# Kinetic Force question

1. Oct 10, 2015

### Richard Noel

Can you help me work something out, please?

I'm writing a science fiction story, and want to work out how much impact energy would be produced by railgun. As a starting point, though I'm sure it should be way too high, if I accelerated a 300kg shell to 290,000 m/s, the kinetic energy should be about 12.6 million megajoules. Given that the US military said a shell fired at nearly 10k mph would give 1.5 megajoules, this seems pretty high. But when I converted this into megatons to get the power, it only gives me 0.003. I tried it a couple of times and checked it on an online calculator and came up with same answer. Which just doesn't work out.

Now I wanted to be able to produce about 40-50 megatons. I know just short of light speed is ludicrous, but I needed a starting point. How do I work this out? I'm sure I've heard that object moving at that speed would go right through the planet, so how do we work that out? Do I have to factor in the stationary object, or does relativity kick in with the mass increasing with speed, in which case I'm lost.

Can anyone help with this?

2. Oct 10, 2015

### Isaac0427

The most important part of that is fiction. While you may want some science in it, invent some new crazy power thing that can do whatever you want it to do. You need to balance out science and fiction. I'm not quite sure how to work the math of it, but that's my advice.

3. Oct 11, 2015

### Richard Noel

Yes, I could do that. But all I really want is to work out fast I'd have to hurl a shell in order for it to have that level of impact force. I like to make the numbers real where possible because it gives you nice consistency and a little realism where you can. I've ignored the laws of physics enough when I've had to say that we have a drive system that can reach speeds of up 3-4 pentameters and hour.

4. Oct 11, 2015

### Isaac0427

Ok, I checked out the math, and you have energy of about 13 terajoules (1.3*1012). You want about 200 pentajoules (2*1017). We are talking about exponentially increasing your value. I am going to stand by my original claim. Try being able to accelerate things beyond the speed of light. I mean think about it, in Star Wars, people can travel across galaxies within hours.

5. Oct 11, 2015

### Richard Noel

I managed to figure it out. The problem is out of stupidity, I calculated the speed of light to be 300k m/s, not 300m m/s as it should be (rounded off I know, but it was only for approximation). This made a significant difference. We then ended up with 1.261x1013 megajoules, or 3,015 megatons of TNT. Way above what was necessary.

With a bit of trial and error, I then came to hurling a 40kg shell at 0.4c, or 120m m/s for east maths. This then have me 68.8 megatons of TNT, which is just right.

HOWEVER, if I wanted an accurate measurement I shouldn't have used Newton's laws of motion. Einstein's laws of kinetic energy would be better suited to working this out at anything over about 0.1cc, because relativity becomes an issue. But I did only need a eurgh idea so I can decide how big to make the guns.

This was useful to work out, because now I need to make sure how fact ships can move so as not to outrun the shells, and I know how much energy is required and therefore how many fusion reactors the battleship would need to keep 18 of these guns firing in sequence at a rate of 1 shell every second.