[Math] Kinetic energy of impact between two moving objects

Well, yes, ofcourse it’s the same, as your calculations are based on momentum.

In the calculations posted in earlier replies the impact calculation is wrong, because due to the way it is calculated, the reference frame is going to determine the energy lost to object A and B, and as such they cannot be directly used to calculate the impact - it’s usable to calculate the loss of kinetic energy in the entire system, yes, but that’s not interesting when you’re calculating the damage of each object. The simplest, least-prone-to-error way of calculating the impact, is to make the impacted object stationary.

My calculations are based on both, momentum and energy.
I calculate the energy lost in the collision.

before collision: 1/2 * 0^2 + 1/2 * 20^2 = 200 J
after collision: 1/2 * 10^2 + 1/2 * 10^2 = 100 J

So 100 J were lost on the collision. And that number is independant of the reference frame.

Yeah… that’s what I said :clue:

The trick with using a “easy” frame of reference is that it makes non closed systems easy to deal with. That is the problem with using a different frame of reference. A wall can bring momentum in and out of a system. If the wall is at zero speed. You no longer need care.

Typically for collisions the correct frame is the center of mass frame as the easiest. Since an unmovable wall has effectively infinite mass. Its rest frame is the correct one.

In games almost all “collisions” are not really closed systems. Seriously hack physics typically ends up as better more fun game play anyway.

Also, the h-bomb only has to get near its target, whereas the impactor has to be a direct hit. And, if you are using a rail gun to fire your impactor, don’t forget the firing ship takes a recoil.

[url=http://www.amazon.com/Risen-Empire-Succession-Scott-Westerfeld/dp/0765319985/ref=sr_1_13?ie=UTF8&qid=1399967458&sr=8-13&keywords=scott+westerfield]The Risen Empire[/url] has a pretty nice kinetic space fight...

Quite enjoyable essey about space combats http://forums.spacebattles.com/threads/essay-on-realistic-space-combat-i-wrote.131056/

Here’s a snippet:

[quote]Let’s say you have a nuclear salt water rocket propelled warship with a mass ratio of 5, which will give it a delta V of 8,421 km/s, and you want to bomb New York. If you expend all your propellant in a single burn in the direction of Earth and then launch a 1 ton missile into New York City it will impact with the energy equal to an 8.48 megaton bomb. Consider that to be able to saturate the PD of enemy warships your ship will probably carry several hundred such missiles. In other words, forget about New York, you can singlehandedly devastate the entire United States. And this is peanuts compared to what you can do if you really want to make a splash: crash your ship into the planet along with your missiles. If your ship weighs 10,000 tons it will impact with a force of 84.8 gigatons.
[/quote]
O_O

I pretty much managed to predict most of the stuff in there, nice to see that confirmed. What I seem to have underestimated is the result of the impact of kinetic missiles, so it’s time to resuscitate this thread!

A missile which after using up all its fuel has a mass of only 1kg which collides with an enemy craft with a speed difference of 20km/sec has the kinetic energy of ~48kilotons of TNT, equal to around two and a half Fat Man nukes. There’s probably not a single material in the world that can stand against such an impact, but that doesn’t necessarily imply a one-hit-kill as the essay assumes. What’s important is the amount of energy that’s actually lost (e.g. converted to heat) in the impact. A kinetic projectile hitting a solar panel isn’t going to cause a nuclear explosion. It’s most likely going to disintegrate the solar panel and possibly severely damage whatever part of the ship that it was attached to, but it’s far from a one-hit-kill. We simply can’t assume that all the kinetic energy of the projectile is converted to heat. We can however assume that the projectile will probably either vaporize or simply break up into millions of fragments no matter how slightly it touches anything at that speed. It would seem as if the important number here is how much speed the projectile loses by penetrating the target. It would actually make perfect sense to design the missile to essentially be round. A spherical missile would require less materials for its volume (for fuel), while reducing the penetration effect compared to a long and narrow missile (maximizing kinetic energy to heat conversion on impact).

