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Old 25th August 2008, 07:06 PM   #1
Gene L
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The Math of why birds don't collide?

That's the question. I'm sure there is a formula, just as there is a formula for why bullets fired in a rain storm don't hit individual rain drops. (Don't ask me, I just know one exists. Something to do with both occupying the same space at the same time.)

Anyway, you see birds, which are pretty mysterious creatures, in a flock, all seeming to swerve at the same time. I've never seen a slo-mo of this, but they all seem to go the same way, with no one in particular in charge. I wonderd why they don't run into each other. Track and field runners, essentially going the same way, run into each other when competing. Birds asumptively aren't competing, but still, in HUGE flocks, they all seem to veer the same way at the same time.

Again, slo-mo films might reveal 1/10000 second difference (metric seconds, of course ) in their wing movement. And it's a matter of occupying the same space at the same time, like a bullet in a rainstorm, but where missing is guided by intellegence and decision, if you can call a bird intelligent. You would think that a bird occasionally makes a wrong decision in the crowded skies, but apparently not.

Maybe this is a water-cooler topic with some, but I've never seen it addressed. Any ideas?
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Old 25th August 2008, 08:56 PM   #2
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Quote:
That's the question. I'm sure there is a formula, just as there is a formula for why bullets fired in a rain storm don't hit individual rain drops. (Don't ask me, I just know one exists. Something to do with both occupying the same space at the same time.)
Somehow, I suspect this formula is
Edited by tim:  Please don't try to bypass the autocensor.
. Do you have a link to more info?

(I don't know if there are any formulas about flocks of birds, of schools of fish, but their behavior would be determined by instincts. You might need a different formula for each different species.)

Last edited by tim; 25th August 2008 at 10:55 PM.
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Old 25th August 2008, 09:03 PM   #3
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http://en.wikipedia.org/wiki/Flocking_(behavior)
http://www.red3d.com/cwr/boids/
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Old 25th August 2008, 09:35 PM   #4
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Originally Posted by Gene L View Post
That's the question. I'm sure there is a formula, just as there is a formula for why bullets fired in a rain storm don't hit individual rain drops. (Don't ask me, I just know one exists. Something to do with both occupying the same space at the same time.)

Anyway, you see birds, which are pretty mysterious creatures, in a flock, all seeming to swerve at the same time. I've never seen a slo-mo of this, but they all seem to go the same way, with no one in particular in charge. I wonderd why they don't run into each other. Track and field runners, essentially going the same way, run into each other when competing. Birds asumptively aren't competing, but still, in HUGE flocks, they all seem to veer the same way at the same time.

Again, slo-mo films might reveal 1/10000 second difference (metric seconds, of course ) in their wing movement. And it's a matter of occupying the same space at the same time, like a bullet in a rainstorm, but where missing is guided by intellegence and decision, if you can call a bird intelligent. You would think that a bird occasionally makes a wrong decision in the crowded skies, but apparently not.

Maybe this is a water-cooler topic with some, but I've never seen it addressed. Any ideas?
When Birds Collide.

Last edited by tsig; 25th August 2008 at 09:36 PM. Reason: change entire meaning
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Old 25th August 2008, 09:36 PM   #5
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Umm... I think animals don't usually run into each other because they are paying close attention to tiny clues such as air or water currents, eye movements of flock mates and so on. They do occasionally collide. But I don't think it has anything to do with math.
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Old 25th August 2008, 10:11 PM   #6
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there is a formula for why bullets fired in a rain storm don't hit individual rain drops.
Considering the speed of rain, and the speed of the bullet , considering rain as an ideally constant repartition of water sphere in a volume, and considering the density of water in a rain storm, we can consider the bullet travelling a path described by a volume, and the relative speed make it so at first approximation all water sphere are fix in space. That would mean that there is a non zero probability that the bullet will have a few rain drop on its path.

The question is , do the shockwave before the bullet push away the raindrops before it hits the bullet ?
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Old 25th August 2008, 10:31 PM   #7
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Originally Posted by Gene L View Post
I wonderd why they don't run into each other. Track and field runners, essentially going the same way, run into each other when competing.
Track and field runners are confined to a certain space and are jockeying for position. Birds in a flock are not confined. The bigger the flock, the larger the space they take up. In a big flock flight there always seems to be considerable distance between birds so that they won’t collide. They simply spread out far enough from each other to have enough room.

