What an interesting problem, I never thought about that.
Half way down this article it explains your problem, see the “frame of reference” sub heading.
As it applies to your game, why not just always use the game landscape as the frame of reference to calc the damage which is a function of kinetic energy?
In a collision the difference in velocity doesn’t mean anything by itself. It’s all about momentum. Especially if you want to calculate damage.
TL;DR: I mainly wanted to calculate the kinetic energy to be able to relate and compare it to the explosive energy of the warhead of a missile for game balance purposes.
I’ve been Googling all day about this. I’m surprised by how little information I could find about this and my other related questions.
First let me take a step back and explain why I’m asking about this. I’m trying to figure out what would happen if two objects collide in space. The reason why I’m interested in kinetic energy is simply because many times space ships are going at extremely high speeds relative to each other, so kinetic projectiles will most likely be the main weapon of many ships. This includes both cannons firing unguided projectiles at extremely high speeds (Gauss cannons or rail guns) and missiles that contain a kinetic penetrator instead of a conventional or nuclear warhead. Example: https://www.youtube.com/watch?v=yHbf-Eb3xak&feature=youtu.be&t=41s My reasoning for kinetic missiles is simply that at some point, the amount of kinetic energy the missile has after accelerating towards the target be so high that the kinetic energy the missile has is higher than the energy released by its explosive warhead, at which point it would be better to optimize the missile as a penetrator and get rid of the explosive warhead altogether. This was the main reason I was interested in calculating the kinetic energy of a projectile; to be able to compare the difference in efficiency.
For small Gauss cannon projectiles, rail gun projectiles and kinetic missiles we can assume that the projectile will simply penetrate into the ship it hits and either exit the ship on the other side at a lower speed or come to a complete stop inside the ship. Therefore I need to figure out how much a projectile is slowed down by passing through X meters of a certain material. This would be a function of the width, mass and speed of the projectile and the density of the material being penetrated. I’ve reached the conclusion that there’s no real reason to go for a realistic approach here so just go with something that works well in the game. The only actual formula I’ve been able to find was this: http://en.wikipedia.org/wiki/Impact_depth which I think makes no sense since it claims that impact depth is not dependent on the speed of the projectile (it does however assume a “high” velocity).
However, things get an awful lot more complicated when the missile has a conventional warhead and is not made to penetrate the armor of the object it hits. In this case we can assume that the projectile will not significantly penetrate the object regardless of speed since the missile will essentially crumble and fragment into millions of pieces almost instantly, which significantly reduces the penetration depth. However, we still need to take the warhead’s explosion into consideration. This gets weird once you realize that the projectile may actually be traveling at a higher speed than the actual explosion of the projectile. To work around this, I’ve decided to only allow a certain type of warhead, namely shaped charges. A shaped charge is essentially a shotgun facing forward that fires a jet of metal particles when it’s triggered. This jet is also optimized to penetrate armor by applying as much energy as possible to a small area of the object hit, but the jet disperses quickly at longer distances. That should allow me to essentially use the same approach as for kinetic projectiles but with some quirks like the damage caused by the jet quickly falling off with distance and the fact that resulting speed of the jet is the speed of the missile when it hits plus the produces by the shaped charge’s detonation.
In the end this is more of a game balance problem than anything else, so I consider the problem solved for now. I’ll just have to experiment until I get it right I guess.
Yeah, not the most cut-and-dry problem. Hardcoded values for weapon properties is probably the most practical route.
That said I’m quite interested in what this project of yours is and how it contains all these things I know and love… :point:
I’ll stay tuned!
I’m trying to sort out the fundamental problems I have before posting much more, but I’ll eventually post about it here. ^^
Regarding the original question: when 2 objects collide, all that is important are the mass and the relative velocities. (obviously)
The question was: what is the reference frame, as this determines the relative velocity of each object.
The issue was that 2 objects traveling at +10m/s and -10m/s would yield different results than one moving at 0m/s and the other one at 20m/s. It is obvious that in reality, the damage to each object would be exactly the same in either situation, because the universe does not take into account our observer’s reference frame for Newtonian physics. (!)
When we want to determine the impact/damage to object A, we set the reference frame to A (making it stationary), and let B hit it.
When we want to determine the impact/damage to object B, we set the reference frame to B (making it stationary), and let A hit it.
Now we can safely say that both objects had the same impact (loss of kinetic energy) on eachother if their masses were equal, regardless of where the observer’s reference frame was.
Observer P may say that object A lost way more kinetic energy than object B gained, while observer Q may say the opposite, but object A and B couldn’t care less about P and Q. Therefore most calculations in this thread should be discarded, because they reason from such irrelevant observers. Setting the reference frame to ‘the game world’ would be such an arbitrary observer, leading all impact analysis to be plain wrong.
Unless you are travelling at relativistic speeds, a nuclear warhead will definitely deliver more energy to the target than any realistic impactor…
Physics results are will be the same no matter what frame of reference you use. So “cheat” and use the one that is the easiest. You can all sorts of math to prove that physics is the same in difference reference frames and that’s all fun. but if you don’t’ really care, just use the simplest frame of reference.
Sure, but people are trying to use kinetic energy to calculate impact/damage, and in that case the reference frame must be the object that was impacted.
Any calculation of an observer that is moving at a arbitrary velocity will vastly complicate the calculations, which, as this thread proves, easily results in plain wrong results. We’re all familiar with the conservation of energy, so if your calculations show that object A gains more energy from a collision that object B loses, it’s a red flag.
I wrote some code that collides two objects 100 times in different random reference frames and calculates the kinetic energy lost in the collision. As expected it gets the same result each time so it really is independant of the reference frame.
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.
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.
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.