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Old April 6, 2012, 10:01 PM   #1
mo84
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barrel pressure between different grains of bullets and recoil

I was wondering if the berrel pressure changes significantly when the weight of the bullet increases just just as the recoil usually becomes heavier. does heavier recoil indicate more barrel pressure or does recoil and barrel pressure not coincide with each other?

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Old April 7, 2012, 08:16 AM   #2
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Yes. If you asked because you plan to reload, do buy a good reloading manual. It will have explanations and ballistics for different weight, and configuration of bullets.
A good manual is the first piece of reloading equipment a beginner should buy.
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Old April 7, 2012, 09:55 AM   #3
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Substuting a heavier bullet, with the same powder charge used with the light bullet, will increase pressure and recoil. Possibly to a dangerous level. Heavier recoil does not always indicate more barrel pressure if using the correct powder charge. The burning rate of the powder comes into play here.
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Old April 7, 2012, 11:14 AM   #4
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That is a very complicated issue.

Momentum is mass times velocity. So the force felt on your shoulder is the product of mass and velocity. If you up the mass, or the velocity, you will feel more recoil if the product of the two is higher.

There may be something subjective to this as my 190 grain loads in my 308 rifles always "hurt" more than my 168's even though they are both maximum. It might be related to barrel time.

If you have a loading manual, you notice that the manual says something like "none of these loads exceed 50, 000 pounds". That is the same pressure limit for heavy or light bullets.

Gunpowder has an exponential slope to the curve and you can easily exceed safe pressures, with light or heavy bullets, by adding too much powder.
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Old April 7, 2012, 02:59 PM   #5
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Buy a copy of Quikload and play with it. Once you have spent some time with it you will see that it is not that easy of an answer. There are generalities but not many absolutes.
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Old April 7, 2012, 03:11 PM   #6
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Recoil comes in two stages:

1: Internal recoil as the bullet is being pushed out the bore the rifle is being pushed backwards, this can be as much as 1/16th of an inch.

2: "External Recoil" which is the "jet blast" as all that pressurized gas pushes out after the bullet leaves the bore.

This is why a max load under a 140 grain bullet in a 7mm Rem Mag can "feel" more powerful than a sedate 175 gr Bullet at a starting load.

When you add up the mass of the powder and bullet you get the total mass leaving the muzzle and pushing back through the rifle into your shoulder. A drop of 35 grains in bullet weight can be totally wiped out by an increase of 10 grains of powder giving back more felt recoil.

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Old April 7, 2012, 07:10 PM   #7
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mo84,

I'm not sure you were trying to say the same powder charge was involved. If not, if you are simply saying that you've noticed heavier bullets tend to recoil more, that's a true generalization. When the same pressure is applied to them they accelerate more slowly, subjecting the gun to the same equal and opposite force for a longer time. That accelerates the gun more to the rear.

Because the nerve endings in the body tend to experience recoil in proportion to energy rather than the acceleration pushing on them, recoil calculations are often done to determine the free recoiling energy of a gun (recoil energy with no shooter or rest absorbing any of it; what it would have by way of energy if it fired free floating in space). SAAMI has a free downloadable00 document describing how to make that calculation, here.
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Old April 7, 2012, 09:53 PM   #8
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In my experience, a heavier bullet will recoil more than a lighter bullet.

Recently reloading for my uncles 300 savage, he was undecided between 150gr and 165gr. I recommended 150, but loaded some of both to test. The heaviest loaded 150 recoiled less than a mid loaded 165....

Of course, his gun has no recoil pad, just a metal butt-plate, so its easy to tell the difference in recoil, and a pain in the shoulder after 4-5 rounds ... On my savage edge which has a nice recoil pad, I didnt really notice a difference between factory 150 and 180gr factory loads.....

