Physics question


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MTMilitiaman
March 3, 2006, 04:12 PM
So I messed around with a few loads from my 10mm. I shot a 175 gr Silvertip through about 4 inches of water into waterlogged sand at the edge of a river. I was on top of a train tressel a good 50 feet or so above the ground. I tried the experiment again with a 180 gr Gold Dot loaded by Double Tap, but was down on the bank underneath the tressel. It got me thinking about the effects of gravity on a projectile when fired downwards from an elevated position.

Does gravity still accelerate a projectile such as a bullet when it is fired downwards? Or does that fact that the projectile is already far past its free-falling terminal velocity mean that gravity can no longer accelerate it, but merely reduce the rate at which is loses velocity due to air resistance? In other words, would that Silvertip have an impact velocity greater than, or less than its muzzle velocity? How much so?

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B36
March 3, 2006, 04:17 PM
Get a copy of Hatcher's Notebook.:)

Answer to question 1 is no. Friction will slow velocity to terminal.

atk
March 3, 2006, 04:33 PM
MTMilitiaman,


I'm not that great with ballistics, but I can answer from a basic knowledge of physics.


Gravity will always pull the bullet towards the earth, whether it is fired up, down, or sideways. So, gravity will be trying to make the bullet accelerate.


Terminal velocity is not a force, but the result of competing forces: gravity and friction of the bullet against the air. The friction is simply trying to stop the bullet's movement - like if you dive into a lake, the water tries to stop you form sinking to the bottom of the lake.

As an object moves faster, it collides with more air particles, more quickly than when it was moving slower. Friction is caused by colliding with particles - in this case, air particles. The more air particles that the bullet collides with, the more friction it will feel.

Terminal velocity comes about when the force of gravity is equal to the force of friction.


The second part of your question asks if gravity will slow the downward deceleration to terminal velocity. The answer seems to b, "yes". However, one should keep in mind that, while the bullet is traveling faster than terminal velocity, friction is stronger than gravity, which is what forces the bullet to slow down.

carnaby
March 3, 2006, 04:35 PM
Does gravity still accelerate a projectile such as a bullet when it is fired downwards? ... In other words, would that Silvertip have an impact velocity greater than, or less than its muzzle velocity? How much so?

...

Or does that fact that the projectile is already far past its free-falling terminal velocity mean that gravity can no longer accelerate it, but merely reduce the rate at which is loses velocity due to air resistance?

Exactly right. The bullet will slow down, but at a slower rate than otherwise, until it reaches terminal velocity when the force of drag and the force of gravity on the bullet are equal. Then it's just turtles all the way down :)

carnaby
March 3, 2006, 05:31 PM
Friction is caused by colliding with particles - in this case, air particles. The more air particles that the bullet collides with, the more friction it will feel.
I don't mean to be a nit picker, but this is not exactly correct. It's not the collisions exactly, just the coming into contact with the particles. But ignore the situation on the particle level. The friction comes from viscosity. If air or water or any other fluid had no viscosity, then there would be no drag due to friction. Actually, there would be no drag due to anything.

This is because, for a bullet, the majority of drag does not come from friction between the air and the bullet, but from the big honkin flow separation that occurs behind the bullet that causes the wake. This flow separation is also due to viscosity, and the geometry of the bullet. Odly enough, if there was no viscosity, there would be no drag, since there would be no friction and no flow separation (D'Alambert discovered this and was perplexed since they didn't know about viscosity and couldn't figure out where drag was coming from). Anyway, the pressure in front of the bullet is not recovered at the back, and the pressure difference, which you can imagine is quite big, leads to drag, since pressure is force divided by area blah blah blah. This is why bullet like this

http://www.questbullets.com/Images/AB%20boattail%20bullet.jpg


has lower drag and better balistics. The flow doesn't separate as "badly" and thus there is a smaller wake and less drag.

Hope that was maybe interesting and not too blah blah blah :p

JohnKSa
March 3, 2006, 10:35 PM
It will impact with less velocity than it had at the muzzle but more than it would have had at the same distance if you had made a shot level with the ground.

Friction will be the dominant force until the bullet slows significantly. Gravity (in your case) would keep the bullet from slowing as much as normal, but it doesn't have the strength to totally overcome the friction at those velocities.

MajorPowerchord
March 4, 2006, 12:33 AM
I think that a mediums (air, water, etc) viscosity leads to greater frictional forces due to particle collisions rather than drag forces.

Viscosity is basically how well a medium flows. If it has a high viscosity, it takes more force to move a volume of medium in a given time frame vs a low viscosity medium. For example, it takes more force to pump a gallon of syrup 10 feet in one second than it takes to pump 1 gallon of water 10 feet in one second). Bottom line, its harder to move the medium.

The nose of the bullet is displacing air...basically splitting it like an axe into a chunk of wood. The slowing down comes from the bullet giving up kinetic energy of motion to the energy it takes to split through the air. If the medium has a low viscosity like air then the rate of slowing down is not very high compared to splitting through syrup. Syrup is not only more dense, but more viscous. Thus the nose of the bullet is hitting more particles per time AND takes more work per particle displaced.

I am not an aeronautical engineer but I think drag (turbulent flow rather than laminar flow) is not as much the cause for decelleration as is the nose pushing air out of the way. It definitely is a contributing factor, I just don't beleive it is the major player on the court. Someone who has studied aerodynimcs...please chime in.

In my defense though, I am about to graduate with a masters degree in nuclear engineer and I have studied hydrodynamic shock propogation in various mediums. Again, if I am wrong, lets discuss. I am more than willing to admit I am wrong if it means learning something new.

MTMilitiaman
March 4, 2006, 01:40 AM
Wow. Entirely more physics here than I ever retained from clear back in high school. Great explanations guys. Thanks.

Waitone
March 4, 2006, 01:41 AM
Let's assume to be assuming you are in a vacuum There is no air, no nuthin', just vacuum. Firing a bullet down you will get a vector sum of acceleration due to the firing of the cartridge plus the acceleration due to gravity. I would suspect acceleration due to gravity be swamped by acceleration due to gunpowder.

So take you understand out of the vacuum and put it into the atmosphere. Add resistance due to air and you slow the projectile down to some extent but not much from a train tressel. Hope this helps.

carnaby
March 4, 2006, 01:58 AM
I am not an aeronautical engineer
Me neither, but I play one on The High Road. Actually, I am an aeronautical engineer. :)

I think that a mediums (air, water, etc) viscosity leads to greater frictional forces due to particle collisions rather than drag forces.
Friction forces on an object moving through those mediums are drag forces. Drag is anything that impedes the motion of an object traveling in a fluid. Drag about a non-lifting body comes essentially in two forms, due either to friction between the fluid and an object (friction drag), or due to pressure differences about the object (pressure drag). There is also drag associated with the creation of lift, etc.
...drag (turbulent flow rather than laminar flow) is not as much the cause for decelleration as is the nose pushing air out of the way. It definitely is a contributing factor, I just don't beleive it is the major player on the court. Someone who has studied aerodynimcs...please chime in.
Drag is not turbulent flow. There can be more or less drag associated with turbulent flow than laminar flow. Laminar flow is simply flow that is "smooth." A turbulent flow would have more friction drag associated with it because more energy has gone into making the swirling turbulent flow, and that energy had to come from, in this case, the kinetic energy of the bullet.

On the other hand, turbulent flow can have lower drag associated with it than laminar flow. Consider the example of a smooth golf ball vs. a dimpled (rough) ball. The roughness induces turbulent flow near the surface of the ball. While this takes kinetic energy to do, it turns out that the thin energized layer of fluid (air) about the ball (refered to as the "boundary layer") results in a smaller wake behind the ball than for the laminar case. This figure is worth more than the next thousand that I could type:

http://www.aerospaceweb.org/question/aerodynamics/sports/sphere-flow-comparison.jpg

The same thing is true for cars, airplanes, cyclists and bullets. In fact, the spinning of the bullet not only stabilizes its flight, but I think it probably helps to induce a turbulent boudary layer which would lower its drag.

