Kinetics - the numbers just get stupid

[Cordane]

Realistic ships facing off against each other would have difficulty maintaining a useful range for very long, assuming they were travelling along non-parallel vectors at any low relativistic velocity. For example, two ships travelling at 0.5% c (1,500 km per second) and at even a 5° angle away from each other after crossing vectors, would see the range between them increase by around 131 km/s. If both ships want to re-engage and immediately perform a 1G burn to kill the outbound vector, they’d need approximately 6,700 seconds (an hour and 51 minutes) to counteract the rate of range increase, and would be over 430,000 km away before they would start moving back toward each other. Increasing the thrust cuts the time and distance covered by the multiple (e.g., 2G burn by both cuts the time to about 55 minutes and separation to 215K km).

Right angles (90°) make it over 2,100 km/s outbound, 15 hours to kill the vector, and over 57 million kilometers away before accelerating back toward each other. They’d also only have about 45 seconds before crossing their vectors and 45 seconds after to shoot at each other, if they can only do so inside of 100,000 km – probably only one shot per mount (maybe a second, but more likely recharging capacitors). Full-on jousting (180°) would be 3,000 km/s, over 21 hours, almost 115M km, and just 70 seconds total, respectively.

 

[CrowScape]

They have FTL. You don't need to get your projectiles up anywhere near up to a real fraction of the speed of light in order to get it onto target halfway across the system in time before your opponent has the opportunity to evade or think about changing course. You just need to be able to temporarily apply your FTL tech to the projectile. Yeah, it might appear to slam into the enemy at a billion x c, but it will still only have the kinetic energy of whatever your gun can impart.

The problem is the game's need to force you to be at the edge of the system for ships to enter FTL.

 

[MichaelJanuary]

Realistic ships facing off against each other would have difficulty maintaining a useful range for very long, assuming they were travelling along non-parallel vectors at any low relativistic velocity. For example, two ships travelling at 0.5% c (1,500 km per second) and at even a 5° angle away from each other after crossing vectors, would see the range between them increase by around 131 km/s. If both ships want to re-engage and immediately perform a 1G burn to kill the outbound vector, they’d need approximately 6,700 seconds (an hour and 51 minutes) to counteract the rate of range increase, and would be over 430,000 km away before they would start moving back toward each other. Increasing the thrust cuts the time and distance covered by the multiple (e.g., 2G burn by both cuts the time to about 55 minutes and separation to 215K km)

Agreed. But this is quite consistent with battle timeframes in Stellaris, with weapon cooldowns measured in days and battles lasting several weeks of game time.

 

[Retry]

Lasers can't deliver damaging energy against a hull at distances anywhere near a light-minute, they can't get a beam waist far enough out to be viable beyond a few light-seconds at best.

Why not?
Select a Gamma Ray with a wavelength of 10^-11 m, and select a beam waist of 1 meter, and you end up with a rayleigh length of pi*10^11 meters. Granted, that's a very large beam waist, but it seems like a lot of people are going for 1km+ ships on this forum, so that size of laser could fit fairly reasonably.

Multiply by the ratio of meters to the distance light covers in one second (1 light-second/3e8 m) and we get the rayleigh length in terms of light-seconds, approximately 1050 light-seconds, or at least 17 light-minutes, for this long-range gamma laser design. If the rayleigh width occurs at the lense, that effectively means an effective range of 1050 light-seconds where the laser's intensity is at least half of our maximum, point-blank intensity. In fact you can shorten the beam waist a little bit to increase intensity while still keeping 50% of your maximum intensity at a range in excess of 1 light-minute. From what it looks like, you could reduce the beam waist up to about .25 meters and get that result, using gamma radiation.

Not that you're going to hit anything that's one light-minute away, but that's not what's being asked.

Okay, so you're talking about "damaging" energy, so knowing how well a beam holds its intensity isn't enough. So, to approximate this damage, let's dig into some heat transfer!

