As I understand it, bolt thrust is proportionate to the internal area of the casehead.
Problem is, the inside of the base isn't flat; it's more like a concave. How does the shape of the area effect the amount of thrust backward? It would seem that more force would be applied outward in vectors against the various parts of the chamber, no?
And so, it would therefor make sense that a case with reinforced web area (such as Lapua from Rigby, or Chey-Tac from Gibbs) would generate less boltthrust for a given pressure rating.
Does anyone have good numbers on the area of the popular casehead sizes ('06, H&H, Jeffery, Rigby, Lapua, Whetherby....)? I'd love to get a hold of them.
Thanks!

You will find a good article on bolt-thrust at Dan Lilja's page, www.riflebarrels.com look for "articles by Dan". He has the simple formulas that allow you to calculate bolt thrust and lug strength.

Sounds like you want to calculate, not measure, bolt thrust.

Pressure always acts perpendicular to the surface it is exerting against. I hope you are up on your trigonometry, you will need it to determine the force vectors in the blend radii.

Scott

Contrary to what some people think, pressure acts against every internal point from ALL directions, not just perpendicular to the surface. So to calculate the rearward thrust that the bolt must resist. Take the LARGEST internal diameter inside the chamber/case and use this to calculate the reaction area. To be on the safe side you can take the case OD as this diameter. This is because if there is any loss of seal around the neck then the shoulder will be the largest reaction diameter. We are talking pistons here, and the cartridge is the piston that is pushing back on the bolt face. Still the piston area of a shotgun shell casing is much larger than most high powered rifle cartridges that would be considered. So long as the barrel liner or replacement barrel will contain the pressure the Bolt should do so as well. The possible exceptions would be some of the bolt actions that only lock up on the bolt handle when using larger high pressure calibers.

Of course, the friction of a dry case on the chamber wall resists the thrust, but I'd ignore it to be on the safe side. There are lots of situations where a cartridge ends up being fired with the case or chamber wall lubricated one way or another. IMO a gun should never be fired with a load that's dependent on the case friction to keep the action stress level safe.

Just my grey matter smoking here, but it seems to me that things like a longer case, concave base, etc., would effect rearward thrust, since the pressure is spread in all directions, and there is more internal surface area (not to mention more friction from casewall to chamber wall).
Now, if it is simply that when in the tens of thousands of pounds realm the effect is negligable, I can dig it. If there simply is no effect on rearward thrust, I would love an explanation I could understand.

Bwana--The base of a case is just like a piston, with force against it and whether the piston is flat from inside of the
sides of the case or concave it is still pushing with the same pressure backward against boltface, like apiston in a
brake wheel cylinder, piston in a motor, or piston in hydraulic cylinder, many of which are of all shapes-flat,
convex,or concave.--Minus what the case sides are able to hold.The formula for bolt thrust is simple, as I laid it out in the bolt-action shotgun thread...Ed.

Basic math is simple, but even if the shape of the head has no bearing (which does make sense at first), then surely the friction coefficient is lower for a shorter case than a longer one (e.g., RUM vs SAUM).
And it seems the thicker web at least decreases the internal area, if even by just a wee bit, and "ought" to increase the FC of the brass/chamber.
To illustrate, a cube of brass with an internal shape of a sphere, when holding enough pressure to make it move (piston) then as it expands, trying to find room to move, it will push out at the thinnest point first, i.e., the tip of the sphere closest the bolt.
In the same vein, imagine a case - 30-06 say - that has a web shaped like a cone, with a point where the flash hole is punched. The boltthrust shouldn't be calculated using the full diameter, because the stresses over the duration of the explosion will be radically different at the primer pocket than in the areas at the fringe.

What we need is a strain gauge, attached to the case head or boltface, or maybe anywhere that will record the movement of the bolt. Maybe at the rear of the lugs?

If you take a water tank 10' tall and 10' across fill it with water, then stand a 10' tall piece of 1/2" copper pipe and fill it with water, the pressure at the base of both will be the same. So maybe if we are measureing bolt thrust along the axis of the cartrige, then the math would be to take the integral along the curve of the inside of the case in the direction of movement. This should be the area straight across at the widest point. The curvature and wall thickness will effect the radial pressure exerting out towards the wall of the barrel. There would have to be a point in the longer case equation that the additional surface area griping the sides of the chamber would not add any additional resistance as the thicker base will not expand enough to exert any sizable friction and the case will stretch at this point if the elestic limit of the brass is exceeded.

