a helicopter that is hovering, the aerodynamic force is vertical and exactly balances the helicopter weight, with no lateral force. The downward force on the air flowing through the rotor is accompanied by an upward force on the helicopter rotor disk. The downward force produces a downward acceleration of the air, increasing its kinetic energy. This energy transfer from the rotor to the air is the induced power loss of the rotary wing, which is analogous to the lift-induced drag of a fixed-wing aircraft. Conservation of linear momentum relates the induced velocity downstream in the far wake field to the rotor thrust per unit of mass flow. Conservation of energy considers these parameters as well as the induced velocity at the rotor disk. Conservation of mass relates the mass flow to the induced velocity. The momentum theory applied to a helicopter gives the relationship between induced power loss and rotor thrust, which can be used to analyze the performance of the aircraft. Viscosity and compressibility of the air, frictional losses, and rotation of the slipstream in the wake are not considered. Momentum theory For an actuator disk of area , with uniform induced velocity at the rotor disk, and with as the density of air, the mass flow rate through the disk area is: By conservation of mass, the mass flow rate is constant across the slipstream both upstream and downstream of the disk (regardless of velocity). Since the flow far upstream of a helicopter in a level hover is at rest, the starting velocity, momentum, and energy are zero. If the homogeneous slipstream far downstream of the disk has velocity , by conservation of momentum the total thrust developed over the disk is equal to the rate of change of momentum, which assuming zero starting velocity is: By conservation of energy, the work done by the rotor must equal the energy change in the slipstream: Substituting for and eliminating terms, we get: So the velocity of the slipstream far downstream of the disk is twice the velocity at the disk, which is the same result as for an elliptically loaded wing predicted by lifting-line theory. Bernoulli's principle To compute the disk loading using Bernoulli's principle, we assume the pressure in the slipstream far downstream is equal to the starting pressure , which is equal to the atmospheric pressure. From the starting point to the disk we have: Between the