Poll: Bullet physics, the two trains

Rattja

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So I were watching this Let's play of Metro Last light, and at one point there is this shooting section on a train, and it made me wonder how this actually works out in real life.
I'll try to explain the best I can, but english is not my main language and I do not have a degree in physics or anything so bare with me here.

The scenario is this:
You have two trains moving next to each other at the same speed in the same direction. Let's call them train A and B.
Now, if you were to fire a bullet at a 90* angle from train A towards train B, would the forward momentum, air resistance or anything else cause you to miss if you were aiming straight at your target? Would you have to lead the shot?


=====(shot)===== (train A) ---> movement direction
|
|
|-20m max.
|
|
=====(target)==== (train B)

In the game the bullets hit behind the target, but people seem to think this would not happen.

For the sake of argument, let's say we are using standard train speed (whatever that is) and a not too powerful gun, like a low powered rifle or a pistol.
Also, let's say the distance between the two trains is 20 meters or less.

Personally I think it would be slightly off, but not by much at that distance, but it would be nice to know for sure how this actually works.
 

Zhukov

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Dec 29, 2009
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If the trains are moving at the same speed and in the same direction then I can't think of any reason why it would be any different to shooting at a stationary target.
 

Redingold

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Mar 28, 2009
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The obvious answer is no. The forwards momentum of the trains will have no effect because they have no relative velocity. As for air resistance, imagine if the trains were sitting still and the wind was blowing at whatever speed the trains were travelling at. This is a physically equivalent situation. Would you expect the wind to deflect the bullet that much?

Anyway, to find out how much it actually got deflected, I used a numerical integrator that I wrote for a university project.

I picked the AK-74 as the weapon, which fires a 5.45*39mm bullet at 900ms[sup]-1[/sup]. Drag coefficient of a bullet is about 0.3, from what I found online. If anyone can suggest a better figure, I'll be happy to update my answer.

Anyway, sticking the trains 20m apart and travelling forwards at 15ms[sup]-1[/sup], I found that the bullet only drops back by about 15 microns. No joke. The travel time is just way too short for the wind to make even the slightest difference, espeically given that bullets are fairly aerodynamic.

EDIT: Looking at what Eleuthera said below, it seems the spinning of the bullet causes deflection, because of various things like gyroscopic drift causing the bullet to be at a slight angle relative to its velocity, which can alter its course. I didn't account for these, and it seems like they might have a substantial impact. Still, I don't expect the bullet to be deflected by any noticeable amount over such a short distance.

DOUBLE EDIT: So it turns out I'm a complete moron, and forgot to divide by the bullet's mass when calculating its acceleration resulting from the drag force. Scratch that 15 microns figure, it's more like 4000 microns. Still insubstantial, but much more likely to be in the right ballpark.
 

Eleuthera

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Sep 11, 2008
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Zhukov said:
If the trains are moving at the same speed and in the same direction then I can't think of any reason why it would be any different to shooting at a stationary target.
There would be a 100mph "crosswind"

OP: according to this guy's [http://www.shootingtimes.com/ammo/dont-blow-a-shot-in-the-wind/] calculations, a 100 mph would result in a 20inch (or 30cm) deviation (but I'm not sure what type of gun he's using...)
 

Zhukov

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Dec 29, 2009
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Eleuthera said:
Zhukov said:
If the trains are moving at the same speed and in the same direction then I can't think of any reason why it would be any different to shooting at a stationary target.
There would be a 100mph "crosswind"

OP: according to this guy's [http://www.shootingtimes.com/ammo/dont-blow-a-shot-in-the-wind/] calculations, a 100 mph would result in a 20inch (or 30cm) deviation (but I'm not sure what type of gun he's using...)
Trains are only 20m apart though. At that range, is the wind going to be much of a factor?

Also, where did you get the 100mph figure?

Eh, I' unno, I'll be the first to admit to not being a ballistics expert.
 

Eleuthera

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Sep 11, 2008
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Zhukov said:
Eleuthera said:
Zhukov said:
If the trains are moving at the same speed and in the same direction then I can't think of any reason why it would be any different to shooting at a stationary target.
There would be a 100mph "crosswind"

OP: according to this guy's [http://www.shootingtimes.com/ammo/dont-blow-a-shot-in-the-wind/] calculations, a 100 mph would result in a 20inch (or 30cm) deviation (but I'm not sure what type of gun he's using...)
Trains are only 20m apart though. At that range, is the wind going to be much of a factor?

Also, where did you get the 100mph figure?

Eh, I' unno, I'll be the first to admit to not being a ballistics expert.
The 100mph was just an assgrab, but seems a reasonable speed for a train at speed.

I forgot to convert the guys 100 yards to ~25 yards, so the deviation should be 1/4 to 1/5 of what I said before. 4 to 5 inches.

EDIT: also in no way an expert, just googled about for a bit for an answer.
 

