ELR optimization theory

F

free_rider_151

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Howdy everyone! I'm new to posting here. I've been reading this forum for a few years now and I think it's the best place to find a good average of information.
I have been shooting a 300 rum for the last 3 years or so. Thus far I had only taken it to 700 yards. I was uneasy about the stock remington action so I decided to have it worked over by Montour County Rifles. I got it chambered in 338 Edge and I am eagerly awaiting it's arrival next week. I am an avid reloader and have done smith work on a number of bolt actions, semis, and pistols. I work for a company that measures, scans, and 3D models anything you can imagine. Now that you know a little bit about me and my background, let’s get into the details of my theory.

Extreme Long Range Cartridges (henceforth ELRC) follow a set of linear characteristic factors. While there are some constants, each ELRC has a progressive yet predictable change in dimension from one chambering to another.
Let’s take a quick look at internal ballistics for a moment and define the primary characteristics of the reaction involved in burning rifle powder.
When the firing pin strikes the primer it ignites the primary explosive and creates a very high velocity shockwave that propagates through the flash hole and into the ELRC. This shockwave is complimented by extreme heat and pressure that in turn ignites the rifle powder. The point of the rifle powder ignition is in the most rearward end of the ELRC and propagates in a semi elliptical shape down the length of the ELRC. This action of deflagration creates a wave of pressure and heat.

For my first linear characteristic element, I will attempt to show how a solid rocket motor is analogous to an ELRC.
In a solid rocket motor you have three parts:
1. Ignition Bulk Head (farthest left end of the picture below.)
2. Fuel Grain
3. Nozzle

epdwg1.jpg

ELRCs have the same general layout and principal model of operation as that of a high power solid rocket motor.
Let’s look at the point of ignition.
On both the motor and ELRC, the point of ignition is opposite the nozzle end.
Rocket motor: The reason for ignition at the top of the motor is due to the considerably faster rate at which the propellant grain is fully ignited. This is because the high pressure/high temperature gases are only able to escape through the nozzle of the motor, therefore, the flame channel burns downwards, not upwards.
ELRC: The point of ignition located in the rearward most end is due to simplicity of adaptation. However, later I will explain why this characteristic is so important to future ELRC development.

Let’s look at the propellant charge.

Solid rocket propellants burn at similar rates as compared to slow burning rifle powder.
(This characteristic only applies to cartridges filled to 90% or more.)

Rocket Motor: The propellant grain is the fuel that is consumed in the combustion process to produce the high-pressure gases that propel the rocket upward. The fuel burns slowly and typical KNO3 motors maintain a pressure of around 3000 PSI in the motor. To successfully make a rocket fuel burn and hold a set pressure, you have to regulate the surface area of the burning grain. As you can imagine, there is no way to “throttle” a burning hunk of propellant because it is made with both the fuel and oxidizer in it. They will burn underwater, or in space. Therefore, since there is no effective way of controlling how much of the grain is burning, we have to get a little more creative. As a rocket fuel grain burns, it is also eroding and flowing out into the atmosphere. Most high power rocket motors use a Bates style fuel grain. This is a tube made of fuel with very thick walls. It will burn on the top face, bottom face, and on the inner diameter of the grain. As the grain burns, the inner diameter grows. This increases the surface area. However, while the inner diameter is eroding and gaining surface area, the top and bottom are also eroding. This shortens the overall length of the grain; reducing the length of the inner diameter. This makes the grain burn a constant surface area, thereby keeping the internal motor pressure stable, and the thrust curve is therefore more linear.
ELRC: The powder is burnt in an elliptical wave front that moves down the length of the cartridge. Not all of the powder is burnt in the cartridge however. Because the wave is creating pressure at the rear of the cartridge, this pushes the remaining powder against the projectile and pushes it out of the cartridge. As the wave front pushes the powder and projectile down the barrel, the powder is consumed. Because the powder is burning in a single wave plane, the surface area remains constant with the exception of the change of the diameter from body to bore.


Let’s look at the nozzle/neck:
Rocket motors and ELRC’s have a divergent cone shape that plays a significant role in performance.

