Disk loading

In fluid dynamics, disk loading or disc loading is the average pressure change across an actuator disk, such as an airscrew. Airscrews with a relatively low disk loading are typically called rotors, including helicopter main rotors and tail rotors; propellers typically have a higher disk loading. The V-22 Osprey tiltrotor aircraft has a high disk loading relative to a helicopter in the hover mode, but a relatively low disk loading in fixed-wing mode compared to a turboprop aircraft. In fluid dynamics, disk loading or disc loading is the average pressure change across an actuator disk, such as an airscrew. Airscrews with a relatively low disk loading are typically called rotors, including helicopter main rotors and tail rotors; propellers typically have a higher disk loading. The V-22 Osprey tiltrotor aircraft has a high disk loading relative to a helicopter in the hover mode, but a relatively low disk loading in fixed-wing mode compared to a turboprop aircraft. Disc loading of a hovering helicopter is the ratio of its weight to thetotal main rotor disc area. It is determined by dividingthe total helicopter weight by the rotor disc area,which is the area swept by the blades of a rotor. Discarea can be found by using the span of one rotor bladeas the radius of a circle and then determining the areathe blades encompass during a complete rotation. When a helicopter is being maneuvered, its disc loading changes.The higher the loading, the more power needed tomaintain rotor speed. A low disc loading is a direct indicator of high lift thrust efficiency. Increasing the weight of a helicopter increases disk loading. For a given weight, a helicopter with shorter rotors will have higher disk loading, and will require more engine power to hover. A low disk loading improves autorotation performance in rotorcraft. Typically, an autogyro (or gyroplane) has a lower rotor disc loading than a helicopter, which provides a slower rate of descent in autorotation. In reciprocating and propeller engines, disk loading can be defined as the ratio between propeller-induced velocity and freestream velocity. Lower disk loading will increase efficiency, so it is generally desirable to have larger propellers from an efficiency standpoint. Maximum efficiency is reduced as disk loading is increased due to the rotating slipstream; using contra-rotating propellers can alleviate this problem allowing high maximum efficiency even at relatively high disc loadings. The Airbus A400M fixed-wing aircraft will have a very high disk loading on its propellers. The momentum theory or disk actuator theory describes a mathematical model of an ideal actuator disk, developed by W.J.M. Rankine (1865), Alfred George Greenhill (1888) and R.E. Froude (1889). The helicopter rotor is modeled as an infinitely thin disc with an infinite number of blades that induce a constant pressure jump over the disk area and along the axis of rotation. For a helicopter that is hovering, the aerodynamic force is vertical and exactly balances the helicopter weight, with no lateral force. The upward action on the helicopter results in a downward reaction on the air flowing through the rotor. The downward reaction produces a downward velocity on 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. For an actuator disk of area A {displaystyle A} , with uniform induced velocity v {displaystyle v} at the rotor disk, and with ρ {displaystyle ho } as the density of air, the mass flow rate m ˙ {displaystyle ^{dot {m}}} through the disk area is: