What's the general consensus on what the best caliber is for ELR (I'm talking over 300 yds)?
Consensus? I do not know, but the good => better => best caliber for extreme long range is the one with the biggest diameter because the bigger diameter, the heavier projectile you can fit, and said combination will give the biggest sectional density, and thus the form factor i in the Ballistic Coefficient formula becomes less significant and forgiving:
SD = BC x i
The G1, BC is based on a theoretical one pound projectile of 100 caliber, or 1.000 inch diameter with a form factor of 1.000 and thus gives a Ballistic Coefficient of 1.000
WARNING!
math follows:
firstly, nothing up my sleeves,
SD = 1.000
mass = 1.000 pound, or 7,000 grains
caliber = 1.000 inch
form factor = 1.000
Ballistic Coefficient = 1.000
since SD = BC x I then 1.000 = 1.000 x 1.000
The closest analogy to compare such mind boggling math is to think back in the 2nd grade when you started to learn about the physics of electronic fundamentals such as Ohms Law, but not so much about Joules law, yet.
You are probably wondering why my experience and education began in the second grade? Well, which is also a deep subject, when I was in the second grade, I bent a tang on a fork 90 degrees, and I still hadn’t learned trigonometry then I stuck the bent tang into the Hot side of a wall plug and my little hand cramped down on the fork handle and I was being electrocuted. I still remember my Dad laughing then he kicked my hand off the fork and said that if we were in Europe and the Nazis didn’t kill me, the 240 volt house voltage would’ve. My Mom was so pissed at my Dad that I remember her smacking him several times as he kept laughing, and I was so proud to have a mom come to my rescue at such a young age and beating down a laughing ogre that was still laughing, until I heard my so called hero mom screaming at my Dad in cuss words and Spanish that y
he ruined her fork.
So much for hero moms.
My Dad being in WWII was a radioman and started teaching me about Electromotive force being measured in volts, intensity of electrical current being measured in amperes, and resistance being measured in ohms, and since he also doubled as a scout sniper anti-sniper hunter, my ballistics education began also.
Three variables in electronic principals E = I X-ray, and three variables in ballistic kinetic energy (Ke) = 1/2 x m x v^2.
Note that incrementing the mass only increments the kinetic energy proportionateply, but incrementing the velocity increments the Ke by the squared value proportionalply.
Now comes Joules Law: Power which is measured in Watts equals the intensity of the current that is measured in Amperes squared and multiplied by the resistance that is measured in ohms, so it looks like this:
W = I^2 x R; similar to Ke = 1/2 x m x v^2, or basically comparatively speaking:
W = Ke
v^2 = I^2
R = 1/2 x m, or m/2
Power = Dynamic Kinetic energy (there is also static potential energy as well as internal energy, calculated only).
velocity = intensity
resistance = half-mass
So, my Dad would tell me that the USS Missouri would fire two ton projectiles at just barely over the speed of sound and they would travel over the horizon, way past the line of sight of the crows nest on the ship, and hit an enemy boat about the size of a mansion, and these were of caliber, or 16, or 18 inch guns that I remember him saying.
So to answer the question?
The biggest and heaviest projectile combination, but with airguns, we need to calculate the barrel length too; as well as the molecular mass of the gas being used to transfer the momentum and kinetic energy to the projectile.
Now, keep in mind the ideal gas law does not apply to air guns as the Volume has a super script gamm function (compressibility of approximately 1.4; but closer to 1.396 according to my experiments at Normal Temp and Pressure (NTP), so at different elevations barometric pressures and temperatures your mileage will vary.
For the average mass of dry air, I use 28.966 daltons, which equates to 28.966 grams of dry air per mole; where a mole is defined as exact to be 6.02214076x10^23 entities, just like a dozen means 12, a score means 20 (“four score and seven years ago” = 1863 - 1776), a myriad means 10;000; etc. where a word means a number).
Now, we shoot lead (Pb) projectiles on average; unless you are in the state of nuts & fruits, and lead has a mass of 207.2 da, or 207.2 grams of lead contain 1 mole of lead molecules, so the ratio of dry air to lead is 207.2/28.966, or roughly 7:1.
Furthermore, the law of conservation of momentum will hold at all cost. I think it should be named the law of Marines holding their position at all cost would be more accurate.
Anyways, the limiting factor is the base area of the projectile, its mass, and the time the gas molecules can strike the base before exiting the muzzle approximately 3 calibers out where the dynamic frictional drag of the projectile against the barrel goes to zero and said energy is transferred as a jump in velocity and the more jump because of higher pressure causes less accuracy, but more power, but keeping in mind that consistency trumps accuracy at range when it comes to hunting at different ranges and environmental conditions.
I better stop here before I run out of text ink.
Thank you all for my increased knowledge from your posts because once I think I got it is when I realize how much more I need to know and how little I really know. Ignorance is bliss.
Numbers do not lie, but you can lie with numbers, and the laws of physics are not just really good ideas.
FJB Out!