Vicarious Reality

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Jul 10, 2011
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Well no, not at that distance and normal train speeds, even with an air rifle
The air would certainly cause the bullet to hit behind your target

Redingold said:
The obvious answer is no. I found that the bullet only drops back by about 15 microns. No joke. .
LOL
My extra fine diamond hone uses 9 micron sized diamond dust
GREEN (E) Diamond - Extra Fine
Sharpen to a razor edge (1200 mesh, 9 micron)
 

Xeorm

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Eleuthera said:
The 100mph was just an assgrab, but seems a reasonable speed for a train at speed.

I forgot to convert the guys 100 yards to ~25 yards, so the deviation should be 1/4 to 1/5 of what I said before. 4 to 5 inches.

EDIT: also in no way an expert, just googled about for a bit for an answer.
http://en.wikipedia.org/wiki/Rail_speed_limits_in_the_United_States Has most mainline track in the US going ~60 mph.

Assuming your link works linearly and is accurate, we'd get about 2.1 inches of deviation.
 

shootthebandit

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May 20, 2009
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Just follow the damn train CJ

If the trains at different speed then youd have to compensate but if they are the same. Say the train is X axis and bullet as Y. There is no X velocity if its at 90[sup]o[/sup] so the movement of the train can be dismissed. A relatively strong wind in X direction over 20m is probably enough to effect small arms fire

 

Thaluikhain

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Forward momentum wouldn't if they are at matched (and constant) velocities...it's like they are standing still or on the same train that is just very wide. If they are both accelerating, this would be an issue.

As mentioned, you would get some cross wind, yes.

...

There are some other things that might affect things, but they aren't likely to apply in this example. The curvature and rotation of the planet, gravity and so on. Unless it's a super fast alien space train, not really going to matter.

And, of course, lots of things that might throw the aim off that have nothing to do with being on a train.
 

Albino Boo

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I would say yes you would have to lead the target. In the sport of biathlon the range length is 50 meters but they have zero weapons in just normal winds speed of 10 metres per second which is 2 to 4 times less that forward motion of passenger train. If you think about for second, take the trains out of it and imagine you are trying to shoot a target with a hurricane force cross wind, you would have to correct for it.
 

spartan231490

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Rattja said:
So I were watching this Let's play of Metro Last light, and at one point there is this shooting section on a train, and it made me wonder how this actually works out in real life.
I'll try to explain the best I can, but english is not my main language and I do not have a degree in physics or anything so bare with me here.

The scenario is this:
You have two trains moving next to each other at the same speed in the same direction. Let's call them train A and B.
Now, if you were to fire a bullet at a 90* angle from train A towards train B, would the forward momentum, air resistance or anything else cause you to miss if you were aiming straight at your target? Would you have to lead the shot?


=====(shot)===== (train A) ---> movement direction
|
|
|-20m max.
|
|
=====(target)==== (train B)

In the game the bullets hit behind the target, but people seem to think this would not happen.

For the sake of argument, let's say we are using standard train speed (whatever that is) and a not too powerful gun, like a low powered rifle or a pistol.
Also, let's say the distance between the two trains is 20 meters or less.

Personally I think it would be slightly off, but not by much at that distance, but it would be nice to know for sure how this actually works.
If the two trains are moving with the same speed and direction, then forward momentum is what makes the bullet hit its target. The wind resistance of the two slip-streams would push the bullet off target, but it's impossible to know how much without knowing how fast the trains are going and how large they are.

Assuming a handgun, you would probably have to lead the target substantially, even at that distance. Probably by about a foot. Handgun bullets are very very slow, and so the slipstreams would exert a greater impulse on the bullets. Rifle bullets are faster and more aerodynamic, so they would be effected less.
 

spartan231490

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Eleuthera said:
Zhukov said:
If the trains are moving at the same speed and in the same direction then I can't think of any reason why it would be any different to shooting at a stationary target.
There would be a 100mph "crosswind"

OP: according to this guy's [http://www.shootingtimes.com/ammo/dont-blow-a-shot-in-the-wind/] calculations, a 100 mph would result in a 20inch (or 30cm) deviation (but I'm not sure what type of gun he's using...)
um . . . 20in =/= 30cm. 30cm is very close to 12 inches.

I also wouldn't trust this guy's math. His wind-speeds are highly suspect. I live in a windy area, and there is absolutely no problem keeping a ball cap on even in wind speeds of 30-40 mph, but he seems to think the limit is 20. He was also doing math for a 200 yard shot, not a 20 meter shot.

I don't know why, but no one but me seems to be accounting for the slipstreams. Both trains would be surrounded by regions of air that would be more dense and faster moving than the surrounding atmosphere.
 

Eleuthera

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Sep 11, 2008
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spartan231490 said:
um . . . 20in =/= 30cm. 30cm is very close to 12 inches.
Yeah, I have no idea how I messed that up, I guess I was thinking miles.

I also wouldn't trust this guy's math. His wind-speeds are highly suspect. I live in a windy area, and there is absolutely no problem keeping a ball cap on even in wind speeds of 30-40 mph, but he seems to think the limit is 20. He was also doing math for a 200 yard shot, not a 20 meter shot.
A 100 yard shot actually, at the end anyway.