We have our laser with that given characteristics: a beam waist of 1 meter, and we're firing at a target that's at the edge of our rayleigh length of 1050 light-seconds. In which case, our effective beam waist at that distance is 1.414 meters from here:

In other words, the laser beam that's impacting the surface of our target has a radius of 1.414m, or a diameter of 2.828m. All that energy getting pumped into the laser, whatever isn't getting reflected, has to be absorbed by the ship's armor. Not a whole lot of materials that I know of have high reflectivity for gamma rays, so we'll assume the absorbtivity is about 1: Or all energy exiting the laser beam must be absorbed by the armor.

Now, the general equation for conduction (Fourier's Law) would be a lot to work with for a general 3D problem. Fortunately, we can simplify the problem up a bit using a conduction shape factor.

Here's the basic idea: Our laser is heating the surface of our target in a circular cross-section of diameter "D". If the armor of our spacecraft (or whatever other target) is "thick", then that energy from our laser needs to conduct its heat into the nearby surrounding armor/structure of the ship. Given the conduction properties of the "armor" (basically how 'fast' heat flows), and whatever external temperature T2 the semi-infinite medium is supposed to be held at, and given the power output of the laser, we can approximate the temperature that spot on the surface would be at if we were to continue holding that laser at that particular spot for a long time (steady-state conditions).

The working equation for this is:

Q=S*k*(T1-T2)

S=Shape factor (for this specific scenario/geometry, S=2D. D=2.828m, so S=5.656m
k=Conduction coefficient
T1= Temperature of the surface being heated, which we want to find.
Q=Heat rate, or the laser's rated output power.
T2= Temperature of the semi-infinite medium, basically the surrounding metal that is not being melted directly.

We'll presume a human crew who likes to be comfortable and not freezing to death on the target vessel. So, let's let T2 be a temperature that's comfortable for said humans to continue to exist, about 300 Kelvins.

Rearranging the equation gives us the following:

Q/(S*k)+T2=T1

The most "famous" laser system currently existing today is fairly small with a power output of 30,000 Watts, and they want to get that up to 100,000 watts and want to test even 300,000 watts on a small sea-faring destroyers. So let's take a fairly conservative gander and say that Q=1,000,000 Watts of power output is reasonable for our huge space laser, which is much smaller than the maximum power output of a fission or fusion reactor.

It's a lot harder to guess what a spaceship or space station would be "armored" with in the future, so I'll go with an aluminum basic structure. We'll look at a table of aluminum k-values vs temperature and pick the 240 W/(m*K) to try and be conservative with our output temperature.

Plugging everything in, we find that:

(1,000,000W)/(5.656m*240W/mK)+300K=1037K=T2

So the surface material at the laser is at 1037K if the laser holds its position there. There's a slight issue: Aluminum melts at about 930K, so this laser will indeed do some damage despite its high beam waist. Granted, that neglects radiation from that heated surface so the effective temperature will actually be a bit smaller, but that issue can be fixed fairly easily just by pumping up the power to the still-reasonable 2 Megawatts.

If we optimize the laser a bit, since we're obviously not going to be hitting anything 16 light-minutes away, so let's reduce that beam waist to a more reasonable level of .25m. That gives us a rayleigh length of only about 1 light-minute away, but we'll benefit by having a smaller area and thus more high-focused laser.

Our new beam width at our rayleigh range is .707m, and our new shape factor is thus 1.414m. Using the same aluminum structure and 1 MW power output:

(1,000,000W)/(1.414m*240W/mK)+300K=3247K=T2

Again, our surface aluminum is going to melt off the longer the beam rests on the surface, since the melting temperature is much lower than the predicted steady-state temperature. And in this case, even faster, due to energy being concentrated in a smaller area (precisely how fast, however, is outside the scope of this analysis). Even taking into account the radiation leaving the immediate vicinity providing an additional cooling effect, I still end up with an estimated equilibrium temperature of approximately 1734K for the aluminum that's unfortunate enough to be in the line of fire.

