Patent Publication Number: US-2020290725-A1

Title: Ducted thrusters

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 16/138,672, filed Sep. 21, 2018 titled “Ducted Thrusters”, which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Ducted main rotors are rarely used on helicopters because helicopter rotors are very large and would require an enormous, and therefore heavy, duct. In addition, there is no straightforward way to attach a duct around the main rotor on a helicopter. However, in U.S. patent application Ser. No. 15/477,582, filed on Apr. 3, 2017, which is incorporated herein by reference in its entirety, a helicopter with a non-ducted main rotor and ducted forward-facing thrusters is disclosed. Tiltrotor aircraft rely on smaller diameter, highly loaded rotors that are more amenable to utilizing a duct. Tiltrotor aircraft generally have two proprotors positioned at the ends of a fixed wing. The proprotors are positioned with the rotor blades in a generally horizonal orientation for a hover, or helicopter, mode, and they are positioned with the rotor blades in a generally vertical orientation for a forward-flight, or airplane, mode. The proprotors on a tiltrotor aircraft generally have a smaller rotor disc area (with higher installed power) than the main rotor on a comparably-sized helicopter. Thus, tiltrotor aircraft can utilize smaller ducts that would not be feasible on a similarly-sized helicopter. Even though tiltrotor aircraft would seem to be a good fit for ducted proprotors, tiltrotor aircraft are rarely fitted with ducted proprotors. However, in U.S. patent application Ser. No. 15/811,002, filed on Nov. 13, 2017, which is incorporated herein by reference in its entirety, a tiltrotor aircraft having segmented ducts for tilting proprotors is disclosed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an oblique view of a helicopter with two ducted forward-facing thrusters, according to this disclosure. 
         FIG. 2  is a top view of the helicopter of  FIG. 1 . 
         FIG. 3  is a front view of the helicopter of  FIG. 1 . 
         FIG. 4  is a side view of the helicopter of  FIG. 1 . 
         FIG. 5  is an oblique view of a tiltrotor aircraft with two ducted tilting proprotors, according to this disclosure, shown in a helicopter mode. 
         FIG. 6  is a top view of the aircraft of  FIG. 5 , shown in the helicopter mode. 
         FIG. 7  is a side view of the aircraft of  FIG. 5 , shown in the helicopter mode. 
         FIG. 8  is a front view of the aircraft of  FIG. 5 , shown in an airplane mode. 
         FIG. 9  is an oblique view of the tiltrotor aircraft of  FIG. 5 , shown in the airplane mode. 
         FIG. 10  is a partially exploded oblique view of a ducted thruster, according to this disclosure, with a partial cutout. 
         FIG. 11  is a front view of a rotor assembly of the ducted thruster of  FIG. 10 , with a partial cutout. 
         FIG. 12  is a diagram illustrating the orientations of rotor blades and stator vanes of the ducted thruster of  FIG. 10 . 
         FIG. 13  is a partial front view of another ducted thruster of  FIG. 10 . 
         FIG. 14  is a partial cross-sectional side view of a thruster assembly of the ducted thruster of  FIG. 10 . 
         FIG. 15A  is a partial cross-sectional side view of a duct of the ducted thruster of  FIG. 10 . 
         FIG. 15B  is a partial cross-sectional side view of a duct of another ducted thruster, according to this disclosure. 
         FIG. 16  is an oblique view of another ducted thruster, according to this disclosure. 
         FIG. 17  is a front view of a rotor assembly of the ducted thruster of  FIG. 16 . 
         FIG. 18  is a front view of the rotor assembly of the ducted thruster of  FIG. 16 . 
         FIG. 19  is a front view of another rotor assembly, according to this disclosure. 
         FIG. 20  is a table showing a modulated angular distribution of the rotor assemblies of  FIGS. 18 and 19 . 
         FIG. 21  is a schematic front view of a thruster assembly, according to this disclosure, showing centerlines of rotor blades as solid lines and centerlines of stator vanes as dashed lines. 
         FIG. 22  is a schematic front view of the thruster assembly of  FIG. 21 , showing the centerlines of the rotor blades as dashed lines and the centerlines of the stator vanes as solid lines. 
         FIG. 23  is a rear view of a stator assembly of the thruster assembly of  FIG. 21 . 
         FIG. 24  is a schematic front view of the centerlines of the rotor blades of  FIG. 21 . 
         FIG. 25  is a schematic front view of the centerlines of the stator vanes of  FIG. 21 . 
