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What happens inside the cartridge until maximum pressure is reached?
New member Hermann Weideman of Peregrine Monolithics in the USA corrected my figure about the equivalent in the universe of the 60,000 psi inside a 30-06 chamber. I compared it to the pressure at the bottom of an ocean 132,000,000 ft deep. I must have done a decimal incorrectly somewhere: the actual comparison of 60,000 psi is at the bottom of an ocean 135,000 ft. deep.
Thank you Hermann.
We all know that rifle propellants do not meet the thermodynamic features to satisfy the common definition of an explosive. Having said that, go limit the expanding volume behind a departing bullet relative to the so called burn rate of the propellant, secure the rifle on a heavy vehicle tire, pull the trigger from behind cover with a string and see that rifle chamber explode in quite impressive fashion. So, despite all the rolling eyes out there - in this discussion I shall refer to the deflagration that takes place inside a rifle chamber as the explosion. :-)
The time of this burn is explosively quick and way outside our normal frame of reference, as is the pressure rise it causes. Misinterpreting this rapid development often is the cause of misunderstanding the dynamics of what happens inside the case and inside the ever-expanding combustion chamber behind the departing bullet. This post is all about that. Here are some first perspectives:
Pressure: The 60,000 psi in say a 30-06 chamber is a very HIGH and very dangerous pressure, being the same as at the bottom of an ocean 135,0000 feet deep.
Time: The application of this enormous pressure (the burn time of the propellant) - is explosively quick - like 0.0005 of a second in a rifle and 0.0001 in a handgun. For a rifle that is one half of one ten thousandth of a second. This means that after having fired one thousand rounds your rifle has experienced only 1.5 seconds of pressure through the average 24” barrel. It is a sober thought that some overbore rifle barrels have only a one second useful life.
In a rifle like the 30-06 this maximum pressure is already achieved after the bullet has only moved about 1.4 inches away from the case mouth, and in handguns it happens with the bullet still in contact with the case. With the relatively small case and large bore diameter of the .458 Win Mag the maximum pressure is attained when the bullet has moved less than an inch after having been expelled from the case mouth.
Despite the considerable amount of published affirmations about the benefits of wide shoulders, steep shoulder angles, short, and super-short, and ultra super short, wide bodied cases - real scientific research has not presented any empirical proof of either a thermodynamic or accuracy gain in such designs. In fact the .375 H&H, 30-06, .303 Brit and .300 H&H are right up there in the top 25 winners of the SA Hunting rifle group shooting competitions where the winner will have shot a .16" group and number 25 will typically have shot a smaller than .30" group. The case geometry has little if any influence on burn efficiency or accuracy during that 1/4 of one ten thousandth of a second of gas generation as discussed below:
1. Rate of Pressure Increase
This time taken by the explosion, or put more correctly: the rate at which the pressure is increased to peak value when the bullet is at the optimum distance away from the case is the most important performance requirement for the propellant. Rate of pressure increase is critical for every different combination of: 1) case volume, 2) the increasing bore volume behind the departing bullet into which the gas must expand, 3) bullet mass, and very important: 4) bullet frictional resistance, and 5) seating depth. Considering each one of these variables which influences rate of pressure increase in turn, and then the combined interaction of these:
1.1 Case Volume. The case volume determines the maximum volume of propellant it can hold and therefor the maximum gas volume it can develop and compress into the increasing chamber volume behind the departing bullet within a set time at the rate of its explosion. This determines the maximum amount of heat energy and therefor pressure that can be obtained, which determines the maximum velocity it can impart to the bullet.
1.2 The increasing bore volume behind the departing bullet. The case volume to barrel volume relationship has a direct bearing on maximum achievable velocity of a specific weight bullet.
1.3. Bullet Mass. Higher bullet mass means higher inertia to be overcome by the gas pressure to start the bullet going. Related to the increasing bore volume behind the departing bullet a heavier bullet in any calibre needs a slower burning propellant in order to prevent a too fast rate of pressure increase than what a lighter bullet would need.