Okay, now shoot holes in my theory. I'm too tired to do the math, but maybe there would be a cross product in the integral to obtain the force in the bolt direction.

Oh, one other thought on the pressure at the primer pocket. The flash hole acts as a short capilary tube to reduce the pressure inside the primer pocket. If the pressure curve is longer, then the pressure in the primer pocket would start to reach an equilibrium with the case pressure and may have higher primer pocket pressure with the same peach chamber pressure. Again, go ahead and swiss cheese me.

I thought basic physics was still taught in high school? Why do these threads just keep going on and on?
Pressure times area = the force on the bolt. Simple.

Bwana
If you want to be super-anal, go ahead and try to derive the equation for the curve of the case wall to circular flat area in the case. Unless you know that equation you'll have a hard time integrating the curve. That is why it is so much more simple and easy to just look in a reloading manual for the size of the base of the case. Its diameter. Now take that with the equation for the area of a circle and multiply it times the pressure. There is your bolt thrust.

All the crap about length of the case and taper and yak-yak-yak-crap is just crap. P x A = F

Dr. Rothschild has spoken.

Oh boy.
It is perhaps unfortunate if my attention to minutia seems "anal." The truth is that I'm simply trying to get at the real answer.
If it satisfies you to take shortcuts, then great. (BTW, you're not even accounting for brass thickness in your equation there, Doc. ) I'd say it's because physics is still taught in school (if you can apply the word "still" to the mid 80's) that I think there's more to this picture than such a simple formula.
In fact, I don't know the formula for accounting for the curve, but it sure seems like there should be one if we are to talk meaningfully about action tolerances.

Bwana-The longer case will grip sides more of course, but
the shorter case at medium to high pressures will grip as much as the strength of the brass sides can hold in carrying its share of the thrust.And you are right that the
cone shaped inside the base will handle stresses different
than a flatter inside, but those stresses are still pushing on a supporting structure, that is the case base, thus the whole structure of the base reacts to the pressure, back
toward bolt.And those stress on the inside is trying to push
the case apart in the corner and if corner is rounded more it handles stress better, but the whole structure is reacting to the rear at whatever psi is being exerted.The gases will they are working in the cone you describe, are being pushed by gases from the center of the case, back
toward bolt.Thus the base structure,and the gases in the
cone are just a combination together making a piston.

As far as testing thrust, somewhere this has been done, thus the formula, and inside shape didn't matter.I read about,I think of military doing it using copper crushers, between breech and case.

With a 30-06 having 7,000 lbs thrust,458WIN 8800 lbs,
a 460 Wea having 13,000 lbs of thrust, 12GA FH having 11,000
lbs at 35k, and so on in actions having a bolt shear rating
of 33-37,000 lbs, the system works, if mistakes(human error) are not made and actions have good lug bearing contact, metalurgy, etcc.They have mutiples of safety built in.Ed.

I am almost afraid to join in on this discussion. It is loaded with misconceptions. Yes, the force is equal to the pressure times the area. F=p*a it is that simple. Here is a though experiment to prove it. Imagine the case with it high internal pressure at an instant in time where the pressure is uniform inside the case. Now, imagine a thin diaphragm spread across the area just forward of the case head where the case has the thickest walls. There is an equal pressure everywhere and the diaphragm would have the same pressure on both sides. The force on the diaphragm is exactly f=p*a on both sides. It makes no difference what the shape of the inside of the case head is. The total axial force is still f=p*a or the diaphragm would move.



Now a large step stressing brain cells. There is a Finite Element Calculation of the bolt thrust from a .243 Win cartridge case with various conditions of friction between the barrel's chamber and the outside of the brass case. You can see the plots of how the load is shared between loading the bolt face and stretching the brass case as various friction coefficients are used.



Here is the link: http://www.varmintal.net/a243z.htm



Good Hunting... from Varmint Al

I still say that, just to be safe, you should plan for a "worst case" scenario of no brass friction resisting the bolt thrust. It shouldn't be dangerous to fire a rifle with an oiled cartridge. That's something that's going to happen a lot in the real world.