But hey, even Mods make mistakes (well.. a mod makes mistakes)
 

giles

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Feb 1, 2009
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A (very) rough estimate using typical numbers for trains and a 9mm handgun using your 20m distance and Stokes Law says the effect would be very small (of order 10^-3m at best).
Even though the wind is "strong", the air viscosity is rather small, the flight time is short and the bullet is small.

Reality may be different though... the best guesses in hydrodynamics are made by computer simulations, not super simple models like mine.
 

Rattja

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spartan231490 said:
The wind resistance of the two slip-streams would push the bullet off target, but it's impossible to know how much without knowing how fast the trains are going and how large they are.
Hm didn't even think about that. Considering the sceene in the game was in a tunel as well, the air flow would be interesting to say the least. No idea what something like that would do to a bullet.

Yes it is small and travels fast, but then it's also rather light.


albino boo said:
I would say yes you would have to lead the target. In the sport of biathlon the range length is 50 meters but they have zero weapons in just normal winds speed of 10 metres per second which is 2 to 4 times less that forward motion of passenger train. If you think about for second, take the trains out of it and imagine you are trying to shoot a target with a hurricane force cross wind, you would have to correct for it.
When I try to picture standing there in a hurricane trying to hit a target, I start to think it would actually miss because of it.

If we know how long a bullet has been in the air after traveling 20m, and then found out how much sideways force the wind would be able to apply during that time, would that not give us the answer? Or doesn't it work that way?
 

Shock and Awe

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Sep 6, 2008
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The bullet maintains the forward velocity of being on Train A, if you are shooting at something moving the same speed in the same direction you would be shooting straight at it. EXCEPT thats if you don't talk about the relative crosswind that would be going on do to your movement. You would compensate for the crosswind, but not your movement.
 

Albino Boo

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Rattja said:
albino boo said:
I would say yes you would have to lead the target. In the sport of biathlon the range length is 50 meters but they have zero weapons in just normal winds speed of 10 metres per second which is 2 to 4 times less that forward motion of passenger train. If you think about for second, take the trains out of it and imagine you are trying to shoot a target with a hurricane force cross wind, you would have to correct for it.
When I try to picture standing there in a hurricane trying to hit a target, I start to think it would actually miss because of it.

If we know how long a bullet has been in the air after traveling 20m, and then found out how much sideways force the wind would be able to apply during that time, would that not give us the answer? Or doesn't it work that way?


I think the best way to calculate the deviation would to treat them as vectors and dot product them together. The resultant vectors angle would the lead need to hit the target. That said, its 22 years since the last time I did a dot product and I cant remember the technique.
 

giles

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albino boo said:
I think the best way to calculate the deviation would to treat them as vectors and dot product them together. The resultant vectors angle would the lead need to hit the target. That said, its 22 years since the last time I did a dot product and I cant remember the technique.
You can just picture the entire thing in a system in which the bullet is at rest and the wind friction is pushing on it for a fixed period of time (the bullet flight time). This gives you the distance it travels off the mark due to wind. If you're then interested in the angle with which you need to adjust your aim, you may simply use elementary trigonometry (the increased travel time due travelling a slightly longer distance is negligible for such small angles).
 

Eclectic Dreck

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Rattja said:
You have two trains moving next to each other at the same speed in the same direction. Let's call them train A and B.
Now, if you were to fire a bullet at a 90* angle from train A towards train B, would the forward momentum, air resistance or anything else cause you to miss if you were aiming straight at your target? Would you have to lead the shot?
Short answer: it depends.

Longer answer: if you simply look at it as a classic physics problem and ignore the effects of air, there is no need to alter your point of aim for two trains moving in parallel at the same speed than when they are standing still because from the frame of reference of the shooter, the target is still stationary.

Air resistance, however, will come into play. To greatly simplify this, I'll simply state that any object moving through the air will be resisted by the air. This resistance is proportional to speed. At relatively low speeds of just a few miles per hours, the air is exerting very little force for a very short period of time across the given distance and while this would have an impact on where the bullet hit, it would not be a significant one.

To use an example, given a wind speed of 10 mph (the two trains are moving at 10mph) and a 124 grain 9mm JHP round fired at 1250 fps (reasonable stats for a handgun), my shot would vary by a mere 0.2 inches at 25 yards. With a 25 mph wind, my point of aim would vary by 0.6 inches. At 50 mph, my point of aim would be off by 1.2 inches. We can carry on like this for quite some time before you'd go from hitting a target at center mass to missing entirely. At the speed of an average train, at 20 yards it should suffice to say that any reasonably quick round would not require leading to make the shot. Only the very high speed trains move fast enough to require leading in this case.

I'd guess that the reason games might require you to lead has to do with a combination of factors. First, many games suggest bullets move very slowly compared to real life. This means the effects of wind, if modeled (and it rarely is), would be exaggerated greatly. More importantly, many video games fail to take into account the motion of the shooter and thus instead of adding together the vectors and arriving at the conclusion that you're shooting at a stationary target (the ideal case where we ignore air resistance), you instead are shooting at a target that is moving perpendicularly at the speed of the train. In short - poor physics modeling lies at the heart of the problem.