Theoretical Question

mp3guy

if you shot a bullet from a gun upwards, and then it slowed, and finally turned to fall back to earth, if it theoretically fell for ever in earths sea level atmosphere what would happen? Would it just keep going? Or end up as gas?

Cute_Button

Hmmm- I am making a presumption that what you are actually stating is once the bullet starts to fall again, and is, through gravity, accelerating towards ground (at a rate varying depending on the atmospheric friction on the bullet, gravity at each point of its trajectory, the final effect of constant gravity at sealevel- ?) Theoretically the bullet would accelerate at an increasing speed to the point where the effect of gravity on the bullet was no longer increasing (however this is also the point at which the atmospheric effects are also greatest)- and reach a constant rate of acceleration.

In your hypothesis there is no final point (of impact or otherwise) therefore acceleration is indefinite and accumulated speed is thus limited by factors other than gravity.

As the speed of the bullet increases, all other things being equal, the mass of atmosphere the bullet must also pass through also increases (and a defineable but not exponential rate).

We now have the increasing effect of atmospheric friction on the bullet. What are bullets mostly made from? Lead- what will happen to lead in increasing friction (heat)- it will melt.

You now have melted lead accelerating indefinitively.

As the molten lead continues to accelerate, it further heats, and in the earths atmosphere would form an oxide and dissipitate as gas.

So yes is the ultimate answer- it would be dissipitated as gas.

Jen

Victor

I generally concur with Cute_Button although the scenario is rather hypothetical.

In reality the bullet will return to earth at or about supersonic speed and still poses a safety hazard. There are incidents where people have been seriously injured by people firing into the air, although the lower the angle the more hazardous the bullet (because it falls sooner and has suffered less air friction).

ApeXaviour

Right lads, I've yet to sleep in the day or two so forgive me if I missed something yis said. But I have to severely disagree.
Let me get it straight.. gravity is constant, air pressure is constant but there is nothing to impact. Well used to these kinda hypothetical questions..

Terminal velocity: under the circumstances listed after a few seconds the bullet would reach terminal velocity ie it would stop accelerating. How does this happen? Well force/acceleration due to gravity is remaining constant at +9.8ms^-2. So as the velocity increases so does the friction as they are proportional. But what is friction but an opposing force. Thus once the friction reaches -9.8ms^-2 there is no net force, the velocity becomes constant.
Since the friction is constant, the heat being supplied to the bullet would well dissipate into the atmosphere before the temperature got anywhere near the bullets melting point (ie thermal equilibrium would be attained).

So in conclusion: after the initial acceleration phase, the bullet with no net force acting upon it would remain intact, at a constant temperature and in "motion" at a constant velocity for eternity.

Woden

/me wades in to survery whats going on.

aye apexaviour has it. terminal velocity is the answer

/me wades out after supplying little to the thread but confident in his assessment

Victor

ApeXaviour wrote:

Thus once the friction reaches

Remind me what friction does to solid materials?

Remind me what heat + air does to metals?

PhoenixRising

hmm, this one got me thinking aswell. ApeXaviour is right - the bullet will reach a terminal velocity (not a particularly high one either) and the heat due to aerodynamic heating would be negligible at low subsonic speeds, so the bullet will remain intact and get no where near it's melting point.

Here's the math!

Terminal velocity occurs when drag = weight of the bullet.

Typical weight of a bullet: 1/2 oz (1.4175 x 10^-2 kg)
Typical coefficient of drag of a bullet: 0.295 (sourced from a nasa website)

I chose an arbitrary bullet diameter of 12mm, which is about the size of most bullets I've ever seen.