You can repeat the calculation using data for steel or titanium as your structural materials, but they'll still melt under these conditions.

There's a few tricks you could do to mitigate the laser's effectiveness. One would be somehow using diamond as your structural material, since it has a very high melting (well, sublimation) point. You could try to find a surface with a very high reflectivity for gamma radiation, so only a fraction of the incoming laser power is absorbed, although I'm not even sure if they exist for that. And there's all the issues that would come with trying to hold a laser down at the same point against a target that's literally light-seconds away. And, of course, you would have to invent a gamma-ray laser, which doesn't yet exist. And of course there's absolutely zero practicality of firing at non-stationary targets more than maybe a few light-seconds away.

But would it be impossible to design a laser that can damage something light-minutes away, provided it can hit? Not in the slightest.

 

[Cordane]

Your explanations are leaps and bounds beyond what I'm capable of. I'm not sure where I read that a laser would have difficulty beyond a million kilometers or so - doesn't matter where, but it was probably dealing with modern lasers, not exotic not-yet-developed ones, and might not have been close to accurate at that. But your last paragraph pointed out one of the biggest issues that I don't think has been touched on enough:

... And there's all the issues that would come with trying to hold a laser down at the same point against a target that's literally light-seconds away. And, of course, you would have to invent a gamma-ray laser, which doesn't yet exist. And of course there's absolutely zero practicality of firing at non-stationary targets more than maybe a few light-seconds away.

A laser weapon needs time to ablate armor and hull - it's not at all a large amount of time, but there's a high probability that the beam would slice across the target's hull rather than being capable of lasing into a narrow zone, assuming a moving target and a moving firing platform (ship and/or turret). A spaceship is only going to be able to mount so much thickness and mass of armor and hull plating, and the properties of the materials will lean toward defending against kinetic deformation over specific wavelength reflection, but it would still be looking for high temperature resistance and dissipation. The armor simply needs to keep enough of the damaging effects of the laser beam from punching through into bulkheads and equipment during the first hit or two over an area. Probably by the time a space empire has developed gamma lasers, similarly advanced empires will have developed advanced materials with properties sufficient to not immediately fail against such a powerful weapon. Fail it will, eventually, but then no defense would likely be impenetrable for long.

 

[Spidee]

Nice reading! Thanks for the lectures guys, keep it going!

 

[Aed]

Why not?
Select a Gamma Ray with a wavelength of 10^-11 m, and select a beam waist of 1 meter, and you end up with a rayleigh length of pi*10^11 meters. Granted, that's a very large beam waist, but it seems like a lot of people are going for 1km+ ships on this forum, so that size of laser could fit fairly reasonably.

Multiply by the ratio of meters to the distance light covers in one second (1 light-second/3e8 m) and we get the rayleigh length in terms of light-seconds, approximately 1050 light-seconds, or at least 17 light-minutes, for this long-range gamma laser design. If the rayleigh width occurs at the lense, that effectively means an effective range of 1050 light-seconds where the laser's intensity is at least half of our maximum, point-blank intensity. In fact you can shorten the beam waist a little bit to increase intensity while still keeping 50% of your maximum intensity at a range in excess of 1 light-minute. From what it looks like, you could reduce the beam waist up to about .25 meters and get that result, using gamma radiation.

Not that you're going to hit anything that's one light-minute away, but that's not what's being asked.

Okay, so you're talking about "damaging" energy, so knowing how well a beam holds its intensity isn't enough. So, to approximate this damage, let's dig into some heat transfer!

We have our laser with that given characteristics: a beam waist of 1 meter, and we're firing at a target that's at the edge of our rayleigh length of 1050 light-seconds. In which case, our effective beam waist at that distance is 1.414 meters from here:

In other words, the laser beam that's impacting the surface of our target has a radius of 1.414m, or a diameter of 2.828m. All that energy getting pumped into the laser, whatever isn't getting reflected, has to be absorbed by the ship's armor. Not a whole lot of materials that I know of have high reflectivity for gamma rays, so we'll assume the absorbtivity is about 1: Or all energy exiting the laser beam must be absorbed by the armor.

