Can we fire the Halo MAC cannon?
May 9, 2011 1:09 AM Subscribe
Can the Mass Accelerated Cannon on the UNSC Pillar of Autumn actually be fired?
Is it physically feasible for the Mass Accelerated Cannon on the UNSC Pillar of Autumn to be fired given:
the mass of the slug is 600 tons and is fired at 40% the speed of light.
Given this it can be calculated that the cannon outputs 4.3 x 10^21 J of energy per shot.
Now if we assume Newton's Third Law (Equal and Opposite Reaction) to be true, is the MAC round able to be fired without:
A. Sending the ship flying backwards, OR
B. Tearing it to shreds?
Is it physically feasible for the Mass Accelerated Cannon on the UNSC Pillar of Autumn to be fired given:
the mass of the slug is 600 tons and is fired at 40% the speed of light.
Given this it can be calculated that the cannon outputs 4.3 x 10^21 J of energy per shot.
Now if we assume Newton's Third Law (Equal and Opposite Reaction) to be true, is the MAC round able to be fired without:
A. Sending the ship flying backwards, OR
B. Tearing it to shreds?
A. Sending the ship flying backwards
The PoA will indeed move backwards, but only with the same amount of energy as the slug. The PoA weighs 30,000 tons (according to the Halo wiki) and so will move backwards (or be slowed if it's moving forwards) somewhat less than 40% of c. My rough calculations say:
Slug speed = 120,000,000m/s
PoA speed = 2,400,000m/s (0.8% of c)
That's still pretty fast, but I guess in the future where they have artificial gravity and faster-than-light travel, they have some kind of super-alloy or inertial dampener that deals with the recoil.
posted by EndsOfInvention at 1:33 AM on May 9, 2011
The PoA will indeed move backwards, but only with the same amount of energy as the slug. The PoA weighs 30,000 tons (according to the Halo wiki) and so will move backwards (or be slowed if it's moving forwards) somewhat less than 40% of c. My rough calculations say:
Slug speed = 120,000,000m/s
PoA speed = 2,400,000m/s (0.8% of c)
That's still pretty fast, but I guess in the future where they have artificial gravity and faster-than-light travel, they have some kind of super-alloy or inertial dampener that deals with the recoil.
posted by EndsOfInvention at 1:33 AM on May 9, 2011
You could have another round going in the other direction, like some recoilless rifles have used in the 20th century. I prefer the idea of woo-woo scifi tech though...
posted by pompomtom at 1:46 AM on May 9, 2011
posted by pompomtom at 1:46 AM on May 9, 2011
EndsOfInvention's answer of 0.8% of c doesn't take into account relativistic effects. I think the answer is actually a little less than 0.3%.
posted by Flunkie at 1:58 AM on May 9, 2011
posted by Flunkie at 1:58 AM on May 9, 2011
Actually in the Halo wiki it does say that for Orbital Defence Platforms with Super-MACs (bigger than the ship-born versions) "a pair of thrusters on the bottom side of the station fire for a couple of seconds to counteract the acceleration imparted to the station". It doesn't specify what ships do, but presumably since the ship MACs are pointed directly forwards (and aimed by pointing the entire ship), the ship's own engines act to counter-balance the recoil.
posted by EndsOfInvention at 3:49 AM on May 9, 2011
posted by EndsOfInvention at 3:49 AM on May 9, 2011
The ship is capable of generating sufficient energy to warp the fabric of space-time. Not to mention artificial gravity. If we're going to give them those, we have to give them the ability to deal with recoil.
posted by valkyryn at 4:56 AM on May 9, 2011 [2 favorites]
posted by valkyryn at 4:56 AM on May 9, 2011 [2 favorites]
Maybe the ship just hops in and out of hyperspace when it's firing to absorb the recoil. Or: repurposed Covenant anti-grav technology. Although if the MACs didn't actually work at all, the start of Halo 2 would make a hell of a lot more sense.
posted by A Thousand Baited Hooks at 5:30 AM on May 9, 2011
posted by A Thousand Baited Hooks at 5:30 AM on May 9, 2011
One nice thing about a coil gun is that you can invest energy in your projectile a little at at time, but your target receives the energy the old fashioned way. All at once. So at any given moment there isn't that much force acting on the PoA.
Depending on what they have in the way of artificial gravity and how it works, suddenly all bets are off. Because if I'm being pulled down to the deck as if the deck were a decent sized planet, but that deck isn't being pulled down to the next deck like it weighs what a decent sized planet weighs, I can have all kinds of fun with acceleration and all that matters is that the tidal effects of my little indiscretions don't throw the gravity generator plates or coils or whatever out of alignment prior to the next shot.