They don’t all change courses immediately. Some change course in reaction to an event. Others follow suit. It takes some time, but birds are pretty fast and one bird will be about as fast as the next bird. I think schools of fish move much faster.
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Old 25th August 2008, 10:34 PM   #8
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Originally Posted by AntiTelharsic View Post
That's very cool!
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Old 26th August 2008, 12:39 AM   #9
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http://www.metacafe.com/watch/1489511/birds_collide/
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Old 26th August 2008, 12:48 AM   #10
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With bullets it has a lot to do with weight. A bullet has a far bigger weight than a rain drop. So if a bullet came near a rain drop the bullet will not be deflected much.

A very small gun (air pistol?) may have a bullet that is lighter than a rain drop. However the probability that it will come near a rain drop is very low.

Edit. One of the above links does not work. Here is the right link.
http://en.wikipedia.org/wiki/Flocking_(behavior)

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Old 26th August 2008, 01:10 AM   #11
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Don't know about birds (or fish, for that matter), but the bullets in rain is simple. The bullet collides with them. The bullet is traveling faster than sound, so the raindrop isn't affected until it is rammed by the air being physically pushed out of the way by the bullet. The turbulence shatters the droplet and supplies heat enough to vaporize most of it. In it's small way, the raindrop absorbs some of the bullet's energy and slows it down with its demise. At long range, rain probably has a considerable cumulative effect.
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Old 26th August 2008, 05:03 AM   #12
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and that's why in the rain scene at the end of Lethal Weapon, both Martin Riggs and Sgt Murtagh had to shoot the baddy - one bullet just wouldn't have been enough.*





*Not necessarily true.
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Old 26th August 2008, 05:13 AM   #13
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Birds in a flock and fish in a shoal only need to keep tabs on their nearest neighbours. It's actually quite a simple strategy.

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Old 26th August 2008, 06:16 AM   #14
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Originally Posted by shadron View Post
Don't know about birds (or fish, for that matter), but the bullets in rain is simple. The bullet collides with them. The bullet is traveling faster than sound, so the raindrop isn't affected until it is rammed by the air being physically pushed out of the way by the bullet. The turbulence shatters the droplet and supplies heat enough to vaporize most of it. In it's small way, the raindrop absorbs some of the bullet's energy and slows it down with its demise. At long range, rain probably has a considerable cumulative effect.

No, a bullet and a raindrop don't collide. A raindrop is pretty heavy, considering, and would explode a bullet traveling at high speed at most, or divert it severely at least. As I said earlier, there is a formula to explain why they don't collide, but I don't have it. As I recall, it has to do with the time a bullet is in the space that a raindrop is in, and the amount of raindrops in a that space at the same time, which is very, very small. It may be possible, but the odds are against it.

The size of a group of, say, 5 shots in rain will be the same as in clear weather. If one or two bullets hit a raindrop, the group would be widely and randomly dispereed, and that's not what happens.

What does happen with shooting groups in rain is the air is saturated with water (moisture, not raindrops) which makes it more dense. The bullets go low, but in the same size group as in dry weather.
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Old 26th August 2008, 06:18 AM   #15
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Originally Posted by leon_heller View Post
Birds in a flock and fish in a shoal only need to keep tabs on their nearest neighbours. It's actually quite a simple strategy.

Leon

Humans collide. You see it in track events, fairly often. You see it on crowded streets as well. The differnce, I think, is birds and fish have 3 dimensions to avoid running in to other birds and fish, humans only have two.

Last edited by Gene L; 26th August 2008 at 06:19 AM.
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Old 26th August 2008, 06:22 AM   #16
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Originally Posted by Gene L View Post
No, a bullet and a raindrop don't collide. A raindrop is pretty heavy, considering, and would explode a bullet traveling at high speed at most, or divert it severely at least. As I said earlier, there is a formula to explain why they don't collide, but I don't have it. As I recall, it has to do with the time a bullet is in the space that a raindrop is in, and the amount of raindrops in a that space at the same time, which is very, very small. It may be possible, but the odds are against it.

