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I used E=MC^2 because it is a commonly known equation that shows the relationship between energy, mass and speed... that is all. From toshiro's examples you can see that the actual equations are quite similar.
Except it's not. E=mc^2 is for finding the rest energy of a "particle". E=(mc^2)/sqrt(1-v^2/c^2) finds the total relativistic energy. If you're looking for the kinetic energy, it's (mc^2)/sqrt(1-v^2/c^2) - mc^2, the first order binomial approximation for which is 1/2 mv^2.
Of course, if we're talking Force, we might as well fall back on Newton and F=ma (or m(dv/d[tau]). Since railguns fire magic particles that never accelerate, that's a bit of a tricky one (the rails start out going the same speed as they end up at).
The easiest way to do this is just momentum conservation. Momentum is mv/sqrt(1-v^2/c^2). We'll disregard relativity (poor Einstein) because the speeds are too low for me to care. Now, we know that the ship has 0 momentum initially because it's not moving (if it is, we just tranform into its frame until it isn't moving). That gives us an initial momentum of 417.6 kgm/s for the rail. After the collision, the rail isn't moving and the ship is, so the 417.6 kgm/s will be the ship's new momentum. If we assume a ship mass of 7000 kg (fairly average), that translates to a velocity of 0.06 m/s - not much, but we're also assuming riducously light rails. Nonetheless, it would become noticable if you got hit by several at the same time. And I would argue that it would be more entertaining to artificially increase the number, say by a factor of ten. :-)
Of course, if we're talking Force, we might as well fall back on Newton and F=ma (or m(dv/d[tau]). Since railguns fire magic particles that never accelerate, that's a bit of a tricky one (the rails start out going the same speed as they end up at).
The easiest way to do this is just momentum conservation. Momentum is mv/sqrt(1-v^2/c^2). We'll disregard relativity (poor Einstein) because the speeds are too low for me to care. Now, we know that the ship has 0 momentum initially because it's not moving (if it is, we just tranform into its frame until it isn't moving). That gives us an initial momentum of 417.6 kgm/s for the rail. After the collision, the rail isn't moving and the ship is, so the 417.6 kgm/s will be the ship's new momentum. If we assume a ship mass of 7000 kg (fairly average), that translates to a velocity of 0.06 m/s - not much, but we're also assuming riducously light rails. Nonetheless, it would become noticable if you got hit by several at the same time. And I would argue that it would be more entertaining to artificially increase the number, say by a factor of ten. :-)
E=mc^2 is a little big picture for this issue. We should be thinking about f=ma and p=mv. Using Toshiro's derived mass, the wiki's velocity numbers, and assuming we're shooting a stationary ship that doesn't move after it's hit and that the projectile has a full second to slow to a stop after hitting its target, Newton's 2nd would say that f = (0.87kg)*(-480 m/s^2) = 418 Newtons (not much.)
Really, we should be looking at conservation of momentum for an inelastic collision. (I like Halliday and Resnick as a physics reference.)
Whichever set of equations you use, even if we assume that the projectile stops in much less than a second, it's not going to affect the target much. I think the main reason for this is the low velocity at which our rails travel. 480 m/s works for VO because of the scale around which everything is built, but a real rail gun would probably travel much faster (and hence yield much more damage.)
For comparison, a .22 rifle bullet has a muzzle velocity in the 365 m/s range. A kilo worth of .22 rounds wouldn't have much kick for the firing ship and it probably wouldn't do much to an armored, ship-size target either.
I would think that a rail gun would rock the shooter and target a bit more too, but based on the numbers that are used for VO I think the effects we see are pretty accurate. I don't think the we're concerned with having perfect physics ingame. (If we were, all our weapons would use active homing techniques and all figting would be BVR. Where's the fun in any of that?)
Really, we should be looking at conservation of momentum for an inelastic collision. (I like Halliday and Resnick as a physics reference.)
Whichever set of equations you use, even if we assume that the projectile stops in much less than a second, it's not going to affect the target much. I think the main reason for this is the low velocity at which our rails travel. 480 m/s works for VO because of the scale around which everything is built, but a real rail gun would probably travel much faster (and hence yield much more damage.)
For comparison, a .22 rifle bullet has a muzzle velocity in the 365 m/s range. A kilo worth of .22 rounds wouldn't have much kick for the firing ship and it probably wouldn't do much to an armored, ship-size target either.
I would think that a rail gun would rock the shooter and target a bit more too, but based on the numbers that are used for VO I think the effects we see are pretty accurate. I don't think the we're concerned with having perfect physics ingame. (If we were, all our weapons would use active homing techniques and all figting would be BVR. Where's the fun in any of that?)
Damn it, I forgot to double-check. Thanks, krazyivan, for 418 N do seem a bit weak. However, it is still twice the force a vulture's engine can exert on the ship, although it's an impact and not a force over time... so, as you say, the numbers work well within VO.
On topic:
It would still be fun to have more weapons obtain some kind of 'stopping power'. It does not have to be concussive force like the rockets, but rather something that 'rocks the boat', requiring the ship's engine to momentarily concentrate all its available power to counter the effects of a slug hitting the ship off-center, and thus slowing down the ship.
On topic:
It would still be fun to have more weapons obtain some kind of 'stopping power'. It does not have to be concussive force like the rockets, but rather something that 'rocks the boat', requiring the ship's engine to momentarily concentrate all its available power to counter the effects of a slug hitting the ship off-center, and thus slowing down the ship.
I like that idea Toshiro...something that could really jolt a ship and maybe even knock it down from turbo speeds, but not a prox-fused rocket. It'd have to be tough to shoot accurately, like a rail. Maybe an L port rail gun that shoots much larger rails or something.
Ok... let's try this then... I used E=MC^2 because it was the only equation I could remember at the time that showed that energy, speed, and mass are interrelated... It was non-optimal but it is a lot simpler then the equations you give. (Well... some of them. Obviously f=ma is simple.)
I offer my abject and non-physicist apologies.
I offer my abject and non-physicist apologies.
Let's not forget kickback. If it's arbitralily decided that the rails from the gun have enough force to knock it's target back a peg, it'd be even cooler to feel the full effect of kickback from simultaneous fire of a fully stocked Hornet.
Force would be cool, but with the current rails, we're assuming very small mass per slug, so with the mass of the ship, it wouldn't do much to move it... on the other hsnd, give us an l-port railgun, and you could generate some serious kickback, which is good.
On a related note, isn't it about time the mass, thrust, torque, etc... of everything got multiplied a few times? I mean, that's a pitiful amount of thrust for a spacecraft, yet no more is necessary given how light it is... does anyone else see anything wrong with this? Combat-ready ships should be MASSIVE... Just about the only ship that should be easy to knock around would be the cent.
On a related note, isn't it about time the mass, thrust, torque, etc... of everything got multiplied a few times? I mean, that's a pitiful amount of thrust for a spacecraft, yet no more is necessary given how light it is... does anyone else see anything wrong with this? Combat-ready ships should be MASSIVE... Just about the only ship that should be easy to knock around would be the cent.