Shotgun Comps

[Wap wap]

Got the worksheet done on the actual ft/lb contributed by the gas (pressure) for each of 3 conditions, handgun, shotgun, rifle. Done in a engineering program with graphs and live calculations (I'm sure someone is interested), but website only allows simple text uploads, any ideas in how to upload RTF to this site or IBM hypertext, or MathML or PDF? Does anyone have the weights of the various comps and brakes such that I can calculate the contribution due to only the weight and seperate out that contributed only by the gas discharge? This would remove alot of the confusion as to effectiveness. ie. a lighter comp with x discharge would have a higher % percentage of contribution than a heavier comp or brake with the same x discharge.

[George]

Hi Wap wap,

The JP mid barrel brake weighs in at under 6 oz. It is the only mid barrel brake on the market to my knowledge so comparisons with the muzzle located ones would be moot. It is also the only brake that has an effect that is really noticeable so it really isn't a comparable thing.

BTW, I just got off the phone with Tim at JP Rifle and the weight given is just an approximation and 5-6 oz is the maximum it weighs, it could be a little less.

--

Regards,

Edited April 25, 2005 by George

[Wakal]

This is a cool thread...mmm....math...

However, I can think of two other mid-barrel shotgun comp makers

Here is one on a Saiga-12:

http://www.dreadnaught-industries.com/imag...s/Saiga12_2.jpg

http://www.dreadnaught-industries.com/imag...s/Saiga12_3.jpg

Shooting a "braked" Saiga-12 and an "unbraked" Saiga-12 is...interesting. The hotter the load, the louder...and flatter...the braked gun shot. The same was not true for the regular Saiga. All it took to make the wee Russian beastie a lot more comfortable...and faster (double tapping slugs)...to shoot was 18 1/8" holes, a larger gas port, and...a brake!

I'm not much of a shotgun shooter, and I don't see a very big point to a ported barrel. But even I can tell the different between a "brake" gun and a "non-brake" gun, when running across a target array.

There are actually two Saiga's with mod-barrel JP-style "brakes" on them (that I know of). The S20 was carefully crafted by our own Professor McCoy, and is a masterpiece of red anodized beautifully fluted precision work. I don't have pictures of that one, of course. The other is Fred's Red Saiga Shotgun Of Death™. A hunk of aluminum, lots of bolts, 18 1/8" holes in the barrel, and generally the fine fit and finish that would be expected of Soviet 50's engineering :lol

The one on Liota's pistol-grip'ed M4-stocked Saiga-20 will (hopefully) look like Kellly's, down to his cute little lizard logo. The one on my Saiga-12 will look, I expect, like a slightly cleaner version of Fred's. My USAS-12 gets nothing and likes it!

Alex

[Wap wap]

George thanks for the hint of posting I will be doing that shortly. However the comparisons can be made regardless of place on the muzzle or the weight -the point is to compare the contribution made by the constituents, weight and gas pressure. Don't get me wrong if a consumer is happy with what they have that is enough reason. I am simply trying to "scale" the topic. Obviously the heavier JP would be better due the weight addition alone- but how about porting in the same location with 6-8 oz of dead weight on the end of the barrel? Obviously not as asthetic as the JP but gives significant insight into the problem as a whole. Also it would be nice if you could get some of JP calculations such that we could enjoy them together.

[George]

You know, an interesting point is that with 14 plus oz of shells in the 10 round mag tube, the shotgun has no perceivable difference in recoil against when the tube is empty and there is just one in the chamber. I am thinking (it will need measurement of course) that weight alone is nowhere near as effective a contributor to recoil reduction as the JP brake alone is.

BTW, Tim at JP did say it can't weigh over 6 oz tops and it may even be quite a bit less. It is aluminum and very hogged out so I wouldn't be suprised if it only weighed in at 3-4 oz. There is no way I am taking it off the barrel on my 11-87 considering how carboned up it is where it attaches.