Thanks to "I Love Bees" I can put "Lt. Cmdr. Weapons Sciences" in the Halo universe on my resume (but hardly ever do).
posted by Kid Charlemagne at 5:34 AM on May 9, 2011 [1 favorite]
Depending on what they have in the way of artificial gravity and how it works, suddenly all bets are off. Because if I'm being pulled down to the deck as if the deck were a decent sized planet, but that deck isn't being pulled down to the next deck like it weighs what a decent sized planet weighs, I can have all kinds of fun with acceleration and all that matters is that the tidal effects of my little indiscretions don't throw the gravity generator plates or coils or whatever out of alignment prior to the next shot.
Thanks to "I Love Bees" I can put "Lt. Cmdr. Weapons Sciences" in the Halo universe on my resume (but hardly ever do).
posted by Kid Charlemagne at 5:34 AM on May 9, 2011 [1 favorite]
Whatever material the cannon mount is made of, it's hard to believe it could sustain that kind of force without tearing loose.
posted by Chocolate Pickle at 8:01 AM on May 9, 2011
posted by Chocolate Pickle at 8:01 AM on May 9, 2011
you can invest energy in your projectile a little at at time
This is true, but since you're accelerating the slug to such a high speed within a relatively short barrel, you're going to have to do it pretty quick after all. Assuming that:
Starting velocity = 0
Ending velocity = 120 million m/s
Barrel length = ship length = 1.17 kilometers
your projectile will be out the barrel 19.5 microseconds after you start it.
note: I know nothing about Halo except what I just read on the wiki, so perhaps I've got my numbers wrong
posted by echo target at 8:39 AM on May 9, 2011
This is true, but since you're accelerating the slug to such a high speed within a relatively short barrel, you're going to have to do it pretty quick after all. Assuming that:
Starting velocity = 0
Ending velocity = 120 million m/s
Barrel length = ship length = 1.17 kilometers
your projectile will be out the barrel 19.5 microseconds after you start it.
note: I know nothing about Halo except what I just read on the wiki, so perhaps I've got my numbers wrong
posted by echo target at 8:39 AM on May 9, 2011
Response by poster: Another issue I'm having is the energy required to fire such a weapon.
The Pillar of Autumn has three nuclear reactors yes, but (according to my physics major friend) the energy required to accelerate a 600 ton round to 120 million m/s, my friend says, would require the total energy of the mass of 15 Nimitz class supercarriers (a full load displacement of 100,000 long tons).
I think he might have gotten his math wrong but I can't be sure.
posted by Catarax at 9:34 AM on May 9, 2011
The Pillar of Autumn has three nuclear reactors yes, but (according to my physics major friend) the energy required to accelerate a 600 ton round to 120 million m/s, my friend says, would require the total energy of the mass of 15 Nimitz class supercarriers (a full load displacement of 100,000 long tons).
I think he might have gotten his math wrong but I can't be sure.
posted by Catarax at 9:34 AM on May 9, 2011
The reactors are probably fusion. Fusion reactions produce more energy than fission, and since we don't really have any in the real world that work yet, there is a lot of latitude to decide how much power they can output.
posted by -harlequin- at 9:41 AM on May 9, 2011
posted by -harlequin- at 9:41 AM on May 9, 2011
The energy isn't so much of a problem. One of the current experimental approaches to fusion being tested is laser implosion. A pellet of fuel is dropped into the middle of a chamber and gets high simultaneously from all sides by hyperpowerful laser beams.
During the instant of firing, the system uses energy at a rate equal to the entire US, but only for a few microseconds. They way they do it is by charging up huge banks of capacitors, and drawing all that current back out again during the instant of firing.
Your hypothetical cannon could do exactly the same thing. It doesn't have to have an actual energy generator capable of producing that much power on a continuous basis; it only needs a big storage bank of some kind, which it can charge up slowly, and then discharge rapidly.
posted by Chocolate Pickle at 11:17 AM on May 9, 2011
During the instant of firing, the system uses energy at a rate equal to the entire US, but only for a few microseconds. They way they do it is by charging up huge banks of capacitors, and drawing all that current back out again during the instant of firing.
