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
Variable-mass system on a body (F = 0) the variable-mass system motion equation reduces to If the velocity of the ejected propellant, v, is assumed have the opposite direction as the rocket's acceleration, dv/d"t", the scalar equivalent of this equation can be written as from which d"t" can be canceled out to give Integration by separation of variables gives By rearranging and letting Δ"v" = "v" - "v", one arrives at the standard form of the ideal rocket equation: where "m" is the initial total mass, including propellant, "m" is the final total mass, "v" is the effective exhaust velocity (often denoted