Blowback designs: Back of envelope calcs

Picture in your head that you are sitting on a motionless platform in the middle of a perfectly flat, level floor. The platform is resting on ball-bearings. You hold a spud-gun in your arms.

For the sake of simplicity, let us suppose that you, the spud-gun and the platform weigh 222.2 pounds and further, let us suppose that the potato in the spud-gun weighs 2.2 pounds.

For the sake of convenience, we will define the center-of-mass for your universe (everything above the floor) as the "zero" of our coordinate system. No matter how you wiggle-and-jiggle atop the platform, the center-of-mass of that universe does not move from the zero which was the creator (me) painted on the floor.

Getting bored, you raise the spud-gun to your shoulder and launch the 2.2 pound spud horizontally at 100 inches per second. The seconds tick off the clock. The center-of-mass of the system remains stationary while the spud moves off at 100 feet per second and you+platform+empty spud-gun move in the opposite direction at 1.0 feet per second.

Counter-intuitive? There were no external forces exerted on your universe so the center-of-mass which was stationary remains stationary even though the individual pieces are moving through space.

Hold that thought...

The CCArms LGB series PCCs

Rounding up, it might be capable of launching a 147 grain bullet and the gasses produced by 7 grains of powder at 1100 feet per second.

An extreme example of a case that bulged in the region where the barrel was notched out to accommodate the extractor and/or feed-ramp.

The residual pressure in the barrel just before the bullet clears the muzzle will be on the order of 7000psi-to-10000psi so there is still the potential of the brass case rupturing if it is unsupported by the cylinder. The tricky part is that it can be partially unsupported and the thin brass wall will bulge and carry the pressure load in membrane mode but it will rupture if the distance is too much or the pressure is too high.

Another, less severe example of bulging

It is assumed that the pressure of the hot gas in the barrel will evacuate very quickly after the bullet's base clears the muzzle.

Skipping a bunch of math, if the head of the case can only move backwards 1 millimeter (0.40") then the bolt must weigh about three pounds. If it can move backwards 2 millimeters then the bolt must weigh about 1.5 pounds. If it can move back 3 millimeters then the bolt can weigh about 1 pound.

Increasing the barrel length to squeeze out a few more fps forces the designer to use a heavier bolt to meet the (admittedly arbitrary) 3mm extraction criteria. The heavier bolt requires a longer receiver and increases the likelihood of the plastic parts being damaged when the weapon is dropped.

In a similar vein, making the barrel shorter would allow the designer to use a lighter bolt, making a lighter and shorter firearm but at a loss of velocity/energy of the bullet.

Secondary factors:

There will be friction between the case and the walls of the chamber. That might reduce the thrust by 15%...or it might reduce it by 0% or by 50%. Friction is goofy and the wise designer doesn't hang his hat on it being reproduceable.

The 147 grain load is not very common. The most common is 115 grains but many shooters like 124 grains. The lighter projectiles will result in less movement of the bolt as the projectile clears the muzzle.

Back to calcs

You will notice that there has been no mention of springs. That is because of the very small distances traveled.

The energy stored in a spring is 0.5*K*d*d where "K" is the stiffness or spring-rate and "d" is the amount of compression from the free-state.

In theory, you could design a mechanism with the spring at its fully extended, free-length when the bolt has the head of the case fully inserted into the chamber BUT nobody ever does that for various reasons.

So you are looking at an energy formula of  0.5 * K * (d2*d2 - d1*d1) where d1 is the less compressed distance and d2 is the more compressed (bolt back) state.

That energy will equal the kinetic energy of the bolt as the bullet clears the muzzle. In our example that would be 1/2 * mass * velocity * velocity. In metric, that would be 1/2 * 0.5kg * 6.8m/s * 6.8m/s or 11.5 Joules. In our example, the backward speed of the bolt is 1/50th the speed of the projectile by virtue of their relative masses and conservation of momentum. You can pencil it out or you can play around with parts and spacers (to adjust pre-compression of the spring) to make it work.

