NAVWEPS DO-ROT-80  APPLICATION OF AERODYNAMICS  TO SPECIFIC PROBLEMS OF FLYING  Thus, the velocity due to rotation varies line-  arly from zero at the hub to a maximum at  the tip.  A typical blade section with  the  forces  acting on it is shown in figure 6.15.  usually means remaining over a particular  spot on the ground, it shall be considered  here as flight at zero airspeed.  This is necessary  because  the aerodynamic characteristics of the  rotor depend on its motion with respect to  the air and not the ground.  Hovering in a 20  knot wind is aerodynamically equivalent to  flying at an airspeed of 20 knots in a no-wind  condition,  and the characteristics will  be  identical in the two conditions.  A summation of the forces acting perpen-  dicular to the plane of rotation (tip path plane)  will determine the rotor thrust (or lift) char-  acteristics while summation of the moments  resulting from forces acting in the plane of  rotation will determine the rotor torque char-  acteristics. As a result of this analysis, the  rotor thrust (or lift) is found to be propoc-  tional to the air density, a nondimensional  thrust coefficient, and the square of the tip  speed, or linear speed of the tip of the blade.  The thrust coefficient is a function of the aver-  age blade section lift coefficient and the rotor  solidity, which is the proportion of blade area  to disc area.  The lift coefficient  is identical to  that used in airplane aerodynamics while the  solidity is analagous to the aspect ratio in air-  plane aerodynamics. The rotor torque is  found to be proportional to a nondimensional  torque coefficient, the air density, the disc  area, the square of the tip speed, and the blade  radius. The torque coefficient is dependent  upon the average profile drag coefficient  of the  blades, the blade pitch angle, and the average  lift coefficient of the blades. The torque can  be thought to result from components  of profile  and induced drag forces acting on the blades,  similar to those on an airplane.  The first point to realize is that the rotor is  subject to the same physical laws of aero-  dynamics and motion that govern flight of  the fixed-wing airplane.  The manner in which  the rotor is subject to these laws is much more  complicated due to the complex flow con-  ditions.  Rotor lift can be explained by either of two  methods. The first method, utilizing simple  momentum theory based on Newton ’ s Laws,  merely states that lift results from the rotor  accelerating a mass of air downward in the  same way that the jet engine develops thrust  by accelerating a mass of air out the tailpipe.  The second method of viewing rotor lift  concerns the pressure forces acting on the  various sections of the blade from root to tip.  The simple momentum theory is useful in  determining only lift  characteristics while  the “blade  element”  theory gives drag as  well as lift characteristics and is useful in  giving a picture of the forces at work on the  rotor.  In the “blade element” theory, the  blade is divided up into “blade elements” as  shown in figure 6.15. The forces acting on  each blade element are analyzed. Then the  forces on all elements are summed up to give  the characteristics of the whole rotor.  The  relative wind acting on each segment is the  resultant of two velocity components: (1) the  velocity due CO the rotation of the blades  about the hub and (2) the induced velocity,  or downwash velocity caused by the rotor.  the velocity due to rotation at a particular  element is proportional to the rotor speed and  the distance of the element from the rotor hub.  As in the airplane, there is one angle of  attack or blade pitch condition that will result  in the most efficient operation.  Unfortu-  nately, the typical helicopter rotor operates  at a near constant RPM and thus a constant  true airspeed and cannot operate at this most  eficient condition over a wide range of altitude  and gross weight as the fixed-wing airplane.  The airplane is able to maintain an efficient  angle of attack at various altitudes, and gross  weights by flying at various airspeeds but the  helicopter will operate with a near constant  rotor velocity and vary blade angle to contend  with variations in altitude and gross weight. 