My experience in handguns is the same but different.... With a lighter bullet the recoil is "sharper", where with a heavier bullet the recoil is more, but also more spread out, so easier to handle, if that makes any sense....
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Old April 8, 2012, 08:23 AM   #9
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thanks for the replys, its been a little while since I could get on. I was refering to just increasing the bullet weight and useing the right amount of powder. To get a little more specific. A 350 grain bullet with a max load of powder has less felt recoil than say a 700 grain bullet at a max load of powder. The barrel pressure could possibly be the same in both loads, just you have more mass pushing out against you with the heavier bullet which gives you the heavier felt recoil?
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Old April 8, 2012, 08:57 AM   #10
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As I said, the difference is due to the difference in barrel time. If the pressure is the same, the 700 grain bullet will only be going half as fast by the time it gets to the muzzle. That means it has spent twice as much time in the barrel being pushed forward by that same pressure. Since essentially that same pressure pushes back equally and oppositely against the gun, the gun, being the same mass it was before, will have been given twice as much rearward momentum because it was pushed back for twice as long.

The concept you actually want is called impulse. It is the application of a force multiplied by the time over which it is applied. The longer the force is applied, the more it accelerates a mass (in this case the gun mass) to a higher velocity. Mass times velocity is momentum, and that's what the gun gets more of. It will feel closer to four times more recoil because your nerve endings will sense in proportion to kinetic energy rather than momentum. That's because your shoulder is stopping twice the momentum in roughly half the time, and that takes four times the force. Recoil should feel roughly doubled when the bullet plus powder charge is about half-again heavier.

The force is just the pressure times the cross-sectional area of the bore. In a real calculation that part of recoil against the breech is actually the sum of the force against the bullet base and an average of about half the powder mass being pushed forward, too, plus you then get the rocket effect impulse added to it. Quite a bit going on there.
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Old April 8, 2012, 11:28 AM   #11
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Unclenick, you never cease to amaze me on your knowledge.


Thanks
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Old April 8, 2012, 01:37 PM   #12
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Thats a pretty good explaination. I pretty much understand what its all about now and how it works. Thanks alot
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Old April 8, 2012, 03:42 PM   #13
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Quote:
Quote:
If the pressure is the same, the 700 grain bullet will only be going half as fast by the time it gets to the muzzle. That means it has spent twice as much time in the barrel being pushed forward by that same pressure. Since essentially that same pressure pushes back equally and oppositely against the gun, the gun, being the same mass it was before, will have been given twice as much rearward momentum because it was pushed back for twice as long.
Not exactly, barrel time has to do with acceleration, the longer the acceleration the lower the peak energy delivered over the recoil impulse. Energy = 0.5mass*velocity squared. And Acceleration = Force/Mass, but that doesn't help us here.

Momentum = mass*velocity. The peak rearward velocity determines peak rearward momentum. Change either velocity or mass and momentum goes up in a linear fashion.

Velocity = distance/time, which gives us speed (but not an acceleration).

So the LONGER a bullet spends in the barrel the LESS momentum you'll get.

Combining the two equations give us; Momentum = mass*distance/time and the larger the time value the smaller the momentum value.

Like I said before, you have to look at everything going out the muzzle of the barrel to get a handle on recoil. A heavier bullet will give you more recoil than a lighter bullet with the same powder charge because "for every action there is an equal and opposite reaction."

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Old April 9, 2012, 09:06 AM   #14
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Quote:
Originally Posted by Jimro
…the longer the acceleration the lower the peak energy delivered over the recoil impulse.
Peak energy is the same as final energy for the gun. It depends on the square of the final velocity of the gun, not the bullet. The gun's mass is not changed when you change the weight of the bullet, so the longer it experiences acceleration at a given level of force, the faster it goes and the more kinetic energy it has.


Quote:
Originally Posted by Jimro
So the LONGER a bullet spends in the barrel the LESS momentum you'll get.
Only if you don't change the mass of the bullet, as we did in the example.

To simplify considerations, assume you adjust powder choice and charge weight so the pressure profiles are the same with respect to distance down the bore for the light bullet and the heavy bullet. In other words, the pressure at the bullet base at any bullet distance along the barrel is the same for both the light and heavy bullet examples. a=F/m, so that as the mass of the bullet gets bigger the bullet's acceleration gets smaller, but the equal and opposite force is the same and the gun's mass is the same, so the gun's acceleration is not smaller. The gun's acceleration is just as big but now lasts longer because the heavier bullet takes longer to clear the tube. The result is the gun has more velocity, and, with the square of that, more energy at the end of the firing event.

