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Blowback Rifle Formula
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  ds1948

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Posted: February 06 2017 at 11:00pm | IP Logged Quote ds1948

Now I know what you are all thinking, how many times is this going to get brought up. Well Im here to surprise you with an alternate to using Orions Hammer all of the time and expanding what Chinn and others have said on blowback systems. The majority of my sources will be Chinn and David Findlay's Firearm Anatomy Book Oneabout the Thompson SMG. I apologize for the long post.

First and foremost, the best formula to use is a derivation of the momentum equation that Orions Hammer used. I can go into my derivation if need be, but the formula is Wb=(dP*A*dT^2*g*12)/(dD). For an explanation of the variables, Wb is the mass of the recoiling parts including half the spring mass. dP is the average pressure in psi in the barrel while the projectile is inside of it. A is the area of the bore in inches. dT is the average time in seconds, or simply half the time the projectile is in the bore. g is the gravity constant 32.2 ft/s^2. That is why you multiply by 12, in order to translate the feet of the gravity constant to the inches that you used for the area. If you use different units make sure to keep track of them. Finally, dD is the average distance that the bolt can recoil before the projectile leaves the bore. This can only be found experimentally. For a thompson, this figure is .059 inches gotten from Findlay. Now I know some of you will disagree that the area is always the bore area and suggest that in bottleneck cases the area is the case head area. This is not the case as Chinn, Findlay, the Oerlikon Pocketbook discussed later, and the Rheinmetall Arms book all mention and list in their formulas that area is of the bore.

Unlike Orion's formula I am sure some of you are scratching your head and wondering how you get the average time and pressure in a rifle. There are three ways of doing this. Using a pressure gauge and putting it on your rifle, using quickload or another software to generate a pressure versus time curve, or experimentally. As the first tow methods are self explanatory, Ill discuss some formulas to estimate the pressure versus time.

First one needs to find out the average pressure in a rifle. The best formula I found to do this is a formula from the Oerlikon Handbook. It mentions that dP=[(Wp+Wg/2)*(V)^2]/(64.4*L*A). Wp is the projectile mass in pounds and Wg is the powder mass in pounds. In order to translate grains into pounds, divide by 7000. Wg is divided by two because it is assumed that half the gas mass contributes to the force experienced by the bolt face. This assertion is supported in the aforementioned sources. V is the velocity of the projectile in ft/s. L is the barrel length in front of the cartridge in feet. Finally a is the bore area. With this formula, you can usually determine the average pressure in rifle type loads pretty reliably. The handbook uses this formula to estimate a 30-06 load. When used on rifles, this formula is spot on. On pistols not so much. It takes the longer pressure curve of rifles into consideration so the quick spike of pistol powder causes the formula to underestimate average pressure in these weapons. The best thing about this formula is that if delta pressure is .4 of the total pressure, then a group of assumptions can be made. From the same book, T=[(2*L)/V]*.946. L is the barrel length in feet and V is velocity of the projectile in feet per second. Once again this is a good formula when used on rifles such as the 30-06. Since delta time is just time halved, that means that both average pressure and time can be found experimentally.

For an example, lets estimate the blowback bolt mass required for a .223 from a 18 inch barrel. Using the average pressure formula you get the following inputs [((55/7000)+(27/14000))*(2900^2)]/(64.4*1.35*.039) This results in an average pressure of 24280 which is nearly .4 of 55000 which is the SAMMI pressure for this cartridge. Therefore, if we use the formula to estimate time [(2*1.35)/2900]*.946 we get a time in bore of .000897. The average time is half this. Notice this is a tad quick as the formula given is meant for a slightly longer barrel and therefore a lower average pressure but it will work for an example. Now we input this into the first formula to find the bolt mass (24280*.039*(.00045^2)*32.2*12)/.019. This will give you a bolt mass of 3.9 lbs. Now remember this is low for two reasons. One reason is that the time is too slow because it assumes the average pressure is .4 of the total pressure while ours is about .44. This is minor. The other issue which is much larger is the dD of .019. Remember how I said it can only be found experimentally? Well this is the dD of a 5.7x28 round fired from a civillian p90. This number was back calculated as I already know the bolt weight, 1.34 lbs. of a ps90. Therefore I can use that to find the dD. As the 5.7x28 round is high pressure, over 50000 psi, it forms a good analog to the .223. Notice the Remington round has a higher psi but this provides a better comparison than the thompson round which is just over 20000. That would be far too low. Therefore, the bolt mass is still higher than this yet though probably not by much. In order to find out for sure, could someone give me a quickload estimate for a 55gr. .223 load out of an 18 inch barrel? If you have a pressure gauge, that is even better. Before you ask, I have neither otherwise this post would have been a whole lot shorter.

While I know the mathematical way of finding the average pressure and time is not the best, it shows that the pressure inside of the barrel is a very dynamic force that is quite a phenomena to analyze. I hope this short report is as exciting to you as it was to me when I derived them.