Now, the general equation for conduction (Fourier's Law) would be a lot to work with for a general 3D problem. Fortunately, we can simplify the problem up a bit using a conduction shape factor.

Here's the basic idea: Our laser is heating the surface of our target in a circular cross-section of diameter "D". If the armor of our spacecraft (or whatever other target) is "thick", then that energy from our laser needs to conduct its heat into the nearby surrounding armor/structure of the ship. Given the conduction properties of the "armor" (basically how 'fast' heat flows), and whatever external temperature T2 the semi-infinite medium is supposed to be held at, and given the power output of the laser, we can approximate the temperature that spot on the surface would be at if we were to continue holding that laser at that particular spot for a long time (steady-state conditions).

The working equation for this is:

Q=S*k*(T1-T2)

S=Shape factor (for this specific scenario/geometry, S=2D. D=2.828m, so S=5.656m
k=Conduction coefficient
T1= Temperature of the surface being heated, which we want to find.
Q=Heat rate, or the laser's rated output power.
T2= Temperature of the semi-infinite medium, basically the surrounding metal that is not being melted directly.

We'll presume a human crew who likes to be comfortable and not freezing to death on the target vessel. So, let's let T2 be a temperature that's comfortable for said humans to continue to exist, about 300 Kelvins.

Rearranging the equation gives us the following:

Q/(S*k)+T2=T1

The most "famous" laser system currently existing today is fairly small with a power output of 30,000 Watts, and they want to get that up to 100,000 watts and want to test even 300,000 watts on a small sea-faring destroyers. So let's take a fairly conservative gander and say that Q=1,000,000 Watts of power output is reasonable for our huge space laser, which is much smaller than the maximum power output of a fission or fusion reactor.

It's a lot harder to guess what a spaceship or space station would be "armored" with in the future, so I'll go with an aluminum basic structure. We'll look at a table of aluminum k-values vs temperature and pick the 240 W/(m*K) to try and be conservative with our output temperature.

Plugging everything in, we find that:

(1,000,000W)/(5.656m*240W/mK)+300K=1037K=T2

So the surface material at the laser is at 1037K if the laser holds its position there. There's a slight issue: Aluminum melts at about 930K, so this laser will indeed do some damage despite its high beam waist. Granted, that neglects radiation from that heated surface so the effective temperature will actually be a bit smaller, but that issue can be fixed fairly easily just by pumping up the power to the still-reasonable 2 Megawatts.

If we optimize the laser a bit, since we're obviously not going to be hitting anything 16 light-minutes away, so let's reduce that beam waist to a more reasonable level of .25m. That gives us a rayleigh length of only about 1 light-minute away, but we'll benefit by having a smaller area and thus more high-focused laser.

Our new beam width at our rayleigh range is .707m, and our new shape factor is thus 1.414m. Using the same aluminum structure and 1 MW power output:

(1,000,000W)/(1.414m*240W/mK)+300K=3247K=T2

Again, our surface aluminum is going to melt off the longer the beam rests on the surface, since the melting temperature is much lower than the predicted steady-state temperature. And in this case, even faster, due to energy being concentrated in a smaller area (precisely how fast, however, is outside the scope of this analysis). Even taking into account the radiation leaving the immediate vicinity providing an additional cooling effect, I still end up with an estimated equilibrium temperature of approximately 1734K for the aluminum that's unfortunate enough to be in the line of fire.

You can repeat the calculation using data for steel or titanium as your structural materials, but they'll still melt under these conditions.

There's a few tricks you could do to mitigate the laser's effectiveness. One would be somehow using diamond as your structural material, since it has a very high melting (well, sublimation) point. You could try to find a surface with a very high reflectivity for gamma radiation, so only a fraction of the incoming laser power is absorbed, although I'm not even sure if they exist for that. And there's all the issues that would come with trying to hold a laser down at the same point against a target that's literally light-seconds away. And, of course, you would have to invent a gamma-ray laser, which doesn't yet exist. And of course there's absolutely zero practicality of firing at non-stationary targets more than maybe a few light-seconds away.

