# A-Square Shock Power Index - A-Square Shock Power Index

ASPI values ​​according to Alphin (Anglo-Saxon measurement system) [ft * lb * in²]
ASPI values ​​metric [Jmm²]
Deformation examples: lead hollow point projectiles fired with cartridges .22lfB subsonic ammunition
Image of a mushroomed bullet, cal. 38 Special

The A-Square Shock Power Index (abbreviated ASPI) or A-Square Power Index is an index to identify a projectile's impact . It is based on the quantities energy and cross-section and thus only represents impact ballistics, but not internal, external or even wound canal ballistics . The projectile properties and effects are therefore not described.

## history

The complex processes involved in hitting a projectile on a target are difficult to grasp. This is partly due to the complex mathematics and the limits of numerical simulation ( FEM , BEM ), but also to the lack of the necessary material parameters in these areas. In addition, it is usually unclear beforehand what and where exactly will be hit. Thus, the assumptions to be made for a calculation are very extensive.

Attempts were made early on to describe the effect of a projectile and the protection against it in a simplified mathematical and physical way. Newton and his calculation of the penetration force or the armor formula are mentioned here. [1]

The ASPI was developed by Colonel Arthur Brent Alphin from his military experience with the stopping action of various calibres. Alphin was the founder and developer of the American ammunition manufacturer A-Square Company , which went bankrupt in 2001 and was taken over by James L. Smith. Alphin has been the technical director ever since. In his book Any Shot you want , published in 1996, Alphin presented a system of indicators with a variant of the penetration index in order to make the performance of calibers comparable. [2] [3]

## meaning

Key figures such as ASPI are particularly important for the police, self-protection and hunting. It is important for hunters to kill the game as gently and without suffering as possible. For this, on the one hand the hit position is decisive, on the other hand the projectile effect. [4] [5] This is legally regulated in Germany in the Federal Hunting Act. [6] However, only minimum calibers and minimum energies are used here. As a rule, hunters seek greater certainty in the choice of caliber.

In practice, therefore, various recommendations are made based on practical experience. [7] The ASPI at least essentially reflects this. [8th]

The ASPI does not reflect the effect of the caliber with regard to e.g. B. Distraction of small calibers by branches, wound ballistics or the effects of the projectile type .

## Calculation and use

The calculation of the ASPI is as follows:

${\displaystyle ASPI=E\cdot r^{2}\cdot \pi }$

With ${\displaystyle E}$ as kinetic energy of the projectile

and ${\displaystyle r}$ as the radius of the projectile

With ${\displaystyle E=1/2\cdot m\cdot v^{2}}$

and ${\displaystyle m}$ as the mass of the projectile

and ${\displaystyle v}$ as the speed of the projectile.

Since energy and speed decrease over the ballistic trajectory, one assumes in practice ${\displaystyle E_{\text{0}}}$ as muzzle energy or ${\displaystyle v_{\text{0}}}$ as the muzzle velocity and remains within reasonable ranges of the target.

Unfortunately, only tables [8] based on the Anglo-Saxon system of inches and foot-pounds instead of millimeters and joules have been published . Thus, ASPI of 200 corresponds ft * lb * in ² (minimum value to wild ) about 170-180 kJmm² in the metric system. However, Alphin uses values ​​from unspecified loads in its publications , (${\displaystyle E_{\text{0}}}$ or. ${\displaystyle v_{\text{0}}}$ remain unknown) which means that, in addition to the purely metric conversion, a correction factor of around 1.3 can be assumed.

In the file ASPI metric , exemplary metric ASPI values ​​(Jmm²) are compiled. These are based on the specified diameter of the bullets of a caliber and the specified muzzle energies and velocities. For some calibers, manufacturer values ​​were used due to the lack of published specifications.

A thicker 7 × 57 mm is considered suitable for high seat hunting and stalking wild boar (ASPI${\displaystyle _{\text{englisch}}}$157 ft * lb * in², metric 120–132 kJmm²), but for a driven hunt an 8 × 57 mm (ASPI${\displaystyle _{\text{englisch}}}$237 ft * lb * in², metric 191–218 kJmm²) recommended. For further recommendations see jasw.de. [4]

The practice with regard to the ASPI is thus well above the corresponding legal requirements of § 19 BJagdG : It is forbidden to use a${\displaystyle E_{\text{100}}}$ It is forbidden to hunt other hoofed game under 1000J with a caliber under 6.5mm and ${\displaystyle E_{\text{100}}}$to hunt under 2000J. Assuming the usual energy loss of commercially available ammunition of${\displaystyle E_{\text{0}}}$ on ${\displaystyle E_{\text{100}}}$This results in a reference ASPI for roe deer of 34 kJmm², for the rest of the hoofed game of 88 kJmm². In terms of hunting practice and fairness to hunts , the ASPI values ​​already mentioned must at least be achieved, particularly in the case of driven hunts and other negative influences on the hit seat. A .223 Remington achieves the legal values, but it can be distracted if there are obstacles (branches, twigs, grass) or the weather (wind, rain). It achieves an ASPI that is comparable to a weak .357 Magnum or .40 S&W , which are normally only used to catch sick game. .308 Winchester or 7 × 57 mm are more suitable on roe deer.