapons in space, considering the likely distances and timeframes involved. And the numbers I came up with kind of floored me:
Let's start with range - I've already given a dissertation here on what distances I think are somewhat realistic for a space battle and why. Basically, if you multiply the basic Range stat by 1,000 km or 1 megameter (1 Mm), it's pretty close to what I think works.
From that we can determine time to impact - an S-slot Mass Driver has a Range of 50, or 50 Mm. At the speed of light (c), a laser would only take about a sixth of a second to impact; at 10% of c, it's 1.67 seconds; and 16.67 seconds at 1%. The time to impact is also the amount of time given to the target to deviate from its course enough to avoid getting hit - the target doesn't need to know when a shot is fired, just that it needs to every so often have an off-vector burn to throw off targeting.
So the goal for the ship firing the kinetic shot is to get that time to impact down low enough to limit the target's ability to evade - this requires getting to a given slug velocity. But it has to get it to that velocity using an accelerator barrel of a given length. For a more realistic space warship, you would use the whole ship's length for a spinal mount - if a ship were, for example, 800 meters in length, you might be able to use 700m of that for a spinal cannon. Given a longer barrel, acceleration can be applied for a greater length of time.
Let's do some math:
Your barrel length is 700m, and you're trying to accelerate a 1 gram pellet to 1% c, so it will require an acceleration of around 655,000,000x the force of gravity at Earth's surface (~9.81 m/s^2), applied for about 0.467 milliseconds. If my math is right, that's about 6.43M Newtons of force, or about 9.64 terawatts of power applied to the pellet (i.e., equal to half of the total consumption of power on Earth in 2005). That power number doesn't count any inefficiencies in the cannon, especially waste heat.
But wait, you don't have 700 meters to work with - you're trying to fire the pellet from a turret. Perhaps the turret has a 60 meter-long barrel (you might be able to go longer if your turret had the barrel balanced over the pivot point like some kind of teeter-totter, but we'll stick with 60m for now). Again, 1 gram, 1% c, and now it's 0.040ms to get to speed, so you need an acceleration of 7.65B times gravity - that's 75M Newtons / 113 terawatts, not counting inefficiencies.
Another "but wait" - we've only been accelerating up to 1% c, when we should be shooting for 10% at least, to actually minimize the chance of evasion. To get twice the velocity, you need 4x the force/power; for 10x velocity, it's 100x force/power. That's 7.5B Newtons, 11.3 petawatts (i.e., total for low end Type-I Kardashev-scale civilization), and now you don't have just mechanical inefficiencies to worry about, but relativistic ones as well.
Oh and you're applying all of these forces in a ship's turret. For a single Tier 1 weapon.
I ran those numbers based on a 1 gram pellet because you don't really need to send anything bigger at that kind of velocity. You may actually be able / be forced to use a (MUCH) smaller pellet - maybe that saves on power and stresses on the system - but all this assumes that you only need to accelerate the pellet and not also some sort of cradle or similar to carry the pellet down the barrel.
In the end, for those of you who are not in any way concerned with anything to do with realism, physics, etc., none of this matters in the least - you want your "pew pew", you get your "pew pew", no questions asked, no answers sought. I just thought it was ridiculous how monstrous the numbers were coming out of this, and thought I would share it with you.
One other thing to keep in mind: the speeds that Stellaris has ships travelling at with even low Tier thrusters (e.g., crossing a 60 AU-wide system in a couple of months) are already close to the 1% c mark (e.g., 1 AU/day is approximately 1,700 km/s or 0.57% c), so maybe that "slow" of a pellet would be harmless to even a civilian vessel, never mind a warship, if they would commonly run into such things just flying along. And those speeds are not actually ludicrous, as you can reach it in about 2 days of 1 gravity acceleration.
Let's start with range - I've already given a dissertation here on what distances I think are somewhat realistic for a space battle and why. Basically, if you multiply the basic Range stat by 1,000 km or 1 megameter (1 Mm), it's pretty close to what I think works.
From that we can determine time to impact - an S-slot Mass Driver has a Range of 50, or 50 Mm. At the speed of light (c), a laser would only take about a sixth of a second to impact; at 10% of c, it's 1.67 seconds; and 16.67 seconds at 1%. The time to impact is also the amount of time given to the target to deviate from its course enough to avoid getting hit - the target doesn't need to know when a shot is fired, just that it needs to every so often have an off-vector burn to throw off targeting.
So the goal for the ship firing the kinetic shot is to get that time to impact down low enough to limit the target's ability to evade - this requires getting to a given slug velocity. But it has to get it to that velocity using an accelerator barrel of a given length. For a more realistic space warship, you would use the whole ship's length for a spinal mount - if a ship were, for example, 800 meters in length, you might be able to use 700m of that for a spinal cannon. Given a longer barrel, acceleration can be applied for a greater length of time.
Let's do some math:
Your barrel length is 700m, and you're trying to accelerate a 1 gram pellet to 1% c, so it will require an acceleration of around 655,000,000x the force of gravity at Earth's surface (~9.81 m/s^2), applied for about 0.467 milliseconds. If my math is right, that's about 6.43M Newtons of force, or about 9.64 terawatts of power applied to the pellet (i.e., equal to half of the total consumption of power on Earth in 2005). That power number doesn't count any inefficiencies in the cannon, especially waste heat.
But wait, you don't have 700 meters to work with - you're trying to fire the pellet from a turret. Perhaps the turret has a 60 meter-long barrel (you might be able to go longer if your turret had the barrel balanced over the pivot point like some kind of teeter-totter, but we'll stick with 60m for now). Again, 1 gram, 1% c, and now it's 0.040ms to get to speed, so you need an acceleration of 7.65B times gravity - that's 75M Newtons / 113 terawatts, not counting inefficiencies.
Another "but wait" - we've only been accelerating up to 1% c, when we should be shooting for 10% at least, to actually minimize the chance of evasion. To get twice the velocity, you need 4x the force/power; for 10x velocity, it's 100x force/power. That's 7.5B Newtons, 11.3 petawatts (i.e., total for low end Type-I Kardashev-scale civilization), and now you don't have just mechanical inefficiencies to worry about, but relativistic ones as well.
Oh and you're applying all of these forces in a ship's turret. For a single Tier 1 weapon.
I ran those numbers based on a 1 gram pellet because you don't really need to send anything bigger at that kind of velocity. You may actually be able / be forced to use a (MUCH) smaller pellet - maybe that saves on power and stresses on the system - but all this assumes that you only need to accelerate the pellet and not also some sort of cradle or similar to carry the pellet down the barrel.
In the end, for those of you who are not in any way concerned with anything to do with realism, physics, etc., none of this matters in the least - you want your "pew pew", you get your "pew pew", no questions asked, no answers sought. I just thought it was ridiculous how monstrous the numbers were coming out of this, and thought I would share it with you.
One other thing to keep in mind: the speeds that Stellaris has ships travelling at with even low Tier thrusters (e.g., crossing a 60 AU-wide system in a couple of months) are already close to the 1% c mark (e.g., 1 AU/day is approximately 1,700 km/s or 0.57% c), so maybe that "slow" of a pellet would be harmless to even a civilian vessel, never mind a warship, if they would commonly run into such things just flying along. And those speeds are not actually ludicrous, as you can reach it in about 2 days of 1 gravity acceleration.