I still hold that the recoil reduction effect of the mid barrel mounted brake is very significant compared to bbl porting alone, or weight additions unless they were in the several pounds, or more range. even just under a pound of shells in the tube imparts almost no recoil reduction that I can notice comparatively.

We really need to set up a transducer test, or maybe a ballistic pendulum test. The math may, or may not model it correctly, but a measurement will certainly define the amplitude of the recoil impulse. Once we have quantified the effect, the math can be worked to fit the data.

I get the feeling that JP Rifles testing method was cut-n-try and settle on a result that works.

--

Regards,

[DA45acp]

I have to agree with George. I am not built to shoot shotgun ( 160 lb.s) so every advantage helps and the JP Open shotgun is by far the softest shooting shotgun I have shot (say that fast three times). I am not much on pen and paper theories but actual use and when a shotgun doesn't kick the crap out of me I am a believer.

[Wakal]

...when your sight stays on, that is.

Alex

[wsimpso1]

Think about how the shotgun mag is constructed, and you will have an idea why the full mag does not feel different from an empty one...

The rounds are held aft in the mag tube by the mag spring. When the gun recoils, the ammo wants to stand still, the gun recoils, and the mag spring compresses some. So the ammo in the tube is really not resisting recoil unless the mag spring bottoms out, and by then, the recoil has already poked the shooter in the shoulder. Yeah, the force from the mag spring is pushing forward on the gun, but it is puny compared to the forces in the recoil impulse. Also, we get that impulse back (in its entirety) when the stack of shells, driven by the mag spring smacks the latches.

The Rem M1100 and M1187 have an intercepter latch that drops down forward of the rim of the next shell when the hammer is released. This prevents trying to feed more than one round, but also captures the first round, so it does recoil with the gun, sort of - there is clearance here too, allowing some motion and thus not showing the recoild reduction. Other semi-autos have similar features doing the same thing for both feeding and for making the ammo have little to do with recoil reduction...

There is a lot of stuff going on during the firing and auto-loading cycle!

Billski

[DA45acp]

...when your sight stays on, that is.

Thats cold man. We are talking about "Brakes not Breaks......)

[George]

Billski,

What you are saying then is that the first round from a full tube (spring compressed to point of coil binding in my 11-87)) will actually show the recoil reduction by weight from a full tube, but from there on, no.

I haven't noticed that this is so. I will pay attention to the difference (if there is any) from a full tube, and with 2 rounds down from full next time I am out at the range. If there is no noticeable difference in perceived recoil between these two mag tube states, then I will have to assume that just under a pound of added weight does nothing noticeable for the shooter (the full tube with bound spring can not exhibit the inertia effect of the rounds moving in the tube and robbing the gun of the recoil damping effect the weight of the shells should produce).

--

Regards,

[wsimpso1]

George,

You could do that experiment, but I can tell you up front that your result is likely to mislead you. If your mag spring is really bound up solid, the ammo will add to the weight of the gun in recoil. But you are unlikely to ever get it that bound up.

Lets get the magnitude of the forces understood here. I answered before without having numbers but knowing that they were big. I went and calculated some example ones. High school physics will give it all to you.

If your bird shot shells make a max of 17000 psi, eight pound gun is accelerating at you at over 600 g at peak, and is still accelerating towards you at 100 g when the ejecta nears the muzzle. Then you get another brief pulse of hundreds of g's when the bore is uncorked. Now during all of this accelerating, the travel moving your shoulder is still miniscule. Mostly, the gun gets moving, the shot leaves the barrel, and then the gun gets stopped by pushing you around.

If the bird shot cartridges were to recoil with the gun, the spring would have to come up with over 60 pounds (yes, pounds) per bird shot cartidge, and would still be around 10 pounds as the ejecta approaches the muzzle. A stack of eight rounds would require a spring force of over 480 pounds to prevent floating completely and 80 pounds would still allow it to float over almost all of the firing cycle. Anything less than 80 pounds and the rounds will be floating on the spring during the entire firing period and participate in recoil reduction to the level of the spring force only while floating.