         FIG. 26  is a schematic front view of the centerlines of the rotor blades of  FIG. 21  showing intersection points with a helix. 
         FIG. 27  is a schematic front view of the centerlines of the rotor blades of  FIG. 21  showing intersection points with the centerlines of the stator vanes. 
         FIG. 28  is a schematic front view of another thruster assembly, according to this disclosure, showing centerlines of rotor blades and centerlines of stator vanes as solid lines. 
         FIG. 29  is a schematic front view of another thruster assembly, according to this disclosure, showing centerlines of rotor blades as solid lines and centerlines of stator vanes as dashed lines. 
         FIG. 30  is a schematic front view of the thruster assembly of  FIG. 29 , showing centerlines of rotor blades as dashed lines and centerlines of stator vanes as solid lines. 
         FIG. 31  is a schematic front view of another thruster assembly, according to this disclosure, showing centerlines of rotor blades as dashed lines and centerlines of stator vanes as solid lines. 
         FIG. 32  is a schematic front view of another thruster assembly, according to this disclosure, showing centerlines of rotor blades as dashed lines and centerlines of stator vanes as solid lines. 
         FIG. 33  is an oblique view of another ducted thruster, according to this disclosure. 
         FIG. 34  is a front view of a rotor blade, according to this disclosure. 
         FIG. 35  is a schematic front view of another thruster assembly, according to this disclosure, showing centerlines of rotor blades as solid lines and centerlines of stator vanes as dashed lines. 
         FIG. 36  is a schematic front view of another thruster assembly, according to this disclosure, showing centerlines of rotor blades as solid lines and centerlines of stator vanes as dashed lines. 
         FIG. 37  is a rear view of a stator assembly of the thruster assembly of  FIG. 35 . 
         FIG. 38  is a front view of a ducted thruster according to another embodiment of this disclosure. 
         FIG. 39  is an oblique view of the ducted thruster of  FIG. 38 . 
         FIG. 40  is another oblique view of the ducted thruster of  FIG. 38 . 
     
    
    
     DETAILED DESCRIPTION 
     While the making and using of various embodiments of this disclosure are discussed in detail below, it should be appreciated that this disclosure provides many applicable inventive concepts, which can be embodied in a wide variety of specific contexts. The specific embodiments discussed herein are merely illustrative and do not limit the scope of this disclosure. In the interest of clarity, not all features of an actual implementation may be described in this disclosure. It will of course be appreciated that in the development of any such actual embodiment, numerous implementation-specific decisions must be made to achieve the developer&#39;s specific goals, such as compliance with system-related and business-related constraints, which will vary from one implementation to another. 
     In this disclosure, reference may be made to the spatial relationships between various components and to the spatial orientation of various aspects of components as the devices are depicted in the attached drawings. However, as will be recognized by those skilled in the art after a complete reading of this disclosure, the devices, members, apparatuses, etc. described herein may be positioned in any desired orientation. Thus, the use of terms such as “above,” “below,” “upper,” “lower,” or other like terms to describe a spatial relationship between various components or to describe the spatial orientation of aspects of such components should be understood to describe a relative relationship between the components or a spatial orientation of aspects of such components, respectively, as the device described herein may be oriented in any desired direction. In addition, the use of the term “coupled” throughout this disclosure may mean directly or indirectly connected, moreover, “coupled” may also mean permanently or removably connected, unless otherwise stated. 
     This disclosure divulges aerodynamic and acoustic improvements for aircraft with ducted forward-facing thrusters and ducted tilting proprotors.  FIGS. 1-9  show examples of aircraft with ducted forward-facing thrusters and ducted tilting proprotors. Any of the various features described below may be incorporated thereon. Moreover, the aircraft shown are for illustration purposes only, and the ducted forward-facing thrusters and ducted tilting proprotors disclosed herein may be utilized on any aircraft, such as, for example, an airplane. 
     Referring to  FIGS. 1-4  in the drawings, a helicopter  100  is illustrated. Helicopter  100  comprises a fuselage  102 , a landing gear  104 , a left wing  106 , a right wing  108 , a main rotor system  110  comprising main rotor blades  112 , a first ducted thruster  114  carried by left wing  106 , and a second ducted thruster  116  carried by right wing  108 . Each of left wing  106  and right wing  108  comprise an inner flaperon  118  and an outer flaperon  120 . Main rotor blades  112 , first ducted thruster  114 , second ducted thruster  116 , inner flaperons  118 , and outer flaperons  120  can be controlled in order to selectively control direction, thrust, and lift of helicopter  100 . 