The size of a group of, say, 5 shots in rain will be the same as in clear weather. If one or two bullets hit a raindrop, the group would be widely and randomly dispereed, and that's not what happens.

What does happen with shooting groups in rain is the air is saturated with water (moisture, not raindrops) which makes it more dense. The bullets go low, but in the same size group as in dry weather.
And your source for this info is?
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Old 26th August 2008, 06:35 AM   #17
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Originally Posted by Doubt View Post
And your source for this info is?
Is that just a nice way of saying, "Pfffft."

If so, I ditto.

I want to see the "formula" for why a bullet won't hit a raindrop. If I don't, I'm going to say, "Pfffft" outright.
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Old 26th August 2008, 06:40 AM   #18
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If you need to drive ten miles in a rainstorm, you will collide with less rain if you drive faster.

(officer)
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Old 26th August 2008, 06:43 AM   #19
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Originally Posted by Rob Lister View Post
Is that just a nice way of saying, "Pfffft."

If so, I ditto.

I want to see the "formula" for why a bullet won't hit a raindrop. If I don't, I'm going to say, "Pfffft" outright.
Nope. Pfffft would happen if there is no info to back up the claim.
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Old 26th August 2008, 06:47 AM   #20
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Originally Posted by quarky View Post
If you need to drive ten miles in a rainstorm, you will collide with less rain if you drive faster.

(officer)
mythbusters did a show on this. I forgot the conclusion, but I think it was you would get "less" wet. that is not to say you wouldn't get wet. I think a bullet would have the same result.
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Old 26th August 2008, 06:48 AM   #21
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Originally Posted by Doubt View Post
Nope. Pfffft would happen if there is no info to back up the claim.
Well, so far....how much has been presented?
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Old 26th August 2008, 07:06 AM   #22
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I remember seeing an investigation on TV into whether it was best to run or walk through rain. I think that one got less wet if one walked, but I'm not certain. My mother always maintained that it was best to dart about at random to avoid raindrops, but I'm quite sure that was wrong.

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Old 26th August 2008, 07:15 AM   #23
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Originally Posted by Gene L View Post
Anyway, you see birds, which are pretty mysterious creatures, in a flock, all seeming to swerve at the same time.
There's the problem. They don't swerve simultaneously. One swerves and then others nearby react by swerving, then others near them do so, then others near them do so. The swerving action spreads across the flock like a wave. (And it can be seen with just your eyes; no slow-motion camera needed.)
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Old 26th August 2008, 07:19 AM   #24
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http://www.snipershide.com/forum/ubb...&Number=637165
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Old 26th August 2008, 07:35 AM   #25
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Originally Posted by Ocelot View Post
I found that discussion too. But still no sources for the info.

Vaporization sounds plausible, but there are many kinds of bullets and guns and powder loads. Add in air resistance and you get a wide variety of velocities for bullets.

I doubt there is a single, simple answer for what happens when bullet meets water droplet.
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Old 26th August 2008, 07:58 AM   #26
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Originally Posted by Aepervius View Post
Considering the speed of rain, and the speed of the bullet , considering rain as an ideally constant repartition of water sphere in a volume, and considering the density of water in a rain storm, we can consider the bullet travelling a path described by a volume, and the relative speed make it so at first approximation all water sphere are fix in space. That would mean that there is a non zero probability that the bullet will have a few rain drop on its path.

The question is , do the shockwave before the bullet push away the raindrops before it hits the bullet ?
Of course not. The bullet is travelling faster than the speed of sound. The shockwaves, obviously, aren't. The bullet hits the raindrops.
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Old 26th August 2008, 08:05 AM   #27
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Originally Posted by Doubt View Post
And your source for this info is?

I'm glad you asked this, since it allows me to restate that I don't have the formula. I will continue to look, however.