But would it be impossible to design a laser that can damage something light-minutes away, provided it can hit? Not in the slightest.

Bear in mind that any hypothetical laser weapon would never be continuous wave like you are supposing. Pulsed lasers are the standard for all laser ablation applications, and taking the absolute state of the art in pulsed lasers at the moment, which is zeptosecond lasers, your peak power will be up to 10^21 higher than a continuous laser.

At those intensities and time periods classical heat equations don't apply, materials are converted directly to plasma before the atoms have time to start vibrating, and literally fly apart. This is also the reason why mirror armour is not a realistic option for defence from laser weapons.

 

[Scribbit]

Your explanations are leaps and bounds beyond what I'm capable of. I'm not sure where I read that a laser would have difficulty beyond a million kilometers or so - doesn't matter where, but it was probably dealing with modern lasers, not exotic not-yet-developed ones, and might not have been close to accurate at that.

It was most likely not dealing with modern lasers, but with grasers, because...

The usual culprit is David Weber and his Honorverse. For any time you feel you have completely solid, logical and physics-based reasons for believing something completely and absolutely wrong about space travel, communications, computers and combat, particularly all the physics involved, you can blame reading that series or reading someone that copied that series. It's not how those things work. It's not how any of those things work.

He's just not good at math and physics. He just makes up for it in volume...of numbers he throws at his readers.

OK, maybe some of the blame rests in the fact that he wrote the series bible back in the 90's. Doesn't explain how he managed to screw up tonnage by several orders of magnitude so blatantly that he had to retcon everything...and that was the easy stuff.

 

[Ur-Quan Lord 13]

Why not?
Select a Gamma Ray with a wavelength of 10^-11 m, and select a beam waist of 1 meter, and you end up with a rayleigh length of pi*10^11 meters. Granted, that's a very large beam waist, but it seems like a lot of people are going for 1km+ ships on this forum, so that size of laser could fit fairly reasonably.

Multiply by the ratio of meters to the distance light covers in one second (1 light-second/3e8 m) and we get the rayleigh length in terms of light-seconds, approximately 1050 light-seconds, or at least 17 light-minutes, for this long-range gamma laser design. If the rayleigh width occurs at the lense, that effectively means an effective range of 1050 light-seconds where the laser's intensity is at least half of our maximum, point-blank intensity. In fact you can shorten the beam waist a little bit to increase intensity while still keeping 50% of your maximum intensity at a range in excess of 1 light-minute. From what it looks like, you could reduce the beam waist up to about .25 meters and get that result, using gamma radiation.

Not that you're going to hit anything that's one light-minute away, but that's not what's being asked.

Okay, so you're talking about "damaging" energy, so knowing how well a beam holds its intensity isn't enough. So, to approximate this damage, let's dig into some heat transfer!

We have our laser with that given characteristics: a beam waist of 1 meter, and we're firing at a target that's at the edge of our rayleigh length of 1050 light-seconds. In which case, our effective beam waist at that distance is 1.414 meters from here:

In other words, the laser beam that's impacting the surface of our target has a radius of 1.414m, or a diameter of 2.828m. All that energy getting pumped into the laser, whatever isn't getting reflected, has to be absorbed by the ship's armor. Not a whole lot of materials that I know of have high reflectivity for gamma rays, so we'll assume the absorbtivity is about 1: Or all energy exiting the laser beam must be absorbed by the armor.

Now, the general equation for conduction (Fourier's Law) would be a lot to work with for a general 3D problem. Fortunately, we can simplify the problem up a bit using a conduction shape factor.