A very interesting way of handling damage in the game would be to give each component of the ship a health value and a heat value. Once heat is above a certain threshold, health starts going down. Some components (fuel tanks, missile storages, reactors, etc) may even instantly explode if they become too hot, so cooling them is a priority. Rail guns, gauss cannons, lasers, reactors and engines all heat up their respective components. Heat in turn slowly spreads to nearby components, while components facing space radiates heat away from the ship. A laser hitting an enemy ship would not inherently do any damage. It would simply heat up whatever ship component it hits, so heat shielding and cooling would be an important aspect of the game. However, missiles can also be made to damage using the heat system. An impact from a projectile in essence just heats up whatever it hits, so why not just simply add a (large) amount of heat based on the speed lost by the projectile when passing through said component? The area-of-effect explosion of the impact will then essentially be handled by the heat spread system, pretty much detonating anything that can detonate in the ship. Both nuclear explosions and explosions caused by ship components detonating would work the same way; just dump a shitload of heat in said component. HYPE!

Any further ideas?

Well if it’s in space where’s there’s little to no air resistance, the missiles could be whatever shape you want:

Nuclear chain shot 8)

Also liking this: Relativistic Kill Vehicle
Their example of a 1kg mass traveling at .99c would impact at the equivalent of 132 megatons, 6 times as much kinetic energy as mass-energy!
Which means the next logical step is to fire 1 kg anti-matter rounds at .99c ;D

Some great end-game weapon tech here, I’d say. Probably tough to balance, though.

I’m not sure if balancing this would actually be that difficult, if you exaggerate some of the inherent drawbacks of each type of weapon.

  • Kinetic missile: Somewhat fast and relatively sturdy since it is made of solid metal. Damage strongly depends on the speed difference between the ships making the missile situational, but at least it’s simple to manufacture.
  • Nuclear missile: Can be extremely powerful without depending on a speed difference, but they have a minimum size and are therefore much bulkier and heavier, making it easier to intercept these missiles. The fact that they rely on fine mechanisms to trigger a nuclear reaction in the warhead further enhances their weakness against missile defense as they are easy to disable (without triggering a nuclear explosion).
  • Anti-matter missiles: Powerful as hell. Also suffers from size problems but not to the same degree as nuclear warheads. Always explodes when destroyed, meaning that a single shot down missile can prematurely detonate an entire volley. Dangerous to store on a ship.
  • Rail guns/Gauss cannons: Useful for missile defense and bombardments of enemy ships. Projectiles weigh almost nothing, so it’s possible to fire a huge number of rounds with sufficient power and cooling.
  • Lasers: Great for missile defense and combat at relatively short distance. Ships equipped with lasers can attempt to get close to enemy ships by protecting themselves with their lasers against missiles and then cut up everything in range without having to worry about running out of missiles.

Nuclear missiles are good against enemies with weaker missile defense. Anti-matter missiles are better than nuclear missiles, but they inherently carry a risk since the anti-matter has to be kept stable. Kinetic missiles are heavy since you need lots of them, but in sufficient numbers they can overcome any missile defense system. Rail guns can easily shoot missiles and also weakly bombard enemy ships at medium range. Lasers bring great defensive and offensive capabilities but are short ranged.

Also factor in the fact that nukes are chump change compared to anti-matter projectiles, depending on how far in the future the game is. And railgun launched kinetic vehicles are just pieces of metal and some energy, can’t get much cheaper than that.

I also don’t know what level of realism you want to retain in the mechanics themselves, for instance, lasers (as in NIF scale plus) are probably effective even at quite a distance, depending on your optics technology etc, and have very little latency. (Although if the kinetic missiles are going .99c then that argument is irrelevant)

Lasers have a pretty heavy damage falloff in the real world. Double the distance and the laser suddenly heats up a 4x as large area on the target. Well, most of this stuff’s just balancing issues. xd

And exactly how much energy is required to get that .99c ?

How much energy are you putting in the laser? A 0.99c peashooter or a 2 zillion watt laser, both would need the same input energy. The difference would be the pea would not diffuse with distance.

A perfect antimatter drive puts all the mass energy of the antimatter/matter into kinetic energy. So a 99% c with a gamma of 7 means that a 1 kg projectile needs 7kg of matter/antimatter to accelerate to that speed.

That is 6x10^17J or a 1GW power plant running for 20 years.

antimatter: nice one. Make it part of the missile so even if it hasn’t reached top speed…it give an extra bang? Engineering problem that.

Half of the energy is released as neutrinos and there is no way you can aim those. So not 100% goes to kinectic energy drive.