Now, consider a fixed machine stand, bolted to a concrete slab and the gun does not budge during firing - under these circumstances, the gun and the stand will experience the forces that the powder applies to the ejecta - ugh, thousands of pounds. That is why aviation machine guns are mounted in recoiling mounts and artillery, tank guns, naval guns, etc all have long stroke hydraulic recuperators. And they all still require substantial spades on ground based equipment.

We humans are shoved by a shotgun, and it really recoils pretty freely for the first few milliseconds when all of this interesting stuff is going on. The forces in gun firing are very big, but also very brief, or we would not be able to have all of this fun shooting and thinking about it.

Anyway, having a mag spring bound up to the point of preventing float in the mag tube is tough to fathom.

Now for the skeptics who really want to test this theory about the ammo floating, you could pull the mag spring, load the mag, and put in something (a spring or chunk of foam rubber) to hold the rounds against the front end of the tube so that the mag carries them all in recoil. Then fire it and compare it back to back with firing with an empty mag. Or you could use some clamps to attach some steel slugs to the barrel. Oh, and watch for the clamps slipping along the barrel during the tests...

Billski

[George]

Hi Billski,

I see your point, but I will also point out that the 10th shell on "My" 11-87 requires a very hard push in and the spring bottoms/stacks just as the shell latches in. You cannot push forward and gain any slack past that point. So mine "will" be a valid test as it is pretty much mechanically locked with 10 in it.

Funny thing, the plastic end cap in my Choate tube always never quite seats no matter how hard I press it in after cleaning and disassembly, but the first round always snicks it in the last 32/nd of an inch like it was nothin'. This is pretty much the effect you are delineating applying a tap on that sucker that I cannot duplicate with a cleaning rod, or dowel ;-)

--

Regards,

[Wap wap]

The difference in the experince as the gun changes weight from an empty mag. is the difference between recoil velocity and recoil in ft/lb. Does anyone have the carrier velocities of an AR, 1100 and the slide velocity on a standard 45?. George says he thinks that the force is about 4 ft/lb, and with it's large mass I can calculate the velocity. The amount of recoil reduction that occurs by the addition of weight by the rounds in the magazine is just that, whether it moves in the magazine doesn't change the weight. There is a calculator on the web- search for recoil and muzzle energy. They will give the recoil in ft/lbs and the recoil in velocity. G forces are a constant.

[wsimpso1]

Wap wap,

I did some of these calculations as part of being a gun and ammo engineer. Now I do other work on vibration isolation as automotive engineer. I know something about moving parts, spring loads, damping, etc. If the computer model accurately represents what we know from experience, it might be a good model. If it does not represent what we know, it is a poor model. And if it neglects to include correctly the physical reality that we do know and describe, it should be discarded or modified to include more of the real world. Let's talk about what we know. Assume a locked breach gas op shotgun.

Guns work with short intense impulses and Newton's Laws.

While the ejecta is in the barrel, an expanding "bottle" of gas keeps pressure on the ejecta, acclerating it toward the muzzle. The total momentum change imparted to the ejecta plus the momentum change imparted to gas is also imparted to the gun structure. The gas operation system has taken a small amount of gas during this process. The acceleration the gun experiences is F= m*a = P*A. m is the ridgid body portion of the gun, a is accleration, P is pressure on the base of the ejecta, and A is the area of the ejecta's base. The g's vary though out the the firing cycle based upon the pressure at that moment... G's are not constant during this process.

When the ejecta leaves the barrel, the "bottle" of expanding gas accelerates towards its local speed of sound, which generally exceeds the muzzle velocity of the ejecta, sometimes by many times. During this interval, the front of the propellant gas cloud will generally pass the ejecta, and then slow down. It slows because it is expanding, its temperature is dropping adiabatically, its local speed of sound falls with it, and it can not expand at a speed greater than its local speed of sound. The momentum imparted to the gun is due to the change in velocity of the gas during expansion outside of the gun. This is how rocket engines work, only rocket engines have nozzle shaped to coax the flow in supersonic expansion, and thus get even more energy from the flow. The acceleration that the rigid body portion of the gun sees is again due to the thrust from the gun gas leaving the muzzle, and reduces as the gases drain out of the muzzle.

