ôMuzzle velocityö 8

[Veemax]

I have a question about the “muzzle velocity” of projectiles fired from a gun barrel! I’ve always assumed that the projectile is still accelerating- providing the rate of burn and energy of the charge is sufficient to continue to overcome friction and inertia as it leaves the muzzle- that the projectile velocity is still increasing, even when it’s left the barrel. Am I correct in saying that only the rate of acceleration decreases, ultimately of course- the velocity decreases.

I’ve read several articles in various shooting magazines, that this is not the case! They appear to suggest that the velocity decreases as soon as it leaves the barrel and that maximum velocity is at the muzzle!

Are we to say that the charge and weight of projectile are perfectly balanced- so that the velocity is constant as it leaves the last section of barrel? If this is not the case, then the projectile could still be accelerating at many tens of g’s, as it leaves the barrel.

 

[Veemax]

Thank you everyone, who has contributed in trying to getting to the bottom of my answer. I’m always very grateful to forums such as this, not only to answers to my own personal questions, but also to the creation of searchable information accessible to other Web users, myself included. It’s a very valuable resource, although sometimes you have to “weed out” the correct information for yourself.

The reply from Ltwine, I thought was really good- “Pop open a bottle of Champaign and observe the change in velocity”. I suppose this is the same as when a Ping Pong ball can be balanced at the top of a vertical air stream flowing from a tube. If there were no force beyond the open end of the tube, then the ball would rest at the open end, not in mid air. Anyone who has fired blank ammunition will know that it can produce pressure waves on quite distant objects. Anyone who is willing to place their hand a few inches from the muzzle, whilst firing a blank round- I would consider very foolish! To say that a projectile is not being pushed beyond the muzzle opening- I would consider wrong!

The reply from SNORGY was very good indeed. IRstuff has stated that- “Output from an interior ballistics simulation puts peak linear acceleration at 161409 g for 7.62 mm round at 30.5 mm travel in a 609.6 mm barrel. Acceleration at the muzzle is only 17022 g. SNORGY has mentioned “instantaneous energy conversion”. If also “instantaneous acceleration” is indeed possible and likewise instantaneous deceleration, then in an instant the projectile would reduce in rate of acceleration from 17022 g to zero g. In theory it seems this is possible, in practice, it may be very different. Let’s look at ““instantaneous acceleration”. If it were possible to accelerate a projectile from zero g to 17022 g when time is zero, we would need an infinite amount of energy! If this were put into practice then we could have barrel of zero length producing phenomenal velocities.

If instantaneous deceleration is not possible after the projectile leaves the muzzle, then it must take time- no matter how short. Lets take the figures of 17022 g to zero g, then between these two figures, the projectile is still accelerating, although the rate of acceleration is reducing, if we have time and acceleration, then we have an increase in velocity- no matter how small.

 

[drawoh]

...

If instantaneous deceleration is not possible after the projectile leaves the muzzle, then it must take time- no matter how short. Lets take the figures of 17022 g to zero g, then between these two figures, the projectile is still accelerating, although the rate of acceleration is reducing, if we have time and acceleration, then we have an increase in velocity- no matter how small.

Do you mean instantaneous deceleration, or instantaneous transition to deceleration? The acceleration will drop to zero or a negative value just as fast as the force does, unless the mass of the bullet changes.

JHG

 

[SomptingGuy]

Veemax,

I think you are mixing up velocity, acceleration and jerk here (or force, momentum, energy, etc).

"accelerate a projectile from zero g to 17022 g" doesn't make sense. You can apply 17022g instantly if you can apply enough force instantly. Energy isn't required until the projectile starts moving.

- Steve

 

[GregLocock]

Instantaneous changes in acceleration or deceleration are possible, if you ignore elastic waves in the body. That's what happens when you stop applying a force.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[CH5OH]

still remain difficult to convince:
a ping pong ball floating on air or a hand in front of riffle fired with a blank.....
mmmm... a bit difficult to compaire those objects with a bullet leaving the barrel (speed of the former=0m/s,the latter=supersonic)
a detonation can only excist in a combustible mixture:
to little gunpowder:the gun powder is burned even before the bullet leaves the chamber
to much gun powder:the excess of gun powder is vapourised and burns when entering the air (lack of oxigen when bullet seals the barrel)
however most of the kinetic energy is derived from the thermal expansion of the gas, not from the detonation of the gun powder(hence longer barrel,more bullet speed).The accelaration is a derrived unit (compairing speed over period of time)it would be impossible for the bullet speed to drop to zero instantly (newtons law), the acceleration however does, the moment you seize the energy supply (when the bullet leaves the barrel)

 

[FeX32]

Many good replies here. Although the OP seems to be in left field. Often is the case.


Fe

 

[Veemax]

Let’s say that we are moving the projectile from rest to an acceleration of 1 metre per second per second at the end of a distance of 1 metre, over the next metre let’s say that with increased energy we’re able to produce 10 metres per second per second, next- let’s say 100 metres per second per second. If we were to try to achieve the same acceleration, with the same projectile, in a shorter time, we’d obviously need more energy, as time approaches zero, then we would need infinite energy to produce the same result. I’ll have to assume that the reverse is also true- that if acceleration went from its maximum to zero in an instant, then infinite energy would need to be dissipated. If this cannot be achieved in an instant, there must be a time when the projectile is still accelerating, with a corresponding increase in velocity.

Perhaps I’m on the wrong track here!! Maybe someone has used a high speed camera to see exactly what happens in practice?

 

[Veemax]

Are inertia forces fictitious?