Rocket Motors: The high-pressure gases produced by the consumption of the propellant create a subsonic flow toward the exit/nozzle. When the gases reach the nozzle, they are accelerated by the convergence of the nozzle. The gas velocity reaches several Mach numbers in the smallest area of the convergent section. As the gases exit the convergent section, they expand to many times their original volume in the divergent section of the nozzle as they are released to atmospheric pressures. It is this expansion in the divergent section of the nozzle that produces the vast majority of the thrust on the rocket.
ELRC: The cartridge has a cylindrical area known as the body, followed by a convergent section known as the neck. The neck angle plays a large role in the efficient burning of the powder. I will explain this more later.


Design characteristic similarities

When firing your gun, the velocity of your projectile is directly related to the pressure and velocity of the propellant gases. If you could imagine your gun as being a rocket motor with a cylindrical section between the convergent and divergent section, you can see how rocket motor design theories can be applied to optimizing ELRC. The one limitation to this is that the rifle powder is not burned while only in the containment of the cartridge. This can create issues with optimizing neck angles due to an inconsistent burning surface area during the cartridge to bore diameter transition.
The inherit similarity in ignition position affords us the luxury of easy development of solid single grain rifle propellants. The physical restriction of rifle powder to the area of the cartridge allows us to take advantage of controllable burning surface area (constant or adaptive pressure transient) and convergent nozzle gas acceleration. In general, rockets reach flight speed and hold somewhat steady at a velocity until the grain becomes structurally unstable and begins to burn out. This requires a constant pressure to avoid detonation during flight. Both rifle powder and rocket fuel burn at a rate that is proportional to the ambient pressure. This means that if a rocket nozzle is too small or a rifle bore is too small, it will build pressure exponentially until it exceeds that of the containing vessel (rocket motor case/rifle chamber). I have witnessed this first hand from 3 feet away when a kno3 rocket motor detonated at upwards of 150000 psi. Lots of blood and a few stitches inevitably followed.
In a rifle however, as the bullet is accelerated down the barrel, the volume for the expanding gases increases proportionally with the projectile velocity. This means that a constant propellant burn rate creates a downward sloping pressure transient. This, in effect, means the projectile acceleration slows down proportionally to the distance from the throat.
With this in mind, it would be advantageous for the design of an ELRC to incorporate an accelerating rate of propellant consumption to make projectile acceleration constant. I have tried several different experiments with this, but thus far, none have been acceptably safe or effective. In doing research on military experiments and development of current munitions, I have come up with a reasonable solution that is tried and currently in use across the world. I will discuss this in summary at the end.

The next linear characteristic design element is the optimization limits of ELRC’s

All ELR rounds have an optimum design that is fundamentally defined by the volume of propellant in the case. This means that no matter what cartridge you are firing, there is a set of design characteristics that is proportionally dependent on powder volume. Let me explain this. If you look at the 300 rum in performance, you will find max velocities around 3400 fps for light bullets and 2800 for the heavy bullets. If you were to balance out velocity with mass energy storage in the projectile, you would find an optimum weight bullet that defined the range usage of the cartridge. As a quick note, heavier Is not always better, as some would believe, however, mass does maintain velocity down range. This cartridge has now met its optimum design and cannot perform any better. Now we will look at a round that out performs the 300 rum; 338CT. This case has additional capacity and therefore more energy available for acceleration. If you were to optimize this cartridge with the perfect bullet, you would find a relationship between powder volume and bullet mass with respect to the 300 rum. This proportional relationship between powder volume and projectile mass from one cartridge to another, allows the design of ground breaking cartridges that are based on currently optimized designs. In effect, one could use these relationships to “scale” current rounds to any range capability they desired.