So, the gun is accelerated with one pulse from powder pressure moving the ejecta one way and the gun the other. Then there is a second pulse as the muzzle is uncorked and the gun gas acclerates out of the barrel. This all happens in a few milliseconds, the travel is puny, but the velocities are getting up there, whether you have shouldered it or are holding it lightly. That is why we compute free recoil energy and free recoil velocity - the recoil that we must deal with is largely a matter of rigid gun mass. Light guns kick harder because they are going faster when they run into us. Hold the gun as tight as you want, it is still pretty close to free recoil during the firing cycle.

When we add in a gas system, part of the mechanism starts rearward immediately when the gas is applied. In fact, we have to accelerate the action bars and slide (or carrier or op rod) to sufficient velocity and store sufficient kinetic energy during this time to operate the whole cycle. And we do. But we also have to try to open the gun after sufficient gas has drained from the barrel to allow this to occur. We do this with free travel that all of these systems have. So we accelerate another mass rearward towards the end of the firing cycle, which can help out in recoil by applying forces forward. The action bars and slide are by the way leaning on their action spring during the travel aft, imposing another force rearward, but the action spring forces are puny compared to the forces that drive the action. Gas ops help one more way - the gas in the barrel starts being drained off at the gas port once the piston has moved a little bit, speeding the drainage from the barrel and reducing the impulse applied to the muzzle, but this effect is pretty small - the gas ports are small, and the gas can go no faster than the local speed of sound in the gas there, so things are pretty restricted. We feel all of this in the difference between pumps and gas op semi-autos. Now these mid barrel brakes are an extra big drain on the gas in the barrel and well as applying a forward impulse to the barrel.

Now some other factors do come into play. Ammo in the mag tube has a spring between its mass and the rigid body part of the gun. Once the gun is accelerating aft, the rounds push on the gun through the mag spring, and the ammo imposed forces working to reduce recoil can be no higher than the spring force, which is generally much smaller than the firing forces. If you have a spring that really does crunch down solid just as the last round goes home, the ammo would add fully add its mass to the gun for the first shot. If the spring really does crunch down another say 0.060" under a 200 pound push, the ammo will float during the most important part of the cycle.

So, the amount of ammo in the mag will not generally play much of a role in felt recoil. Gun weight will play a big role. Gas systems will help. And ported barrels will make significant reductions in recoil, resulting in huge differences in shooter perception of recoil.

[George]

Good Stuff Billski,

It definitely explains the last 32nd of seating my mag end plug gets from a full tube on the first shot that I can't get with any amount of pushing with a cleaning rod.

BTW, I just replaced the mag spring that was binding just at 10 shells with a new spring from Grams Engineering and it gives me the same free spring length, same spring force, but I can almost stuff 11 rounds in now. The bind at the 10th round is gone (and I don't miss it) and function is still 100%.

BTW, BTW, this is one of the best fundamentals of function threads going here ;-)

--

Regards,

Edited May 3, 2005 by George

[shred]

The momentum imparted to the gun is due to the change in velocity of the gas during expansion outside of the gun. This is how rocket engines work, only rocket engines have nozzle shaped to coax the flow in supersonic expansion, and thus get even more energy from the flow.

<Pedantic Mode>

Rockets work by throwing mass out the back end, most easily demonstrated with the child- and parent-soaking toy known as the water rocket. The supersonic flow and expansion fruferall is icing on the cake.

</Pedantic>

The remaining explanation is excellent, thanks

[wsimpso1]

Thanks. I am glad that you guys like the explanations. Not that it has much influence on knocking down targets, but it does explain why some of the things we do work and why some other things do not. If you have other gun op details that you want explaned, let me know. I *might* be able to help. And I promise to keep the sarcasm small.

