Can my chronomancer dodge bullets?

November 11, 2009 1:11 PM

I have some weird, tricky physics questions based on a fantastic (non-real) premise, involving bullet speed and potential injury.

I'm toying with the writing of a fantasy-action story/novel set on the battlefields of the first World War. One of the characters is a wizard-type with the ability to control his own personal flow of time. The simplest explanation is that he can make it so that for every one second that passes for the rest of the world, ten seconds pass for him. I'm not sure how this would work if someone was able to do it in reality, but for purposes of the story, it means both that he moves ten times as fast as everyone else, in a fast-forward sort of way, and that anything that might be able to affect him moves 1/10th the speed.

My questions involve the effect of bullets shot at him. He's on the side of the Allies, so as his major concerns are German bullets, I've been referencing this, this, and this Wikipedia page, but I just plain don't know how to do the physics anymore.

Based on my premises, it seems that the effective muzzle velocity for a German rifleman shooting at him should be 87.8 m/s, instead of 878 m/s as the Gewehr 98 page places the real velocity. My first question is, would a bullet going that fast be visible or dodgeable?

Second, the ammunition page says that the weight of the 1905 version of the round (which is the one they used in the war) is 9.9 grams. If I'm doing my math right, that means the momentum of the bullet should be 0.86922 kg*m/s. However, I have no idea how to turn that into force, or what in general it means in terms of it actually hitting the protagonist. If he were hit in his time-shifted state, how much would it hurt him?

Third two-part question: if he could not dodge bullets at 1/10th speed, how much would he have to "slow time" to be able to dodge them. If 1/10th speed bullets would still be lethal, at what point would they not be lethal?

Finally, as a bonus question, what could he do to his enemies? If he were to throw a punch while time-shifted, what effect would that have on the punchee, given that he's effectively throwing his punch in 1/10th of the time as a normal punch is thrown? Would that be ten times the force? One hundred times the force? What would that do to someone in real world terms?

I would be happy to just be given a decent idea of the answers I'm looking for, but if anyone can show me how to do the physics despite the strange starting premise, I'd be really thrilled. Thanks!

posted by Caduceus to science & nature (31 comments total)

1) 88 m/s = ~196 miles per hour. So yes, certainly could be visible (though bullets are small -- cars moving at ~200mph are sort of blurry) and/or dodgeable under the right circumstances (given that your wizard knows he's being shot at, and from a distance).

2) I am not a physicist, but I would think the general approach here (and with your punching question) has to do with the amount of energy administered PER UNIT TIME. His punches should be 10x as strong because, basically, they deliver a single punch's energy over 1/10th the time. Similarly, bullets are 1/10th as dangerous to him because their force is administered over (effectively) 10x the time.

3) I think my answer to (1) gives you a pretty good idea. As a frame of reference, walking speed is about 3mph. I can easily get out of the way of say, a car, moving at 20mph. However, cars are bigger than bullets, and therefore easier to notice.
posted by axiom at 1:19 PM on November 11

Erm, in my answer to question #2, I really meant "force" not "energy."
posted by axiom at 1:21 PM on November 11

Kinetic energy varies with the square of the speed. A bullet going 10% as fast as a typical bullet will therefore pack 1% of the punch of a typical bullet.

Similarly, his punches will pack a hundred times the, er, punch of a normal punch.
posted by Flunkie at 1:24 PM on November 11 [1 favorite has favorites]

Just confirming that 87.8 m/s can probably be dodged under the circumstances that axiom puts forth - it's a bit less than the speed of a paintball (300 ft/s). He's in trouble at short range, however.
posted by McBearclaw at 1:24 PM on November 11

88m/s is actually quite close to the speed of an average arrow (arrow speeds tend to be around the 70-80m/s range).

Arrows were a pretty effective way of killing people a few centuries ago; people generally didn't get time to think "Hey, there's an arrow coming towards me. I'll just dive over here". A bullet is much less easy to see coming than an arrow.