All this is spelled out in the SAAMI document I linked to in post #7. I recommend downloading a copy and working a few examples to satisfy yourself that it's true.
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Old April 9, 2012, 11:29 AM   #15
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I love threads like this ... gives me something to think about when I kick back and pound down a few beers after a morning of cutting and splitting fire wood. Too windy to go to the range and shoot here in NY. You guys might force me to actually do some math for my 7mm Rem Mag with light and heavy bullets just so I can understand this better.
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Old April 9, 2012, 11:54 AM   #16
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Note that as long as the bullet's going down the barrel, the rifle and everything on it is moving backwards. After the bullet's left the muzzle, the jet effect adds a bit more recoil backwards. This is the main reason heavier recoiling hand-held firearms are more difficult to shoot accurately.

Even the recoil during the time the bullet from a .22 short rimfire round's in the barrel on target pistols used for international rapid fire events is minimized by the pistol's design. The barrel is aligned almost perfectly with the shooter's arm so it stays pointed at the aiming point while all things causing recoil doesn't move the sights up and off the target's center. 'Tis important when you're getting off 5 shots in 4 seconds and wanting all shots in the 4-inch 10-ring at 25 meters.
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Old April 9, 2012, 06:12 PM   #17
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Quote:
Peak energy is the same as final energy for the gun. It depends on the square of the final velocity of the gun, not the bullet. The gun's mass is not changed when you change the weight of the bullet, so the longer it experiences acceleration at a given level of force, the faster it goes and the more kinetic energy it has.
Yes, forward energy imparted to the bullet at the muzzle, plus energy lost to muzzle blast should equal the rearward energy of the rifle in a perfect system.

But you missed the point, VELOCITY is dependent on TIME. The longer the time, SPEED = DISTANCE/TIME the slower the velocity. Acceleration is not the same as barrel time which is a velocity. A bullet that leaves the bore at 2200 FPS will have a LONGER barrel time than the same bullet leaving the bore at 3200 FPS. The faster bullet from the same barrel had a greater acceleration to get to that final velocity, and therefore less TIME in the barrel.

Acceleration is given in distance per time per time, such as feet per second per second. Newtonian physics again, the greater the acceleration on the bullet, the greater the acceleration on the rifle.

Follow me on a thought experiment. Two bullets of different mass have the same barrel time. The barrel time being the same means that the recoil should be the same? Obviously not. It takes more energy to push the heavier bullet at the same velocity.

Second, the "jet blast" effect of all that hot gas shooting out the muzzle at around 5,200 fps. This is where the bulk of felt recoil comes into play. That heavier bullet with the same barrel time as the lighter bullet is going to have more pressure behind it when it leaves the muzzle, and this is where you are going to get the biggest portion of recoil.

E = 0.5mass*velocity squared, so that bullet with a 150 grain mass going 2800 fps pushed against the rifle less than that 45 grains of powder going 5200 fps.

Lets take it to the other extreme, two bullets of different mass that never leave the bore, now we have a perfectly closed system where recoil is only a product of "internal ballistics." In this closed system we don't have to deal with muzzle blast so it becomes obvious that the longer the barrel time, the slower the bullet is moving down the bore, the less recoil there will be in terms of either Energy (because velocity is slower), although momentum equals Mass*Velocity, so if mass was large enough it could outbalance the disadvantage of velocity.

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Old April 10, 2012, 01:42 PM   #18
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Quote:
Originally Posted by Jimro
]Yes, forward energy imparted to the bullet at the muzzle, plus energy lost to muzzle blast should equal the rearward energy of the rifle in a perfect system.
No, it looks like I caused this confusion. When I said, "Peak energy is the same as final energy for the gun", I meant the peak energy of the recoiling gun will equal the final energy of the recoiling gun at the moment the bullet and gas have cleared the muzzle; not that the gun energy will equal that of the bullet and powder mass. It won't come close. A typical hunting bullet has about 2000 ft-lbs of muzzle energy, but a typical hunting rifle firing it will have only about 15 ft-lbs of free recoil energy. It is momentum that is equal and opposite, not energy.