Billski

[Wap wap]

recoil worksheet.rtf

recoil worksheet.pdf

The above sites offer a math worksheet on recoil, pressure on a standard gun model (no porting), in .233 cal. and 20 inch barrel.

[wsimpso1]

Did anybody else read the pages that Wap wap is pointing us at?

This is not what I would call a high example of engineering arts. I can not let this "analysis" lie unanswered, simply because other people who might read this might also think that this is an engineering document that is correct and covers the topic of recoil correctly.

First off, the stream of consciousness style of writing makes reading and interpreting it difficult, but not impossible. The lack of organization and punctuation may benefit writer in that it confuses the reader, but most of us who have a well done description of a topic would prefer that our writing be understood.

Aside from the document being difficult to read, is the physics correct? Sometimes yes, but in many important places, the physics and underlying arguments are not correct… So, let's check out the issues. I will cover them in the order that they appear.

The usual way of capturing the pressure curve of a firearm is to place pressure transducer in the barrel, either at the chamber and reading through the case wall, or in the barrel just forward of the throat. Both work well. In modern firearms, placing of pressure sensors further down the barrel do not demonstrate significant differences in pressure from the breach mounted one. They do serve to tell you of the bullet's passage at each point, but this has proven unnecessary because the bullet passage at the muzzle shows a distinct change in pressure that allows you to calibrate your calculations of drag.

If all that you want to know is the average of soemthing, people educated in statistics will tell you a minimum of eight samples is needed. Likewise, if you want to know something about the variability and distribution of something, 33 is the statistician's minimum number. This is because we have an unbiased estimator of variation called the standard deviation, and it pretty much quits changing after the sample size reaches 33. 100 samples is overkill and produces little information that 33 does not.

The author suggests a number of methods for calculating or modeling pressure data. With real data, who needs a math model? The author then discusses how pressure alone does not describe the ability of the cartridge to do work, and the author is correct, but the simplest method of describing why is not covered. In reality, the area under the Pressure-Time curve is the impulse applied to both the ejecta and the gun while the ejecta is still in the gun. The friction of the ejecta on the bore is frequently neglected due to its being small compared to the other forces, but could be included in a rigorous analysis. Where friction is included, the size of the friction estimate is checked by integrating the pressure*area – drag curve over time once to get bullet travel and checking that travel is correct.

The author asserts that the gas impulse exerts its greatest force when the base of the bullet is flush with the opening of the port or brake. I wonder how the author gets that. The forces driving the bullet are simply the gas pressure applied to the area of the bullet's diameter, and this is at its highest when pressure is highest, when it is back near the breech. Now if the author is discussing the impulse of gas leaving the barrel and impinging upon the muzzle brake, the author appears to have missed the purpose of such devices.

Let's get some concepts squared away.

First, the powder gas of most guns is capable of traveling much faster down the bore than the ejecta is moving when it leaves the bore. If it is going slower than the ejecta , it is no longer pushing the ejecta to higher speeds, and most guns will shove their ejecta to higher speeds if you use a longer barrel. It is possible to have a barrel so long that the powder pressure falls below the bullet drag and see velocities dropping, but that is rare. 22 LR subsonic match ammo will start slowing down after it travels 16" or so in the barrel, and has a very small report, but this is a rare case. Where we have a big report, the gases are capable of going much faster than the ejecta.

