It's usually no more than a 5-10% maximum difference. But it is a difference. .5*m*v^2 doesn't work because of hop-up. Different weight of bb needs a different amount of backspin to create the same hopup effect... and energy goes into that. They have to generate a different amount of lift, is why there's a difference. heavier bb's have to have more spin applied... so if you ended up working it out (I refuse to do so), you have a much larger increase in energy output if your linear output (.5*m*v^2) is within 5-10% of the other weights.
You will also see much bigger distances down-range though. Slower moving bb has less drag and therefore less frictional losses. So at the same range, a heavier bb will more likely still be carrying more energy.
Then you have to consider all the effects that whiskey mentioned.
Then you have to add in randomized occurances.
Or you can just do the rule of thumb measurements we take... fps should be ____ or less with ___g bb's.
Axisofoil is right about the rotational energy and drag. There's going to be a lot of drag, unless you're shooting in the vacuum. Drag is a function of velocity of the bb, which in turn is a function of the mass of the bb. The actual kinetic energy curve vs. mass is going to be a curve that can be optimized. If you would like to,
Total Energy in X Direction = Kinetic Energy - Rotational Energy - Drag
E = .5mv^2 + .5Iw^2 + .5vpCA
I = moment of inertia, spheres having (2/5)mr^2
So substituting it back in,
E = .5mv^2 + (1/5)mr^2w^2 + .5vpCA
Where
m = mass
v = velocity
r = radius of the sphere
w = angular velocity
p = density of air
C = drag coefficient, dependent on shape (spheres are about .47)
and A = projected area, a bb being a circle when it hits the air
So what you could do is measure how fast you shoot with each BB, plot the energy as a function of mass and velocity, and then you could optimize that curve for the maximum amount of energy by simply taking its derivative and setting it equal to zero. You got two variables so you'll need to do partials.
Actually, if you wanted to avoid partials, what you could do is plot velocity vs. mass, and fit a regression to that (something tells me it's going to be first or second order... simple), take that function and then substitute it into that energy equation I gave you for E. Then you have one big equation for energy in terms of mass or velocity (you choose), and you'd just take the first derivative. It cannot be worse than a fourth order equation, which means that you may have two maxima. Just find whichever one is larger and use that one for more energy.
Not difficult at all.
](*,) Why couldn't I think of that before? haha, I'm no math matician, failed simple calculus, but makes sense I guess :?: Either way, as stated before, by Whiskey 11, there is quite a bit of space between the barrel and BB. Thus, we have to remember that, also, with random factors of wind, etc., that the energy of the BB, no matter the muzzle energy it has, is always going to vary.
I can't believe how off topic this has gotten haha.
