Respect the Science
August 12th, 2009
Published on August 12th, 2009 @ 04:12:24 am , using 872 words, 388 views
For the past three weeks, I have been fielding comments that the damage output of our weapons is too low--that they should be way higher than a crossbow or longbow. Despite my simple arguments, people still seem to think that a 13 gram bullet should be doing more damage than a 450 gram arrow...and not a single increase in die damage (1d6 to 1d8). We are talking if a longbow does 1d10, then an M16 should be doing 3d6.
Firstly, you have to understand how much energy they carry. Bullets have a lot of energy in their release, but they are light. A knife or an arrow moves a lot slower, but they weigh a heck of a lot more. An arrow has its shaft to carry additional energy in a way your arm does when it pushes in a blade. This why arrows and knives can actually penetrate most bullet proof vests. If you have ever seen an arrow in slow-motion, you'll notice it flexing as it passes through the air. When it impacts, that stored energy in the shaft (flexional energy, I looked it up) causes it to straighten, transferring that power back into its tip. It's more than the fact that arrow tips are pointy and most bullets are not (or at least not as). In fact, mass can have as much or a greater impact on damage to the target than velocity. Expert bowman had seen the damage potential of their tools, penetrating deeper than even high powered rifles.
Consider this thought experiment. Fire a baseball to bowling pins and see if that ball can carry enough energy to knock all 10 pins...compare that to the slow speed of a rolling 16 lbs resin ball. And don't bring up the Hollywood effect of people being thrown off their feet. Anyone who watches Mythbusters knows...it all just wires. That being said, even though a baseball can hit harder with a baseball when thrown by a MLB pitcher than an archer's arrow, the baseball probably won't get through plate mail. The shape does matter.
Now, at some point, velocity does become an issue. For those still paying attention, it's called hydraulic force. This is the shock wave that resonates from a bullet hit in the soft tissue after impact. This causes the internal bleeding and bruising and what not. Arrows, though large, are never fired with enough velocity to create significant hydraulic shock (it actually deals with momentum, and yes, momentum and velocity is different). However, this depends on a variety of issues including range and point of impact. A bullet looses momentum quickly but we can't factor that in the rules. Additionally, we can't include body locations, which can also greatly affect the amount of tissue damage.
So we have a balance. Despite the bullet carrying amazing power, the arrow will penetrate further. That is fact. It's proven. The bullet can cause wound damage from hydraulic shock because of its velocity, which an arrow cannot replicate. This is also fact, also proven. We also balance this with the fact that a GREATSWORD does 2d6 damage. This is a gigantic chunk of sharpened steel that carries penetration and blunt force trauma. It can kill you without even breaking skin. Sooo...Pistols do 1d4-1d6, rifles do 1d8 to 1d10, and heavy weapons do 1d10 and up.
Here is an example I found online. If one fills a 5 gallon plastic pail with sand and fires both a .357 magnum and a heavy hunting arrow at it, the bullet will be stopped by the sand, while the arrow will penetrate the pail completely. The .357 magnum handgun has a 158 grain bullet traveling at 1250 fps, for a momentum of 0.83 slug-feet per second, and a kinetic energy of 520 foot-pounds. A 710 grain arrow at 183 fps has only 0.57 slug-feet per second of momentum, and a mere 52 foot-pounds of kinetic energy. These are actual combinations used to demonstrate the penetration power of a heavy hunting arrow. A major factor between the bullet and the arrow is the increased resistance force met by the higher velocity bullet. While the bullet has ten times more kinetic energy, and 37.5% more momentum, than the arrow, it's almost seven times higher velocity causes the bullet to be met by nearly fifty times as great a resistance force as that encountered by the arrow! Another major factor between the handgun’s bullet and the arrow is the longer time period of the arrow’s impulse; which results from its higher mass. Though the arrow is traveling much slower than the bullet, and has less momentum than the bullet, it derives a greater percentage of the momentum it does possess from its mass. It is "heavier". The heavier (and lower velocity) arrow “decelerates” more slowly than the bullet or, if one prefers, it has a longer time period over which the force acts. Force multiplied by the time it acts equals the impulse. The heavier arrow retains a higher percentage of its force for a longer period of time than does the bullet. The bullet’s total net disposable force, though very high relative to the arrow, is entirely dissipated in milliseconds.
Can I put this to bed now?
(Thanks to Ed Ashby for his science)