Second, momentum is conserved through physical interactions. Momentum of a moving object can be calculated in several ways. m*v and F*t are common versions, both resulting in units of force times units of time, lb-sec or N-s (Newton-seconds). In guns, the gun and ejecta mass have equal and opposite momentum. With friction small enough, a force applied for a certain time will accelerate a mass to a certain velocity. It really is that simple, and an English nobleman named Newton described this stuff pretty well a long time ago. Likewise, if you have several forces, each applied for small times, and you add them up, you can calculate the velocities at the end of each of the times. Extend this a bit and it becomes integral calculus, also invented by that Newton, and coincidentally, by Liebnitz the same summer. They were both working on ballistics too…

So, with the bullet at the muzzle at a certain velocity, we can multiply its mass by its velocity and know what impulse was applied to it, and thus to the gun in the opposite direction. And the mass of the gunpowder has been transformed to gas, with it expanding and traveling at different velocities down the bore and driving the bullet to accelerate. If we take the mass of the powder and multiply it by one half the muzzle velocity of the bullet, we will describe the impulse applied to accelerate the gases and likewise applied to the gun in the opposite direction. This is the state of things with the bullet at the muzzle, but still keeping the gun gas inside the barrel.

Once the buller leaves the bore the gun gases accelerate to whatever velocity they can, adding their impulse to the gun.

Anyway, the author states that the gas impulse is greatest when the bullet is flush with the opening in the brake… Given that we now know that the impulse is the change in direction of the gas flow applied to the brake, the position of the bullet is not terribly important… What matters is that the gasses are being redirected by the baffles, and the resulting impulse on the baffle is forward, opposite all of those other unavoidable impulses, subtracting from the total impulse accelerating the gun towards you.

The author cites that the gases are leaving the gun at the same velocity as the ejecta leaves, in the case of 223 Rem 3300 ft/s. I doubt it. You get a big muzzle report with 223 Rem, and longer barrels produce higher muzzle velocities. I suspect that the local speed of sound at the muzzle is quite a bit above muzzle velocity. the author does appear to have the rest of the physics right on AR15 operation – the reason for the exceptional accuracy of the AR15 is because the bolt and carrier are left alone by gun gas until after the bullet has flow free. Other gas operated guns with pushrods and the like have all sorts of gas system and barrel vibrations disturbing the barrel before the bullet is free. Part of the accurizing process for these guns is figuring out how to minimize the disturbances.

The author suggests that a muzzle device for reduction of recoil is not a brake, but that it could easily be a break… Merriam Webster's Collegiate Dictionary carries its description of brake as "a device for arresting or preventing motion of a mechanism", and "something to slow down or stop movement or activity". Since the device is intended to reduce rearward motion of the barrel, it would seem to me that brake is correct. The author even goes so far as to ask what is braked. Come on now, the gun is accelerated aft by normal unavoidable gun forces, and then it is slowed some by the brake…

In fairness, break is also described with some 34 examples starting with violently parting or destruction, violation, disruption, disclosure of bad news, and so on. While one could describe the redirection and separation of propellant gases to reduce barrel motion in some of these ways, it does seem to me that "brake" fits better, and is a less complicated application of the word to what its job is. Break really is the "wrong word" here.

After this our author starts talking about first, second, and third moments… I have three engineering degrees from one of the better engineering schools in the world, two of them in mechanical engineering and a bunch of Physics and Calculus, and I have never heard force, acceleration, velocity, and distance described this way before, so I had to interpret a little. I believe that our author is saying that the total recoil impulse is less important than the free recoil velocity, and I think that we all agree that a heavier gun generally hurts less than a lighter one firing the same ammo. Work out the m*v of the ejecta, the powder, and the gases out the muzzle and that all equals the m*v of the gun coming back at you. More m on the gun, less v to have to stop on your shoulder. We just proved the obvious...

Then, our author implies that we do not get rocket engine effects from our gun. First the author describes rocket thrust as force in N*s*s. Sorry, it does not work that way. Force is force, and force units are pounds or Newtons. Just go visit http://www.estesrockets.com/Engine_Facts1062.html and look. They cite thrust in Newtons, and oh, there it is rocket impulse in the same units we had earlier of N-s. The way that rockets and jets work is that mass is ejected at a velocity. Same as we have in a gun. That fact that our gun neither has an efficient nozzle nor does it have high fuel/payload ratio does not mean that it is not a rocket, it just means that it is a poor rocket. Since it is not meant to be a good rocket, I do not get bummed out about it.