So no, he most likely wouldn't dodge a bullet.
posted by le morte de bea arthur at 1:27 PM on November 11 [1 favorite has favorites]

To put this in a slightly more real world example, 87 mps works out to 285 fps. Most paintball guns shoot at around 300 fps and are very visible albeit not all that easy to dodge. So yes, while small it would be able to be seen, but about as easy to dodge as a paintball, so... maybe?

A lot of this would depend on how far the shooter was and if the dodger was able to see that the gun was fired at him giving him some additional warning.

As to what he could do; the obvious answer is that he could speed up on a shooter in an unnatural way and simply shoot them, but a more physics spooky way of doing it might be to have him use a thrown bayonet which would simply appear in someone's body as if by magic.

Or hurl a grenade at them. I imagine one moving at ten times the maximum speed of a strong thrower would hurt like hell completely aside from what it would do when it went off.
posted by quin at 1:33 PM on November 11

To dodge bullets at 87.8 m/s, you need to know his reaction time. Human visual reaction time is about .18 s, which means that from 100m away, if he spotted the bullet at the moment it was shot then by the time that he is able to react to it, the bullet has traveled 15.8m, and is now 84.2 m away, which gives him roughly 1 second to dodge. Let's say that he can dodge a bullet in .25 seconds, that leaves .75 seconds of slop. So basically from 100m, he has 3/4 of a second to spot the bullet.

Tricky. 87.8 m/s is still close to 200 miles per hour. How much space do you leave when you cross a highway on foot?

To get the energy in bullet, you want 1/2mv², where m is the mass and v is the change in velocity, assuming it comes to a dead stop you can use the bullet's muzzle velocity. For the bullet, that's 6700 Joules of energy. See here for a similar discussion.
posted by plinth at 1:40 PM on November 11

so as his major concerns are German bullets

I don't know if it matters to you in terms of verisimilitude, but the big killer in WWI was artillery, not rifles and machine guns. Both explosive shells and gas rounds tallied up far more bodies than the smaller weapons.
posted by Chocolate Pickle at 1:40 PM on November 11 [1 favorite has favorites]

For reference, the average major league baseball pitch is 91 mph = 40 m/s. Your bullets are a little over twice as fast.

Bullets are tiny. By the time he could see it coming, it would probably be too late to dodge.
posted by qxntpqbbbqxl at 1:46 PM on November 11

But an arrow is much heavier than a bullet, and conversely has a much larger surface area. Not saying that a bullet fired at the speed of an arrow wouldn't be fatal. but I don't think it's that cut and dried. If the wizard was wearing appropriate armor it would turn an arrow/bullet pretty easily, albeit with some injury.
posted by muddgirl at 1:52 PM on November 11

Paintballs (at a legal field) are shot at or below 300 fps.

I play paintball, and I regularly dodge paint at long range. In fact, last week, I had a very annoying exchange with a fellow at the other end of the field. He was taunting me by standing in the open, waiting for me to take the shot. Then when he heard/say me fire, he'd jump a foot sideways, causing me to miss. When I opened up on him full auto, he simply jumped and then walked behind a tree.

But this isn't the matrix. He was about a hundred yards away from me, at the maximum range of a paintball. At twenty feet, you can't dodge it. I'd say that the minimum dodgeable range is somewhere between sixty and eighty feet. And that's when you're aware of who's shooting at you, and see them take the shot.

You can see the paintballs if you're standing near its axis of flight (you can actually see normal bullets in this situation, too, for that matter), either as the shooter or the target. If you're standing to the side of them, there might be a vague blur, but nothing you could be sure of. And you certainlu couldn't guess its location.

As for what damage would be done if a bullet hit: it would suck. A paintball, which is made to break and splash, often leaves a fairly substantial welt. I'm quite certain that a bullet would cause deep bruising, would break small bones (fingers, nose, teeth, cheeks), would seriously fuck up joints, and would cause concussions. It probably wouldn't penetrate though.