But for the rest of it, the source is personal experience, and training as a LEO sniper at the Army Marksmanship Training Unit. The course was two weeks, and it was called the PC "Counter-Sniper Instructor's Training." They made a point that bullets don't hit raindrops. I'm not sure if they gave the formula, but gave a synopsis of why. I've read the raindrops/bullet thing several times and seen reference to the formula, but wouldn't be able to repeat it even if I saw it. I believe it from shooting rifles, and sure enough of the claim that I would be willing to bet you couldn't hit a falling raindrop with a bullet on demand.

Basically, relying on memory, the idea is to think of 1 bullet and one raindrop, both falling at the speed of gravity, with the bullet also moving at a forward velocity, and the infintesimally small time each is exposed to the other. For them to hit, they would both have to occupy the same space in that small time, and it ain't likely.

As for shooting groups in damp air, I know from experience that the groups shoot lower, since resistance is greater. A headwind will also make bullets hit lower, more air over the bullet (decreased velocity.) In dry air, groups will rise a bit becuse there's less friction. Groups at higher elevations, where the air is thinner, will rise a bit over sea-level groups. This is pretty well known among benchrest shooters. None the less, group size remains pretty much the same, impact just changes a bit.

Last edited by Gene L; 26th August 2008 at 08:12 AM.
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Old 26th August 2008, 08:24 AM   #28
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Originally Posted by Gene L View Post
I'm glad you asked this, since it allows me to restate that I don't have the formula. I will continue to look, however.

But for the rest of it, the source is personal experience, and training as a LEO sniper at the Army Marksmanship Training Unit. The course was two weeks, and it was called the PC "Counter-Sniper Instructor's Training." They made a point that bullets don't hit raindrops. I'm not sure if they gave the formula, but gave a synopsis of why. I've read the raindrops/bullet thing several times and seen reference to the formula, but wouldn't be able to repeat it even if I saw it. I believe it from shooting rifles, and sure enough of the claim that I would be willing to bet you couldn't hit a falling raindrop with a bullet on demand.
I can see where the probability of striking a rain drop may be low. But that is like saying nobody ever wins the lottery because the odds are so low.

Having been through a few military training courses, I do know they don't always have their facts straight. Last time I looked at it the land navigation manual it still said the reason the North Pole existed was that their were large iron deposits in Northern Canada.
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Old 26th August 2008, 08:25 AM   #29
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Originally Posted by Gene L View Post
Basically, relying on memory, the idea is to think of 1 bullet and one raindrop, both falling at the speed of gravity, with the bullet also moving at a forward velocity, and the infintesimally small time each is exposed to the other. For them to hit, they would both have to occupy the same space in that small time, and it ain't likely.
That simply makes it unlikley that a bullets would interact with a particular raindrop, not impossible. Multiply that probability by the number of raindrops and the the liklihood increases. Essentially it is the liklihood of a raindrop being on the bullet's path at the time of firing. In heavy rain that seems quite likely indeed.

The question then becomes what happens when raindrop and bullet do interact. Does the pressure wave push the raindrop out of the way? Is the raindrop splattered with little effect on the bullet? Does the bullet explode?

Well I can answer that last one. Bullets do not explode when they hit water. In fact firing bullets into a hydroballistics tank is an everyday mundane experience for some.
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Old 26th August 2008, 08:30 AM   #30
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Originally Posted by Gene L View Post
the idea is to think of 1 bullet and one raindrop, both falling at the speed of gravity
Speed of gravity?

Quote:
with the bullet also moving at a forward velocity, and the infintesimally small time each is exposed to the other. For them to hit, they would both have to occupy the same space in that small time, and it ain't likely.
Saying that any particular bullet is unlikely to hit a raindrop is not the same thing as saying that bullets simply don't hit raindrops. The former may be true, the latter certainly isn't.
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Old 26th August 2008, 09:04 AM   #31
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Originally Posted by Ocelot View Post
That simply makes it unlikley that a bullets would interact with a particular raindrop, not impossible. Multiply that probability by the number of raindrops and the the liklihood increases. Essentially it is the liklihood of a raindrop being on the bullet's path at the time of firing. In heavy rain that seems quite likely indeed.

The question then becomes what happens when raindrop and bullet do interact. Does the pressure wave push the raindrop out of the way? Is the raindrop splattered with little effect on the bullet? Does the bullet explode?