One of the beauties of a carbine is that you can absorb all (or nearly all) of the recoil in your spring. The packaging and handling constraints make that impossible in a handgun. If you made the spring stiff enough to absorb all of the energy in the limited length of travel, it would be impossible to rack. Consequently, much of the energy is dumped into the frame when the slide hits the stops at the end-of-rearward travel. That impact plays hell on the frame due to the stresses it creates.

...it is their right, it is their duty...

The lovely Mrs ERJ and I were listening to some music from 1970.

My beautiful wife suggested this piece

Good stuff.

And isn't it odd that quoting historical documents that were key to the formation of our nation are now likely to get one added to a terrorist watch-list?

Worrisome.

Potatoes are in the ground

Potatoes are in the ground.

90 feet of Kennebec. 45 feet of Red Pontiac. 135 feet of potatoes pulled from storage that had not sprouted very much and were sound. Varieties not known but some were probably Russet Burbank.

I was aiming for 200 feet of row and ended up with 270, which is half as much as last year. They are in a very good spot and if I do my part with fertilizer, weed control, Colorado Potato Beetle control and irrigation when needed, they should do well.

AND....the tulips are blooming.

Liberty apple trees are in full bloom. 187 Growing Degree Days base-50. By comparison, 2023 was 149, 2022 was 118, 2021 was 205 and 2020 was 72 GDDb50 on this date.

3-D printed 9mm video

A guy "running" one at a Falling Steel Match. 2.5 minutes long. No dead-time.

PLA resin is one of the industry work-horses and is not the most expensive resin.

PCC (Cumberland Saga)

Amira's challenge was outside of Samson's expertise. His specialty was LONG distance, precision shooting, not bar-room brawl distance shooting. He needed to consult with some experts. He wasn't going to deliver something that didn't address the issues Amira had pointed out.

The next morning Samson walked to the eastern edge of the Cumberland Plateau and found a position on the cusp of the Tennessee River Valley where he could visually see the eastern suburbs of Chatt. He was a quarter mile east of the official boundary of Copperhead Cove.

He moved around a bit until he had three bars of signal on his cellphone and then started typing...

Launch App: Rypt_Cord Server

A spinning clock icon appeared on the display of his phone. Then...

....Encryption achieved.....

Login:Not_Marinept25MOA

PW:*********

Ring:SemperfiAtl

Subgroup:PrcnShttrs 

Samson tapped on the icon for "Start new Thread" and then tapped out

Subject: Advice needed re weapons for indig personnel

Background: Twenty small-stature to very-small-stature potential combatants need weapons with following characteristics

• Accurate enough to hit paper-plate at 50 meters with minimum training
  
• Very low recoil and muzzleblast
• Detachable magazine
• Enough projectile mass to disrupt central nervous system from frontal center-of-mass hit at 50 meters
• Compact, lightweight (six pound max)
• Low cost platform and ammo. Many potential combatants, low funds.

Need recommendations.

Over.

Trip1805 wrote: Hello NotMarine

Have you considered M1 Carbine. Designed to replace M1911 .45 ACP handgun for use by cooks, truckdrivers and REMFs.

Sounds exactly like what you are looking for.

Over.

NotMarine wrote: Cost and availability?

Over

Trip1805 wrote: $1500 for used, not matching serial numbers. $2000 for new with +6 month waiting list.

Over

Not_Marine wrote: That is not going to work for me. I need 20 copies in less than a month.

Over

WndwLiqr wrote: Have you considered .22LR semi-auto like 10/22? Can be had for $400.

Over

Not_Marine wrote: Great weapon. Not sure it can punch through chest or beer-gut, hit spine and disrupt CSN.  Also, twenty copies at $400 way above budget. Can you suggest something between M1 Carbine and 10/22?

Over

Time passed and much internal discussion within thread. The various plusses and minuses of several semi-auto platforms were discussed. Then...