 

[GregLocock]

Depends on your frame of reference.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[SNORGY]

Veemax:

Did we share the same thought or the same beer tonight?

Maybe the energy of *motion* can instantaneously change provided that the conversion to other forms of energy occur over some duration of time. These might include:

* plastic deformation
* heat
* light
* sound

Maybe that's where one can reconcile the paradox of "infinite energy required" for instantaneous acceleration / deceleration. My college introductory physics books seem to read this way: they explain that the energy that is apparently "lost" when one tries to apply conservation of energy to problems involving plastic collisions is not "lost" at all - it goes into other things that aren't as readily quantified.

Regards,

SNORGY.

 

[GregLocock]

In reality if you apply a force to a solid body it deforms locally and series of stress waves pass backwards and forwards and sideways through the body. Eventually this damps out and the body ends up accelerating as a whole. If the speed of vibration in the body length L is a, then any discussion of events that last less than a time of the order of L/a can no longer afford to ignore this.

However to try and wrap it up, as the shell leaves the barrel it is being pushed out by a pressurised gas that is capable of travelling faster than the shell (beacsue it is pushing on it). When it leaves the barrel the shell will be surrounded by an expanding jet of gas that will initially be faster than the shell, and so will accelerate it further. However very soon the gas will slow down, and so slow the shell.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[Veemax]

Thank you very much once again SNORGY. I’m afraid I don’t know whether I’m correct on the understanding of this problem, I have my point of view and would like to think that it is correct. Socrates was well know for his inquiries and debates between individuals with opposing viewpoints based on asking and answering questions to stimulate rational thinking and to illuminate ideas. I’d like to think that I’ve learned a lot from this debate!

I should have mentioned earlier that “Veemax” derives from Vmax (Maximum Velocity), I’d liked to have used that, but it had already gone- quite quickly!!

 

[FeX32]

Fig's 16 and 17 are interesting here:

http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA417311

Fe

 

[ione]

The added boost (acceleration) from propellant gases to the bullet, after it exits the muzzle, should be lost approx 10 feet from the muzzle and so it is of very little practical interest, anyway it exists. Doppler radar is probably the best way to get the bullet’s peak velocity.

 

[handleman]

over the next metre let's say that with increased energy we're able to produce 10 metres per second per second

Maybe that's where one can reconcile the paradox of "infinite energy required" for instantaneous acceleration / deceleration

Just looking for a starting point here... both of these posts reveal fundamental lack of understanding basic concepts.
Have either of you guys ever taken a Calculus or Physics course?

-handleman, CSWP (The new, easy test)

 

[SNORGY]

Yes...but it was long, long ago.

My knowledge is apparently decelerating very rapidly.

Perhaps someone ought to shoot me, since it probably wouldn't hurt me, given that I evidently don't know how to stop a bullet.

Regards,

SNORGY.

 

[handleman]

Haha! Fortunately for the universe, its laws continue to operate regardless of our ignorance of them!

SNORGY, going back to your earlier post, it made a bit more sense. Due to elasticity in everything, it is almost impossible to instantaneously stop applying force to an object. However, when the force does stop, the acceleration stops. Acceleration does not continue due to "inertia" or something. In fact, acceleration would not even occur if you instantaneously removed friction. All that would happen is that deceleration would cease to occur. Velocity would then remain constant until some other force was applied. In your example of pushing/throwing things, objects will most certainly not continue to accelerate away from you after release. When you stop contacting and applying force, acceleration stops. Velocity continues, but acceleration stops.

Force causes acceleration.
The continued application of force over distance transfers energy to an object during its acceleration.
Infinite force for zero time over zero distance is zero energy. Infinite acceleration for zero time is zero energy. There is no paradox here anywhere. Zero force over infinite time and infinite distance is zero energy.

-handleman, CSWP (The new, easy test)

 

[SNORGY]

Actually...

"Infinite force for zero time over zero distance" would, I think, mathematically, be *undefined*, not zero.

i.e., F(infinite) x [{0 time}/{0 distance}] = undefined

That said...

F = ma
dF/dt = d(ma)/dt
dF/dt = m(da/dt)
[1/m]dF/dt = da/dt m > 0, m = constant

So, if you can *instantaneously* remove a net applied unbalanced force, you can have an *instantaneous* rate of change in acceleration. My confusion arises from trying to get my head wrapped around the idea that at some point in time, acceleration is some non-zero quantity, and then in a *mathematical instant*, it is zero. Similarly, the net unbalanced applied force goes from "something to nothing" in a mathematical instant. The only way this can happen, unless I am missing something, is if the acceleration is non-zero and zero at the same time; similarly, the force is non-zero and zero at the same time. It has to be at the same time because there is no change in time.

But...I suppose if you can draw a cusp, it's possible to have one.

Consideration of some measure of elasticity and, in a convoluted way, the dynamics of energy conversion and transfer, are perhaps being improperly brought into the discussion in an attempt to understand things a bit better.

My brain (the part that hasn't yet been killed by beer) hurts.

Regards,

SNORGY.

 

[Ltwine]

"However, when the force does stop, the acceleration stops."

Excuse my ignorance. How about motion after impact. I need to check on impulse & momentum.

 

[SomptingGuy]

If you want a refresher on impulse, momentum, kinetic energy, etc, get hold of a Newton's Cradle and play with it. Everyone knows that raising and dropping one ball at one end will result in one rising at the other. It seems amusing, but not too challenging.

Now raise two balls and drop them together. Why do two rise from the other side? Why not one, twice as far? When you can comfortably explain that, there is hope.

- Steve