Well I can answer that last one. Bullets do not explode when they hit water. In fact firing bullets into a hydroballistics tank is an everyday mundane experience for some.
The pressure wave cannot build up in front of the bullet because the bullet is moving faster than the speed of sound. Pressure waves preceding a moving object (like a car or train) is a sub-sonic phenomena.

There is no pressure wave in front of a super sonic object. This is extremely obvious. I wish people would stop saying it exists.
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Old 26th August 2008, 09:15 AM   #32
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I saw a short documentary years ago which included a POV of a fly on a breakfast table. The argument was that the fly thinks much, much faster than we do so, to it, we are moving in slow motion. Because of this, the fly escaped when someone tried to swat it with a newspaper.

I think there was a general correlation between metabolism, lifespan and the speed of thought.

If any of this still holds water (or ever did) then perhaps the same principle applies to birds (ever tried to catch one?). This might also explain why two birds can chase each other through the branches of a tree, seemingly without hitting a twig. Maybe, to them, it's really not that amazing?
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Old 26th August 2008, 09:27 AM   #33
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It's relatively straightforward to figure out whether a bullet in a rainstorm will strike a raindrop during its flight by calculating the mean free path of the bullet between successive collisions with raindrops. Let's do it:

Assuming a uniform number density of spherical raindrops in the space through which the bullet is flying, the bullet's mean free path will be*:

<br />
$\lambda = \frac{1}{\sigma\, n}\, ,$<br />

where

\sigma = \pi {(R_b + R_r)}^2

is the cross section of bullet-raindrop collisions, R_b is the bullet's radius, R_r is the average raindrop radius, and n is the average number of raindrops per unit volume in the rain storm.

Let's find some typical rough numbers for these quantities, to get an idea of the order-of-magnitude of \lambda:

Suppose, for example, that we are using a 9mm bullet. Then

R_b \approx 4.5\times {10}^{-3}\, \text{meters}.

This PowerPoint presentation I found at the University of Illinois website mentions a distribution of 1000 1-mm raindrops per cubic meter. Supposing this is roughly typical, we then have:

R_r \approx 0.5\times {10}^{-3}\, \text{meters}

and

n \approx 1000\, {\text{m}}^{-3}.

Plugging these numbers into the formula above for the mean free path yields:

\lambda \approx 12\, \text{meters}.

Thus: 12 meters (on average) between bullet-raindrop collisions. Of course, the numbers I used were rough, so this may be off by a factor of 2 or 3 or whatever, but it does seem to suggest that a bullet will probably strike a handful of raindrops on its journey, unless you are shooting at a target only a few meters away.


*: This expression can be derived by considering the cylinder swept out by the combined bullet-raindrop radius moving a distance x. The number of raindrops in this cylinder is distributed according to the Poisson distribution. By looking at the probability that the bullet will have NOT hit a raindrop after a distance x, you can get this expression for the average distance between collisions. (I've left out most of the steps, but it's straightforward.)

By the way: The fact that the rain is falling makes little to no difference to this expression, since the bullet's speed and the raindrop's falling speed are so different.
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Old 26th August 2008, 09:57 AM   #34
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Originally Posted by AndyD View Post
I saw a short documentary years ago which included a POV of a fly on a breakfast table. The argument was that the fly thinks much, much faster than we do so, to it, we are moving in slow motion. Because of this, the fly escaped when someone tried to swat it with a newspaper.

I think there was a general correlation between metabolism, lifespan and the speed of thought.
I always thought it was because flies detect the air movement caused by the newspaper long before it gets anywhere near them.

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Old 26th August 2008, 10:02 AM   #35
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Originally Posted by Gene L View Post
No, a bullet and a raindrop don't collide. A raindrop is pretty heavy, considering, and would explode a bullet traveling at high speed at most, or divert it severely at least. As I said earlier, there is a formula to explain why they don't collide, but I don't have it. As I recall, it has to do with the time a bullet is in the space that a raindrop is in, and the amount of raindrops in a that space at the same time, which is very, very small. It may be possible, but the odds are against it.

