Transonic and Mach 1.8 Issues On Bullet Accuracy.

Transonic (Mach 0.95 - Mach 1.1), and Mach 1.8 Issues.

Much of the following may be old hat to the advanced rifleman - but the question still gets asked repeatedly: "What influences bullet accuracy at transonic velocity? And: and why is Mach 1.8 another issue?

It is going to be a comprehensive chat because aerodynamics is too interesting to be expressed in simplistic slang - it needs to be enjoyed thoroughly, and step by step.

When a bullet from a .22 short is travelling at below the speed of sound it sends out pressure waves ahead of it at the speed of sound. These pressure waves literally prepares the air in front of the bullet to partly seperating in advance to best stream around and over the bullet's geometric shape. The free air in front of the bullet acts as if it is incompressible and responds to the pressure waves advancing ahead of the bullet. The pressure waves running ahead at the speed of sound act as the mechanism which decreases the number of air molecules directly in front of the stagnation area on the bullet's frontal profile.

There also is a boundary layer of stationary air molecules that is attached to the bullet and moves with it and this stationary layer partly drags other air molecules along with it and causes what is called friction drag. The frontal area which directly collides with those stagnating air molecules creates an additional drag force on the bullet. At the subsonic velocity of a .22 Short the compressed thickness of this stagnation radius (or stagnation point in case of a pointed bullet) determines the amount of frontal or profile drag. For a fixed round or pointed nose profile this profile drag is purely dependent on the velocity of the bullet.

Ballistic Coefficient

The faster the bullet travels the thicker does this stagnation layer become. The total drag force increases with the bullet velocity - being squared each time the velocity is doubled. So right after the bullet leaves the muzzle the total drag is at its highest and it decreases rapidly as bullet velocity decreases. The frontal shape and therefore the size of the stagnation area, plus the friction drag and mass of the particular design gives a bullet a specific drag coefficient. Drag causes velocity reduction while higher mass for the same drag causes better bullet momentum en therefore better velocity retention. The optimum weight for a bullet from a 30-06 case is 193 gr and retains velocity better over long distance than a 125 gr, even though the latter starts out

The drag coefficient integrated with the total drag force of the bullet at any velocity and with its mass is used to calculate a bullet's "ballistic coefficient" (BC) for that velocity. The same bullet has a lower BC between 0 - 300 yards and a higher BC beyound 500 yards. Velocity retention determines flight time of the bullet over distance and therefor the amount of drop of the bullet over that distance. "Flat shooting" has become a selling point and bullet manufaturers typicall supply the high BC figure for their bullets while users of the bullet will use it 99.9% of the time over the low BC distance. The implication of this false marketing is axiomatic.

As the muzzle velocity from a subsonic .22 short to a barely supersonic .22 LR, to a Mach 1.6 .22 Magnum, to a Mach 2.5 30-06, to a Mach 3.1 .300 RUM approaches and passes the speed of sound the this stagnation layer is compressed more and its thickness decreases as the air density inside the layer increases. and more into the free air in front of the bullet.

For hunting purposes, there are no subsonic bullets in the practical sense - even a .50 flintlock musket shoots its round ball of 183 grains at about Mach 1.5 (1,600 ft/sec). The drag force caused by the compressed supersonic air on this bullet is about 10x as much had it been shot at a mere 1,000 ft/sec (about Mach 0.9).

The rate of slow down of the Mach 1.5 bullet will also be about 10x faster than that of a similar shaped bullet fired at 1,000 ft/sec) or a bullet having slowed through the transonic speed range. The critical drag rise Mach number by supersonic compressed air around the bullet depends on the aerodynamic shape of the bullet and starts at anything from about Mach 0.95 to Mach 1.1. This critical rise in drag force is due to 90 degrees standing shock waves forming on and around the bullet. Beyond Mach 1.2 the drag force reduces sharply as the 90 degrees, high drag standing shock wave pattern flattens into a cone around the bullet and the bullet flies inside a virtual vacuum (not really an airless vacuum, but protected from the drag of the earlier compressed air shock waves standing 90 degrees on the bullet shank as they do during the transonic speed range.