Here's the basic idea: Our laser is heating the surface of our target in a circular cross-section of diameter "D". If the armor of our spacecraft (or whatever other target) is "thick", then that energy from our laser needs to conduct its heat into the nearby surrounding armor/structure of the ship. Given the conduction properties of the "armor" (basically how 'fast' heat flows), and whatever external temperature T2 the semi-infinite medium is supposed to be held at, and given the power output of the laser, we can approximate the temperature that spot on the surface would be at if we were to continue holding that laser at that particular spot for a long time (steady-state conditions).

The working equation for this is:

Q=S*k*(T1-T2)

S=Shape factor (for this specific scenario/geometry, S=2D. D=2.828m, so S=5.656m
k=Conduction coefficient
T1= Temperature of the surface being heated, which we want to find.
Q=Heat rate, or the laser's rated output power.
T2= Temperature of the semi-infinite medium, basically the surrounding metal that is not being melted directly.

We'll presume a human crew who likes to be comfortable and not freezing to death on the target vessel. So, let's let T2 be a temperature that's comfortable for said humans to continue to exist, about 300 Kelvins.

Rearranging the equation gives us the following:

Q/(S*k)+T2=T1

The most "famous" laser system currently existing today is fairly small with a power output of 30,000 Watts, and they want to get that up to 100,000 watts and want to test even 300,000 watts on a small sea-faring destroyers. So let's take a fairly conservative gander and say that Q=1,000,000 Watts of power output is reasonable for our huge space laser, which is much smaller than the maximum power output of a fission or fusion reactor.

It's a lot harder to guess what a spaceship or space station would be "armored" with in the future, so I'll go with an aluminum basic structure. We'll look at a table of aluminum k-values vs temperature and pick the 240 W/(m*K) to try and be conservative with our output temperature.

Plugging everything in, we find that:

(1,000,000W)/(5.656m*240W/mK)+300K=1037K=T2

So the surface material at the laser is at 1037K if the laser holds its position there. There's a slight issue: Aluminum melts at about 930K, so this laser will indeed do some damage despite its high beam waist. Granted, that neglects radiation from that heated surface so the effective temperature will actually be a bit smaller, but that issue can be fixed fairly easily just by pumping up the power to the still-reasonable 2 Megawatts.

If we optimize the laser a bit, since we're obviously not going to be hitting anything 16 light-minutes away, so let's reduce that beam waist to a more reasonable level of .25m. That gives us a rayleigh length of only about 1 light-minute away, but we'll benefit by having a smaller area and thus more high-focused laser.

Our new beam width at our rayleigh range is .707m, and our new shape factor is thus 1.414m. Using the same aluminum structure and 1 MW power output:

(1,000,000W)/(1.414m*240W/mK)+300K=3247K=T2

Again, our surface aluminum is going to melt off the longer the beam rests on the surface, since the melting temperature is much lower than the predicted steady-state temperature. And in this case, even faster, due to energy being concentrated in a smaller area (precisely how fast, however, is outside the scope of this analysis). Even taking into account the radiation leaving the immediate vicinity providing an additional cooling effect, I still end up with an estimated equilibrium temperature of approximately 1734K for the aluminum that's unfortunate enough to be in the line of fire.

You can repeat the calculation using data for steel or titanium as your structural materials, but they'll still melt under these conditions.

There's a few tricks you could do to mitigate the laser's effectiveness. One would be somehow using diamond as your structural material, since it has a very high melting (well, sublimation) point. You could try to find a surface with a very high reflectivity for gamma radiation, so only a fraction of the incoming laser power is absorbed, although I'm not even sure if they exist for that. And there's all the issues that would come with trying to hold a laser down at the same point against a target that's literally light-seconds away. And, of course, you would have to invent a gamma-ray laser, which doesn't yet exist. And of course there's absolutely zero practicality of firing at non-stationary targets more than maybe a few light-seconds away.

But would it be impossible to design a laser that can damage something light-minutes away, provided it can hit? Not in the slightest.

Thanks! This sorta math analysis is exactly what I was hoping for. Superb.

I try to imagine there being as little abstraction in the game as possible. It's more fun for me that way.

