Advanced Marksmanship Recoil and muzzle breaks, some physics

[CoryT]

At Justin's request, here's a new thread from the free recoil POI discussion that went off on a tangent to the physics of recoil itself.

Justin maintains that the jet effect of the powder gasses leaving the muzzle is the cause of recoil, or at least a primary component of the recoil force.

I do not believe that it is more than a VERY small part of the recoil force.

It is true that the bullet leaving the barrel is like popping the cork out of a bottle. Whatever pressure there is in the barrel is instantly released from a small diameter hole. That pressure lasts only a few milliseconds, since there is only a small volume of gas, basically the weight of the powder charge.

That small mass, even under a very high (40K-50K psi) pressure, over such a short time interval, disposes very little energy. Compared to moving the weight of the bullet over 20 to 40 ms, the recoil force of the gas jet is negligable.

Why then, one asks, does a muzzle break reduce recoil? Well, it's not due to redirecting the gas jet. It is using the pressure and mass to work against a surface in the same way it moved the bullet, in this case the surface is attached to the gun. By impacting the baffles of the break, the gas is trying to drive the whole rifle foreward just like it drove the bullet. How well that works depends on how much of the gass can be forced onto the baffle surfaces.

 

[sinister]

Re: Recoil and muzzle breaks, some physics

One of the better texts that explains the technical workings of firearms (particularly muzzle brakes):

 

[bohem]

Re: Recoil and muzzle breaks, some physics

Cory-

I didn't delve into the other thread in depth but I did note a couple comments all dealing with energy and conversion of solid propellant into expanding gasses.

I didn't see anybody mention the fact that energy is not conserved.

The conservation of momentum approach is applicable, conservation of energy is not.

Based upon the mass fraction of the 2 moving parts and based upon that approach the recoil momentum balance is appx 38% induced via propellant gas expulsion.

Also,
Where does your stated value in this time interval come from?

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">...Compared to moving the weight of the bullet over 20 to 40 ms...</div></div>

Based on QuickLoad simulations and pressure traces the bullet exit time from the point at which the primer is struck is under 5ms, in fact (depending on barrel length), likely less than 1.5ms


Based upon spark shadowgraphs and Schlieren photography it is known that the Mach Disc on a high velocity rifle round leaves the barrel in excess of Mach 5 and depending upon the bullet geometry can be much faster than that.

Due to unity in the system the propellant gasses are not moving faster than the bullet in the bore, however upon the bullet breaking the muzzle that jet effect over the course of less than a millisecond both releases the bullet (and the substantial portion of the mass being expelled) but also allows the gas to rocket from the muzzle. This includes the gas still in the bore as the bullet breaks seal with the muzzle and everything in the bore gets to accelerate down the barrel too.

Let's ignore the brake for a second and discuss the recoil impulse without it, then add it back in for clarity:

Energy is not conserved and therefore a momentum balance equation is the way to consider this discussion.

The bullet leaves with a given momentum (mass*velocity) as well as the expanding gasses.

The gasses accelerate down the bore as the pressure drops upon bullet exit and gain a significant bump in velocity (remember the mach disk quickly passing the bullet during shadowgraph experiments).

Let's assume, for simple numbers that the propellant gasses leave the barrel at Mach 5 or appx 5625fps.

The 338LM has some easy numbers to work with (let's just keep this in mixed units for making the algebra easy to follow):

300gr bullet at ~2750fps
~90gr of propellant gas at 5625fps

The momentum sum of those two pieces is
m_bullet*V_bullet + m_gas*V_gas

300gr*2750fps + 90*5625fps = 825,000+506,250 = 1,331,250

The propellant momentum upon release at the muzzle is 506,250/1,331,250 %, appx 38% of the recoil impulse


While it may not be the primary force, it is a substantial fraction.


I agree with the brake explanation.

 

[CoryT]

Re: Recoil and muzzle breaks, some physics

All true, but the example includes the powder charge weight at bullet velocity as part of the jet itself, when I've already counted that as part of the recoil force.

The accelerated portion of the gas is what one would consider the 'jet effect'. Clearly this is only a rough approximation, I don't have the math to get any closer.

300gr*2750fps + 90*2750 + 90*2875fps = 825,000 + 247,500 + 258,750= 1,331,250

Which makes the jet itself more like 19% of the force. that's actually more than I would have expected, and I am corrected, it's more than 'negligable', but still not a signifigant portion.

I neglegted to consider the acceleration of the gas on the bullet departing.