One question I have: if your wizard is perceiving time at 1/10 the normal speed, how does that relate to bullet penetration of cover? For the sake of argument, let's say your mage is crouched behind a piece of corrugated steel when a German takes a shot. At 300 fps, the bullet would merely dent the metal and bounce off. At 2800 fps, it's going to punch right through the metal like rice paper. I don't have an answer... I'm just hope you remember that there's a difference between cover and concealment; and you often shoot through both.
posted by Netzapper at 1:59 PM on November 11

Yeah, now I'm thinking we're gonna have some barn door paradoxes here. In one reference frame the bullet has enough velocity to penetrate steel, but in the wizard's frame it doesn't? I don't think that can work.
posted by muddgirl at 2:06 PM on November 11

Arrows were a pretty effective way of killing people a few centuries ago; people generally didn't get time to think "Hey, there's an arrow coming towards me. I'll just dive over here". A bullet is much less easy to see coming than an arrow.

Actually, from what I've seen and heard, at reasonable range, there's plenty of time to dodge an arrow if you know it's coming. I have lots of stories from friends about deer who were spooked by the sound of their bow and then leaped out of the way of the incoming arrow.

Not to mention that an arrow penetrates by being sharp and hard. If a heavy rifle bullet were made of steel and as sharp as an arrow, it'd work okay at 300 fps. (I had thought that an arrow was heavier than a bullet, but upon looking up some modern carbon arrows, they come out about the same as a rifle bullet.)
posted by Netzapper at 2:09 PM on November 11

if your wizard is perceiving time at 1/10 the normal speed, how does that relate to bullet penetration of cover?

It shouldn't make any difference, from the bullet's and the cover's frame of reference, it's still operating at normal speed. (Unless the wizard somehow pulls the cover into his speed-plane when he casts the spell...)
posted by quin at 2:11 PM on November 11

I think your wizard would see everything in a reddish tinge as light waves become slowed down for him and revert down the spectrum.

If you want to read something similar to what you're describing, Larry Niven's novella ARM posits a machine that can speed up time for whoever is inside its bubble, and is a pretty realistic depiction of what that would look like from a hard-SF point of view.
posted by drinkcoffee at 2:11 PM on November 11

It shouldn't make any difference, from the bullet's and the cover's frame of reference, it's still operating at normal speed. (Unless the wizard somehow pulls the cover into his speed-plane when he casts the spell...)

What about any body armor that the wizard might be wearing? I don't think that 1/10 the speed would be enough to stop a bullet from penetrating skin, considering that an arrow can easily do so.
posted by muddgirl at 2:16 PM on November 11

Your wizard in his altered state will be able to move ten times as fast as anyone. If your wizard were to, say, punch someone, it wouldn't as much be the force that you would be concerned with as the momentum. Physical contact in that way is in the realm of collisions, so you can consult this: wikipedia page on inelastic collisions. Without needing to go too far into it though, the basic momentum equation is p = mv. Him moving at ten times the speed means ten times the momentum.

You need to decide whether you want the wizard to slow down time everywhere in the universe, or just speed up his own time. For the reasons that follow:

If you only sped up the wizard's time, all of the momentum from something like a bullet in a standard frame of reference would need to be conserved in the shifted frame of reference if you are actually interested in obeying physical laws. Since v = d/t, if you have only sped up the wizard's time, the velocity of the bullet is still x meters in y seconds. Not in the wizard's frame of reference, but it seems like it would be the original velocity of the bullet that would matter here. If you assume that the bullet is traveling at a slower speed because to the wizard it is moving slower, where has that momentum gone? Does all that energy just disappear?

The way I would need to think about it is not that the bullet is moving slower, but that the wizard is moving faster and reacting faster. So no matter how much he could slow time, if a bullet hit him, it would still be lethal; he just might be able to watch as it penetrates his skin in slow motion or something. A lot of physics doesn't necessarily apply here, since time-shifting is, as far as we know, not possible (special relativity excluded). But this would also avoid the red-shifted light mentioned above.

This sounds like it would be a very interesting read when it is finished, Caduceus. Let us know how it goes!
posted by battlebison at 2:53 PM on November 11

Arrows are very sharp. The fact that they are very sharp allows them to concentrate the brunt of their force into an extremely small area. Bullets, not so much.

