Muzzle velocity design. In a side by side comparison with the .50 BMG, the titanium round "of any caliber" released almost 28 times the energy of the .50 BMG, with only a 27% mean loss in momentum. Energy, in most cases, is what is lethal to the target, not momentum. In conventional guns, muzzle velocity is determined by the quantity of the propellant (burn speed, expansion), the mass of the projectile, and the length of the barrel. A slower-burning propellant needs a longer barrel to burn completely, but can, on the other hand, use a heavier projectile. A faster-burning propellant may accelerate
Group velocity amplitudes diminish as they approach the leading edge. The longer waves travel more slowly, and their amplitudes diminish as they emerge from the trailing boundary of the group. The group velocity is defined by the equation: where is the wave's angular frequency (usually expressed in radians per second), and is the angular wavenumber (usually expressed in radians per meter). The phase velocity is: . The function , which gives as a function of , is known as the dispersion relation. One derivation of the formula for group velocity is as follows. Consider a wave packet as a function of position