Optimization of current cartridges with current technology
Take a quick look at a tank cannon. The M1 Abrams is armed with a Rheinmetall 120mm smoothbore cannon. This cannon is capable of 5200fps and an effective range of 4400y-8700y (depending on the load). If you scale this cartridge down using the previously discussed relationships, you would find a massive discrepancy in useable range. This is where my discussion of the similarities of rockets and firearms comes into play. Tank rounds have a flash tube that the ignition flame propagates thru. This creates a cylindrically expanding surface of burning propellant. Because it burns in an expanding cylinder, the volume of expanding gases grows exponentially. This exponentially increasing volume of gas creates a constant acceleration throughout the length of the barrel. Unlike conventional ELRC’s the tank projectiles accelerate to a higher final velocity with respect to propellant volume. Optimization of ELRC’s with a flash tube could theoretically increase the useable range of the cartridge.
The other aspect that effects the efficiency difference in tank rounds is that the propellant is for the most part (from what little I know) contained and burned in the cartridge. This allows the subsonic propellant gases to be accelerated in the convergent bottleneck section to bore velocities high enough to achieve 5200fps+. Incorporating fixed propellant in ELR rounds will not only effect a higher muzzle velocity, but will also reduce fouling. When the powder in conventional ELRC’s is burned down the bore, it deposits carbon and binding compounds in the rifling. This fouling can be minimized by the extreme temperatures exhibited at the convergent bottleneck of the cartridge. Because of the flame pressure front burning in a radial direction, the binding compounds would be more prone to affixing themselves to the cartridge wall. This will increase barrel life, aswell as increasing the intervals between cleaning.

In summary
I am theorizing that once a round is optimized with current tank round technology, it can be effectively “scaled” to any desired size needed to reach a specific target range.


Ok, so I’ve been writing this for the last 5 hours… so I’m getting tired and lazy. Hence the 1 sentence summary.
Please correct me on any facts I may have wrong. I’m no expert on this, so there are bound to be flaws in my logic. If you have any insight into my theory, please speak up. I want to begin development of an extremely efficient scalable round for elr. Thanks for sticking with me and reading this…. If you made it to the end, you have a longer attention span than me…..
 
I tried to read it all, but most is way beyond my mechanics level engineering. But sounds cool. I have wondered why no one has developed a smooth bore fin stabilized sabot for an ELR platform, but I imagine since I can reach out beyond a mile with my 300WM there isn't much of a need for it.
 
So just for a good ol boy summary: You're proposing using finned/saboted projectiles, smooth (no rifling) barrels, and fixed propellant for ELR cartridges?

If so, here's an article on a laser guided finned projectile: Laser-Guided Bullets: Sub-MOA at Over a Mile - Guns.com
I'm far from an expert on tank rounds, but how do they measure and obtain accuracy at those ridiculously long ranges? Are their projectiles guided? If not, how will the accuracy of this technology compare to a 338LM or 375CT at 1000yds, a mile, etc.?

I think the most difficult thing would be the fixed (as opposed to powder) propellant in a standard rifle case. I can't think of a way to reload a case with fixed propellant as an individual which really diminishes the value.

Or maybe I'm over thinking this. Dammit my BC powder stash is running low...
 
Ok I guess I didnt make that clear enough... im not talking about designing a fin stabilized round, rather I was pointing out that the rifle powder burns similarly to rocket fuel except that rocket fuel is fixed where as rifle powder is not. If the rifle powder was fixed, you could use the bottleneck of the cartridge as a sort of nozzle to further accelerate the gases that push the bullet out of the bore.
On the note of the fin stabilized round, it is possible to fire a specially designed round out of a certain suppressors. The gun would have to be custom throated to allow this round because it would need to be longer than the first two baffles.
Tank fin stabilized du penetrators are not guided. They are extremely consistent in loading and the ballistic comps are insanely powerful. Also doesnt hurt to fly at 5500 fps with a bc thats gotta be over 150. The penetrator its self is like 27lbs.

Sent from my SM-G730V using Tapatalk
 
You mean stuff like this:

935153_695788070444719_1280273634_n.jpg


We're starting to see technology from other areas creep into the ELR Field. These have your cone, hollow underneath as well there is a bit more to the tail than found on standard bullets.

Also it is being combined with a ceramic paste to help with throat and bore wear.