1.4. Bullet Frictional Resistance. Bullets with relatively high surface friction like the original Barnes “X” have higher resistance to initial moving and this adds to the higher inertia or reluctance to start out, and typically needs a slower burning propellant than conventional bullets to prevent an overpressure condition. Conversely, bullets like the GS Custom series with narrow drive bands that have very low friction coefficients need propellants of typically 2-3 steps faster burn rate than standard bullets of the same weight to obtain the rated pressure needed for the required velocity.
1.5 Seating Depth. Together with the bullet’s inherent frictional resistance any other immediate mechanical hurdle which temporarily delays immediate movement will delay the rate at which the volume behind the bullet increases into which the gas can expand, will cause a quicker rate of pressure build-up and possible over pressure.
Bullets like the Barnes series and particularly the original “X” series with known high friction coefficients must have an easier start by not having them immediately against the mechanical resistance of the lands.
The very low friction of the GS Custom bullets with drive bands benefits from the extra delay offered by contact with the rifling. This is particularly so where the ratio of case capacity to bore volume is low like the 30-30 and the .458 Win Mag. Adding a tight crimp to the .458 bullet will also assist towards a steeper pressure slope.
2. The Complete Picture:
2.1 Gas Generation and Pressure (1). Pressure starts slowly increasing after the firing pin has ignited the primer, then a very short-duration, rapid rise in pressure at first ignition of the propellant follows, and then immediately a zero rise in pressure for a short while followed by a gradual rise to about 10% of maximum pressure, all in about ¼ of one ten thousandth of second.
2.2 Gas Generation and Pressure (2). At 10% of maximum pressure the bullet starts moving out of the case and the volume of the combustion chamber behind the bullet starts increasing exponentially. This is the critical and determining phase for under of over pressure. Too little bullet mass or a very slippery bullet with a lot of freebore ahead moving out too easily, combined with a propellant that has a slow rate of pressure increase due to low burn rate or low gas volume from a small case relative to bore volume (30-30 and .458 Win Mag) may not reach rated pressure and muzzle velocity.
Too much bullet side friction (Barnes “X”) or already touching the lands causing added resistance against moving out may cause a too rapid rise in pressure and reaching maximum gas volume before the departing bullet had created the optimum bore volume, which will result in over pressure. It is to be noted that the gas temperature rise is inter alia a function of the pressure rise. This means that a too easy bullet move-out and slower rate of pressure increase also limits the temperature rise and the eventual level of energy attainment and therefor velocity.
2.3 Gas generation and Pressure (3). Inside the chamber and contained by the action the following happens:
If there is no weakness in the metallurgic integrity of the vessel the failure mode when the pressure is increased past the ultimate strength of the metal will be radially onto the large side wall surfaces and not rearwards or forward onto the small surface areas. In a barrelled action the weaknesses are the stress concentration radials of the acute angles of the threads in the action and the barrel.
Inside the barrel the gas expands in a controlled and relatively slow manner into the ever increasing volume behind the departing bullet. The pressure force in all directions decreases as the bullet moves out of the case mouth and past the peak pressure position about 1.5" further.
In the rifle the designed weak point in the temporary pressure vessel (the cartridge case in the chamber) is the safety pressure plug (the bullet) in front of the cartridge. The cartridge itself is tightly shaped inside the chamber and pressed radially to the sides due to the flexibility of the relatively thin brass walls. The highest force by far is radially onto the flexible case walls pressing them tightly against the chamber walls. This radial pressure acts like old style drum brakes on a vehicle, preventing or limiting rearward movement of the case.
The volume of the pressure chamber is slowly (in relative terms) being increased as the pressure relief plug (bullet) is pushed out and as it moves forward, while chamber pressure forces are slowly decreasing in all directions. Pressure decreases progressively in ALL directions as the volume behind the moving bullet increases. There is NO resultant vector of pressure forces forwards or rearwards. All the time the biggest pressure is radially to the sides, pressing the flexible, elastic brass tightly against the chamber walls.
As the total pressure which is the same in all directions and also on the base of the moving bullet decreases with increasing bore volume the case walls (and their braking grip onto the chamber walls) relax into their designed shape. So called "bolt thrust" is negligible with normal operating pressures.
