How much do collisions slow an object?
 

The moving object could be a car, a rock, or in my case, a superhuman with 300 HP, 100 DR, and multiple levels of IT:DR flying at mach 2 with no morals.
When this creature decides to fly through the buildings in a city block, or say, a mountain, how far do i reduce the distance traveled? Is it just a matter of "you do 2250d collision damage this second, you're at a dead stop when you cease to obliterate things in your path, or does the first hit reduce the velocity for the next, etc. until velocity is zero (first hit is 2250d, next maybe 2249d, etc)?

Re: How much do collisions slow an object?
 

I don't think you need to do that reduction. You do one computation for damage based on speed and hit points. That amount is a total. When you apportion the damage among a succession of targets, you are effectively apportioning the speed among the same targets; each target takes damage in proportion to the speed reduction that it causes. That is,

(Spd1 + Spd2 + ... + SpdN)HP = (Dam1 + Dam2 + ... + DamN),

and Dam1 = Spd1HP, Dam2 = Spd2HP, and so on.

Re: How much do collisions slow an object?
 

If you want to do this, probably the easiest way is to just assume the crushing damage the character takes from slamming through a wall has normal knockback, and the knockback reduces their velocity. Of course, they could potentially get back up to speed between hits. The easiest way to handle that aspect would be to track how much the character has accelerated this turn (if at all - if they started at top speed, no acceleration needed); any leftover Move can be used to recover from the knockback reductions, but once they'd accelerated an amount equal to their full Move, no further acceleration is possible for this round.

So, say you have a character with Move 10/100 that is currently moving at 95 yards/sec. The character has 10 HP (but a mess of IT:DR, plus DR, to avoid getting seriously hurt slamming into things). At the start of their turn, they accelerate to Move 100 (using up 5 of their Move 10) then slam into a wall. The wall deals 25 cr to them before breaking; with a knockback threshold of 8, that's 3 yards of knockback, dropping their current movement rate down to 97 yards/sec. They accelerate back up to 100 (using up a further 3) then hit another wall; this one is a bit sturdier and deals 35 before breaking, for another 4 yards of knockback, dropping movement down to 96 yards/sec. The character can use their final 2 yards/sec/sec of acceleration to get back up to 98 yards/sec, but can't accelerate any more this round.


An alternative is to note that a barrier that isn't broken through by definition reduces move to 0 and work backward from there. The rules for acceleration are the same, but rather than using knockback to figure out how much the character is slowed, you base it on how much damage you rolled vs how much it took to get through, and reduce move proportionally. If the character rolled 40 damage against the wall that took 25 to break through, the character has 15 left over. 100*15/40 = 37.5, so the character gets slowed down to 37.5 yards/sec. Personally, if going this route, I'd have a wall you break through slow you down by less than that - when working on more realistic armor performance, I settled on dividing DR by 3 for layers that were penetrated (this works out to roughly approximate a "difference of cubes" approach, which is more realistic, without being so cumbersome). In this case, that means the 25 it took to break through the wall gets reduced to 8.33, meaning 31.67 got through. 100*31.67/40 = 79.175, so the character gets slowed down to 79.175 yards/sec.

In either case, it would probably be realistic to call for a control roll if the collision slowed the character down by more than their maximum deceleration rate, with penalties following the Pushing the Envelope guidelines (although as they aren't doing it to themselves, it might be appropriate to halve such penalties).

Re: How much do collisions slow an object?
 

If the objects stay intact and are are mostly not elastic(think bowling ball vs pins), it becomes a basic physics problem involving vector math. If one or more are soft and squishy(bowling ball vs basic human) it gets a lot more complicated. Also complicated if one or both shatter.

In the case of your super villain(SV), does the villain keep thrusting during the fly through attempt or is it rendered unconscious on first impact and basically becomes a projectile?

You may want to account for the angle of impact. Possible the SV richotet's off without losing a lot of velocity or causing much damage.

Also, most buildings are largely empty space, unless your SV manages to hit perfectly on a floor level. Possible your SV could hit the glass on one side, miss all the furniture and people and break out the glass on the other side while causing almost no damage to the structure of the building. Any people inside may have to hope they are out of the way of the spray of glass shards....

Re: How much do collisions slow an object?
 

The reality is that the GURPS collision rules are only marginally related to reality, so you have a choice between being consistent with GURPS and being consistent with physics. However, I would treat it as a single damage roll.

Re: How much do collisions slow an object?
 

To say it less negatively, GURPS isn't trying to simulate the physics of two objects colliding. It's just interested in the damage they take from the collision. If you want physics, a physics textbook will have the answers.

Re: How much do collisions slow an object?
 

It's wrong about that part too; in reality, collision damage to both parties is almost entirely determined by the mass of the smaller object.

Re: How much do collisions slow an object?
 

So in this scenario you almost certainly aren't trying to do physically serious collision modeling...

And, evidently, you're expecting your impactor to punch through a bunch.

So why not calculate its damage as a projectile and then let it punch through that much cover DR of obstacles before being stopped? If it's not stopped you could reduce the speed by the fraction of its damage that it 'used up'. This isn't even trying to be real, but it does seem to play nicely into mechanics.

Re: How much do collisions slow an object?
 

Well the total energy available to do damage basically is - wlog you can consider the more massive object (M) initially stationary, call the smaller mass (m), and use the difference in velocities v and determine in an inelastic collision the dissipated energy is 1/2 m v^2 (1-m/(M+m)). Which shows you the mass of the heavier object only matters to how much it [reduces] the total damage - the closer M gets to m, the less total damaging energy there is, going to a limit of half as much energy when they're equal as when M>>m. Given we are talking very approximately here anyway for a damage formula, a possible factor of 2 it pretty minor.

But on the question of which one takes how much of the damage, depends on how the energy gets partitioned between them, and that's a [very complex] problem. It's customary to assume it's equal, but really that only holds when the two objects are made of the same stuff and v is substantially greater than the speed of sound in that material.

From the standpoint of a game though, it is often close to equal, made even closer by taking the square root (damage being sqrt(E) in GURPS), and a lot of the differences between materials are going to be reflected in their having a different DR, which you are presumably going to apply. Might as well call them equal and proportional to sqrt (1/4 mv^2)

Re: How much do collisions slow an object?
 

There's an argument for each participant's DR affecting the damage taken by the other -- at relatively low velocities most of the damage will be taken by whichever yields first, which is presumably the lower DR -- but it's probably overly complex.