The reason a starbase hydroponics farm can produce as much as a low level planetary farm? A combination of 1. All the output is owned by the government, and 2. Starbases are just that huge.

Similarly, when a Corvette takes many months worth of the whole public alloy output of year 2200 Earth to build... That corvette is a big ass ship! Way bigger than an aircraft carrier already. That's why I go for the 1km corvette to 15km battleship in my imagination And a 15km ship can definitely power a meter wide laser, and also can be hit pretty easily at large distances. The mechanical accuracy of the turret would have more impact than any actual evasion!

Meanwhile... The idea that year 2200 Earth is still using fission reactors and red lasers, that part I have to edit out in my head as "the developers could have started at gamma lasers, but then they'd have to either invent new names for shorter wavelengths or just called it gamma laser 1-5".

 

[Dmitrius]

I can still remember the sense of betrayal I felt when someone told me that the soldiers in EU4 are not, in fact, 100 miles tall.

I was all, like, why do they need ships to cross oceans when they could literally just walk across and only get their giant boots wet? Why don't the 100 mile long ships cause mega-tsunami and devastate coast lines when they move? How could something that large even sail in oceans only a few miles deep? But *apparently* the map in grand strategy and 4x games isn't meant to be taken literally.

This is why we need a funny button. I disagree with comment, but enjoyed it immensely.

A like in lieu.

 

[Nitrousoxide]

Couldn't you use a toroid accelerator with an exit point to essentially have a infinitely long barrel to spread the acceleration over an arbitrarily long period of time? You'd obviously have bigger waste heat issues since you'd be dealing with it changing vectors in the toroid as you continue to accelerate it, which need to be resisted to contain it, but you could apply a MUCH more gentle acceleration over a few seconds rather than fractions of a second to get your slug up to a desired speed.

 

[Orimichi]

I don't wanna do the math, but seriously, 9.85 TW half the consumption of earth in 2005. Watt is a power unit not energy, you cannot consume it in a year... (and with our technology we have petawatt laser)
If you have doing the math the energy correctly of one shot is about 1 MJ, it's a lot but again we have laser which can do that in one pulse.

About the use of mirror armor and laser: http://toughsf.blogspot.com/2018/05/lasers-mirrors-and-star-pyramids.html
So yes you can use them

 

[Scribbit]

Couldn't you use a toroid accelerator with an exit point to essentially have a infinitely long barrel to spread the acceleration over an arbitrarily long period of time? You'd obviously have bigger waste heat issues since you'd be dealing with it changing vectors in the toroid as you continue to accelerate it, which need to be resisted to contain it, but you could apply a MUCH more gentle acceleration over a few seconds rather than fractions of a second to get your slug up to a desired speed.

Multiple problems here. Facilitating the vector change is going to cost more energy than is saved. The system is always using the same amount of total energy for final acceleration, but now you're requiring extra energy to be used to change the vector. Finally, all that extra energy used is going to generate its own heat. And once you get your lump of matter to a fraction of c inside your toroid...well, have you seen what a particle accelerator looks like? Because you'll need that but scaled up. That's not saving space.

You are far better off going with massive capacitor banks if it's a choice. And if it isn't, you're much better off with lasers, drones and missiles.

 

[Cordane]

I don't wanna do the math, but seriously, 9.85 TW half the consumption of earth in 2005. Watt is a power unit not energy, you cannot consume it in a year... (and with our technology we have petawatt laser)

I'll admit, I had two things wrong in bringing over the reference:
1) It should have been half of the "average total power consumption of the human world"
2) The year should have been 2013, not 2005 (I grabbed that from the line above it)
One other thing to keep in mind is that a watt is a rate statistic (1 joule per second), so if a laser only fires (or can only fire) for a nanosecond, it might only use one-billionth of its stated power capability.