The rifle designers do build in a safety factor of
3 to 8 times, depending on case size, to allow for slippery cases.As the link above shows the amount of thrust increases
are not astronomical for more polish to the chamber, or
slippery cases.In example polished chamber 4565 lbs thrust,
same chamber with grease, 4787 lbs thrust...Only a 5%
increase....And in a rifle design, with a lug shear
rating of over 30,000 lbs of thrust.Ed.

I know that if you polish your cartridges with Brasso, then wipe them with a little BreakFree CLP and fire, they come out fireformed very nicely. I do this with my .375 H&H into .375 Weatherby.

I like to reduce the stretch.

Bwana,

I a perfect system, such as a mythical perfect rifle, having a perfect chamber made from perfect steel that will not stretch, and machined so perfectly that to load 'n' fire you Super-Glue a primer over the firing pin hole, drop a bullet down through the chamber, drop a load of powder after the bullet and then install the bolt. Upon firing, the peak gas pressure, times the area of the face of the bolt will give you the push exerted on the bolt.

Gas expands and exerts force (pressure) in all directions at once, like being under water, the water presses exactly the same as on the top as on the bottom.

This occurs inside the ballon (the brass case). The ballon stretches to fill the chamber. For any given area, it does not matter what the shape is, whether it is a star, an egg-shaped ovoid or a perfect square, if the area is the same, the force exerted by the pressure is the same. If you glued the cartridge case into the chamber and somehow made the primer fire, you could watch (assuming you have a very high speed camera) the ballon begin to expand and the casehead extrude from the chamber.
In the chamber with the bolt in, gas pushes out in all directions at once, at the smae pressure over the given area. So if there is no movement, there is no stretch. In a tight fitted chamber with zero headspace, there will be a little plastic flow of the brass forward into the neck. This would take several firings to see though, depending on the pressure.

I do not know if I could explain it any better. I would suggest you find a university in your area and ask a physics professor, taking in a fired cartridge case and one that is cut in half down the length so they can see the inside. Many professors have no idea what firearms look like, let alone the ammo. They could do a better job and show you the math behind it.

Bwana-be,
Varmit Al is correct, but please take note that the whole "ultimate tensile strength" was used in Dan Lilja's article when lug shear was calculated.

The tensile strength should always be reduced by roughly 58% in steels for pure shear forces, and therefore the F.S.(factor of safety) to permanently/inelastically deform is only around 2 to 3 times SAAMI maximum rated pressures for old military rifles, assuming the cases do not adhere to the walls, but they actually do. The brass would give out way before the action is damaged, unless the bolt lugs/action was too soft.

The reason I believe in case wall adhesion is due to the fact that Col. Hatcher reduced the lug pads on a 1903 bolt from 0.400" to only 0.100". He fired two or three 52,000 service loads with no deformation, but the first 70,000 psi blue pill broke the lugs off. If he had greased the cases, I'll bet the testing would have ended early with the first service round.

I used an Excel spreadsheet for calculating about a dozen different military and modern bolt lugs, and worst case of all lug shears are the M98s built on magnum cases. Second worst case was a 30-348 Winchester Ackley Improved on a P-17 action due to the larger internal case base aree. Still, all of the FS's (with no case/chamber wall adhesion)were all around 2.

Hotshot

Bwana-You are right that the thicker part of the web is
taking force, along with the center near flashhole, But it is the part of the case that isn't sticking to the sides.It is in essence part of the base, supported by bolt, and supported partly by its connection
to the sides that are sticking due to pressure...Ed.

Hotshot-Lilja used half of the yield strength to figure what McBros action lug shear strength. That is standard
everywhere that I have seen it applied to lug strength
where the force is at right angles to lug attachment.And when it comes to wall adhesion cases due help out, but from
Al's article it is apparent that even with greased cases
that the adhesion of the sides of the case is more than what the strength of the brass sides next to tha base can hold in thrust.And even greased cases the safety factor
is 3 to 8 times depending on cartridge.Like a 30-06 with
7000 lbs thrust in a rifle with 33,000 of lug shear rating
with dry cases and the greased version adding 5% to the
thrust, you are not changing safety factor very much.Case
wall adhesion is a constant that doesn't change much whether
cases are greased or "improved".Of course using last term might really get this thread going..Ed.