The actual value of that "bolt thrust" force: At 55,000 psi in a .303 case the radial pressure force on the chamber wall surface by the walls of the case is a whopping 152,000 lb. (55,000 psi times the case inside wall surface area) - the very reason why over-pressure failures are always into the chamber walls in any rifle. This radial force is countered by the thickness of the metal walls of the rifle's chamber. This designed thickness is conditional on the quantum of the radial pressure plus the tangential stress vectors it causes, and the metallurgical integrity of the barrel steel. Typically under European CIP specifications the average wall thickness around the cartridge web is about 2x calibre and tapers off forwards. The barrel profile can in fact be seen as a graph of the highest stressed sections.
If there had been no braking effect to rearward movement of the case as is caused by this huge clinging radial force, the total pressure on the bolt face via the inside rear end surface area of the case will be 6,930 lbs. force - or 30,130 psi. Due to the braking effect of the radial pressure force on the case walls In practice the rearward force is a great deal less. Even if it is assumed that the braking effect did not exist the force exerted onto a Lee Enfield bolt is less 20% of the force onto the 1/2" chamber wall thickness, which is sufficient to contain that full 152,000 lb radial force.
In actions with front locking lugs the rearward "thrust force" is countered by the compression resistance of the full length of the receiver rearwards of the lugs, aided by the compression resistance of the metal from the bolt face to the contact surface of the locking lugs with the receiver. Furthermore, these are aided by the tensile resistance of the barrelled action forward of the lugs.
On the Lee Enfield action with locking lugs to the rear of the bolt the pressure against the bolt face is countered by compression resistance offered by the full length of the bolt from face to the lugs, aided by tensile resistance of the full length of the receiver forward of the locking lugs (3 inches of locked steel), including the added rigidity from the mated barrel it pulls against. There exists no popularly available empirical values for these compression and tensile forces or a measured relative ability for the above two designs to counter these pressures without measurable elastic compression / extension and spring back. Rough calculations indicate that there is no difference in elastic response between the two lock-up designs, and in fact that the longer linear shock absorbing dynamics of the Lee action may render it more resilient to brittle failure than the front lock-up design of the Mauser type bolt.
2.4 Gas Generation and Pressure (4). Within the next ¼ of a ten thousandth of a second the bullet has moved about 1.5 inches and pressure rises to the typical 60,000 psi of a 30-06. The 180gr bullet in a 30-06 chamber is now accelerating at 160,000 g. (When I pulled the ejection seat handle in a jet fighter three cartridges in my seat fired in quick succession, shot me out and 3/4 of a second after pulling the trigger I was hanging in my open parachute 300’ above the aircraft, with a fractured back vertebra due to the 32g kick).
3.1 Energy General. Being a scalar entity we all know that energy by itself of course can not do any work, but energy being released as measurable heat causes the generated gas to expand and pressured into the enlarging combustion chamber behind the bullet; this pressure forces the bullet out of the case, through the bore, and a residual pushing force of about 575 lbs (7,000 psi) expels the .308" diameter bullet out of the muzzle of a 30-06.
3.2 Energy Specifics. The most popular30-06 propellant in South Africa for a 180gr bullet is Somchem S365 which has the following thermodynamic properties. Understanding these values will enable the serious reloader to choose exactly the best propellant from any brand in the world for a specific cartridge:
Flame Temperature: 4,932 degrees Fahrenheit. This is the immediate temperature of the conflagration impulse and determines the final energy output as inhibited by the burn rate retardant chemicals.
Specific Energy Release: 1,050 joules per gram of propellant (1 gram=15.4 grains). This means that 55.9 gr of S365 generates 3.811 kilojoules of energy to expand the generated gas to cause a pressure of 58,872 psi to propel a PMP 168 gr bullet at 2,846 ft/sec.
Heat of the Explosion: 3.983 kilojoules per 15.4gr of propellant. See Carbon Volume below:
Carbon (graphite) Volume: Less than 1 gram per cubic centimeter. This is an indication which, together with he total heat of the explosion determines the amount of unburnt residue in the rifle's bore. Somchem propellants, after 20 shots typically leave a originally mirror bore with a dull appearance but no visible residue.
Load density: 22.45gr of propellant per cubic centimeter case capacity.
% velocity deviation: Less than 0.7% deviation from the reference velocity for that batch. The full history from the beginning of time for every batch is available.