 

[Spidee]

I don't wanna do the math, but seriously, 9.85 TW half the consumption of earth in 2005. Watt is a power unit not energy, you cannot consume it in a year... (and with our technology we have petawatt laser)
If you have doing the math the energy correctly of one shot is about 1 MJ, it's a lot but again we have laser which can do that in one pulse.

About the use of mirror armor and laser: http://toughsf.blogspot.com/2018/05/lasers-mirrors-and-star-pyramids.html
So yes you can use them

If you look at how power plants and power consumption is in MW/h.

 

[Ur-Quan Lord 13]

If you look at how power plants and power consumption is in MW/h.

It's in MW*h

Power * time = energy

Consumption is measured in energy. Just like the joules or calories in the food you consume.

 

[Ur-Quan Lord 13]

I'll admit, I had two things wrong in bringing over the reference:
1) It should have been half of the "average total power consumption of the human world"
2) The year should have been 2013, not 2005 (I grabbed that from the line above it)
One other thing to keep in mind is that a watt is a rate statistic (1 joule per second), so if a laser only fires (or can only fire) for a nanosecond, it might only use one-billionth of its stated power capability.

It is not a "rate statistic" but a rate.
It uses all its power. Just for a shorter time period.
It uses less energy, since energy is equal to power times time.

There is no "1s limit" on watts, or any unit of power. 10 petawatts is 10 petawatts whether it lasts 1us, 1s, or 3 months.

 

[Orimichi]

Ok, there is a lot of mistakes in the math :
1 g at 1% of c with a 700m cannon:
time of accelaration 4.67 us
Energy 900 GJ
Power 192 PW
Force 1.28 GN

 

[Cordane]

Ok, there is a lot of mistakes in the math :
1 g at 1% of c with a 700m cannon:
time of accelaration 4.67 us
Energy 900 GJ
Power 192 PW
Force 1.28 GN

I'm confused - where in my calculations below did I mess up?
distance = 1/2 acceleration x time^2
2 x distance / acceleration = time^2
time = sqrt (2 x distance / acceleration)
distance (barrel length) 700 m
acceleration 6,419,679,696 m/s^2 (654,401,600 gravities x 9.81 m/s^2)
time 0.000467 seconds
exit velocity 2,997,924.54 m/s (speed of light 299,792,458 m/s^2)

force (Newtons) = acceleration x mass
mass 1 gram = 0.001 kg
force 6.42M Newtons

power (watts) = Newtons x mass (kg) / time (sec)
power 9.62 trillion watts (9.62 terawatts)

Reversing your numbers on the time factor show that you were trying to reach the full speed of light instead of 1%:
acceleration = 2 x distance / time^2
acceleration = 64,193,975,853,894.5 m/s^2 (64.2 trillion vs 6.42 billion above)
velocity = acceleration x time
velocity 299,785,867.24 m/s^2 (99.9978% c)

There's also a doubling in there somewhere from mine to yours once you start looking at energy, power, and force, beyond the magnitude differences in the time for acceleration. Not sure where that would come from, as conversions to Newtons and then to watts are straightforward.

 

[anamiac]

If a vessel is cruising along at 1% c, and runs into an effectively stationary object (assuming it's a very slight fraction of the vessel's mass), would you expect that object to do much damage to the vessel? No, because the vessel would have been designed to travel at that speed, or else it wouldn't go that fast.

Yea, this makes no sense.

If a car is cruising around at 100 mph, and runs into a stationary cement filled pole, would you expect that object to do damage to the car? The car is designed to go well over 100 mph.

Of course it would damage the car! The car is designed to go 100+ mph on an unobstructed road! Jets are designed to fly through unobstructed atmosphere, and utterly fail to fly through any other substance. At just a few hundred mph, even small objects can cause humongous damage to an aircraft. Similarly, the spaceship is designed to go 1% c in unobstructed vacuum! At that speed, any stationary object it hits will do damage far greater per mass than it would to a slower moving vehicle, such as a car. The faster the craft is traveling, the smaller the kill projectile has to be. If the spaceship is going fast enough, you could destroy it just by venting atmosphere in its path.