Quote:
Originally Posted by Jimro
But you missed the point, VELOCITY is dependent on TIME. The longer the time, SPEED = DISTANCE/TIME the slower the velocity. Acceleration is not the same as barrel time which is a velocity. A bullet that leaves the bore at 2200 FPS will have a LONGER barrel time than the same bullet leaving the bore at 3200 FPS. The faster bullet from the same barrel had a greater acceleration to get to that final velocity, and therefore less TIME in the barrel.
But you missed the point. The object of the discussion is not either velocity or speed, but what causes felt recoil to change with bullet weight. That is not dependent on elapsed time alone, but rather depends on the recoil energy which varies with the combinations of gun mass, time and force applied to the breech of the gun. For an extreme example of there being no unique dependence on time, having a small grandchild sit on your lap for five seconds would not have the same felt effect as having morbidly obese aunt Bertha sit on your lap for five seconds. Even though the amount of time is the same, you will feel the difference in force imposed by gravity on these two affectionate creatures.

Similarly, in the gun, there are two ways to increase the barrel time. One is to reduce powder charge, which lengthens barrel time by reducing the force accelerating the bullet, simultaneously reducing recoil. The other is to increase the bullet mass so the exact same increase in barrel time is needed to get it out of the muzzle, but that does not reduce the accelerating force. So now you have the same original force applied for a longer time, accelerating the gun mass more, increasing recoil.

In the real world its not that simple because progressive powder will burn faster and make more pressure with a heavier bullet because it can't push the greater weight to increase the powder burning space (expansion) as quickly. So powder charge has to be reduced or the load has to be switched to a slower powder to keep the pressure profiles the same.

Quote:
Originally Posted by Jimro
Acceleration is given in distance per time per time, such as feet per second per second. Newtonian physics again, the greater the acceleration on the bullet, the greater the acceleration on the rifle.
For a given gun mass, that's only true if you keep the bullet mass the same. The premise of the OP, however, is that the bullet mass will be changed.

Quote:
Originally Posted by Jimro
Follow me on a thought experiment. Two bullets of different mass have the same barrel time. The barrel time being the same means that the recoil should be the same? Obviously not. It takes more energy to push the heavier bullet at the same velocity.
Yes, we agree that more energy in proportion to mass has to transfer to the heavier bullet to give it the same velocity, though that's not what is normally done. We normally limit the force on the bullet in both cases by limiting pressure to something the gun can withstand. That means accepting lower velocity with longer barrel time for heavier bullets. Indeed, typically, if guns are optimally loaded for each round by adjusting powder burn rate and quantity, the heavy and slow bullets exit with similar levels of muzzle energy, but the recoil energy is not the same. Again, energy is not equal and opposite, only force and its resulting change in momentum are, and accelerating the gun rearward for a longer time with the same level of force will give it more velocity and more momentum and with that comes more recoil energy.

Quote:
Originally Posted by Jimro
Second, the "jet blast" effect of all that hot gas shooting out the muzzle at around 5,200 fps. This is where the bulk of felt recoil comes into play. That heavier bullet with the same barrel time as the lighter bullet is going to have more pressure behind it when it leaves the muzzle, and this is where you are going to get the biggest portion of recoil.
That would happen if the heavier bullet were driven to the same velocity as the lighter one, but, again, that's not normally the case because that would require a pressure increase.

I will add that while it is true with some overbore guns that muzzle blast can be the majority contributor to recoil energy, with most common calibers, like a .308, it's responsible for about a third of the recoil energy. That's because it gets about a third of the momentum and only momentum, not energy, is equally and oppositely created in the gun.

Quote:
Originally Posted by Jimro
E = 0.5mass*velocity squared, so that bullet with a 150 grain mass going 2800 fps pushed against the rifle less than that 45 grains of powder going 5200 fps.
The root of the problem is expressed there. It is that you are calculating energy on the assumption it will be equal and opposite in the gun and ejected mass. If you apply the same force to the bullet and gun breech in opposite directions, you'll find the acceleration of the bullet and the gun mass are inversely proportional to their masses. That makes the resulting velocities at the end of the barrel time inversely proportional to their masses. If you multiply these oppositely directed masses by their oppositely directed velocities you end up with two equal and oppositely directed quantities. Velocity times mass is momentum, so momentum is what those equal and oppositely directed quantities are called.