Drag = Cd.(0.5).rho(air).V^2.S

Cd = Coefficient of Drag
rho(air) = density of air = 1.225 kg/m^3 (assuming sea level conditions)
V = bullet speed in m/s
S = frontal surface area of bullet = 11.3 x 10^-5, given radius of 6mm

Weight of bullet = (1.4175 x 10^-2).(9.81) = 0.14 N

Drag = (0.295).(0.5).(1.225).(11.3 x 10^-5).(v^2)

At terminal velocity, drag = weight of bullet so,

0.14 = (0.295).(0.5).(1.225).(11.3 x 10^-5).(v^2)

V^2 = 6856.8

V = 82.8 m/s = 298.1 km/hr

So the bullet will reach 298.1 km/hr and then stops accelerating. Kinematic heating for Concorde, travelling at Mach 2.0, is only in the region of around 400 degrees C. Our bullet only reaches Mach 0.24, and aerodynamic heating is negligible at these low subsonic speeds. So even if the bullet was made from lead which has a very low melting point of ~328 degrees C, it's temperature would get nowhere near this, so no chance of it vapourising!

Capt'n Midnight

ApeXaviour wrote:

But I have to severely disagree.
Let me get it straight.. gravity is constant, air pressure is constant but there is nothing to impact. Well used to these kinda hypothetical questions..

A/
The acceleration towards the earths surface is not constant - it lessens with height. Also the earth rotates so at the equator you get about 1 mile/s spin. If the bullet were to reach a vertical height of 36000Km with no more forward velocity it would not fall back as it would be in geo-synch orbit.

Neglecting air resistance a bullet fired horizontally at a speed of 16,000mph would orbit the earth every 90 minutes. (of course the bullet would have to be fired faster westward while eastword would not need as much speed since the earth rotates.)

Any faster and it would orbit the earth further out until at escape velocity, the bullet will leave the earths gravitational well and orbit the Sun, the Sun has an higher escape velocity and provided the bullet was going in the right direction it would join voyager in leaving the solar system. Higher speeds still would be needed to leave the galaxy / local group etc.

B/ air pressure is not constant - PV=nRT etc. the pressure of the air above means air is denser lower down. Also the temperature affects air viscosity so that is another factor that changes with height.

Lets modify the original question...
If you had a supergun (iraq style) and a projectile with an ablaltive coating then it would come out of the gun at more than 16,000mph and be slowed down by air resisitance and the coating would burn off, so that when it had cleared the atmosphere it would then be travelling enough to orbit and you'd only loose about 5% of the mass. - Since you don't have to carry reaction mass etc. its a cheap way of getting mass into orbit. Solid state electronics could be potted in resin to survive the acceleration and water/ice carried in to orbit this way could be photolysed to produce rocket fuel for later on.

The problem with this and with the bullet is that your speed is highest where the air is densest, unlike a reentry where you are gradually (relative) slowed down by increaseing deanse air. This means that if the bullet is going to melt it would be on the way UP not down.

Bullets travel at supersonic speed - so the Mach 0.24 bullet earlier would not melt.

ApeXaviour

Victor wrote:

Remind me what friction does to solid materials?

Remind me what heat + air does to metals?

Okay I know this has been addressed already but I'd like to take a different angle in explaining it so you can appreciate the why of it. We've established that once it is travelling at a constant speed, friction will also be constant. Think of the friction now as a constant supply of heat to the metal. This will begin raising the bullets temperature. But as it's temperature raises, heat begins to radiate and conduct into the atmosphere from the bullet. The more the temp rises the more heat is lost and quickly it becomes equal to the supplied friction heat. Heat lost = heat gained, no net change in temperature at this point. As has already been stated, at .24 mach the friction heat is low so the bullet wouldny heat up that much.

Capt'n Midnight wrote:

A/
The acceleration towards the earths surface is not constant
B/ air pressure is not constant .

Yeah that's pretty obvious. If you had read the original question though you'd have seen it was posed as a hypothetical situation where gravity and air pressure are constant.

EDIT: Nice filler tho..

Victor

The hypothesis says nothing about gravity being constant. Isn't gravity proprotional to distance from centre of gravity?

PhoenixRising wrote:

Our bullet only reaches Mach 0.24, and aerodynamic heating is negligible at these low subsonic speeds.

How come muzzle velocity is typically Mach 3 then?

ApeXaviour

mp3guy wrote:

if it theoretically fell for ever in earths sea level atmosphere what would happen?

