What happens after the Maximum Pressure Moment (MPM)?
As was stated in the discussion on internal ballistics (the initial thermodynamic phase immediately after ignition) the maximum pressure inside the chamber of our 30-06 rifle occurs when the bullet has reached a position about 1.4" in front of the case mouth.
This does not mean that gas generation and expansion is now complete - far from it. It only means that as more gas is generated and expanded this pressurisation happens inside a combustion chamber the volume of which is expanding very rapidly. As the gas is generated it expands into an increasing space and the pressure starts dropping from say 62,000 psi at MPM to about 6,800 - 7,000 at the muzzle departure moment (MDM). This phase is what causes the following:
The final (muzzle) pressure at the moment of bullet departure determines the final value of the bullet's muzzle velocity.
The time difference for bullet acceleration from the MPM to MDM determines the impulse of the momentum value at bullet departure and partly determines the measurable recoil.
The value difference between P.max at MPM and P.min at MDMdetermines the felt recoil and also is the physical determining value for the final muzzle pressure and therefor muzzle velocity - but this is only part of that equation- as
-the base physical reason for the value of P.min at MDM is the actual volume of gas generated within the parameters of 1-3 above.
Associated with the thermodynamics touched on above are the inertial dynamics caused by the bullet accelerating down the bore - mechanical issues which have to do with the interactive forces between the bullet and the barrel, the barrel and the action, the barreled action and the stock, and finally the complete rifle and the shooter holding it.
The bullet engages the rifling. The bullet is forced from behind into the rifling - which normally is spiralling clockwise viewed from the rear - and as the lands engrave the bullet there is a radial force from the lands onto the bullet, forcing it to spin to the right.
/ displacementThe counter force by the bullet is an anti clockwise torqueing action on the lands and therefore into the whole barrel. This force increases as the bullet encounters less and less barrel stiffness moving away from the breech. Typically in a 1:12" twist rate barrel the bullet does two complete rotations before it leaves the muzzle, exerting an anti clockwise elastic torqueing deformation / displacement to the more flexible muzzle end of the barrel.
High speed tracing of a laser beam emanating from the crown indicates that the nett movement of a 24" standard profile barrel with a clockwise twist is a typical 2-3 microns to the left with corresponding shift in impact points of the bullets. Vertical separation of the bore centre point at bullet departure appears to be neglibly minute.
As the barrel heats up during repeated firing the increase in temperature exacerbates any post rifling-cutting residual metallurgical stresses in the metal and the displacement pattern of the barrel will change with every shot as the barrel heats up - even if the barrel does not make any contact with the stock channel.
The standard displacement is repeated with every shot and in barrels that have been stress relieved (as all European and South African made barrels) the difference between five shots will not be more than about two microns (two thousands of a mm at the muzzle. This relates to an impact displacement of .25 mm at 100 yards which is so small it can be disregarded. Any barrel that has residual stresses from the very stressful rifling forming process will display random displacements orders of magnitude bigger than this. This is why the South African Hunting Rifle Group Shooting Competitions where only bona fide hunting rifles and PMP factory ammunition is used has the top ten shooters obtaining between 4mm and 5mm groups, and number 25 from the top typically at 6.5mm at 100 yards over a standard sandbag rest in front and no rest at the rear.
The bullet leaves the crown. The torqueing, bending force on the barrel is ongoing as the bullet acellerates forward and continuously and progressively increasing the amplitude of displacement of the barrel against its elastic rigidity. The moment the bullet leaves the crown the displacing force is removed and the barrel springs back due to its own mechanical elasticity and typically does two vibratory oscillations before settling in its original position. This is a pure, very short term, elastic, damped vibration and has no influence at all on the bullet which by then is happily on its way to the heart of the animal it was aimed at.
In American gun media the term barrel harmonics is often used and how this affects the bullet during departure - as if it is an outside influence on the bullet. The term "resonance" is already incorrect at it refers to a part of any structure which vibrates in harmony with an outside vibratory input due to the particular elastic similarity to the input vibration - the simbiotic harmonics of the input vibration and the reactive response by the resonating part. The terms resonance and harmonics by definition are reactive and outside of mechanical connection between the input energy and the reactive vibration. It does not apply to a barrel and a bullet.
The term barrel harmonics which supposedly can affect the departure point of the bullet is incorrect terminology. Any post departure vibration of the barrel as explained above is due to the barrel's elastic return after having been mechanically displaced by the bullet. A harmonic or resonance is a form of auto-stimulation to to a vibratory input and not related to a barrel and a bullet.
Behind the bullet, and sealed off from the outside atmosphere exists the inside atmosphere which is at a temperature of about 1,500 degrees centigrade and having a pressure of about 7,000 psi. In front of the bullet existed the earth's atmosphere at a pressure of about 14 psi. The bullet forces this column of air out at about Mach 2.5 and this creates a supersonic shock wave in the air in front of the muzzle slightly ahead of the bullet.
Behind this shock wave, at that incremental moment before departure there exists a temporary vacuum in front of the muzzle into which the bullet acellerates, being pushed from behind and then gets overtaken by the gas pressure which expands into this partial vacuum at a speed in excess of Mach 3. So straight after having left the braking friction of the rifling the bullet still gains speed for a short while. This moment of freeing itself from the rifle is crucial to accuracy and will be discussed in this section of intermediate ballistics.
This moment of freeing itself from the rifle is crucial to accuracy. Accepting that every part of the barreled action and interfacing with the stock is linear and concentric (some models of the Ruger Mk. 1 and earlier Ruger M77s were so horribly eccentric that it was not worth to spend any money on gunsmithing), and that the barrel had been properly stress relieved, the only remaining causes for inherent inaccuracy in any rifle / bullet combination are the following two issues:
The perfect concentricity and squareness of the bore crown with the bore centreline.
The perfect squareness to the shank and concentricity of the base of the bullet.
The minutest deformity in the bore crown will cause uneven release of the base of the bullet, some wobbling, a lot of profile drag and poor airtime performance.
Similarly, the minutest inaccuracy in the base of the bullet - and this particularly is the risk with boat tail bullets - will cause similar uneven release from the crown, but more so a marked effect by the dense atmospheric pressurised gas overtaking and shoving the bullet from behind just as it leaves the crown.
This wave of very dense gas enveloping the bullet from the rear, for a short but significant time that apart from influencing the attitude of an inaccurately designed bullet, causes it to fly without any airflow from the front over it. First the bullet has a slight rear to front airflow as it flies behind the shockwave front of the expelled air from the muzzle; then there is a momentary true vacuum around it, and then there is the fast, flaming hot, high pressure gas surrounding and passing it from behind. Only once this interaction between the gas and the environment atmosphere has dissipated does the bullet enter a condition of free stream airflow over it and then its design aerodynamics come into effect.
Next issue for discussion will be about recoil - what causes it, how total recoil is calculated and the difference between calculated and felt recoil, and the factors influencing the latter.