How can the mechanical stress exerted by DG cartridges on the action be estimated? Peak pressure alone is not a solution

Peak chamber pressure (e.g., in N/cm² or MPa) by itself does not fully describe the mechanical stress experienced by the firearm. However, it is a commonly used metric to assess the mechanical stress. Certainly, this is not the whole story because besides peak pressure, bolt thrust, pressure time curve, the weight of the powder charge, the friction of the cartridge case, and the bullet impulse all play a significant role.

I am interested whether a single index can describe the mechanical stress.

In order to stimulate a discussion on this issue I have selected some DG rounds and metrics were calculated with AI
Below is a structured comparative estimate for the selected cartridges using typical modern factory loads with common bullet weights.

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Assumptions Used
Representative loads (modern factory equivalents):

1. Bolt Thrust (Primary Structural Load on Locking Lugs)
Formula:
Case head area
A = π(d²)/4
Bolt thrust
T = P × A
Results:

Key Observation
.460 Weatherby produces ~26% higher bolt thrust than .375 H&H.


2. Momentum (Projectile Impulse)
Momentum = (bullet gr ÷ 7000) × velocity



3. Pressure–Time Curve Considerations
This is critical but often overlooked:
High-pressure (sharp curve)

• .460 Weatherby
• .416 Remington Magnum
• .458 Winchester Magnum
• .375 H&H Magnum

These produce:

• Higher peak bolt load
• Sharper stress rise
• Greater lug setback potential
• More receiver ring stress

Low pressure (longer curve)

• .416 Rigby
• .505 Gibbs
• .404 Jeffery
• .450/400 NE

These produce:

• Lower peak stress
• Longer impulse duration
• Smoother load transfer
• Reduced action battering (despite high recoil)

4. Receiver Hoop Stress = Circumferential Stress (Simplified)
Thin-wall approximation:
σ ≈ (P × r) / t
Where:

• = internal pressure
• = inner radius
• = wall thickness

Relative comparison proportional to P × case radius.
Relative to .375 H&H:



How would you rank theses rounds based on the mechanical stress on the action? Is there a possibility to find a single proxy? How much weight should be given to the different metrics shown above? How can the friction of the case be considered?

To start the discussion here is my personal ranking which is based on gut feeling rather than on scientific grounds:

1. .460 Weatherby
2. .416 Remington Magnum
3. .458 Winchester Magnum
4. .375 H&H Magnum
5. .416 Rigby
6. .505 Gibbs
7. .404 Jeffery
8. .400/450 Nitro Express

.416 Rigby and .505 Gibbs are probably sharing similar ranks.

Interesting, but how relevant are such parameters in practice?

It is certainly good to know that when you select a cartridge for hunting DG to be sure that you also bought a suitable firearm for it, but I would not do that only based on such criteria.

Interesting. I was with you till #3. Need a bit more explaining after that. Interesting that you have calculated 404 based on 2300 fps velocity for 400 gr ammo. Presumably this is Hornady factory ammo. The concensus seems to be they put way too much gas in their stuff. Most prefer the old standard 2150 fps as a benchmark. I haven't chronoed my loads but literature seems to indicate around 2200 fps and that's almost too much recoil for me.

I guess it could be possible to make case friction calculations using area of case surface and pressure. Shouldn't be that difficult. It would not be precise given irregular shape of most cases (shoulders and belts) but could be used for general comparison? I think you are correct in assuming case friction must have some effect on chamber pressure. Fatter and/or longer cartridge cases have the potential to disperse outward pressure on the chamber over a greater area. Theoretically this must effect the pressure on the bolt face.

You also need to consider back trust on the bolt face.
Force = pressure X area.
It is the chamber pressure multiplied by the area of the rim. If it is a rebated rim then use the base diameter,

Sorry I now see you had back trust.
It is debateable as to how much is transfered to the bolt face as cartridge taper and chamber finish all influence how much back thrust is actually transferred. But assuming all aspects are equal then the relative values are valid.

@grand veneur
For example, with a similar amount of work the Mauser 98 system can handle both the .416 Remington Magnum and the .404 Jeffery. I would definitely opt for the .404, as it causes less mechanical stress. Or, as a Ruger No. 1 fan, I would always prefer a .416 Righby to a .416 Remington.