Some other formulas to check out are the Lu Duc formula and the formula for acceleration listed below. a=(dP*A*g)/(Wp+Wg/2). as acceleration is equal to dV/dT this is another way to estimate the average time. dV is the average velocity which you can find out using the Lu Duc formula (that is a post in and of itself as it can get quite involved.

In order to find the sources that I mentioned, check out Weaponsman as well as Forgotten Weapons for some free firearm pdfs. Findlays book is available on amazon. In addition to this, all of my formulas are also included in the attached excel sheet with my own notes. The excel is rough but it will allow you to toy around with formulas and see what factors impact bolt weight more than others.

As a final note, I hope this is in the right forum and that it does not go against the rules of conduct. None of the formulas are my own, they can all be found in the above sources, but how they are combined and used is all my own and it took a lot of work getting them to mesh and work together. Feel free to move this if need be but please learn from it. No offense to Orions Hammer, but their is more than one way to calculate bolt mass.
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  backbencher

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Posted: February 07 2017 at 6:55am | IP Logged Quote backbencher

It's been known for some time that Orion's Hammer's chart was cautious.  You've got way too much math in your post for me to follow this early in the morning, but I applaud your efforts.
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  ronzor

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Posted: February 07 2017 at 11:01am | IP Logged Quote ronzor

Please post the ''attached excel sheet''
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  ds1948

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Posted: February 08 2017 at 3:41pm | IP Logged Quote ds1948

I guess the attachment didnt work, I compressed it into a zip file and attached it. I hope that works. Its an excel document.
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  ds1948

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Posted: February 08 2017 at 3:44pm | IP Logged Quote ds1948

I guess the attachment didnt work, I compressed it into a zip file and attached it. I keep getting this error though

Server object error 'ASP 0177 : 800401f3'

Server.CreateObject Failed

/forum/functions/functions_upload.asp, line 375

800401f3
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  ronzor

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Posted: May 25 2017 at 5:00am | IP Logged Quote ronzor

Please post the ''attached excel sheet''
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  backbencher

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Posted: May 26 2017 at 8:02pm | IP Logged Quote backbencher

The mice in the server are no longer accepting uploads.  That makes them run too fast on the wheel.

You can put it into any number of file sharing sites, and post the link.
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  ds1948

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Posted: May 27 2017 at 7:01pm | IP Logged Quote ds1948

alright lets try this. This is the full document mistakes and all. This includes a lot of ramblings and side discussions but it was a blast to make. http://dropcanvas.com/x797c
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  backbencher

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Posted: May 29 2017 at 8:06pm | IP Logged Quote backbencher

ds1948 wrote:
alright lets try this. This is the full document mistakes and all. This includes a lot of ramblings and side discussions but it was a blast to make. http://dropcanvas.com/x797c


http://dropcanvas.com/x797c

Looks good.  Thanks for posting the link.  I just made it hot.
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  Tanner Frisby

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Posted: June 03 2017 at 9:03am | IP Logged Quote Tanner Frisby

Thank you for the write up and the excel sheet. Results publications are very much appreciated.

Tanner Frisby
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  ds1948

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Posted: June 05 2017 at 1:28pm | IP Logged Quote ds1948

Tanner as you have built a couple blowback weapons, could you let me know what weight your .380 slide was and your gas delayed 7.62 bolt was? This will help me make my formula better with actual examples. That and Im writing an add on for gas delayed firearms.
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  Tanner Frisby

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Posted: June 07 2017 at 8:39am | IP Logged Quote Tanner Frisby

I don't have the parts nor files in front of me, but I'll get back to you within a week on that.

The 380 was never finished and has slipped into the nebulous of forgotten builds. It was more a machining exercise for my new mill, and the design proved excessively complicated for a good working model to come out of it. I did calculate a slide weight though, so I'll find the figure and post it.

The 7.62 x39 was delayed blowback, so I don't know if that will compare well to the figures you are calculating. Improper materials were used and it beat itself to death within 5 rounds. It appears to have functioned very well for the first round (based on spent case inspection), so I'll estimate the bolt weight and post that figure as well.

Also, I haven't had the time to parse through your document, but at least one instance of "10-22" [Ruger] has been converted to "10-22" [22 Oct 17] by Excel. It took me a while to figure out what gun it was; I'm sure others figured it out more quickly.

I've got a blowback .22lr from Mossberg that I'll try to measure as well. I did a modification on the charging handle and it actually weighed too much and wouldn't cycle. I'll throw those weight estimates in also.

Keep up the good work,
Tanner Frisby
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5 most recent builds as of this post:

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7.62 x39 v1
Mosin Nagant

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  backbencher

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Posted: June 07 2017 at 11:44am | IP Logged Quote backbencher

Tanner Frisby wrote:
  The 7.62 x39 was delayed blowback, so I don't know if that will compare well to the figures you are calculating. Improper materials were used and it beat itself to death within 5 rounds. It appears to have functioned very well for the first round (based on spent case inspection), so I'll estimate the bolt weight and post that figure as well.

