Bypass ratio the velocity of a very large volume and consequently mass of air produces a very large change in momentum and thrust: thrust is the engine's mass flow (the amount of air flowing through the engine) multiplied by the difference between the inlet and exhaust velocities in—a linear relationship—but the kinetic energy of the exhaust is the mass flow multiplied by one-half the square of the difference in velocities. A low disc loading (thrust per disc area) increases the aircraft's energy efficiency, and this reduces the fuel use. The Rolls–Royce Conway turbofan engine, developed in the early 1950s, was an early
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