Ed,
Here are two more detailed analysis of bolt lug strength.

http://www.varmintal.net/abolt.htm

http://www.varmintal.net/abat85.htm

The highest shear stresses are at the aft junction of the bolt lug and the bolt cylinder. Also, notice the elastic deflection of the bolt face under load. It is not zero!

Good Hunting... from Varmint Al

Al--The fact that the point of greatest stress is at
the back of the lugs,, where in essence they are trying to
be pulled and sheared from the thrust, is the reason engineers only use half of the yield strength of the metal
in figuring how much thust lugs can take, in a relatively simple formula to use safely.. It is a very interesting
hobby we have..Ed.

The events in a chamber occur in the following sequences. The primer firing pushes the case forward.
The chamber pressure holds the case forward by friction to the wall. The primer pushes back until it
touches the bolt face. This is why a rifle with headspace may show a protruding primer when fired.
With a dry chamber the case stays forward until about 40 kpsi then friction is over come and the case comes back
stretching to fill the chamber. This is why reduced loads may develop headspace. When the case comes back if
the primer has protruded it is bulged a bit and pushing it back in the seat gives a "rivet" look to it.
If the case is oiled it dosen't adhere to the wall and comes back against the bolt face. The case isn't stretched, this is
a good way to fire form cases. When the case comes back it has the same force on the bolt oiled or not.
That is why the old timers oiled cases for "proof testing". With low pressure rounds the only time the case
pushes back is when it is oiled. Ackleys tests with a 94 Winchester with the locking bolt didn't prove anything.
In fact an "improved" cartridge will push back just as hard as a standard case.
Good luck!

Clark--it is nice to see your correct conclusions about
improved cases and bolt thrust.Ed.

IRV--You stated--""With a dry chamber the case stays forward until about 40 kpsi then friction is over come and the case comes back
stretching to fill the chamber.""
If dry case sides have 40k against them there is no chance of the case sliding back as that 40k psi holds it there.What moves back is the base with the sides stretching
just above base, if there is headspace for it to move,and/or
bolt,lugs,reciever stretch.When cases are oiled the major part of case at 40K doesn't move, but a little more of it above base, compared to dry case, slides so that stretching
is spread out and less thinning in like a ring occurs.Also
lubed case allows brass to flow into sharper shoulder on
bottleneck cases, when fireforming.Example is a 460 Wea
case.The brass just above base can hold about 6000 lbs thrust before they start stretching and if the sides have 40k pushing them into
chamber walls(in the area above base to the front) with a coeffient of friction of .4 for smooth chamber the case is held in place with a force of about
40,000 lbs so the case will stretch before the whole case moves.With oiled case the COF is .2 so case is still held
with a force of 20,000 lbs and whole case won't move but a little more of the sides above base will slide thus spreading out the stretch...Ed.

Hubel458 et al,

I have done a dynamic FE analysis of the effect of chamber friction on bolt thrust. You might be interested at reviewing the calculation results. Currently a test is underway to better measure the friction coefficient between 416 stainless steel and cartridge brass for various finish conditions. The calculations show the load on the bolt face as a function of time as the pressure in a 243 Win case is increased and then returned back to zero.

Here is the info: http://www.varmintal.net/a243z.htm

I would be very much interested in your comments.

Good Hunting... from Varmint Al

hi
I don't know about the kind of steel and hardness in my savage 340 bolt action. can you tell me if it could be rechambered to the modern 307 winchester? i love this old rifle because it is so handy ana I wish i could get more power from it.
best regards
danny

Al,

I loved the page. Mucho informative. I use Breakfree CLP on my Brasso polished Winchester H&H brass to fireform it to the .375 Weath. chamber Frank Wells did for me. That chamber shines.

The problem with a grease is it takes up more space than a thin coat of oil. I usually put a few drops on the paper towel and twirl the case, making sure there is no excess, as it has to go someplace when the pressure expands the case. I will see if I can get some Lubriplate EP and do some experimenting.