1493215_691985867491606_753900806_n.jpg


This design along with the Gain Twist Barrel I am using should allow me to push this harder than traditional bullets of the same or similar weight.

I completely agree, heavier does not mean better. Take the 300gr bullet in a 338LM, it's not being pushed hard enough by this round to take advantage of the weight. So if you want the very best out of a 338, you want to stick closer to the 285gr weight instead of stepping up to 300.

But with this, the driving bands, paste, gain twist all working together we should see some better results. Testing has just started up with this new design, and weather has been a factor. But we are moving forward. (By "we" I mean the designer, I am just shooting them for results downrange)
 
Ok I guess I didnt make that clear enough... im not talking about designing a fin stabilized round, rather I was pointing out that the rifle powder burns similarly to rocket fuel except that rocket fuel is fixed where as rifle powder is not. If the rifle powder was fixed, you could use the bottleneck of the cartridge as a sort of nozzle to further accelerate the gases that push the bullet out of the bore.
On the note of the fin stabilized round, it is possible to fire a specially designed round out of a certain suppressors. The gun would have to be custom throated to allow this round because it would need to be longer than the first two baffles.
Tank fin stabilized du penetrators are not guided. They are extremely consistent in loading and the ballistic comps are insanely powerful. Also doesnt hurt to fly at 5500 fps with a bc thats gotta be over 150. The penetrator its self is like 27lbs.

Sent from my SM-G730V using Tapatalk

Where the rocket analogy goes south is a nozzle trades pressure for velocity. In the case of supersonic flow, very inefficiently at that. If you extend the rocket nozzle with a tube and plug it with a bullet the pressures on either side of the nozzle will be too close to produce supersonic flow.

One misconception in your dissertation above is that the flow in the neck of the nozzle is many machs. Supersonic flow can not be produced in a converging nozzle. Mach 1 will be achieved if the area and pressure ratios are sufficient. In the case of the rocket, the flow in the converging nozzle will be above the speed of sound for normal ambient temperatures, but it will still be at or below Mach 1 for the propellant gas temperature. The diverging section of the nozzle is required to produce the supersonic flow. This is important because we get that the only way for the propellant gas to keep up with rifle bullet velocities is by heating it. If you want big velocities, you need big temperatures as a first condition. That's probably why that barrel only lasts 50 - 250 rounds. Having enough propellant mass to keep the pressure high enough to keep the bullet accelerating without exceeding the actions peak pressure limitation is the next problem.

I did like reading about that gun. If you scale the bullet back to 30 caliber, it's only 36 grains. It's insanely long and made from a material 1.7 x as dense as lead. The SD is through the roof.

As a simpler exercise, I multiplied the weight and BC of a 223 90 grain SMK by 1.7 and ran it through Quickload on a 300 RUM. Taking some liberties with pressure got it to 3500 fps. PM ballistics calculated it to go transonic at 2200 yards at sea level. The stability also goes through the roof. So if you made a copy of that SMK out of depleted uranium and a 308 sabot, it'd be an interesting round.

If you were to extend that concept to shapes like the Lowlight round things could get really crazy. The thing might even transition.
 
Lowlight, where did you get the gain twist barrel? I've been wanting to try that. Let me know how it works out.

OF&B you are quite correct. What would happen if you had little or no friction between the bullet and the bore? The only force acting on the pressures would be the mass of the bullet. Actually after thinking about that, it wouldn't matter unless the bullet was already traveling at mach1.
Does anyone know where to get depleted uranium? I have always wanted to machine some rounds from it.
 
Interesting thought experiment. Have wondered before if a flash tube in a large magnum caliber will help to keep the propellant inside the case instead of traveling down the barrel (and eroding the throat). Maybe a way to get longer barrel life?

