GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: rsterne on February 28, 2019, 04:27:46 PM
-
I have been collecting penetration data in "melt-and-pour" soap for a few years now, for a lot of pellets and a few bullets.... The bullets have a lot of variation in nose shape, and the data is therefore scattered.... but if I take out all the Hollowpoint pellets and look only at those which don't expand, I get a very close correlation with theory.... The data lays quite nicely along a linear trendline....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Penetration_zpsnph0fkit.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Penetration_zpsnph0fkit.jpg.html)
The basis for the theoretical penetration is the Sectional Density of the pellet multiplied by the Velocity, times a constant.... For the soap I use, a constant of 2 gives a penetration in mm with good correlation to what I have measured.... I didn't remove any pellets from the data except Hollowpoints, so there are datapoints in the above graph for wadcutters and pointed pellets in addition to domed, round nose, and others.... Hollowpoint pellets, which are designed to expand, and do so to a varying degree depending on the velocity.... may penetrate only about half the distance of their solid cousins or less, which is why I did not include them....
The theory only applies to non-expanding projectiles which do not tumble inside the impact media.... The fact that the data gathers around a linear trendline is quite good, considering all the variation in nose shape.... I feel it confirms the basic theory that penetration is proportional to the product of velocity and SD....
Bob
-
Interesting!
I wonder what it would look like if you used energy as a variable rather than velocity.
-
If you used energy instead of velocity, the result would be a parabola, since you square the velocity to get the energy.... For a given projectile you need to double the velocity to double the penetration, which increases the energy by 4 times.... If you think about it, using the Sectional Density and Velocity is the same as using the Momentum and Bore Area.... just a different constant required.... Using the Sectional Density allows the comparison of projectiles of different calibers....
SD = Weight in lbs. / Caliber^2 = W / 7000 / C^2.... so SD x Velocity = W x V / C^2 divided by a constant
Momentum = Mass (slugs) x Velocity = W x V / (32.16 x 7000).... Bore Area = C^2 x PI/4.... so Momentum / Area = W x V / C^2 divided by a constant
It is well known that penetration in a given calber, without expansion, is proportional to the Momentum, not the Energy.... This data confirms that fact....
Wound Channel volume, however, is roughly proportional to the Energy.... For a given caliber, if the Momentum M x V is the same (and therefore so is the penetration), but one pellet has more energy than the other (ie is lighter but moving faster), it will create a larger diameter wound channel.... For a given projectile, if you double the velocity, you get the same penetration, but the wound channel will be roughly 1.4 times the diameter, so that the wound channel volume is 4 times as great to match the FPE, which is M x V^2....
All of this requires a uniform medium to measure the penetration, and no expansion or tumbling of the projectile, of course....
Bob
-
If you used energy instead of velocity, the result would be a parabola, since you square the velocity to get the energy.... For a given projectile you need to double the velocity to double the penetration, which increases the energy by 4 times...
Indeed.
There is a rather lovely study done by a certain W.H. Noble of the Ordnance Select Committee back in 1863 (referenced here (http://www.archive.org/stream/reportofbritisha67brit/reportofbritisha67brit_djvu.txt) but sadly it's poorly scanned text with no illustrations and jumbled up tables) which is quoted in Ian Hogg's excellent "A History Of Artillery" (https://www.abebooks.com/book-search/title/a-history-of-artillery/author/hogg-ian-v/):
A 68 pounder smoothbore and a 7 inch Armstrong gun firing 200 lb shot had been fired at 4.5 inch plate backed by 18 inches of teak. The 68 pounders had penetrated the target, while the 200 pounder had made hardly any impression on it. Noble showed that the answer lay in the relative velocity of the two projectiles. The 68 pounder had been moving at 1,425 feet per second when it struck, while the 200 pounder was loafing along at a mere 780 feet per second. On the face of it, the 200 pounder with 156,000 foot-pounds of energy should have out performed the 68 pounder with 96,900, but the low velocity of the heavier projectile allowed the plate to deform and resist the blow, whereas the higher velocity of the 68 lb shot tore through the plate before it could begin to absorb the blow.
As Noble said in his paper, "What is wanted is velocity; if you sacrifice it to weight you will only be able to keep knocking at the door without entering."
-
Fascinating!
Subscribed!
Thanks Bob for running a test to move our understanding of airgunning forward! Great job! :D