Quote:
Originally Posted by ILLusion
It does correlate with velocity, but also in combination with the mass of the projectile. It's a function of all three variables.

Hi everyone, I am new from Southern Ontario.
Disclaimer: None of the below statements have been logically proven, and a margin of error exists. If you do not agree with the information posted, please feel free to debate. Please do not take this as an insult. I voice this objectively simply to make typing this easier. Sorry for necromancing a 1 year 8 month 27 day old topic.
Actually, since the projectile in question has a velocity much much lower than 299792458 mps (c) and a wavefunction with wavelength much much smaller than we really care about in terms of uncertainty, the formula for kinetic energy is simply
E=1/2*m*v^2.
so, 1=1/2*1/5000*100^2
However, after diligent research, I have found that kinetic energy actually tends to increase with BB weight. This may seem counter intuitive, since each pull of the spring uses the same amount of energy, but according to the second law of thermodynamics, entropy must always increase, so there will always be an energy inefficiency. the efficiency simply increases when using a heavier bb. I have a theory for why this is. When the spring is released, it exerts a force which varies according to Hookes law, but more importantly, it is accelerating its own mass, the piston, all the air in the cylinder, and lastly, the lowly bb. E=F*d, so the more massive the projectile, the greater proportion of the force from the spring it gets, so the more energy is imparted onto it. In an ideal system, the "inefficiency" in this case would actually be the kinetic energy of the piston, air, and spring. The energy equivalence theory only works in an ideal system with a massless spring, massless piston, massless, ideal gas, and massive BB.
Do I have evidence to back this up? well, yes I do. While this is not directly relevant to the present comparison, and other factors(bb quality etc) may be involved, I have found that the velocity .12g is, as a function of velocity(fps) with .2g, f(v1)=1.075*v1+41. If the energy were constant, then it should be f(v1)=sqrt(5/3)*v1 (yes, I realize there is an intersection at about 69 fps, but keep in mind that my sample contained no elements less than 210fps, and that the function is an average linear trendline) . additionally, I actually calculated the energy of the samples, and the energy (joules) of .12g as a function of .2g is f(e1)= 0.791e1+0.0735, clearly less than of .2's(very strong correlation too). I will do a similar study for .2g vs .25g when convenient.
As for the question of range, I will assume that you are referring to range with hop up set for flat trajectory, at angle of 0, at height 1.2 meters. Honestly, this is a little beyond my scope, but I'll try at least.
Hop up is caused by the Magnus effect, derived from the Bernoulli effect. The amount of lift created is described by F=S(ω×v) where ω is vectored angular velocity, v is vectored linear velocity, S is dependent on the average of the air resistance coefficient across the surface of the object, and × denotes the vector cross product. Omega can be adjusted, while S is dependent on BB, while v will regress over time described by F=ρ*v^2*C(d)*A. A, ρ, C(d) are constant, so that leaves v^2. I can't go any further without a good grasp of calculus, so I'll simply state my unscientific opinion. I believe that under a certain velocity, the lighter bb will go further, while over it, when v^2 exceeds some variable k*v+b, the heavier bb will prevail.
Good to be here B).