I found the following YouTube video

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interesting, but wondered if a .505 Gibbs might be a bit too much for a Ruger No. 1 conversion in the long run. Based on the above estimates, the .505 will not cause any problems, but I believe that a .460 Weatherby Magnum should not be used, even though it is possible (see, for example, Africahunting ‘Ruger No. 1 460 Weatherby’). Of course, there is no need to discuss the terrible recoil of both cartridges or the rationale of these conversions.

I own a custom rifle caliber 460 Weatherby Magnum built with a Brevex Mauser action, with which I have fired hundreds of rounds over the last 30 years. No sign of any wear.

@BlackRhino I love your analysis!

I purpose a slightly different hypothesis;
There are two factors that must be considered for action strength, Hoop Stress and Bolt Thrust.

• Hoop Stress, or not exceeding the Circumferential Stress limit of the close cell pressure vessel that the combination of the action, barrel, and base of the bullet traveling through the barrel keeps that assembly from functioning as a grenade.
• I think that firearm actions are designed to provide at least 1.5x strength over the maximum mean working pressure of the cartridges that the barrels joined to those actions will be chambered in.
• M98 with good metallurgy are routinely used for cartridges with 62,000 maximum mean working pressures. I cannot confirm this but I believe that the better of these actions do not become grenades until they exceed 98,000 psi (or more).
• Bolt Thrust, or not exceeding the Longitudinal Strength of the action keeps the barrel and the bolt, breach block, of standing breach from separating.
• Maximum blot thrust is a very important factor in the chambering’s of break action, i.e. double rifle. A little too much bolt thrust over too many shots will slowly loosen an action.
• I remember reading somewhere in the last 50+ years once or twice of blot actions’ bolts sheering the bolt lugs and being thrust rearward into the shooter’s face. I cannot presently find any examples of this. Maybe I am dreaming…

I believe that hoop stress is the most important factor for safety of any firearm. In a strong bolt action, the bolt thrust is important but should be within the operating limits of the action.

In a break action, bolt thrust while not as important as hoop stress, becomes an important factor since the break actions are not as strong longitudinally as bolt actions. Break actions may handle high pressure cartridges but what would an overpressure of 80,000 psi do to these actions? Even within the safe working pressures of high pressure cartridges like the .458 Win Mag, 62,000 psi, over time break actions will suffer plastic deformation little by little and the barrels will become loose against the standing breach.

Bottom line is hoop stress is most important but bolt thrust is an important design consideration, especially in break action rifles.

I made a short post in January about bolt thrust on a new .44 Mag double rifle by Pedersoli.

460 Weatherby shoots 500 gr bullets @ 2600 fps! Wow. Did not know that. I'm surprised there is an action, not to mention a shooter, built to take that kind of abuse.

I went looking for "projectile impulse" explanation and this is what I found.

"Impulse (J) is the product of the average force (F) applied to the base of the projectile and the time (t) that force acts:
Δ=×Δ "

The length of the barrel and muzzle velocity determines the Δ factor. The longer the barrel the more time gasses will be pressed against the base of bullet. The greater velocity = greater pressure on that bullet per unit of time. I am assuming all calculations were made with barrel of same length.

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@BlackRhino Thank you for putting up your calculations. I was breaking out my caculator.

@Mark A Ouellette Your analysis on the actions is spot on.

@Ontario Hunter The 460, 416,378 weatherby's all have serious recoil not just in Ftlbs of recoil but also in the fact that they come back an a very high speed.

Ontario Hunter said:

I went looking for "projectile impulse" explanation and this is what I found.

"Impulse (J) is the product of the average force (F) applied to the base of the projectile and the time (t) that force acts:
Δ=×Δ "

The length of the barrel and velocity determines the Δ factor. The longer the barrel the more time gasses will be pressed against the base of bullet. The greater velocity = greater pressure on that bullet per unit of time. I am assuming all calculations were made with barrel of same length.

Click to expand...

Regardless of this,
"Impulse (J) is the product of the average force (F) applied to the base of the projectile and the time (t) that force acts:
Δ=×Δ "

Longer barrels do not affect peak pressure.

Peak pressure is generated when the bullet is being swaged into the rifling. Increased pressure in the closed cell pressure vessel causes smokeless powder to increase its burn rate, then again, and again…
When the bullet is fully swaged into the rifling and starts traveling through the barrel, the resistance to movement is less, and the volume of the pressure vessel is increasing. Both reduce the pressure and that lessens the burn rate of the powder. See the pressure curve below,



Note: Athough pressures curves vary in peak and slopes, be they for smokeless loads in rifle, shotgun, for handgun, in general they all appear similar to this.