     Fuselage  102  comprises a front end  122 , a tail end  124 , and a length therebetween. First ducted thruster  114  comprises a first duct  126  having a first central longitudinal axis  128  that is generally parallel to a vertical plane bisecting fuselage  102  along the length thereof and a first thruster assembly  130  supported within first duct  126 . Second ducted thruster  116  comprises a second duct  132  having a second central longitudinal axis  134  that is generally parallel to the vertical plane bisecting fuselage  102  along the length thereof and a second thruster assembly  136  supported within second duct  132 . 
       FIGS. 5-9  illustrate an aircraft  200  with a first tilting proprotor  202  and a second tilting proprotor  204 , that enable aircraft  200  to operate in a helicopter mode when first and second tilting proprotors  202  and  204  are in a generally horizontal configuration, referred to as a helicopter position (as shown in  FIGS. 5-7 ), and in an airplane mode when first and second tilting proprotors  202  and  204  are in a generally vertical configuration, referred to as an airplane position (as shown in  FIGS. 8 and 9 ). Aircraft  200  includes a fuselage  206  with a front end  208 , a tail end  210 , a top portion  212 , and a bottom portion  214 . A first set of wings  216  that provide lift in airplane mode extend bilaterally from bottom portion  214  proximate front end  208 . A second set of wings  218  that provide additional lift in airplane mode extend bilaterally from top portion  212  proximate tail end  210 . First set of wings  216  are angled toward tail end  210  and second set of wings  218  are angled toward front end  208  such that the tips of first and second sets of wings  216  and  218  join at first and second tilting proprotors  202  and  204 . As such, aircraft  200  is configured as a negative stagger joined-wing aircraft. However, first and second tilting proprotors  202  and  204  may be used on any aircraft that would benefit from vertical lift in one mode and propulsive thrust in another. 
     First and second sets of wings  216  and  218  both include control surfaces  220  proximate the trailing ends thereof. Control surfaces  220  may comprise flaps, ailerons, spoilers, or any combination thereof. Control surfaces  220  may be used to increase or decrease lift or drag, change pitch, or roll aircraft  200  while in airplane mode. A vertical tail fin  222  extends from top portion  212  proximate tail end  210 . Vertical tail fin  222  includes a rudder  224  to affect yaw of aircraft  200 . 
     First tilting proprotor  202  comprises a first duct  226  having a first central longitudinal axis  228  that is generally parallel to a vertical plane bisecting fuselage  206  along a length thereof and a first thruster assembly  230  supported within first duct  226 . First tilting proprotor  202  is rotatable about a first tilt axis  232  that is generally perpendicular to first central longitudinal axis  228 . First thruster assembly  230  comprises a first rotor assembly  234  rotatably coupled about first central longitudinal axis  228  within first duct  226  and a first stator assembly  236  coupled within first duct  226 . First rotor assembly  234  comprises a first rotor hub  238  and a plurality of first rotor blades  240  extending from first rotor hub  238 . First stator assembly  236  comprises a first stator hub  242  and a plurality of first stator vanes  244  extending from first stator hub  242  to an interior surface  246  of first duct  226 . 
     Second tilting proprotor  204  comprises a second duct  248  having a second central longitudinal axis  250  that is generally parallel to the vertical plane bisecting fuselage  206  along the length thereof and a second thruster assembly  252  supported within second duct  248 . Second tilting proprotor  204  is rotatable about a second tilt axis  254  that is generally perpendicular to second central longitudinal axis  250 . Second thruster assembly  252  comprises a second rotor assembly  256  rotatably coupled about second central longitudinal axis  250  within second duct  248  and a second stator assembly  258  coupled within second duct  248 . Second rotor assembly  256  comprises a second rotor hub  260  and a plurality of second rotor blades  262  extending from second rotor hub  260 . Second stator assembly  258  comprises a second stator hub  264  and a plurality of second stator vanes  266  extending from second stator hub  264  to an interior surface  268  of second duct  48 . 