Also, an interesting point to look at is how much of that Mach ring of gas is actually working against the firearm. A fair bit of that energy is actually being expended into the air and dissapated as sound. Without a nozzle to contain and focus that gas, how much actually presses the firearm itself to the rear? Certainly the whole of the muzzle area is affected, but beyond that, how much does that expanding ball expend the energy onto the firearm?

 

[bohem]

Re: Recoil and muzzle breaks, some physics

I misread what you posted and thought you had discounted the mass of the powder, I see what you meant before.

Based on that, ~ 20% would be the other component that I was pointing out.

It is a mass based equation, for the same reason that a rocket motor produces thrust in a vacuum. The rocket thrust is based on mass efflux out the nozzle and the velocity at which it leaves the nozzle.

The nozzle is there to increase the exit speed of the mass flowing through it.

 

[CoryT]

Re: Recoil and muzzle breaks, some physics

True, but it can also provide a working surface similar to the muzzle break. For example, my Vickers MMG has a muzzle cup which increases the recoil impluse by that gas pressing against it. Without the cup in place, not enought force to run the gun.

In a rocket nozzle, the acceleration of the gas occurs while still contained within the motor. In the rifle that increase in velocity takes place outside the vessel, so not all the work is being done against the rifle, much is being done against the air

 

[bohem]

Re: Recoil and muzzle breaks, some physics

OK, I'm not sure what your point is though. I thought the discussion was regarding what input the propellant gasses had in terms of felt recoil and as we discussed above they're not insignificant.

I'm not arguing with your explanation about how the brake works, just that the recoil impulse from propellant is not " a VERY small part of the recoil force", as I don't call even 20% insignificant. If it was 2% I would agree, but 20% is still pretty substantial.

http://en.wikipedia.org/wiki/Rocket_engine

 

[CoryT]

Re: Recoil and muzzle breaks, some physics

My point is that the acceleration, which is getting us the extra 2875fps and that 20% is not taking place inside the rifle, but in open air.

In the rocket, the gas is accelerated to it's exit velocity within the chamber of the rocket motor and exit nozzle, where the force is therefore transmitted to the rocket.

In the rifle, the gas accelerates to Mach 5, AFTER leaving the barrel, due to unrestricted expansion. What is not clear to me is how the force is transmitted to the rifle.

To me, I don't see the differance between this expansion into open air and an explosion, like a firework of 90 grains in weight detonated right at the muzzle.

How much of this explosive force is directed into the firearm beyond the flat plate area of the muzzle? I can't see how more than a small fraction of that 20% is transmitted to the firearm as recoil force.

 

[bohem]

Re: Recoil and muzzle breaks, some physics

It is happening in the barrel as well, as soon as the bullet breaks the crown the gas expands through the whole column of gas and accelerates, including everything from the case web to the crown. Conservation of volume requires that to happen. You don't have a jump discontinuity at the muzzle.

 

[The Mechanic]

Re: Recoil and muzzle breaks, some physics

If the gas jet was the only or at least most effect on recoil, you would never get a 1911 to unlock upon firing.

 

[CoryT]

Re: Recoil and muzzle breaks, some physics

Now that chart makes sense to me. Note the large protion of the recoil force is generated well before the bullet leaves the barrel. Note also the duration if the impluse compares to the small, short duration bump from the gas exit.

Thanks Mechanic for locating that!

 

[TiroFijo]

Re: Recoil and muzzle breaks, some physics

Cory, the momentum equations bohem shows and explains are very well proven in many experiments and tests with free recoil guns on a test cradle.

For the 338 LM load discussed the contribution of the accelerating gas to the recoil impulse is in the order of 38% of the total amount, very significant.

For handguns is in the order of 10-15%. Magnum handguns about 20%.

For the M80 7.62 NATO Ball is about 31%, for the 5.56x45 about 35%.

For artillery about 50%.

With the free recoil tester the acceleration of the gun with and without brake can be measured. The muzzle brakes reduce the recoil by diverting some of the escaping gas, either to the sides (zero value) or to the rear (negative -pull- value).

 

[bohem]

Re: Recoil and muzzle breaks, some physics

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: CoryT</div><div class="ubbcode-body">Now that chart makes sense to me. Note the large protion of the recoil force is generated well before the bullet leaves the barrel. Note also the duration if the impluse compares to the small, short duration bump from the gas exit.

Thanks Mechanic for locating that! </div></div>

The short duration shows that the work done is lower during brake operation than while the bullet is being accelerated down the bore.

Work = Force * Distance

Since the time scale can be directly correlated to the distance traveled by the bullet and the rifle then the brake's Work Done is easily related to the integral of the curve that Mechanic posted.

ETA: Hit "post" too soon.