As long as the pressure remains within the elastic range of the barrel and action metal, nothing permanently changes. But if the pressure exceeds that limit and plastic deformation occurs, there is a safety problem and the firearm may be ruined! The threshold of plastic deformation varys pertaining the the steel/steel alloy the barrel and action are made of.

Ontario Hunter said:

I went looking for "projectile impulse" explanation and this is what I found.

"Impulse (J) is the product of the average force (F) applied to the base of the projectile and the time (t) that force acts:
Δ=×Δ "

The length of the barrel and muzzle velocity determines the Δ factor. The longer the barrel the more time gasses will be pressed against the base of bullet. The greater velocity = greater pressure on that bullet per unit of time. I am assuming all calculations were made with barrel of same length.

.

Click to expand...

For some reason parts of the formula were snuffed when publishing that post. Delta P = F × delta t. Presumably delta P is change of pressure or projectile impulse.

So would cartridge design affect back thrust? Think of 300 H&H vs some 40 degree Ackley Improved. One of the professed benefits of less taper is to reduce case lengthening, which suggests that longitudinal pressures are involved. Or is something else going on?

Ontario Hunter said:

460 Weatherby shoots 500 gr bullets @ 2600 fps! Wow. Did not know that. I'm surprised there is an action, not to mention a shooter, built to take that kind of abuse.

Click to expand...

grand veneur said:

View attachment 749767

View attachment 749768

Click to expand...

Good grief! 2700 fps. The box should come with a hospital bed illustration on it not an elephant.

@BlackRhino
Great to see math…
A couple of points:
1. For the bolt thrust, I use the rim diameter- the head groove diameter as the pressure goes thru this area, not the rim area. I use the axial pressure instead of the radial, which is app. 85% of the radial (see QL)
2. I use QL to find the distance from the breech face when the peak pressure occurs. This determines the barrel diameters I use for the barrel stress.
3. The Hoop stress is only the tangential stress. There is also a radial stress equal to the peak pressure. I also use the thick model (why not, excel does the work) which includes the outside diameter & outside pressure ( sea level psi and usually can be ignored). Von Mises shows how to combine the tangential & radial, sqrt((hoop+radial)^2), which is significant if ignored.
If you follow this, you will match a 3D static pressure simulation.

I have read that case design has a large impact on bolt thrust. Less case taper= less bolt thrust, more taper= more bolt thrust. I recall reading about an experiment PO Ackley did with a lever action chambered in 30-30, then rechambered to 30-30 AI. The AI version had much less bolt thrust, demonstrated by shooting the AI version with locking block removed from the rifle with no ill effects, bolt was held closed by the lever only. Reportedly this is because the case walls are able to grip the chamber more with a straighter case. Theoretically this could increase hoop stresses though I suppose.

Many thanks for all your valuable inputs! Good points!

While hoop stress can be easily better simulated by the thick model, I have no idea how the case design can be estimated and then to be added to bolt thrust when a tapered case is considered.

A rapid and a slow pressure curve can result into an identical bullet impulse. However, it is obvious that a rapid pressure curve as was mentioned by AZDAVE for the Weatherby rounds provides more mechanical stress. How can a different pressure curve be considered?

But back to my question. We can calculate several factors, but which weight should be given to these factors in order come up wth a single index? Let's say that for simplicity we only consider three Factors:

(1) bolt trust
(2) bullet impulse
(3) hoop stress.

What's your weighting?

All of the factors that you have outlined are related to pressure. Failure of the chamber or lugs would occur at peak pressure, so that is surely the main factor. So engineers will determine the weakest link, ie chamber or lockup. Then determine the failure pressure for that component and reduce pressure by a safety margin.

In practise, bolt thrust is less than absolute pressure because the brass grips the chamber and also contains the pressure more in the base area (thicker brass).

One would also assume that any decent engineer would design the first failure point at the safest point. In my mind, that would be the chamber as that is furthest from the shooter. A bolt flying backwards is sure to do more damage. So they simply overdosing the lockup and then use chamber pressure to determine safe margins on the chamber.

You could run different scenarios through Solidworks or Autocad to develop stress illustrations.