       FIGS. 10-15  show various components of a ducted thruster  300  for use on an aircraft as a tilting proprotor or forward-facing thruster. Ducted thruster  300 , shown in  FIG. 10  attached to a wing  302 , comprises a duct  304  having a central longitudinal axis  306  and a thruster assembly  308  supported within duct  304 . Thruster assembly  308  comprises a rotor assembly  310  rotatably coupled about central longitudinal axis  306  within duct  304  and a stator assembly  312  coupled within duct  304  downstream of rotor assembly  310  with respect to a direction of the airflow through duct  304 . Rotor assembly  310  comprises a rotor hub  314  and a plurality of variable-pitch rotor blades  316  extending from rotor hub  314 . Stator assembly  312  comprises a stator hub  318  and a plurality of stator vanes  320  extending from stator hub  318  to an interior surface  322  of duct  304 . 
     Duct  304  has a substantially axisymmetric shape about central longitudinal axis  306 , described hereafter with reference to  FIGS. 15A and 15B . Corresponding elements shown in  FIGS. 15A and 15B  are labeled with common element numbers, with an (a) or (b) for  FIG. 15A  or  FIG. 15B , respectively.  FIG. 15A  shows a first exemplary shape of interior surface  322  of duct  304  and  FIG. 15B  shows a second exemplary shape of interior surface  322  of duct  304 , as well as an exterior surface  324   b . In  FIG. 15A , duct  304   a  includes a collector  326   a , corresponding to a portion of interior surface  322   a  generally upstream of rotor assembly  310 , and a diffuser  328   a , corresponding to a portion of interior surface  322   a  generally downstream of rotor assembly  310 . Collector  326   a  comprises a convergent inlet nozzle  330   a  and a cylindrical portion  332   a  extending from inlet nozzle  330   a  to rotor assembly  310 . Diffuser  328   a  comprises a cylindrical portion  334   a  extending from rotor assembly  310  downstream, a frustoconical portion  336   a  extending from cylindrical portion  334   a  downstream, and an outlet  338   a . Rotor assembly  310  is mounted in duct 304a so that its rotor blades  316  rotate within cylindrical portions  332   a  and  334   a . Each of rotor blades  316  has a pitch-change axis  340 , wherein pitch-change axes  340  define a rotor plane  342   a  in which they rotate and which is substantially perpendicular to central longitudinal axis  306 . Collector  326   a  has a length  344   a  along central longitudinal axis  306 , and diffuser  328   a  has a length  346   a  along central longitudinal axis  306 . Collector  326   a  includes inlet nozzle  330   a  with a constant radius  348   a  and cylindrical portion  332   a  with a length  350   a  along central longitudinal axis  306 . Diffuser  328   a  includes cylindrical portion  334   a  with a length  352   a  along central longitudinal axis  306 , frustoconical portion  336   a  diverging from cylindrical portion  334   a  with a half-angle  354   a , and outlet  338   a  with a constant radius  356   a.    
     Length  344   a  of cylindrical portion  332   a  should preferably be between 2% and 8% of a diameter  358  of cylindrical portion  332   a . A minimum magnitude of length  344   a  of collector  326   a  (radius  348   a  plus length  350   a ) should be approximately 10% of diameter  358 . Radius  348   a  of inlet nozzle  330   a  should be approximately 8% of diameter  358 . The position of rotor plane  342   a  is defined as a function of a chord length  360  of rotor blades  316 , their positive pitch angle, a distance  362  between their leading edges and their pitch change axes  340  (wherein distance  362  is approximately 40% of chord length  360 ), and a maximum deformation of rotor blades  316 . Length  350   a  should be greater than the sine of the maximum pitch angle times distance  362  plus the maximum deformation. In order to avoid any overhang of rotor blades  316  in front of cylindrical portion  332   a , an additional margin of 1.33% of diameter  358  may be added. Length  352   a  of cylindrical portion  334   a  of diffuser  328   a  may be between 1% and 3.5% of diameter  358 . Length  352   a  is preferably less than the sine of the maximum pitch angle times the difference between chord length  360  and distance  362 . Half-angle  354   a  of frustoconical portion  336   a  is preferably between approximately 5 degrees and approximately 20 degrees. 
