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October 25, 2009, 11:39 AM   #6
Bartholomew Roberts
member

Join Date: June 12, 2000
Location: Texas and Oklahoma area
Posts: 8,462
Some good science and math on the issue from the Ammo Oracle:

Quote:
 The importance of rate of twist in wounding is a frequent subject of what we politely call "ballistic myth." Any projectile that has a "center of pressure" forward of the center of gravity will tend to tumble. You can illustrate this to yourself by trying to balance a pencil on your fingertip. Spin, given to the projectile by barrel twist, puts a projectile into a state described as "gyroscopically stable." The projectile might be momentarily disturbed but will return to nose-forward flight quickly. To describe how stable a given projectile is we use the gyroscopic stability factor (Sg). Generally you want a factor of 1.3 or greater for rifle rounds. 1.5-2.0 is a generally accepted value for 5.56 rounds. For M193 the following variables apply: axial moment of inertia (A) = 11.82 gm/mm2 transverse moment of inertia (B) = 77.45 gm/mm2 mass (m) = 3.53 grams reference diameter (d) = 5.69 mm Using the gyroscopic stability formula: Sg = A2 p2 / (4 B Ma) and assuming sea level we use an air density of 1.2250 kg/m^3 and discover that this this projectile will need on the order of 236,000 rpm for good stability (Sg > 1.3). At 3200 fps M193 is typically spun up to more like 256,000 (1:9" twist) to 330,000 rpm (1:7") so that Sg approaches 1.9 or 2.0. 1:12" rifles will spin rounds at around 192,000 rpm and 1:14" rifles around 165,000 rpm. You can see why 1:14" rifles might have had trouble stabilizing M193 rounds. Clever math types will see that density of the medium traversed (air in this case) has a dramatic effect on the spin required to maintain the Sg (density being in the first term's divisor). This is why cold conditions tend to dip "barely stable" rounds below the stability threshold. Without doing too much calculus it will be seen that an increase of three orders of magnitude (1000) in this variable will be a dramatic one for spin requirements. To balance things spin must be increased to compensate. Through human flesh (which varies from 980 - 1100 kg/m^3 or about 1000 times the density of air) something on the order of 95,000,000 - 100,000,000 rpm is required to stabilize a projectile at speed. Given these differences it will be seen that the difference between a 1:12 or 1:14" twist when it hits flesh and a projectile launched from a 1:9 or 1:7" weapon is so small as to be beyond measuring. But the game isn't over yet. Gyroscopic stability of 2.0 or so is sufficient for a M193 projectile to recover from an upset quickly, return to nose-forward flight and not be over stabilized. To prevent the upset in the first place, particularly when a sudden and very extreme change in density (and therefore drag and pressure applied to the center of pressure) requires FAR more stability. To grant enough stability force to prevent the upset of a M193 projectile encountering a sudden 1000 fold increase in density a factor of as much as 10 to 50 times (speaking VERY conservatively) the required gyroscopic stability for a steady state flight through a medium of that density would be required. In other words, unless the projectile is spinning at nearly a BILLION rpm it is going to be upset by such a transition. Even at this rpm it is like to be upset somewhat. In summary, and to take the most extreme case, a M193 projectile spinning at 350,000 rpm (from a 1:7" rifle) is going to upset in flesh (yaw) exactly as fast as one spinning at 150,000 rpm (from a 1:14" rifle).

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