Ok granted he doesn't state it explicitly, but it seems implied from above ("fell forever"?). That's why I stated it at the beginning in the "making sure I got it right" bit.

Victor wrote:

How come muzzle velocity is typically Mach 3 then?

Because there is exploding gunpowder forcing it out, not gravity..

Hagar

/Wanders in. Looks around.

All bullets aren't supersonic.
12mm diameter bullets are huge, 1/2" more or less. This is what the US would call a "50 caliber". These would be supersonic.

Capn Midnight wrote:

The acceleration towards the earths surface is not constant - it lessens with height

At sea level there is no height variation. I'm lost here.

At sea level would there be sea water? Aha I think I have yiz there. Would it stop the bullet from melting?

Would the bullet fall straight back down pointed end first or become ballistically unstable and tumble end over end as many are designed to for maximum target damage? After all most of the weight is at the rear of the bullet. What effect does variable wind resistance have in this scenario?

Do you know what Ted, yer man asking the questions is a bit mad. Isn't he really though?

/Wanders back out to reality.

Jim

Twas in a film I saw once. Brad Pitt's mate got shot in the head from a bullet that was fired into the air and came back down.

No, seriously, Brad Pitt.

/me blinks

PhoenixRising

Victor wrote:

How come muzzle velocity is typically Mach 3 then?

I was talking about the bullets descent back to earth under gravity, and not it's initial velocity as it leaves the gun.

The original poster was wondering if the bullet would vapourise if it descended forever under gravity....I think .

amen

Bullets hitting someone and killing them after been shot into the air is commonal called a "Beirut haircut" due to the number of ppl killed in Beirut by this method


as for the Iraq super gun, the V2 rockets bascially worked on the same principal. They were launched into high altitude (I think 20-60 miles up) and then they dropped back to earth.

gravity is not a constant 9.81ms it varies at sea level depending on your location on the planet I think New York for instance has a slighly lower g than dublin

civdef

amen wrote:

Bullets hitting someone and killing them after been shot into the air is commonal called a "Beirut haircut" due to the number of ppl killed in Beirut by this method

Bullets from small arms fired vertically don't pose a major safety risk, the problem is the yahoos who fire up in the air generally don't check to see if they're aiming perfectly perpendicular to the ground - Think of the famous clip of Saddam Hussein firing his rifle at around a 45 degree angle over his fans, if that connected with you, it'd do harm.

Gen. Julian S. Hatcher supervised experiments to determine whether a bullet returning by gravity from rifle fired vertically represented a danger.

Hatcher's Notebook, Chapter XX, "Bullets from the Sky," summarizes the relevant research and reports upon his studies, saying:

"One of the shots that hit the platform was a Service .30-'06, 150 grain flat based bullet, which came down base first (as that bullet usually does) and bounced into the water after striking the edge of the lower platform. It left a mark about 1/16 inch deep in the soft pine board."

"It was concluded from these tests that the return velocity was about 300 feet per second. With the 150 grain bullet, this corresponds to an energy of 30 foot pounds. Previously the Army had decided that on the average, an energy of 60 foot pounds is required to produce a disabling wound. Thus Service bullets returning from extreme heights cannot be considered lethal by this standard."

"Most .30 caliber bullets seem to attain about this same final velocity and it doesn't make any difference how far they fall. Even if a bullet were fired downward from a very high plane, it would still reach the ground at about the same velocity. That is because the air resistance increases very rapidly indeed with increases in speed."

"For larger calibers, the terminal velocity of fall is higher, as the weight is greater in relation to the diameter. An ordinary .50 caliber machine gun bullet having a weight of 718 grains would have a terminal velocity of fall of nearly 500 feet per second and a final energy of something less than 400 foot pounds. A 12-inch shell weighing 1000 pounds and fired straight up would return with a speed of between 1300 and 1400 feet per second and over 28,000,000 ft. lbs. of striking energy."

StupidLikeAFox

well im off to buy me a rifle and check it out so as to prove you all right / wrong