Our author goes on to cite that the powder to ejecta mass ratios of handguns and shotguns is lower than with a rifle. This does truthfully indicate how much you can do with a brake relative to the ejecta. So we can not do as much with a shotgun. This does not mean that we can not do anything useful with it, just that we can not do as much as say with a rifle.

The author also cites that brakes and other compensators are not used on 40mm AA guns, 16 in deck cannons, and 105 howitzers. Sometimes true, sometimes not. You have to understand that if you fire a 120 mm smoothbore gun on an M1 tank with a brake on it, the blast will not only knock over anybody standing in their station, it will damage radio antennas, and may set off reactive armor. Some armored vehicle guns do use a substantial muzzle brake, but most do not. First off, all of these guns are in recoiling mounts to greatly reduce the forces applied to ground or vessel. In the case of artillery, you do want the guns spades to stay put so that all of the rounds in a barrage will go where you intend. If the recoiling mechanism is not used, the spades would have to be much bigger to keep the gun from shifting around on every shot. Similar mechanisms allow less heavy duty mountings of shipboard guns of many types. Next issue with big guns is that the ground, ship's hull, etc, does not really care about exactly how much force is applied to it as long as we stay below the strength of the parts. And the recuperators are designed to keep the forces to a certain level. Yeah fatigue is in there, too, but that is the essence. But us silly humans, we care about things like how hard it pushes and how fast it recovers from recoil, and we are not linear sensors. If the recoil is just above our limit of where we are comfortable, it bothers us. If it is 10% lower, we do not hurt 10% less, it becomes below our comfort level and is just fine with us. Likewise, if it speeds up recovery by a few percent, it can take recovery inside our ability to notice it, and it becomes what feels like instantaneous to us… We are not machines, and thus we have different requirements.

So, we have found out that our author has his physics more than a little off kilter. So what, you say? I say, that if your model starts off out of shape, you can not count on where it will take you. Garbage In, Garbage Out. But let's follow him through.

The author then gives some hypothetical pressure info, which is a little low on the pressures down barrel, but close enough for demonstration. The author calculates the force on the bullet and plots it, and cites that rockets have different shaped curves than this. So what? As I said above, guns are not good rockets, just that we get some of the same types of effects.

The author then attempts to calculate forces at several places along the barrel, and the author ends up with units of kg^2/s^2*ft/lb?!? I have no idea. Force is pounds or is kg*m/s^2 or N. This mixture of metric and English units looks like nothing that I am accustomed to. Perhaps he was attempting to avoid converting back and forth between m/s and ft/s, but this sort of mixing usually just creates mistakes…

Then the author cites work done in accelerating the bullet to velocity as the integral of force through a distance. Good. This is also equal to ½*m*v^2, which the author solves for v and calculates velocity of the bullet as it travels down the barrel. OK, the author does know how to do some of the math – his numbers are pretty good, but I still do not get his mixed units…

The author then describes how the bullet's acceleration sags while the pressure behind the bullet drops, and how this means that less energy is also available to make the brake work. True, but that does not mean that nothing useful can come from the gas left at the muzzle. As those of us who use them can attest.

The author also cites that the steeper the velocity and kinetic energy (work) curves, the sharper the recoil. What does the author mean by that? The steeper the curves, the greater the forces applied to the gun by the powder gases. Now we know that the greater the forces, the more the gun is accelerated towards us and the more velocity the gun has that we will have to stop… true, and if that is what he means by sharper, I have to agree.

Then the author plots kinetic energy versus velocity, which seems pretty silly to me. Kinetic energy and velocity are intimately related by KE = ½*m*V^2. The deviation from the smooth curve appears to match the number of deviations from a smooth curve in the pressure table at the beginning… GIGO again.

And nowhere does he calculate recoil impulse from driving the bullet and gases to the muzzle, the recoil impulse of the gases accelerating out of the muzzle, nor the impulse from redirecting the gases out the brake… Which would seem to me to be the object of all of these mathematical gyrations. How much recoil comes from the bullet, the gas, and how much can the brake do? The author not only does not do the calculation, he does not even talk about how to do that part of the calculation.