     As shown in  FIG. 15B , duct  304   b  includes a collector  326   b , corresponding to a portion of interior surface  322   b  generally upstream of rotor assembly  310 , and a diffuser  328   b , corresponding to a portion of interior surface  322   b  generally downstream of rotor assembly  310 . Collector  326   b  comprises a convergent inlet nozzle  330   b  and a cylindrical portion  332   b  extending from inlet nozzle  330   b  to rotor assembly  310 . Diffuser  328   b  comprises a cylindrical portion  334   b  extending from rotor assembly  310  downstream and a frustoconical portion  336   b  extending from cylindrical portion  334   b  downstream. Rotor assembly  310  is mounted in duct  304   b  so that its rotor blades  316  rotate within cylindrical portions  332   b  and  332   b . Each of rotor blades  316  has a pitch-change axis  340 , wherein pitch change axes  340  define a rotor plane  342   b  in which they rotate and which is substantially perpendicular to central longitudinal axis  306   b . Collector  326   b  has a length  344   b  along central longitudinal axis  306   b , and diffuser  328   b  has a length  346   b  along central longitudinal axis  306   b . Inlet nozzle  330   b  may comprise a quarter elliptical or quarter super-elliptical shape with a semi-major axis  364   b  and a semi-minor axis  366   b . Semi-major axis  364   b  may be between 10% and 90% of a total chord length  368   b  of duct  304   b , depending on the application, but semi-major axis  364   b  will generally be equal to about 30% of chord length  368   b  for most applications. Cylindrical portion  332   a  has a length  350   b  along central longitudinal axis  306   b . A leading portion  370   b  of exterior surface  324   b  may also comprise a quarter elliptical or quarter super-elliptical shape with a semi-major axis  372   b  and a semi-minor axis  374   b . While semi-major axis  372   b  is shown as being equal to length  344   b , it may be greater or less than length  344   b , depending on the application. The magnitude of semi-minor axis  366   b , of inlet nozzle  330   b  may be approximately 1.67 times the magnitude of semi-minor axis  374   b  of leading portion  370   b . Alternatively, the magnitude of semi-minor axis  366   b , may be defined as a percentage of total airfoil thickness  376   b  of duct  304 , wherein total airfoil thickness  376   b  is equal to the sum of the magnitudes of semi-minor axes  366   b , and  374   b . The magnitude of semi-minor axis  366   b , may be between 5% and 95% of total airfoil thickness  376   b , depending on the application, but will generally be equal to about 62.5% of total airfoil thickness  376   b  for most applications. The position of rotor plane  342   b  is defined as a function of chord length  360  of rotor blades  316 , their positive pitch angle, distance  362  between their leading edges and their pitch change axes  340  (wherein distance  362  is approximately 40% of chord length  360 ), and a maximum deformation of rotor blades  316 . Length  350   b  should be greater than the sine of the maximum pitch angle times distance  362  plus the maximum deformation. In order to avoid any overhang of rotor blades  316  in front of cylindrical portion  332   b , an additional margin of 1.33% of diameter  358  may be added. 
     Diffuser  328   b  includes cylindrical portion  334   b , with a length  352   b  along central longitudinal axis  306   b , frustoconical portion  336   b  diverging from cylindrical portion  334   b  with a half-angle  354   b , and a transition section  378   b  between cylindrical portion  334   b  and frustoconical portion  336   b  having a radius  380   b . Length  352   b  of cylindrical portion  334   b  of diffuser  328   b  may be between 1% and 3.5% of diameter  358 .Length  352   b  is preferably less than the sine of the maximum pitch angle times the difference between chord length  360  and distance  362 . Half-angle  354   b  of frustoconical portion  336   b  may be between 0 degrees and approximately 20 degrees. Radius 380b will be determined by manufacturing constraints, desired diffusion, length  346   b  of diffuser  328   b , and half-angle  354   b . Radius  380   b  may be equal to zero when half-angle  354   b  is equal to 0 degrees. When half-angle  354   b  is greater than 0, the following expression may define the relationship between radius  380   b , half-angle  354   b , a radius  382   b  of cylindrical portion  334   b , a length  384   b  of transition section  378   b  and frustoconical portion  336   b , and a duct radius  386   b  at an exit of diffuser  328   b : 
     
       
         
           
             
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     A trailing portion  387   b  of exterior surface  324   b  is a curve that is tangent with leading portion  370   b  at the junction therebetween and intersects frustoconical portion  336   b  at a trailing edge  388   b  at an angle that provides acceptable camber to the rear of trailing edge  388   b , preferably such that a tangent of  387   b  at trailing edge  388   b  forms an angle relative to central longitudinal axis  306   b  that is approximately equal to half-angle  354   b.    