Energy, on the other hand, is proportional to half the square of velocity times the mass, so square the velocity ratio and divide by the mass ratio (same magnitude) and also by 2. If the mass ratio is about 250:1, rearranging you have: 250²/(2×250)=250/2= or 125 times more energy in the bullet and gas mass than in the gun. The bottom line is the bullet gets more energy out of the powder than the gun does, basically as a result of having less inertia and therefore being easier to move.

So, now we see momentum rather than energy is equal and opposite, let's run a calculation based on the momentum.
150 gr = 0.0214 lbs.
45 gr = 0.0064 lbs.

0.0214 lbs + (0.0064 lb/2) = 0.0246 lbs × 2800 fps = 68.9 lb-ft/s momentum added to the bullet and half the powder mass during their time in the barrel.

0.0064 lb × 5200 fps = 33.3 lb-ft/s momentum added to gas expelled at muzzle.

68.9 lb-ft/s + 33.3 lb-ft/s = 102 lb-ft/s total momentum.

The gun weighs 8 lbs with scope. Momentum will be equal and opposite, so:

102 lb-ft/s / 8 lb = 12.8 ft/s gun recoil velocity.

For kinetic energy, the lbs in ft-lbs is pounds force (commonly also written as lbf), the amount of force needed to accelerate 1 lb of mass (1/g slugs) at 1 ft/s². The gun weighs 8 lbs on a scale because gravity imposes enough enough force on it to do that. But gravity isn't involved in the force from gas pressure in the gun. That force acts on the mass of the gun, not its weight, so we have to get that mass from the weight by dividing by gravity.

8 lb/32.2 ft/s² = 0.248 slugs.

mV²/2 = 0.5 × 0.248 slugs × (12.8 ft/s)² = 0.124 slugs × 163 ft²/s² = 20.3 ft-lbs recoil energy.

If you rework this example for a 9 lb rifle, you wind up with 16.0 ft-lbs of recoil, so you can see how gun weight is a significant factor.
That bullet had 0.5 × 0.0214 lb/32.2 ft/s² × (2800 ft/s)² or 2610 ft-lbs of energy. Lets switch to a 180 grain bullet also propelled to 2610 ft-lbs of energy by 45 grains of a slightly slower burning powder (so the pressure doesn't increase). It will be traveling at about 2560 fps.

We now have:
180 grains =0.0257 lbs
45 gr = 0.0064 lbs.

0.0257 lbs + (0.0064lb/2) = 0.0289 lbs × 2560 fps = 74.0 lb-ft/s momentum added to the bullet and half the powder mass during their time in the barrel.

0.0064 lb × 5200 fps = 33.3 lb-ft/s momentum added to gas expelled at muzzle.

74.0 lb-ft/s + 33.3 lb-ft/s = 107 lb-ft/s total momentum.

The gun is still 8 lbs, so:

107 lb-ft/s / 8 lb = 13.4 ft/s gun recoil velocity.

8 lb/32.2 ft/s² = 0.248 slugs.

0.5 mV² = 0.5 × 0.248 slugs × (13.4 ft/s)² = 0.124 slugs × 180 ft²/s² = 22.3 ft-lbs recoil energy.

Reworking for a 9 lb gun it comes out to 17.6 ft-lbs.
Bottom line, firing the heavier bullet to the same energy level, as is common since the case only can hold so much stored energy, the heavier bullet recoils more.
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Old April 11, 2012, 06:58 PM   #19
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Quote:
Similarly, in the gun, there are two ways to increase the barrel time. One is to reduce powder charge, which lengthens barrel time by reducing the force accelerating the bullet, simultaneously reducing recoil. The other is to increase the bullet mass so the exact same increase in barrel time is needed to get it out of the muzzle, but that does not reduce the accelerating force. So now you have the same original force applied for a longer time, accelerating the gun mass more, increasing recoil.
We aren't disagreeing, but you pointed out this

Quote:
When the same pressure is applied to them they accelerate more slowly, subjecting the gun to the same equal and opposite force for a longer time. That accelerates the gun more to the rear.
was slightly confusing because it sounds like longer barrel time increases acceleration, which it by definition cannot. What you should have written is:

Quote:
When the same pressure is applied to a heavier bullet greater inertial and bullet to bore friction resistance causes them to accelerate more slowly, subjecting the gun to the same equal and opposite force for a longer time. This longer time interval allows acceleration to result in a greater final velocity.
Because even if acceleration is less because of increased barrel time, final velocity can be increased because you have more time to build up velocity.