Ed: Of course you are right. I should have said the base moves back. An "improved" chamber is usually
set to minimum headspace for forming without stretching. If the standard cartridge is oiled cases will form
perfectly in a chamber with some headspace. I have done alittle testing with force sensitive film on the
case head. That is where I reached the conclusion that once the case head moves back it has the same force
as a dry case. This summer I plan to do a better controlled test.
Where are you in Michigan ?. I am around Big Rapids, which is why I shoot in the summer.
Take Care!

Irv- I am at Brinton, east of you 30 miles.Yes I learned a lot in my testing and wildcatting. I took belt back on 458

years ago to make headspace longer and checked thinning

after firing many rounds.I found dry cases thinned in a narrow band just ahead of belt, but that if the first inch

from base forward was lubed the stretching was spread out

to a longer area of the sides.I also reamed the chamber

50 thousands longer so as brass lenthened from dozens of reloads(with proper headspace)I didn't have to trim.Gave more powder area,and that is what started me on the longer case wildcatting.Ed.

Is there a reference somewhere that covers cartrige brass and heat treatments to go from dead soft, annealed to 1/4 or 1/2 hard..... Will heat treatment only get you so far? to what point? I would imagine that work hardening would be required to harden past that point.

Very interesting site Al.

Varmint Al,
Thanks for posting that.
It was nice to see such a good job after I spent time this week with a calculator[not programable] and piece of paper.

I wondered what the peak pressure advantage of small primer brass over large primer brass for 7.62x39mm.

Stension = tension stress of brass on primer pocket wall due to pressure in primer with unsupported extractor groove
Scompression = compression stress in primer pocket wall due to bolt thrust
Ac = inside area of case in combustion area
Appw = cross sectional area of primer pocket wall
P = peak pressure in case
Ff = friction force
S total = total stress on primer pocket wall due to tension and compression.

Scompression = Ac P /Appw - Ff
Stension [hoop stress] = P [inside diameter of primer] /[2 primer pocket wall thickness]

S total = [[Scompression]^2 + [Stension]^2 ]^1/2
The tension stress is <10% of compression stress and becomes only .5% as important as the compression stress when after the r.m.s. calculation.
Stotal = [approximately] = Scompression

Bolt Thrust = P Ac - Ff = S Appw
Ff = P Ac - S Appw
P = Appw S / Ac + Ff/Ac
Ac = pi r^2 = [ .4"]^2 pi/4 = .126 sq. in
Appw [large rifle primer pocket and .372" extractor groove] = A[OD] - A[ID] = [[.372"]^2 - [.210"]^2]pi/4 = .074 sq. in of brass
Appw [small rifle primer pocket and .372" extractor groove] = A[OD] - A[ID] = [[.372"]^2 - [.1775"]^2]pi/4 = .108 sq. in of brass

My large rifle primer test data:
Win brass lubricated with Imperial sizing wax, CCI200, 2.190" 180 gr Sierra
21.1 gr 296 cratered, no extractor groove growth, Quickload: 60 kpsi
22.5 gr. 296, primer fell out, .008~.012" extractor groove growth, Quickload: 72 kpsi

Assume the large primer brass case is good for 60 kpsi pressure per the above experiment.
Assume the brass material is good for 63ksi per the following post:
http://yarchive.net/gun/ammo/cartridge_expansion.html

Ff = 60kpsi .126 - 63ksi .074 = 2898 lb
friction force effective chamber pressure = 23 kpsi

P[small primer] = [.108] 63ksi/.126 + 2898/.126 = 77 kpsi
much better than the 60 kpsi for the large prmer brass.

Lapua and Win make large primer 7.62x39mm brass.
Remington used to make small primer brass.
I got a quanity of RP from Ebay.
Lapua 220 Russian is small primer brass, but paying 50 cents and necking it up to .311 is undesirable.

Lar45,

There is a table of cartridge brass properties down near the bottom of the same page: http://www.varmintal.net/a243z.htm

I would post the table of brass properties here, but don't know how to format a table on this forum.

There is also an interesting side by side calculation of a Full Hard case next to one that was inadvertently annealed. It shows why one doesn't want to anneal the case head and how dangerous it is to do so!