NAVWEPS 00-8OL80  AiRPlANE PERFORMANCE  angle, and is a function of some proportion of  the flight velocity, V, and the velocity due to  rotation which is mD at the tip.  The pro-  portions of these terms describe the propeller  “advance ratio”, J.  it is more appropriate to define propeller effi-  ciency in the following manner:  ‘ )~= output propulsive power  mput shaft horsepower  where  vP= propeller efficiency  T= propeller thrust  V= flight velocity, knots  BHP= brake horsepower applied to the  propeller  J=propeller advance ratio  V=flight velocity, ft. per sec.  n=propeller rotative speed, revolutions  per sec.  D = propeller diameter, ft.  where  The propeller blade angle, fi (beta), varies  throughout the length of the blade but a  representative value is measured at 75 percent  of the blade length from the hub.  Many di,fferent factors govern the efficiency of  a propeller. Generally, a large diameter pro-  peller favors a high propeller efficiency from  the standpoint of large mass flow.  However,  a powerful adverse  effect on propeller efficiency  is produced by high tip speeds  and conipressi-  bility effects. Of course, small diameter pro-  pellers favor low tip speeds. In addition, the  propeller and powerplant must be matched for  compatibility of output and efficiency.  Note that the difference between the effec-  tive pitch angle, 4, and the blade angle, 8,  determines an effective angle of attack for the  propeller blade section. Since the angle of  attack is the principal factor affecting the  efficiency of an airfoil section, it is reasonable  to make the analogy that the advance ratio, J,  and blade angle, 8, are the principal factors  affecting .propeller efficiency. The perform-  ance of a propelleris typified by the chart of  figure 2.19 which- illustrates the variation of  propeller efficiency, ~a, with advance ratio, J,  for various values of blade angle, 8.  The  value of vP for each fl increases with  J  until a peak is reached, then decreases.  It is  apparent that a fixed pitch propeller may be  selected to provide suitable performance in a  narrow range of advance ratio but efficiency  would suffer considerably outside this range.  In order to appreciate some of the principal  factors controlling the efficiency of a given  propeller, figure 2.18 Uustrates the distribu-  tion of rotative velocity along the rotating  propeller blade. These rotative velocities add  to the local inflow velocities to produce a  variation of resultant velocity and direction  along the blade. The typical distribution of  thrust along the propeller blade is shown with  the predominating thrust being located on the  outer portions of the blade. Note that the  propeller producing thrust develops a tip  vortex similar to the wing producing lift.  Evidence of this vortex can be seen by the con-  densation phenomenon occurring at this Ioca-  tion under certain atmospheric conditions.  In order to provide high propeller efficiency  through a wide range of operation, the pro-  peller blade angle must be controllable.  The  most convenient means of controlling the  propeller is the provision of a constant speed  governing apparatus.  The constant speed  gov-  erning feature is favorable from the standpoint  of engine operation in that engine output and  efficiency  is positively controlled and governed.  The component velocities at a given propeller  blade section are shown by the diagram of  figure 2.18. The inflow velocity adds vec-  torially to the velocity due to rotation to pro-  duce an inclination of the resultant wind with  respect to the planes of rotation.  This incli-  nation is termed + (phi), the effective pitch  147 