Your hypothetical cannon could do exactly the same thing. It doesn't have to have an actual energy generator capable of producing that much power on a continuous basis; it only needs a big storage bank of some kind, which it can charge up slowly, and then discharge rapidly.
posted by Chocolate Pickle at 11:17 AM on May 9, 2011
The PoA will indeed move backwards, but only with the same amount of energy as the slug
Yeah, but what energy? At .4c, your relativistic mass is about 109% of your rest mass, at the scales we're dealing with, we can handwave this away -- esp when I start rounding. 600 tons (assuming US short tons) = 1.2 million pounds or 554,310kg, + change.
Velocity is .4c, in cm/sec that's 11,991,698,320 cm/sec. Now that I have mass in grams and velocity in cm/sec, I can solve for ergs. E in erg= mv2/2. v2 is huge -- 1.48x1020th, we multiply by 554,310,000g and divide by two and we end up with 3.98x1028thergs, or, wow, we're going to have to reach up the order of magnitude scale, and it comes out to be, oh, 3,985 exajoules, or near as doesn't matter to 4 zettajoules, which is meaningless to us, so we convert to 950 gigatons of TNT, which is also meaningless to us.
This is 10 times the entire annual energy consumption of Earth.
Nothing survives firing this. Nothing survives being hit by it. Someone upthread mention 19μsec to fire it. Average Power is ΔW over ΔT, or work over time. Work, here, is in joules. Time is in seconds, so average power is watts (1J/s=1W), and 4zettajoules over 19 microseconds is 210,526zettawatts, or about 210yottawatts. That's really close to the luminosity of the sun. You have the entire energy output of the sun in that barrel.
In short: The expanding cloud of vapor that is the PoA will be moving outwards at quite a clip.
posted by eriko at 11:52 AM on May 9, 2011
Yeah, but what energy? At .4c, your relativistic mass is about 109% of your rest mass, at the scales we're dealing with, we can handwave this away -- esp when I start rounding. 600 tons (assuming US short tons) = 1.2 million pounds or 554,310kg, + change.
Velocity is .4c, in cm/sec that's 11,991,698,320 cm/sec. Now that I have mass in grams and velocity in cm/sec, I can solve for ergs. E in erg= mv2/2. v2 is huge -- 1.48x1020th, we multiply by 554,310,000g and divide by two and we end up with 3.98x1028thergs, or, wow, we're going to have to reach up the order of magnitude scale, and it comes out to be, oh, 3,985 exajoules, or near as doesn't matter to 4 zettajoules, which is meaningless to us, so we convert to 950 gigatons of TNT, which is also meaningless to us.
This is 10 times the entire annual energy consumption of Earth.
Nothing survives firing this. Nothing survives being hit by it. Someone upthread mention 19μsec to fire it. Average Power is ΔW over ΔT, or work over time. Work, here, is in joules. Time is in seconds, so average power is watts (1J/s=1W), and 4zettajoules over 19 microseconds is 210,526zettawatts, or about 210yottawatts. That's really close to the luminosity of the sun. You have the entire energy output of the sun in that barrel.
In short: The expanding cloud of vapor that is the PoA will be moving outwards at quite a clip.
posted by eriko at 11:52 AM on May 9, 2011
it only needs a big storage bank of some kind, which it can charge up slowly, and then discharge rapidly.
In Halo canon (pun intended), this is in fact how MACs work - their firing rate is limited by the recharge rate of their capacitors.
posted by EndsOfInvention at 1:41 PM on May 9, 2011
In Halo canon (pun intended), this is in fact how MACs work - their firing rate is limited by the recharge rate of their capacitors.
posted by EndsOfInvention at 1:41 PM on May 9, 2011
Momentum. It's momentum that's conserved. And because the slug is traveling at relativistic speeds, you need to use the relativistic mass to calculate its momentum.
posted by exphysicist345 at 2:41 PM on May 9, 2011
posted by exphysicist345 at 2:41 PM on May 9, 2011
[On preview: as exphysicist345 says] the PoA will recoil to match the momentum of the slug, not the energy. The ship's mass is 50 times that of the slug; the slug's γ is 1.09; the ship's γ is essentially 1; its recoil will be 0.9%c. I think.
I agree that the real answer is that as far as momentum and energy conservation is concerned, if you have artificial gravity and FTL travel you can break all the rules.
posted by hattifattener at 10:51 PM on May 9, 2011
I agree that the real answer is that as far as momentum and energy conservation is concerned, if you have artificial gravity and FTL travel you can break all the rules.
posted by hattifattener at 10:51 PM on May 9, 2011
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posted by Jairus at 1:31 AM on May 9, 2011