I like the kid and fat aunt analogy, because both are being accelerated at -9.8m/s/s for 5 seconds. Time of acceleration is immaterial as the acceleration still results in a velocity of zero (providing the chair don't break). But here is another analogy, if two different balls are dropped from 20 feet up, the time it takes for them to hit the ground is exactly the same, the time of drop is exactly the same, but the impact is different, you can see my point that barrel time isn't the deciding factor in impact, but the energy required to get the balls to 20 feet to begin with. It all comes back to energy, not time.

Sorry to argue so intensely over precision, but I hope some folks have found it amusing if not educational.

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Old April 12, 2012, 05:12 PM   #20
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My second sentence should simply have been, "That accelerates the gun to a higher rearward velocity". That would have cleared the ambiguity.

Quote:
Originally Posted by Jimro
you can see my point that barrel time isn't the deciding factor in impact
Actually, that was the point I was trying to make. Your earlier sentence made me think you had that confused, when you said:

Quote:
Originally Posted by Jimro
But you missed the point, VELOCITY is dependent on TIME.
You should have written: "…VELOCITY is dependent on TIME, IF the FORCE is constant and the MASS is unchanged". And that's pretty much where I was going, too. Change the time OR the force OR the mass and you get a different acceleration over a different time with different resulting final velocity. The length of the barrel being constant is assumed.

You and I should get together and write a textbook. Between us we'll get it edited correctly in the end.

Slightly OT, but relevant to the discussion: One of the confounding things for people trying to keep their rifle loads tuned is that velocity and barrel time don't always track well enough to do that. You can't just change powders and load to the same velocity and be tuned because the barrel times won't match. If you pick a charge of a fast powder and a companion charge of a slow powder that both produce the same velocity with the same bullet in the same rifle, the fast powder charge will produce the shorter barrel time.

The above happens because, even though both charges have the same average pressure over the bullet trip down the bore, the fast powder achieves that average with a higher peak pressure and lower muzzle pressure. It therefore does a greater portion of its acceleration earlier in the bullet's trip, letting the bullet cover the remaining bore length at a higher average velocity. The slow powder has a lower peak pressure and a higher muzzle pressure, so it spreads the acceleration out more over the length of the barrel, and the bullet velocity just catches up to the fast powder bullet velocity at the very end of the journey.

So barrel time has a pressure profile dependency, with average pressure being the integral of the powder pressure function with respect to either time or bullet base position in the tube. Since the average pressure comes out the same for both the fast and slow powder at the end, the resulting imparted momentum and transferred final energies are still the same.

"First contemplation of the problems of Interior Ballistics gives the impression that they should yield rather easily to relatively simple methods of analysis. Further study shows the subject to be of almost unbelievable complexity."

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Old April 12, 2012, 06:30 PM   #21
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An open source "XYZ's of Reloading" aka "the big book of everything you never needed to know explained in precise detail" sound about right? One of these days an enterprising young editor is going to comb the archives and combine the best of the most interesting.... Ever think that in a hundred years people might read our ramblings the way we read Hatcher's Notebook?

Anyways, when people want to talk "ballistics" and I ask "Interior, exterior, or terminal?" they usually look at me funny. But interior ballistics is a lot like magnets, they are pretty simple in concept but when you have to actually explain how they work.... it gets technical quickly. Then again the English language isn't exactly user friendly.

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Old April 13, 2012, 11:21 AM   #22
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Yep. Esperanto, here we come.
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Old April 13, 2012, 12:18 PM   #23
Jim243
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Then again the English language isn't exactly user friendly.

And Greek or Latin are?

Jim
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Old April 13, 2012, 03:31 PM   #24
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I don't speak German but I usderstand it is pretty good for technical descriptions.
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