There is another effect that is due to having to move the mass of air or water or whatever out of the way, but that is a little different. When you accelerate through a fluid. This effect is termed added mass (http://en.wikipedia.org/wiki/Added_mass)
Added mass is the weight added to a system due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. The added mass force opposes the motion, and acts as a kind of drag force.

More interesting stuff on drag here (http://www.centennialofflight.gov/essay/Theories_of_Flight/drag/TH4.htm).

I hope I wasn't too much of a jerk :o and that that clears some things up. My Masters thesis was on this stuff, but I've since switched to control systems and all that. :)

carnaby
March 4, 2006, 02:11 AM
Let's assume to be assuming you are in a vacuum There is no air, no nuthin', just vacuum. Firing a bullet down you will get a vector sum of acceleration due to the firing of the cartridge plus the acceleration due to gravity. I would suspect acceleration due to gravity be swamped by acceleration due to gunpowder.

This is true in a vacuum or in a tub of pudding. The only difference is that you have to also add drag to the vector sum in the pudding.

Further, in a vacuum, the effect of the acceleration due to the firing of the cartridge imparts a high initial velocity, while the acceleration due to gravity will keep speeding up the bullet till it hits something in its path, or passes through the center of the earth, assuming you shot it down an evacuated tube that went that far :)

brickeyee
March 4, 2006, 08:42 AM
Comparing air flow at supersonic speeds to flow over a sub-sonic golf ball is about as apples-and-oranges as you can get.
Even the Bernoulli equations fail when the flow becomes compressible.

As Yeager and a lot of others found out, flow becomes very different above the speed of sound. AS a note, to this day no one flies ‘at the speed of sound’. You fly above or below to avoid the buffeting of Mach wave development. The routine maneuver is to make a shallow dive through the speed of sound and has been called a ‘dipsey doodle’.

The drag coefficient increases as the square of speed to around 90-95% of the speed of sound. At that point the flow becomes supersonic over portions of the bullet. Until about 105% the drag coefficient actually changes little. Above ~105% the coefficient starts to decrease as the Mach angle reduces.
The gravity will have very little effect on the actual speed of the bullet since it is ~32 ft/sec^2. It only has a few milliseconds to act on the bullet. Any gain will likely fall well within the shot to shot variation of even the best ammunition.
See http://www.pejsa.com/ for a very good basic book on ballistic theory.

JMusic
March 4, 2006, 09:11 AM
I'll have to confirm the friction coeficient part. I cannot recall a factor for gravity for ballistic speeds. Short story

We were taught ballistics by a chemistry major who was a genius at math. However when we did our first calculations for the distance of a 22 LR the correct number came out to be over 200,000 ft! The instructor swore by this but was not a shooter. The shooters in the class told him he was WAY off, that you would be lucky to get a mile (5280 ft.) out of it. The argument lasted the rest of the class. The next day one student found the correct calculation in an old NRA magazine. The missing factor? Friction coeficient of the atmosphere. We were doing our calcs in a vachum.
Jim

JMusic
March 4, 2006, 09:20 AM
I've seen several comments about buffeting due to passing the speed of sound. Question how much does that actualy affect a bullet while accelerating? Chances are it has already passed that speed while still in the rifle barrel. Is it realy a factor?

Kentak
March 4, 2006, 09:55 AM
Just to reiterate what has already been posted.

Without gravity, any object hurled downward (or any direction) in air or any other fluid medium, would have a terminal velocity of zero. It would eventually loose it's momentum due to friction, drag, etc., and come to rest.

Another hypothetical. Given gravity, but no air, a bullet fired downward would *increase* in velocity, and continue to accelerate until something stops it's travel.

