mcb
Member
So playing around try to visualize the four dimensional space that is mass, velocity, momentum, and kinetic energy. This is far from perfect since my four dimensional holograph is on the fritz but after playing around with numbers and Excel for awhile I came up with the following two graphs, one inset in the others and thought I would share and hope it would help someone else's intuition on these four interconnected values often used with projectiles.
Click here for full size.
Hopefully if you click on the link below the image you can see the full resolution version so you can read all the fine print.
The data for each cartridge is, for simplicity sake, take from SAAMI's publish P&V tables in the front of the Pistol and Revolver volume and the Rifle Volume. The other odd ball projectiles are taken from googling the needed data. For each cartridge I took a bullet of weight I thought most representative of the cartridge, this was usually a slightly heavy for caliber but rarely the heaviest of those show in the table. No doubt some of these cartridges are common loaded to higher performance than the SAAMI table but these are based on standard ammo and I thought the fairest representation for each cartridge.
The inset graph is for showing what mass vs velocity is used to calculate the momentum and kinetic energy in the larger graph for each projectile. The horizontal axis in the inset graph is logarithmic.** This spread things out better so you can actually read all the cartridge names.
On the main graph the vertical axis (kinetic energy) is likewise plotted on a logarithmic** scale this was done so you could actually see the pistol cartridges that otherwise all ended up in a little messy cluster in the bottom left corner of the graph otherwise.
The dotted lines on the main graph represent constant mass (red) and constant velocity (black) lines. If you move back and forth along a constant velocity line you are increasing or decreasing mass, conversely if you move along a constant mass line you are increasing or decreasing velocity. If the vertical axis was not logarithmic the black constant velocity lines would be straight lines and the red constant mass lines would be parabolas as expected.
Sorry if your favorite cartridge is not there, I tried to pick relatively mainstream cartridges. If there is interest I might add more data to the graph. The odd-ball projectiles like the Nerf dart and baseball are there to try to help add some more intuition to this endeavor. Along with other cartridge I would love to add some other non-bullet projectiles to the graph to help with that intuition. Suggest away.
Any mistakes, though unlikely
, feel free to point out and I will do my best to correct.
I am sure some will want to jump into a lethality discussion and that's fine but be prepare for me to say that its not that simple. This post was not intended to make any assertions with regard to lethality but to simple visualize the relationship between mass, velocity, momentum (P=mv), and kinetic energy (E = 0.5mv^2).
**If you not familiar with logarithmic scales each minor line between the labeled major lines is a multiple of the left line. The third line over from 10 is 40, the fifth line over from 100 is 600.
Click here for full size.
Hopefully if you click on the link below the image you can see the full resolution version so you can read all the fine print.
The data for each cartridge is, for simplicity sake, take from SAAMI's publish P&V tables in the front of the Pistol and Revolver volume and the Rifle Volume. The other odd ball projectiles are taken from googling the needed data. For each cartridge I took a bullet of weight I thought most representative of the cartridge, this was usually a slightly heavy for caliber but rarely the heaviest of those show in the table. No doubt some of these cartridges are common loaded to higher performance than the SAAMI table but these are based on standard ammo and I thought the fairest representation for each cartridge.
The inset graph is for showing what mass vs velocity is used to calculate the momentum and kinetic energy in the larger graph for each projectile. The horizontal axis in the inset graph is logarithmic.** This spread things out better so you can actually read all the cartridge names.
On the main graph the vertical axis (kinetic energy) is likewise plotted on a logarithmic** scale this was done so you could actually see the pistol cartridges that otherwise all ended up in a little messy cluster in the bottom left corner of the graph otherwise.
The dotted lines on the main graph represent constant mass (red) and constant velocity (black) lines. If you move back and forth along a constant velocity line you are increasing or decreasing mass, conversely if you move along a constant mass line you are increasing or decreasing velocity. If the vertical axis was not logarithmic the black constant velocity lines would be straight lines and the red constant mass lines would be parabolas as expected.
Sorry if your favorite cartridge is not there, I tried to pick relatively mainstream cartridges. If there is interest I might add more data to the graph. The odd-ball projectiles like the Nerf dart and baseball are there to try to help add some more intuition to this endeavor. Along with other cartridge I would love to add some other non-bullet projectiles to the graph to help with that intuition. Suggest away.
Any mistakes, though unlikely
, feel free to point out and I will do my best to correct.I am sure some will want to jump into a lethality discussion and that's fine but be prepare for me to say that its not that simple. This post was not intended to make any assertions with regard to lethality but to simple visualize the relationship between mass, velocity, momentum (P=mv), and kinetic energy (E = 0.5mv^2).
**If you not familiar with logarithmic scales each minor line between the labeled major lines is a multiple of the left line. The third line over from 10 is 40, the fifth line over from 100 is 600.