Keep up the good work,
Tanner Frisby


Tanner, if I remember aright, your "gas-delayed" blowback 7.62x39mm had similar issues to the original Nazi "gas-delayed" blowback 7.92x33mm rifle in the 2nd WW, namely the gas port was WAY too far forward to provide an effective delay, unlike the HK P7 or Walther CCP.  Fortunately, the German rifle had a sufficiently heavy bolt that it functioned as a mass-delayed blowback - yours did not have a heavy enough bolt, and as it was a bullpup, you almost ended your engineering career precipitously early.  It beat itself to death b/c the bolt was WAY too light.  Post the weight only as a cautionary tale.
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  ds1948

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Posted: June 07 2017 at 1:25pm | IP Logged Quote ds1948

Thanks Tanner! All of that is much appreciated. Whenever you find those Ill appreciate it. And sorry about the slop in the excel sheet. I originally never planned on posting it anywhere until I kept seeing people putting down individuals that suggested blowback rifle caliber guns. Therefore I decided to create an account and post it to show quite the opposite, and without a ridiculously heavy bolt.
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Posted: June 08 2017 at 9:21am | IP Logged Quote backbencher

ds, you should have a look @ the just released CMMG .45" ACP Guard.  Using delayed blowback via mechanical disadvantage - very clever system, and will fit in a standard AR upper receiver.
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  ds1948

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Posted: June 14 2017 at 11:03am | IP Logged Quote ds1948

That delayed blowback system reminds me of the Scotti and SIA series of machine guns. They also utilized a greater than 4 degree angle to provide a delay in the opening of the bolt and utilized a rotating bolt. Forgotten Weapons did a video on the Scotti X Rifle that shows the bolt in detail. It is funny to see old designs resurrected. The camming surfaces shouldn't be too difficult to calculate.
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Posted: June 14 2017 at 6:40pm | IP Logged Quote ds1948

Hmm I like the look of that carbine. Also that bolt reminds me of the scotti or the sia machine gun. Both of those had angled lugs that worked at a mechanical disadvantage to delay the bolt opening. I love when weapons dig up old concepts. That is also quite a a weight savings. The bolt looks to weigh only .6 pounds or about the same as an ar 15 bolt and carrier.
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  Tanner Frisby

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Posted: June 19 2017 at 7:07pm | IP Logged Quote Tanner Frisby

It seems like weaponeer is down every time I come here. Sorry for the delays.

My Jenning's 9mm handgun (Zamak 3 gun / Hi point / Saturday Night Special / etc) is a blowback. I weighed the slide and recoiling components at 7/8 lbf on a grocery produce scale with a 1/32 lbf resolution (my digital postage scale seems to have stopped working since I last used it years ago).

My home brew blowback .380 had a design weight of 1/2 lbf.

I haven't had a chance to weigh the bolt of my Mossberg 702 Plinkster bolt as it is in a different location. I will try to add these weights in as well.

I also feel like the recoil spring's stiffness should play a non-negligible roll in the equation as well. I don't have a good way to measure the "k" of these springs, but it might be a relevant variable.

backbencher wrote:

Tanner, if I remember aright, your "gas-delayed" blowback 7.62x39mm had similar issues to the original Nazi "gas-delayed" blowback 7.92x33mm rifle in the 2nd WW, namely the gas port was WAY too far forward to provide an effective delay, unlike the HK P7 or Walther CCP.  Fortunately, the German rifle had a sufficiently heavy bolt that it functioned as a mass-delayed blowback - yours did not have a heavy enough bolt, and as it was a bullpup, you almost ended your engineering career precipitously early.  It beat itself to death b/c the bolt was WAY too light.  Post the weight only as a cautionary tale.


You are absolutely right about my lack of safety when I test fired my build, but I have to disagree with almost everything else in the quote.

I will make a thorough write up on how the gas delayed system works and how to design an action around gas delay, with a few theoretical examples worked out. I'll try to write and post this in about a week.

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5 most recent builds as of this post:

.380 Blow Back
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7.62 x39 v2
7.62 x39 v1
Mosin Nagant

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  backbencher

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Posted: June 19 2017 at 7:12pm | IP Logged Quote backbencher

Good to hear from you, bud.  You back in the States?

I finally actually built a rifle from "scratch".  Cut off the end of an AR trigger jig, and put it into an AR thumbhole stock - instant single shot.  Have sent off a trigger jig to a new friend who has an AR 5.7 upper w/ a 50 round magazine in the upper. 
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  ds1948

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Posted: June 20 2017 at 11:06am | IP Logged Quote ds1948

Thanks for those weights Tanner! Now I just need to go to ballistics by the inch and use those velocities. As for the spring, Chinn, Rocha, and the others have said that the spring mostly just contributes to the return bolt velocity and is used to assume rate of fire. That assumes though that you are not using a spring meant for a bmg on a .22lr. The spring does contribute to the overall weight of the system. Half the spring weight, and any other mass that reciprocates with the bolt, is added to the bolt weight. So it does help some.
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