The end result of my comment is to illustrate why even with a brake the rifle still maintains some felt recoil on there.

Nice plot, I couldn't find it when I was looking the other day.

 

[CoryT]

Re: Recoil and muzzle breaks, some physics

Tiro, understood, but I was looking at just the jet effect, not the gas as a total. that's certainly understood to be part of the accelerated mass.

I've somewhat understated the acceleration after the bullet leaves, which is actually about 19 percent of the force, where I expected only 4 or 5. Even at that, looking at the duration and magnitude as displayed on the chart, I doubt many would notice it's absence as a signifigant reduction in felt recoil.

The experiment would be shooting with no brake, then a break that balanced only the jet effect. That would be pretty hard to setup, and I'm not sure it would have any value except curiosity.

10 or 20 percent of a large short duration impluse is probably tough to note, kind of like the differance between a 200gr bullet and a 300 grain bullet. Is it there? Certainly. Could I tell in a blind test? I doubt I personally could, others may be more discerning.

 

[TiroFijo]

Re: Recoil and muzzle breaks, some physics

Cory, Uuups!! sorry I missed that part...

I agree on your assessment, where roughly half of the recoil impulse due to the gas is experimented after the bullet exit.

And also in the brake explanation.

I think with a test cradle and accelerometer the effect of the blast after bullet exit could be clearly seen.

 

[The Mechanic]

Re: Recoil and muzzle breaks, some physics

I am sure you guys have already guessed that my graph is a .50BMG so obviously recoil for lighter rounds will differ. Also a .50 can make a butt load of gas for a brake. Pun intended.

 

[Massoud]

Re: Recoil and muzzle breaks, some physics

Gents,
Good info so far, I'm scanning all my muzzle brake/recoil papers to add some quotes/cites.

One thing I wanted to add is that first, that's a great graph, but also, we need to see one of a rifle without a brake. Recoil begins to rise at gas exit, then drops abruptly and goes into the negative G territory. From where they mark "powder gas exit" to where they mark "powder gas hits brake" there is a drop in positive G's, but the time lapse is around .1 ms and it's already in the Negative G's by the time they mark "powder gas hits brake". While an interesting chart, I think it has limited relevance relative to a chart of an unbraked rifle.
More later,
Justin

 

[The Mechanic]

Re: Recoil and muzzle breaks, some physics

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Massoud</div><div class="ubbcode-body">Gents,
Good info so far, I'm scanning all my muzzle brake/recoil papers to add some quotes/cites.

One thing I wanted to add is that first, that's a great graph, but also, we need to see one of a rifle without a brake. Recoil begins to rise at gas exit, then drops abruptly and goes into the negative G territory. From where they mark "powder gas exit" to where they mark "powder gas hits brake" there is a drop in positive G's, but the time lapse is around .1 ms and it's already in the Negative G's by the time they mark "powder gas hits brake". While an interesting chart, I think it has limited relevance relative to a chart of an unbraked rifle.
More later,
Justin</div></div>
I must respectfully disagree.
To me it shows that you have at most a 1/5th increase in recoil as compared to recoil energy while the bullet is still in the barrel. This is also a .50 with a 32 inch barrel and should have the highest amount of useable braking gas. Also note that as pressure in the barrel decreases rapidly from complete combustion and cooling of gasses the amount of time that the jet of gasses are responding to the movable air mass in front of the barrel is small compared to the actual use of some of that gas to impact the non movable (compared to actual rifle) baffles to "pull" the rifle forward, with an amount of high speed gas that is very dependent on brake design, velocity of gas, volume of gas, and time said gas has to impart a force on the brake.

You need to break out the thousand page QL book (if you have Quick Load) and give it a read. It has some amazing info if you can really put yourself into it. You can see the actual acceleration is highest from a dead start. Not to say that the acceleration stops just that it is the highest according to QL as the pressure peaks. I REALLY have a hard time putting my head around significant added recoil from escaping gas from the end of the barrel, according to what I have read. YMMV

 

[Massoud]

Re: Recoil and muzzle breaks, some physics

I'm not sure how you see that in the chart. Peak force upon gas exit looks to be at or just above 200g's. Peak force at the .5ms mark is labeled as 540g's. Just from that alone, muzzle gas exit is producing over a third of the recoil force of the bullet-in-barrel force.

All of that is moot, however, as the muzzle brake interupts our force diagram so we don't really get to find out what happens after the bullet exit sans muzzle brake. So the chart is interesting but again, we need the chart shot without a brake.

Again, maybe you missed some of the examples I posted in the other thread, but it's not hard to envision the release of pressurized gas causing propulsion. One example I gave was the little race cars that run on a pierced CO2 cartridge.