DieTrd wrote: How about Pistol Cartridge Carbine? 9mm PCC approximately 3X .22LR mass and performance. Simple blow-back. Price about $400 per copy for cheapest option.

Over

Not_Marine wrote: Price still too high.

Looked at M1 Carbine. Magazines are junk. Need robust magazines.

Over

Even more time passed

Md_scntst wrote: If I remember correctly, you have access to 3D printing. Many designs for PCC available on the graynet. Some use Glock magazines. PM me for details.

Over

Please advise regarding projected cost.

Over

Looking at a bulk buy for CHMSL barrels, roughly a C-note per copy.

Over

PM sent.

Over

End Session:

The prototype showed up in six days and was tinker-toyed from many AR parts because they are abundant and ergonomically excellent. For example, the fire-control groups were scrounged from the builder's parts drawer. Triggers are one of the items most frequently upgraded from "stock" ARs and "stock" was plenty good-enough for Amira's specification. Ditto for the buffer-spring that powered the bolt which the builder had fabricated from laminated steel, similar to the core of a low-voltage transformer.

Samson was delighted with the additional AR parts. He saw them as inventory-on-the-hoof. They were fair-game to cannibalize should the high-end weapons need those parts.

The 6" 9mm Luger barrel was pressed into a 16-1/2" long tube to make it legally a long-arm. The receiver was 3-D printed and it even had a serial number on it (CCArms, LGB-A001) to make it legal. The mag-well accepted Glock magazines and the forearm had a dovetail for a light and posts for a sling. The sights were on the barrel-tube, a tall ghost-ring rear and a simple, hooded post in the front.

Samson took the weapon out for first firing and he encountered some short-stroking. He determined that the bolt had some burs on it that were scraping the molded-in metal guides that trapped the bolt. He stoned the bolt to slightly chamfer the rough edges and reran the test with only two failures of the bolt to travel far enough back to pick up a new round. 

Samson reread the notes the builder sent with the "build" and learned that there were spacers in the buffer-tube to increase the preload on the spring. He started playing around by removing spacers and deliberately "limp-wristing" the wimpy, generic, white-box 9mm ammo in an attempt to make it not-cycle. He stopped removing spacers when it ran ten-in-a-row even in limp-wrist mode.

Once he was happy with how the rifle was tuned in, he filed the front sight to raise the point of aim to a 75 meter zero and then invited Amira, Sarah and Sig to shoot it.

Bracing the weapon against a tree trunk, simulating shooting from a doorway, Amira was able to keep ten shots at fifty meters in a group no larger than a softball.

Sig suggested that the front post should be thicker for better low-light visibility. He also suggested that wooden butt-stocks could be fabricated in Copperhead Cove to reduce cost at a penalty in weight.

"How soon can we have all 20?" Amira asked.

Samson frowned. "There are always bugs that don't show up until the lead units get enough exposure to several different shooters and different types of ammo. I want to make five and get them out to shooters of different heights and get some rounds through them."

"After we bubble-up and solve the issues on those, I want to make another batch of five" Samson replied. He had anticipated the question. "Point being, if we have the parts in-hand, they are much easier to modify as loose-parts. If I build them into working rifles then we risk damaging the receivers if we have to do a full disassembly. The receiver is just plastic, after all."

"I want one of the first ones" Amira said.

"If it is alright with Sarah and Sig, you can have the one you are holding" Samson said.

That brought a BIG smile to Amira's face.

"The next question is, where are we going to get $2000 for the parts and another $1000 for ammo, extra magazines and other odds-and-ends?" Samson asked.

---Note to my readers---

 Thank-you for all of your comments on the previous Cumberland Saga post!

This is a work of fiction and undoubtedly many of my more sophisticated readers are already thinking..."but it doesn't work that way...". My challenge as a writer is to produce vaguely technical sounding text that seems plausible and paints pictures in the reader's heads while not strangling the story with excessive detail.

I will be disappointed if some commenters don't take me to task, though.