To answer your question, a bullet fired downward has essentially two forces acting on it. One is the sum of the resistance forces, friction and drag. The other is the accelerating force of gravity. Just for fun, let's say the resistance has a value of -20 (negative since it is opposing the forward motion) and gravity has a value of +5 (positive since it is acting forward). This means the net force is -15 opposing forward motion, and the bullet will decelerate, but not as rapidly as if there was no gravity, in which case the net force would be -20.

Of course, as the bullet slows, the resistance forces decrease until a balance is reached with gravity, and terminal velocity is achieved. (We won't quibble about the fact that the density of air increase as you go downward, so actually the bullet would continue to slow. But just a bit)

K

BigFatKen
March 4, 2006, 09:56 AM
The only practical thing here is: A bullet that is ALWAYS sub sonic will be more accurate than a bullet that starts super sonic then goes sub sonic before hitting the target. e.g. A .22LR standard velocity will be more accurate than a high velocity at >100 yards. by a tiny amount. However, a self defence 10mm slug hitting a BG, even if it makes the super/sub change, will make no decernible difference on a center of mass shot. Use the ammo you shoot best with and hit your target. As is often said, shot placement is of most importance. As said before, the few fps shoting downhill is meanless on you target.

carnaby
March 4, 2006, 11:58 AM
I've seen several comments about buffeting due to passing the speed of sound. Question how much does that actualy affect a bullet while accelerating? Chances are it has already passed that speed while still in the rifle barrel. Is it realy a factor?
Right, as others have pointed out, this will not affect the trajectory since the bullet exits the barrel supersonic.
Comparing air flow at supersonic speeds to flow over a sub-sonic golf ball is about as apples-and-oranges as you can get.
Even the Bernoulli equations fail when the flow becomes compressible.Well, it is and it isn't. Bernoulli fails because it is a simplification for incompressible flow. Navier-Stokes still applies and you have, I think, three regions of interest, around the bullet behind the shock (or shocks if there's more complicated stuff going on), the shock, and the region ahead of the shock. The shock shows up in the N-S PDE's, but good luck solving for it :)

I will agree that supersonic flow (i.e. compressible flow) is a different animal, and I didn't study it much. And here's what my text has to say, very interesting stuff I did not know :D
Supersonic drag is composed of skin friction drag, wave drag, and base drag. Base drag refers to the drag produced by the pressure acting on the blunt rear end (base) of a body, such as that pictured (turns out to be a bullet :)) The base drag was not stresed in Chapter 4 since, in subsonic flow, the shape of the base affects the flow over the rest of the body ahead of it, so the base was viewd as simply an integral part of the overall pressure drag. In supersonic flow, however, the base oes not affect the flow ahead of it, so it is convenient to treat it separately.

...

Generally, the base drag is affected by the thickness of the boundary layer just ahead of the base (note: boundary layer still important => viscosity still important, etc.) ... so depends on the body shape, [B]surface condition, and Reynolds Number (ratio of inertial forces to viscous forces). That's from Aerodynamics, Aeronautics and Flight Mechanics by McCormick, 1995. So I wasn't totally wrong, but I did forget to consider the fact that this is compressible flow. Whoops :p

xsnydx
March 5, 2006, 12:54 AM
Being 3 months from finally being an aero engineer, I agree totally with carnaby. We talked about this sort of thing in our supersonic aero course and the only thing you missed was the way the "base" of the bullet is shaped. (most)Supersonic bullets have a "boat-tail" shape (they neck down) to decrease the "base" area, and therefore help mitigate the pressure issues that create a large portion of the total drag on the bullet.

Wow...that might be one of the first times I've shared my aero knowledge in public...
Thanks for listening...

-xsnydx

depicts
March 5, 2006, 05:12 PM
Again, as many times in the past, I', wicked impressed with the people in this group and am proud to be among you...well,...most of you :)

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