I may have ascribed too much force to the exiting gas by saying it was the majority of recoil force (other thread) because I looked at the brake from a purely reductionist standpoint, i.e. redirecting forces that would have otherwise contributed to recoil, instead of a positive mechanism, i.e. actually creating negative g's, pulling the rifle forward, that the graph suggests. However I would still like the original source for that chart and all the background info as well as the chart without a brake if there is one.

I found the equations in a gun design book that I have here. It's like 3 pages worth of stuff so I can't just post it all but I'll put it here little by little. It will take a bit cause I've been pretty busy lately.
Justin

 

[cali_tz]

Re: Recoil and muzzle breaks, some physics

an interesting youtube video, showing alot more flex of various components than I would have imagined. It's a 50BMG, and maybe its a poorly designed rifle, but it sure moves around alot. Also, the muzzle flash at the end precedes the barrel whip... could help the discussion here.

<object width="425" height="350"> <param name="movie" value="http://www.youtube.com/v/s5pVya7eask&feature=related"></param> <param name="wmode" value="transparent"></param> <embed src="http://www.youtube.com/v/s5pVya7eask&feature=related" type="application/x-shockwave-flash" wmode="transparent" width="425" height="350"> </embed></object>

watching this one next, also most of the barrel flex comes after the bullet appears to leave the muzzle.

<object width="425" height="350"> <param name="movie" value="http://www.youtube.com/v/ozyw84Swmb4"></param> <param name="wmode" value="transparent"></param> <embed src="http://www.youtube.com/v/ozyw84Swmb4" type="application/x-shockwave-flash" wmode="transparent" width="425" height="350"> </embed></object>

 

[bm11]

Re: Recoil and muzzle breaks, some physics

UH, you think the Accuracy International AS-50 is a "poorly designed rifle?"

 

[cali_tz]

Re: Recoil and muzzle breaks, some physics

I said 'maybe', and in any case, I don't have an opinion on AI other than my perception is they are a top brand. The amount of flex there seems like it would be almost destructive over many firings.

edit: reviewing the 50BMG video, I am amazed at how much that S&B scope flexes... I need to take a similar high speed video of my 338LM...

 

[chain]

Re: Recoil and muzzle breaks, some physics

How do you guys do that shit?? I try to learn those equations and my brain slips downstream. I am sticking to the framing square. My hat is off to you.

 

[ctressler]

Re: Recoil and muzzle breaks, some physics

I have a hard time believing that 38% of the felt recoil is induced via propellant gas expulsion.

That spike in the graph where the bullet leaves the barrel, is ~40 Gs, so that's less than 10% of the total Gs

The gas pressure on the crown is proportional to the cross-sectional area of the crown. I've shot two rifles one after the other in the exact same caliber with the same load and nearly the same weight, and the recoil was the same even though the crown of one was nearly have the area of the other.

Just my .02

 

[noname]

Re: Recoil and muzzle breaks, some physics

the recoil equation contains the powder charge as part of the ejecta, but doesn't contain the parameters we need so switching to a thermodynamic model helps, also the bullet is not a solid mass . The amt. of recoil contributed would be the wt. of the ejecta mass minus the powder charge if the system were 100 % efficient. The amt. of force and work the gas does against any surface area will only depend on that surface area. The remaining kinetic energy will not be transferred to the device, but instead dissipated in a more less spherical fashion as the pressure gradient decreases to atmospheric levels. The conservation of momentum dictates that the small mass molecules must be accelerated to some value to balance (usually around 4000 to 5000 fps) the net energy equation. This is the amt. of force or work usable if the system were 100% efficient, not the 10 or 15% that is more probable. This force is the pressure x the surface area, and the work is the integral of this force. In short distances the force (newtons) is usually about 3 orders of magnitude greater than say 16 inches down the barrel in a 20 inch ar as an example.
By definition the device does not "brake" the gun unless a vector force is acting in the opposite direction. (although it is breaking gas) and this of course depends on the angle of the baffles and their surface area and in this context devices that are not angled are not brakes. Large parachute or sail devices such as JP claim better utility by this principle. Little if any comparison is done comparing the differential decrease in recoil made by increases of weight to the device against differential increases in surface area of the device.
Analogies using co2 containers or pop the cork examples are really good "pictures" of how the expanding gases contribute to the muzzle flip more than an example of jet effect. Its an impulse not thrust and not comparable. also jets and rockets are pushing against other molecules not a "sold" device. (because of their size the efficiency is decreased in simply heating up the atmospheric gas molecules.)