I'm not saying "obviously a 1/10th speed bullet wouldn't hurt"; I'm merely saying that "arrows kill people at 1/10th the speed of a bullet" is not a good argument for the efficacity of a 1/10th speed bullet.
posted by Flunkie at 3:12 PM on November 11 [1 favorite has favorites]

Your wizard in his altered state will be able to move ten times as fast as anyone. If your wizard were to, say, punch someone, it wouldn't as much be the force that you would be concerned with as the momentum. Physical contact in that way is in the realm of collisions, so you can consult this: wikipedia page on inelastic collisions. Without needing to go too far into it though, the basic momentum equation is p = mv. Him moving at ten times the speed means ten times the momentum.

Momentum is only relevant to figuring out how fast the target will travel as a result of the bullet hitting him. That is, not very. What's relevant is the amount of energy transferred from the bullet to the target. This is basically equal to the kinetic energy of the target, which, as noted above, varies with the square of velocity, not linearly with velocity.
posted by Flunkie at 3:17 PM on November 11

I think your wizard would see everything in a reddish tinge as light waves become slowed down for him and revert down the spectrum.

As lower-frequency light moved out of his visible range, higher frequency light would move into it. Outdoors in daylight it would be something of a wash; he'd be seeing by UV instead of by "visible" light.

Indoors under artificial lighting would be a different matter because light bulbs are tuned to produce frequencies visible to normal people.
posted by Chocolate Pickle at 3:26 PM on November 11

What's relevant is the amount of energy transferred from the bullet to the target. This is basically equal to the kinetic energy of the target

Doh, I mean "... of the bullet", of course.
posted by Flunkie at 3:29 PM on November 11

I think what you're saying isn't that "the universe is slowed down 10x," it's that the wizard perceives everything as if time were moving more slowly.

So his reaction time is improved, but the kinetic energy of things hitting him isn't lessened.

And what happens when the bullet makes contact with him? Whether the bullet's kinetic energy is lessened or not, the wizard's flesh, as part of him, will move at 10x in response to a 1x impact. So I think he will take normal damage no matter how the time slowdown happens so long as he (and his flesh) move and exist at a higher speed.
posted by zippy at 3:59 PM on November 11

I think what you're saying isn't that "the universe is slowed down 10x," it's that the wizard perceives everything as if time were moving more slowly.

Why do you think that? I think the question was pretty clear that the opposite was the case: "with the ability to control his own personal flow of time" ... "he can make it so that for every one second that passes for the rest of the world, ten seconds pass for him" ... "anything that might be able to affect him moves 1/10th the speed".

It's not merely that his reaction time is improved and he becomes fast. It's that time is passing at a different rate for him than it is for the rest of the universe.

So his reaction time is improved, but the kinetic energy of things hitting him isn't lessened.

I disagree, because (again) it's not merely that his reaction time has improved. The objects really are travelling slower. So their kinetic energy has decreased.
posted by Flunkie at 5:10 PM on November 11

Thanks for the thoughtful answers so far, everyone. I just want to clarifying that, because it's magic, he very specifically does shift into a frame of reference where, as far as he, specifically, is concerned, everything else is really, effectively moving at 1/10th the speed. So bullets really will only have 1/10th the momentum hitting him as they would anything else. As far as everything else views it, he's moving ten times as fast, but from his perspective, he moves normally and everything moves 1/10th as fast and has 1/10th the momentum. He's not just speeding up his own metabolism and reaction time, he's actually changing the way time flows for him. If it helps to use a familiar bit of technobabble, think of it as him shifting "out of phase" so that physics is working in a recognizable way, just 10 times slower. I'm not sure that helps, but that's all I have time for at the moment.

Thanks again!
posted by Caduceus at 5:13 PM on November 11

87 meters per second is still pretty damn fast. One second, the bullet is on the other end of a football field, the next second, it's hitting you in the forehead. No way is someone going to dodge that based on seeing it coming in midair.

On the other hand, imagine trying to aim at someone running laterally to you at normal speed. Now imagine trying to hit them when they're moving 10x faster. It seems nearly impossible.

I can't even really wrap my brain around what happens when our wizard comes into contact with something. Take for example, billiard balls. Cue ball hits other ball. Cue ball stops, other ball flies off with same velocity as initial cue ball. Momentum is conserved. In the wizard's world, the cue ball hits the other ball which can only move off at 1/10th the velocity...cue ball flies back at .9 initial velocity? Obviously the cue ball is a stand-in for the wizard's fist in this scenario.

Maybe I'm wrong to try to think about it in terms of velocity instead of time.

But still, you have to think about it in terms of how is this time shift manifesting itself. Are the wizard's clothes moving the faster rate? If not, how does that even work, does he have to accelerate and decelerate his clothes at fantastic rates every time he moves?

I need to stop thinking about this before my head explodes.
posted by cali59 at 7:16 PM on November 11

So the Chronomancer's time bubble means time outside his bubble moves at 1/10th the normal rate. Things in his bubble, however move at the normal rate.

Now, let's go back to a bullet striking the Chronomancer. The bullet is moving at 1/10th normal speed due to the Chronomancer's effect on time. However, what happens when it comes into contact with him?

If it hits him, does his flesh move at the same speed as the bullet (1/10th normal), or does it fly away at 1x normal, as an effect has now crossed into his bubble and gone from 1/10th time to 1x time?

There might be interesting issues regarding transfer of energy that I am not sure how to handle with classical mechanics.

Breathing would be interesting too. He exhales at a normal rate (to him), but outside of his field the gas diffuses at 1/10th speed, so he might be surrounded by a CO2 cloud. He'll also deplete oxygen in enclosed spaces as fast as 10 people.

this plate of beans is fun at any speed
posted by zippy at 10:26 PM on November 11

87 meters per second is still pretty damn fast. One second, the bullet is on the other end of a football field, the next second, it's hitting you in the forehead. No way is someone going to dodge that based on seeing it coming in midair.

Read the paintball comments upthread.

Just last saturday, I poked my head around a bunker, saw a greenish blur headed toward me, and pulled my head back in just before the paintball splattered on the tree behind me.

I guess, though, that the paintball is decelerating in a way that the hypothetical timeshifted bullet would not. By the time it got to me, it probably wasn't doing 300 fps anymore.
posted by Netzapper at 10:28 PM on November 11

IANAP, but just re. the punching thing; if, as pointed out upthread, his punches have 100x the momentum of a normal punch, doesn't that mean that the force on his fist is 100 times greater as well? So he'll need reinforced knuckles and wrist bones if he's to punch his way through the Germans.
posted by primer_dimer at 1:50 AM on November 12

doesn't that mean that the force on his fist is 100 times greater as well

From the Germans' point of view, they're being hit by an extremely fast punch, and it'll hurt like hell. From the wizard's frame of reference, he's punching extremely hard/stiff people, because if they move slow, then they're also less elastic. He won't necessarily need a fully-reinforced glove, but it should hurt his hand more than a normal-speed punch to the face hurts the puncher.

Honestly though, it'd make more sense to hit them with a pipe-wrench (at 10x speed). This is war, after-all. Superheroes may not kill, but soldiers can and do.
posted by explosion at 8:11 AM on November 12

I think that the conservation of energy and matter would ensure that only the hero's perceptions could be faster than normal but the effects of external bodies on his would be same regardless. If a bullet hits the hero and it imparts the energy that corresponds to the perceived speed rather than the actual speed, where does the remaining energy go? It can't disappear.

Similarly, where does the extra energy of moving faster come from? How do the muscles work faster?
posted by dantodd at 10:39 PM on November 12

I think that the conservation of energy and matter would ensure that (...)

I think the principal of conservation of energy is based solely upon evidence that is completely dissimilar to the base assumption of the question.
posted by Flunkie at 6:05 PM on November 13