Depending on the design of the bullet its centre of mass may be forward or rearwards of the centre of the aerodynamic drag force created by the airflow over it. The bigger this lever arm is with the centre of mass to the rear of the centre of the aerodynamic forces the higher will be the destabilising force caused by the interaction of the aerodynamic and inertial moments forced on the bullet. To prevent the bullet from wobbling or even tumbling the bore rifling imparts a spin to the bullet which causes a stabilising inertial force called gyroscopic rigidity. The magnitude of this force is dependent on the mass of the bullet times the speed of rotation.

Often there will be posters on internet forums who vehemenently argue against bullet weight being a factor in gyroscopic rigidity, citing simplistic popular equations for twist rates to ensure gyroscopic rigidity. Fact is that the stabilising force of gyroscopic rigidity is an inertial moment and therefore solely depends on the mass of the rotating bullet and the rate of rotation of that mass. The thinking shooter needs only consider the relative stabilities of mass against airflow of two similar calibre and design and length bullets against opposing aerodynamics forces - one made of styrofoam or balsa wood and the other of pure copper.

It will also be clear to the reader that the length of a bullet determines the distances between the centre of mass of the bullet and the centre of the aerodynamic drag force on it. A bullet made of pure lead will be shorter than a bullet made of pure copper; the latter being of a longer length than the former with a longer distance between the centre of mass and the centre of the aerodynamic drag force on the bullet. This longer distance means that the copper bullet may need a higher spin rate to generate the same stability ability than the shorter lead bullet depending on the relative positions of the centre of mass and the centre of aerodynamic force. Simple algebra will show that if the centre of mass of the bullet is forward of, or very close to the centre of aerodynamic drag force a much lower grysocopic rigidity force will be needed, no matter the length of the bullet.

Just as there is a high drag rise at the onset of supersonic airflow around a bullet, there is another spike in unpredictable shockwave drag rise at Mach 1.8 to about Mach 2.0 on a bullet. It is a dynamic and complex situation to explain without employing algebra but has its origins in the flattening of the shock cone around the bullet and the random attachment and detachments of the shock cone to the frontal and rear ends of the bullet, and therefore an increased attack on the stability of the bullet. Particularly do bullets with pronounced ogives and long boat tail designs display instability issues from Mach 1.8 to about Mach 2.0, and particularly when impacting the differing plasma/bone/sinew and flesh density of an animal. This very well may have been part of the reason of the early failure to penetrate of 500 gr bullets from the .458 Win Mag on Cape buffalo and elephant with their 1,900-1,800 ft/sec launch / impact velocities.

When entering the variable and very higher environmental densities of say Cape buffalo and giraffe and elephant 1” thick tough skin, very tough and slippery tendons, very dense, convex shaped shoulder and 1" thick rib bones this attached shockwave is greatly intensified and wobbling is almost certain to ensue with immediate failure to penetrate. This phenomenon caused the original research and design by GS Custom Bullets in South Africa for the flat nose bullet which causes “super cavitation” to minimise the contact and drag force by the animal tissue on the bullet. This was taken up by Peregrine bullets, and the concept of a virtual flat nose also by Impala Bullets.

Another way for maintaining penetration stability on large soft skinned and soft boned animals is to have a bullet which is heavy in any particular calibre to combine a flat nose and pre-impact velocity below Mach 1.8. The highest mass for the calibre is required to still ensure a suitable impact impulse force per square millimetre frontal area at the low impact velocity of below Mach 1.8 to ensure both stability and retained penetration momentum in order to ensure mechanical breaking down of all the drag forces (skin, sinew, convex bone and flesh), and to reach and cut open the heart top chambers for a quick kill.

The above was the thinking behind my contention that the best calibre-bullet weight combination for the exceedingly dangerous little bushbuck hunted at short range in its dense, dark forest habitat would be a .358" flat nose calibre bullet of 270 gr with a muzzle velocity at nothing higher than 1,800 ft/sec (well below Mach 1.8) - and the reason to have a Marlin 30-30 rebarreled to a 30-30/.358".

Bushbuck have such exquisite meat and beautiful cape that one does not want to spoil any with a fast, expanding bullet.

The flat nose Peregrine / GS Custom / Rhino / Impala monolithic solids or solid shanks already make a 4x calibre permanent inside wound channel (calibre size entrance and exit holes in the skin) with zero meat damage and therefore may even be suitable for kudu out to 100 yards - but the 24" Marlin in this 30-30/.358" chambering will be a dedicated bushbuck rifle.