9mm seemed like the only choice. It is the cheapest centerfire ammo and really does replicate .22LR ballistics with three times the mass out of a 6" barrel. Longer barrels only gain about 100fps compared to a 6" barrel according to Ballistics By The Inch.

Ballistics: 2" high at 50 meters with a 75 meter zero and 3" below the line-of-sight at 100 meters. With a muzzle velocity of 1100fps, velocities of 1020fps at 50 meters and 960fps at 100 meters. Getting plunked in the noggin or heart/lungs by 124 grains at 960fps will quickly end the party for you, even if the bullet is going too slowly to expand.

The final nail in the coffin of 9mm vs .22LR is that most centerfire arms are less likely to be damaged by dry-firing than most rimfire arms. When ammo is dear and noise is to be avoided, dry-firing is your friend. It makes flinches disappear.

To the Marines out there: Samson was not a Marine but is allowed to be on the ring by virtue of being able to shoot as well as a Marine.

---End notes---

"Shingled" time-horizons for inherent resilience

One of the recent sub-themes in the Cumberland Saga is the use of "shingling" or overlapping time-horizons to create resilience.

Amira observed something like "There will always be another crisis coming along. It is just a matter of time."

The idea comes from the strategy of having a "ladder" of Certificates of Deposit of varying maturities to supply a steady flow of income. If the income is not needed, then they can be reinvested like a link in a caterpillar track.

The people in Copperhead Cove expanded their short maturity food crops and applied fertilizer to maximize yields. They also invested in cows which have a much longer time-horizon than annual crops. A cow can live five-to-fifteen years depending on care and upon the owner's willingness to tolerate lower milk production in later years.

The small-fruiting bushes are even longer-horizon than the cows. They will start fruiting in their second year in the ground and some of them will spread on their own. A thirty-year life span in a home garden is not unreasonable. Small fruits are also very resilient with respect to the weather. Given a little bit of snow-cover, most of them can sustain -30F.

Reportedly a 700 year-old Sweet Chestnut tree

The chestnut orchard is the investment with the longest time-horizon and it occupies the least desirable land. They might start producing nuts in four or five years (if fertilized and weeds are controlled). Some will die of blight but others will have resistance. On a favorable site, a single chestnut tree can live and produce human-quality food for hundreds of years. Nut pines, Black Walnut trees, oak with sweet acorns, persimmon, olives and pear trees can last just as long. Apples are a 30-to-50 year enterprise. Most stone-fruits are 5-to-20 year enterprises.

Small projects

The rabbits are already hitting the apple root-stock I planted. I am surprised that they are eating the MM-106 but left the G.214 alone. That might change.

I tooled up with a length of pipe, a stack of copy paper, glue stick and "white glue" to make temporary shelter for the vulnerable root-stock. Putting a fence around the enterprise is on my list of things-to-do. I got my cycle time down to around 15 seconds per copy by the time I was done. I could probably squeeze another five seconds out if I had to make another thousand.

I purchased some steel T posts at a salvage yard. They were charging $3 each which was not a great price but it was a fair price. I only had $60 cash in my wallet so I bought 20.

Ichthys

Approximately 1/6th scale

The church that I attend has a food pantry that supplies supplemental food to people who ran out of pay-check before they ran out of food.

The distribution point is WAY back in the extreme opposite corner of the parking lot from the entry way and it is masked by other buildings.

I committed to making a stencil to be used on the pavement to indicate the directions to the distribution point.

The Ichthys symbol seemed appropriate. My current plan is to make the "fish" thirty-six inches long from nose-to-end-of-tail with the lines 1-1/4" wide and painted with white pavement marking paint. The fish will be supplemented with an arrow indicating actual direction the vehicle should travel.

The Ichthys symbol not only represents a fish (food) but was an early symbol for Christ and evangelization (John 21:11). The 153 fish may have represented the entire, known world since it was believed at the time that there were only 153 species of fish in the world.