Saberhagen's C+ Cannon, So What is The Impact Energy?

[BigDon]

Since there are real scientists here I was wondering about that one. One of the better weapons against the Berserker threat were ships that could mount a "C+" cannon. You have a one (metric) ton lead slug with a small FTL drive engine attached. On the way to the target it would skip in and out of "real" space and was computer timed to impact just as it was re-entering real space to give it a virtual speed of, well, C+. These were needed because your average planet killer sized Berserker was 50 miles across and built dense as there were no passage ways needed for crews and such. Heavily armed and with multiple layers of thick armor and force fields.

Aside from the fantasy aspect of C+, how much energy is the energy release of a metric ton (rest mass) of material hitting a solid object at let's say 99% the speed of light? (I don't know what equations to use) Would it be a big difference if the target was stationary as opposed to moving a good clip its own right?

[The Supreme Canuck]

Er, define "good clip." Relativistic? Not? Probably won't make much difference with the projectile at 99% c, but I'm curious.

[Ronald Brak]

E=mc2

so E = 1,000 kg by 300,000,000 m/s squared

E = 90,000,000,000,000,000,000 joules

Which would be enough force to lob a navel battleship at the moon and leave a jolly big crater.

[01101001]

This topic only makes me think of
Pachelbel's D Canon (http://en.wikipedia.org/wiki/Pachelbel's_Canon)

[BigDon]

Thanks Mr Brak, I wasn't sure if that was the equation to use or not. Well, the stories always mentioned the hits being devastating even to the larger units.

011, the one I thought of as I was typing it out was: If a C+ cannon was so effective think what a B+ or an A- would do for you.

Okay,then the next part of my question would be, what would the mass gain be on one tonne accelerated to that speed?

[Ronald Brak]

Thanks Mr Brak, I wasn't sure if that was the equation to use or not.

Don't thank me yet. There is a good chance someone will point out that I've totally messed up the calculation.

Okay,then the next part of my question would be, what would the mass gain be on one tonne accelerated to that speed?

Well, I found a table on the internet that says that at 99% the speed of light an object's mass will be 7.1 times greater.

[Tog_]

If this is just the impact force why wouldn't it be the mv2 one? Or 1/2 mv, or whatever the real formula is (as opposed to the version I know that uses grains and FPS to get foot pounds).

1000 kg= 15,432,648 grains
0.99c=973,733,270 feet per second

V*V*M/450451= 3.248 e19 ft lbs or 4.406 e13 Mega joules (I thnk). According to this site (http://www.convert-me.com/en/convert/energy), that puts it about the same as 10.5 Gigatons of TNT. Before you do the 7.1 mass increase.

[Ronald Brak]

Boy I am really stupid!

Sorry, that last statement was unethical towards myself. I should have said, Boy, sometimes the things I write are really stupid.

Ignore what I wrote, look at what Tog wrote. E=mc2! That is not the equation to use! So embarrassing! No wonder I never win the Nobel Prize for physics!

[BigDon]

Thanks again for the replies guys.

Tog, thank you, ten and a half gigatons? Can you say duck? Sounds a little like that nuclear artillery round that had a blast radius that exceeded its maximum range. :think:

I thought only the rest mass counted in impact calculations like this.

Ronald, can you get banned for Ad Homming yourself? :)

Actually, wouldn't this be even more complicated? Wouldn't the object being impacted contribute significantly to the reaction as well? (I'm not asking for a new calculation!) From the projectiles point of view it just got hit with several billion tons of Berserker at near light speed.

I read on that physics in movies website that the ships in Independence Day that hovered over the cities were 15 by 2 miles. The weight calculation by the engineers on the site was 2 billion tons. Not something you'ld like dropped on your hometown. Larger Berserker units were 50 by 30 miles. Without a lot of passageways.

[Ronald Brak]

Speaking of Independance Day, Why didn't the mothership just hover above the earth in line with the moon and allow the increased tides to take out humanity's cities? It was that big.

[BigDon]

Did you go to that site? They mention that. They had its mass and orbital range (both from the movie) and estimated it had 2000 times the pull of the moon.

[Tog_]

Thanks again for the replies guys.

Tog, thank you, ten and a half gigatons? Can you say duck? Sounds a little like that nuclear artillery round that had a blast radius that exceeded its maximum range. :think:

I thought only the rest mass counted in impact calculations like this.

Actually, wouldn't this be even more complicated? Wouldn't the object being impacted contribute significantly to the reaction as well? (I'm not asking for a new calculation!) From the projectiles point of view it just got hit with several billion tons of Berserker at near light speed.

That IS the rest mass...

Also, that's just the kinetic energy it brings to the table, what happens froom the instant of impact is a different matter. I have no idea how to calculate the heat release from something like that, but I don't think it would be an issue of blast radius.

It would also depend on the density of the projectile and the density of the ship. A lead slug would be a really poor choice since it's so soft. "bug on a windshield" is a term that comes to mind. This is why tank use depleted uranium rounds. They are very dense which means they pack more mass into a smaller package. For a penetrator, I'd imagine you'd want a smaller surface area made of incredibly hard material.

[Ronald Brak]

No, I didn't go to that site. Before I'll do I'll mention a couple of other things about the movie. Notice that the aliens didn't change their technology or even their security codes for fifty years? Talk about being lax. I mean why even bother having a security code if you are going to keep the same one for fifty years?

Then there was the fact that dispite having an impenertratable shield around their saucers, they still felt the need to send out fighters to deal with the human planes instead of say, oh flying towards the humans planes and splatting them against the shield like bugs. Or just ignoring them. I guess the aliens must have really been bored and wanted to go out and shoot down some hominids in planes. Their xbox must have been broken or something.

Then there was the convenient fact that for some reason the aliens had to use their city buster beam from low in the atmosphere instead of from a million miles away giving human planes a chance to take them out.

An if you can see through the shield that means light can pass through it, which means a decent amount of energy from an atomic bomb should pass through. And why did the humans stop after one atomic bomb failed to work? Weren't they curious to find out just how much that shield could take?

[Ronald Brak]

At 99% the speed of light I don't think it would make much difference if you were hit by a ton of steel or a ton of marshmallow. Against a 50 mile berserker ship I guess all that energy is going to be transferred to the ship. You wouldn't want the mass of plasma the projectile would become blowing out the other side as some of its destructive potential would then be wasted.