So let's talk about that a little.

When the bullet is at the muzzle, the gases are still under some pretty significant pressures and temperatures, even if they are down to "only" 4000 psi and 1500 F. When the bullet pops loose, the pressure behind the gases will accelerate out around the bullet. The pressures are high enough to cause incredible acceleration, but by some interesting behavior described well in thermodynamics, these gases can not flow faster than the local speed of sound except in some very specific circumstances. Rocket motor and jet engine nozzles actually exploit this to obtain gases at speeds greater than sound… The local speed of sound in a gas is a function of molecular weight of the gases and is very high at high temperatures and diminishes as the gases expand and cool (adiabatically). Even at the muzzle, the local speed of sound exceeds the ejecta velocity in most guns, as is obvious in high speed photographs of the bullet with glowing gases ahead of it for some distance…

So, how much impulse is generated at the muzzle? Well, let's go back to the math for impulse – m*v or F*t… If we have a simple muzzle, we can calculate what is going on just as the muzzle is opened. We divide the gas in the barrel up into many small packets, and we know the mass of each packet, how fast it is going, what each packet's temperature is. We can also calculate the momentum of each packet as the muzzle is uncorked. Then we expand all of the gas out of the muzzle, knowing that each packet of gas accelerates to its local sonic velocity just beyond the muzzle. So we can compute the change in momentum of each packet of gas between when the muzzle was uncorked and when the gases are all expanded out. In a simple muzzle this impulse is computed by summing up the change in momentum of the gases to give the muzzle impulse.

Add a brake to the muzzle, these gases still accelerate out of the bore, but shortly after they get out of the bore they are redirected sideways or upwards by the baffles of the brake and their momentum is changed again. This impulse is primarily forward, opposite the one that has been applied so far. There may also be ports directing gasses upward to push down on the muzzle. And the impulses are always the sum of the changes in velocity times the mass of the little packets of gas.

So, while I did not do the calculations, I have told you how it might be done. While agree that the brake is a device.

Billski

[George]

Hi Billski,

Thanks for the analysis. I perused it as deep as I could and felt that there was a possible problem, but didn't have the engineering depth to noodle out the inconsistencies.

Your description of the process is dead on as far as my understanding goes. You da man!

I said it before and I will say it again. This is the best "in depth" technical thread going on the Forums ;-)

--

Regards,

[shred]

Good explanation..

I also like Hatcher's treatment of recoil in Hatcher's Notebook. It's absolutely amazing how many internet-questions like this are answered in there.

[wsimpso1]

Hatcher's Notebook is great.

Glad you like the responses...

Billski

[wsimpso1]

Oh man, I just detected a couple of omissions and wish to correct them. The typos I will leave be.

First, you integrate the total force (gas pressure*bore area - ejecta drag) once to get velocity and twice to get travel. And you can check your calculation by seeing if you indeed get muzzle velocity at the muzzle, and you indeed get the travel down the barrel when you get the place where travel should end.

Next omission. Tanks and artillery pieces have skipped brakes for other reasons too. There are driving bands on conventional shells that are supposed to stay on the shell but that can come off as the shell clears the muzzle. If there is a brake on the muzzle, the shell's flight will be grossly disrupted by the band snagging the brake, and accuracy can be terrible, to the point of it falling on friendly forces. Then there a sabot rounds, where the sabot is discarded from the rest of the round in flight shortly after leaving the muzzle. It is important that the sabot come off of the round without disturbing it or, again, the accuracy will be none-existent. A brake will interfere with the sabot. Then there is danger to local personel if debris is residing on the brake when the gun is fired, launching the debris locally.

[George]

Never thought about the sabot tank rounds having trouble with a brake.

I wonder if shotgun wads and shotcups get disturbed passing through a brake located at the end of a shotgun barrel. Slug accuracy degredation?

Interesting....

Thanks again,