The size of a group of, say, 5 shots in rain will be the same as in clear weather. If one or two bullets hit a raindrop, the group would be widely and randomly dispereed, and that's not what happens.
Sorry, but I don't buy this explanation at all.

As someone else pointed out, compared to a bullet, you could consider the falling drops of rain to be holding still. At any moment, in a nearly straight line (actually a segment of a very large parabola), there are bound to be rain drops in the line of fire. The question is what happens when they hit.

The energy is the mass and the velocity. A bullet has a lot*. Raindrops have very little. The effect of the raindrop on the bullet is pretty small (probably negligible in most cases). There would probably be a noticeable effect in heavy rain at a greater distance (hitting more drops). On the other hand, when shooting greater distances, I imagine people usually use a higher-powered gun (bigger bullets fired at a higher velocity, I guess?).

*This is why a bullet, even with relatively little mass can be fatal but killing someone with one blow of a 2 x 4 is pretty difficult. Better yet, killing someone by throwing a 2 x 4 at them from any distance is darn near impossible.
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Old 26th August 2008, 10:21 AM   #36
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Joe - two by fours tend to have a ton of kinetic energy, probably at least the same as a bullet. They don't kill because they apply their force over a larger surface.

As an example, knives and kevlar. Kevlar isn't great at stopping the force of the knife (especially if you put your body weight behind it).
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Old 26th August 2008, 10:29 AM   #37
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Originally Posted by GreyICE View Post
The pressure wave cannot build up in front of the bullet because the bullet is moving faster than the speed of sound. Pressure waves preceding a moving object (like a car or train) is a sub-sonic phenomena.

There is no pressure wave in front of a super sonic object. This is extremely obvious. I wish people would stop saying it exists.
Yes you are absolutely right. What you do have is a thin layer of air molecules that are being physically compressed by the bullet or by other molecules being pressed out of the way as it is making its way through them. They cannot extend that compression outward to the front but they do extend their disturbed behavior to the side at the speed of sound, creating the wakes of sound that appear to trail the object.

At or above the speed of sound one cannot propagate energy by compression, shear or transverse wave phenomena traveling through the medium, but that certainly doesn't mean you cannot accelerate particles of that medium as high as you need to (in fact, supersonically) in order to move them out of the way.
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Old 26th August 2008, 10:30 AM   #38
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Ok. Back to the theory that birds don't collide. I don't buy it but failing me finding a video of birds colliding, I certainly can't prove it. I suspect they collide as often as cars on I-95. Not often, but it happens...and with less litigious results.

Opps! guess what...they do.

http://www.ebaumsworld.com/video/watch/750719/

all of somebody's base are belong to us.

erm...no lawsuit is pending, so far as I know.

Last edited by Rob Lister; 26th August 2008 at 10:44 AM.
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Old 26th August 2008, 10:50 AM   #39
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Originally Posted by shadron View Post
Yes you are absolutely right. What you do have is a thin layer of air molecules that are being physically compressed by the bullet or by other molecules being pressed out of the way as it is making its way through them. They cannot extend that compression outward to the front but they do extend their disturbed behavior to the side at the speed of sound, creating the wakes of sound that appear to trail the object.

At or above the speed of sound one cannot propagate energy by compression, shear or transverse wave phenomena traveling through the medium, but that certainly doesn't mean you cannot accelerate particles of that medium as high as you need to (in fact, supersonically) in order to move them out of the way.
Certainly true, but saying a layer a few molecules thick could possibly deflect anything is absurd. It's certainly nothing like the large and powerful pressure fronts that build up in front of near-sonic objects.

Those 'wakes' are in fact the shockwaves mentioned earlier, which is why shockwaves never deflect anything from the projectile (if they're occurring, the projectile is outrunning them, unless it suddenly goes subsonic).
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Old 26th August 2008, 10:58 AM   #40
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Originally Posted by GreyICE View Post
Certainly true, but saying a layer a few molecules thick could possibly deflect anything is absurd.
Stop there and reflect upon your assertion. It is not only NOT absurd, it is a fact beyond refutation.

Let's at least be accurate in our debunking.
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