The main problem limiting muzzle velocity is that the action has a PEAK pressure limit (due to mechanical limitations), and the ‘pressure trace’ grows, peaks and then decays fairly quickly long before the bullet leaves the barrel, especially on long 28-32” rifle barrels. A web search for pressure trace pictures show it peaking at 30 to 50 microseconds (0.3 to 0.5 ms) after ignition (for 6BR, 30-06, 308 calibers, pistol calibers are very different of course). Pressure trace is simply the profile (plot) of chamber pressure vs. time, and can be measured with a low cost strain case glued to the action, and connected to high speed electronics to record the pressure sensor signal. Or you can invest in a more expensive but more accurate piezoelectric pressure sensor. [BTW: The strain guage option is within reach of most reloaders.] This gradual drop in pressure that occurs after the peak pressure point is ‘lost opportunity’ in terms of achievable muzzle velocity.

Also barrels beyond 36” does not buy you much additional speed, so not worth it with current designs.

If we continue with the thought experiment (for the fun of it): Imagine we had a way to reliably ignite an additional (small) volume of powder say 50 microseconds after ignition, so just after peak pressure is achieved, so you could boost pressure a second time. What kind of rifle design would be required to speed up a 750 gn 50 cal bullet in a BMG action to over 4,000 fps? Try a 40” barrel? Maybe add a small (like 223) cartride loaded with a faster burning propellant (and no bullet) that sits in a second chamber 1/3 rd down the barrel and this second powder charge is ignited by the flame front passing by (via a small hole drilled in the barrel connecting the barrel and the additional action)...? Add a second 223 action 2/3 rds down the barrel with a faster burning powder... Pick the hole size to correctly regulate pressure. And just maybe if you did not blow up your weird looking rifle with the two additional actions mounted to the rediculously long 40” barrel, you have a way to keep pressure above 55,000 psi until the bullet leaves that very long barrel.

Some burning gas always leave the barrel before the bullet exits... so some risk of preignition....

Disclaimer: Just a fun concept to brainstorm. NOT really seriously proposing this as a workable design, and please don’t go build one and blow yourself up!

But if you have the equipment, please invite me if you do, bullet proof glass can be found. High speed camera might be better though. ?

Yes there is clearly a risk that this ill conceived device can blow up! But it would be interesting to at least build a finite element simulation to see it the idea has merit or not....
 
Interesting thought experiment. Have wondered before if a flash tube in a large magnum caliber will help to keep the propellant inside the case instead of traveling down the barrel (and eroding the throat). Maybe a way to get longer barrel life?

The main problem limiting muzzle velocity is that the action has a PEAK pressure limit (due to mechanical limitations), and the ‘pressure trace’ grows, peaks and then decays fairly quickly long before the bullet leaves the barrel, especially on long 28-32” rifle barrels. A web search for pressure trace pictures show it peaking at 30 to 50 microseconds (0.3 to 0.5 ms) after ignition (for 6BR, 30-06, 308 calibers, pistol calibers are very different of course). Pressure trace is simply the profile (plot) of chamber pressure vs. time, and can be measured with a low cost strain case glued to the action, and connected to high speed electronics to record the pressure sensor signal. Or you can invest in a more expensive but more accurate piezoelectric pressure sensor. [BTW: The strain guage option is within reach of most reloaders.] This gradual drop in pressure that occurs after the peak pressure point is ‘lost opportunity’ in terms of achievable muzzle velocity.

Also barrels beyond 36” does not buy you much additional speed, so not worth it with current designs.

If we continue with the thought experiment (for the fun of it): Imagine we had a way to reliably ignite an additional (small) volume of powder say 50 microseconds after ignition, so just after peak pressure is achieved, so you could boost pressure a second time. What kind of rifle design would be required to speed up a 750 gn 50 cal bullet in a BMG action to over 4,000 fps? Try a 40” barrel? Maybe add a small (like 223) cartride loaded with a faster burning propellant (and no bullet) that sits in a second chamber 1/3 rd down the barrel and this second powder charge is ignited by the flame front passing by (via a small hole drilled in the barrel connecting the barrel and the additional action)...? Add a second 223 action 2/3 rds down the barrel with a faster burning powder... Pick the hole size to correctly regulate pressure. And just maybe if you did not blow up your weird looking rifle with the two additional actions mounted to the rediculously long 40” barrel, you have a way to keep pressure above 55,000 psi until the bullet leaves that very long barrel.

Some burning gas always leave the barrel before the bullet exits... so some risk of preignition....

Disclaimer: Just a fun concept to brainstorm. NOT really seriously proposing this as a workable design, and please don’t go build one and blow yourself up!

But if you have the equipment, please invite me if you do, bullet proof glass can be found. High speed camera might be better though. ?

Yes there is clearly a risk that this ill conceived device can blow up! But it would be interesting to at least build a finite element simulation to see it the idea has merit or not....

I think you’re referring to something like this:

B1FC91AB-E9B3-441F-96F3-0627A5751E6E.jpeg


https://howwegettonext.com/space-guns-fa2dda0561ec

You can see this idea has been around a while. I think this has been attempted in the not so distant past by countries trying to develop space guns, really just super long range heavy artillery. A interesting concept but I think it would be very hard to regulate powder ignition, burn rate, etc., especially on small caliber weapons.

Mike
 
One way to optimize current (legacy) cartridges is to use a denser projo (i.e., sintered tungsten powder) like Powell River Lab (DRT cartridges) uses.

The USAMU found they are very, very good at bucking winds, albeit at a much higher price per bullet. The bullet profile of a Sierra 190 but weighing 250 grains or more makes for a dandy ballistic coefficient.
 
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I think you’re referring to something like this:

View attachment 7012126

https://howwegettonext.com/space-guns-fa2dda0561ec

You can see this idea has been around a while. I think this has been attempted in the not so distant past by countries trying to develop space guns, really just super long range heavy artillery. A interesting concept but I think it would be very hard to regulate powder ignition, burn rate, etc., especially on small caliber weapons.

Mike

Very impressive, and invented in the 1890’s! Was not aware, thanks for finding it Mike.

Wonder if modern high speed electronics can do a better job at accurately timing the sequential ignition of the cartridges....

Btw: The way that liquid fuel is injected in tiny but accurately metered quantities in a direct injection (stratified injection) via piezoelectric transducers might one make a liquid powered canon a real possibility...

Fascinating topic!
 
One way to optimize current (legacy) cartridges is to use a denser projo (i.e., sintered tungsten powder) like Powell River Lab (DRT cartridges) uses.

The USAMU found they are very, very good at bucking winds, albeit at a much higher price per bullet. The bullet profile of a Sierra 190 but weighing 250 grains or more makes for a dandy ballistic coefficient.

Hi,

This paired with cartridge cases made from an alloy that can handle higher pressures is going to be a great combination.
For example: Blackwater ammunition has a new alloy BMG case that they have been testing and operating at over 70k with no problems (And it is 35% lighter in weight than standard brass BMG case) which is big difference from the normal 52k something of the brass BMG case.

Sincerely,
Theis
 
Sorry did not mean to hijack the thread. Getting back to rocket propelled bullets: I bet it would be possible to produce a rifle round that uses some form of solid rocket fuel, with electronic (spark) ignition, or a flash tube and a primer. If you can tightly pack the fuel in layers, so it won’t move around and get mixed up, you likely could build a round that has constant pressure for the duration of the barrel dwell time and get MV up by 500 fps or more, using long barrels. Denser bullets would clearly help to maintain all that newfound speed. Equivalent to burning through different layers of powder with way different burn rates.

Likely will be more expensive to produce them, but don’t see a good reason why it won’t work....
 
Hi,

We already have more MV and Internal ballistic advancements than the available barrel and cartridge case technology can handle.
There are some BMG based wildcats that are being limited purely from BMG brass being so weak.
There are some wildcat/projectile combinations that put up so much MV that barrels are gone within a couple hundred rounds.

"Advance" those 2 key items and IMO I think we will see a new generation of ELR weapon systems.

Sincerely,
Theis
 
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Fair point!

I wonder how a finned Tungsten sabot projectile in a new ultra modern case designed for 95,000 psi, shot through a smooth 36” barrel would do. Or can we do away with the need for a case completely....