     The first exemplary shape shown in  FIG. 15A  may be more suitable for use on a tiltrotor that is likely to be utilized more often in helicopter mode as the wide radius  348   a  may increase hover efficiency in helicopter mode but will increase drag in airplane mode. Whereas the second exemplary shape, shown in  FIG. 15B , is optimized for increasing thrust on a fixed forward thruster or a tiltrotor likely to be utilized more often in airplane mode. It should be understood that if duct  304  is intended primarily for safety and/or noise reduction, rather than increased thrust/hover efficiency, other modifications may be included. For example, chord length  368  of duct  304  may be reduced, cylindrical portions  332  and  334  may be omitted, frustoconical section  336  may be curved instead of being frustoconical, etc. 
     Referring now to  FIG. 10 , rotor assembly  310  is rotationally coupled within duct  304  and is driven by a gearbox (not shown) within stator hub  318 . Stator hub has a substantially cylindrical external shape and is coaxial with central longitudinal axis  306  and is secured to interior surface  322  of duct  304  by stator vanes  320 . The gearbox in stator hub  318  is driven by a drive shaft (not shown) passing through a sleeve  390  and wing  302  and connected to a main gearbox (not shown). Sleeve  390  is arranged in duct  304  substantially in the place of one of stator vanes  320 . Rotation of rotor assembly  310  within duct  304  creates a guided flow of air which provides thrust in the direction of central longitudinal axis  306 . In order to vary the amplitude of this thrust, stator assembly  312  and/or rotor assembly  310  comprise a mechanism for collective control of the pitch of rotor blades  316 . 
     Stator vanes  320 , fixed in duct  304  downstream of rotor blades  316 , recover the rotational energy of the airflow downstream of rotor blades  316 , by straightening out the airflow towards the central longitudinal axis  306  and generating a supplementary thrust. As shown in  FIG. 12 , two rotor blades  316  which rotate with rotational speed U=ΩR have been represented diagrammatically upstream of two stator vanes  320 . This speed U is combined with the axial inlet speed Vo 1  of the air in order to give a relative speed W 1  of the flow of air at rotor assembly  310 , this latter speed establishing a pressure field around each rotor blade  316 . This field then gives rise to an aerodynamic resultant R 1  which may, on the one hand, be broken down into a lift force Fz 1  and a drag force Fx 1  and, on the other hand, gives rise to an axial thrust S 1  of direction orthogonal to the direction of the speed U of rotation of rotor blades  316 , and in the opposite direction to Vo 1 . 
     As a consequence of the first obstacle constituted by each rotor blade  316 , the air leaves rotor assembly  310  under different speed conditions, and the outlet speeds triangle makes it possible to discern a new speed W 2  relative to rotor blade  316 , less than W 1 , and an absolute speed V 2  which acts on a stationary stator vane  320  facing it. The speed V 2  fulfilling, for the stationary stator vane  320 , the same role as did the speed W 1  for the moving rotor blade  316 , V 2  establishes a pressure field around each stator vane  320 , and this field gives rise to an aerodynamic resultant R 2  which, on the one hand, is broken down into a lift force Fz 2  and a drag force Fx 2  and, on the other hand, gives rise to an axial thrust S 2  which is an additional thrust adding to the thrust S 1 . Upon leaving stator vanes  320 , the airflow is straightened and its speed V 3  may be practically axial (parallel to central longitudinal axis  306 ) by a suitable choice of the asymmetric aerodynamic profile of stator vanes  320 , and in particular their camber and angular setting with respect to central longitudinal axis  306 . 
     In ducted thruster  300 , the arrangement of stator assembly  312  with profiled stator vanes  320  downstream of rotor assembly  310  in duct  304  makes it possible to produce a compact, balanced and rigid thrust generating device which, without modifying the power required for driving rotor assembly  310  gives increased thrust. The efficiency of such a thrust generating device is thus linked to the characteristics of rotor assembly  310 , the performance level required to fly the aircraft depends mainly on the choice of diameter of rotor assembly  310 , and therefore of duct  304 , on the peripheral speed of rotor blades  316 , the number of rotor blades  316 , their chord length  360 , and on their profile and twist law, to the characteristics of stator assembly  312 , when it exists, and particularly on the number of stator vanes  320 , their chord, their profile (camber, setting, etc.), as well as to the characteristics of duct  304 . 
     In addition, acoustic optimization of ducted thruster  300  is ensured by distributing acoustic energy over the entire frequency spectrum, by adopting an uneven angular distribution of rotor blades  316 , termed azimuth modulation or phase modulation, and by reducing the acoustic energy level emitted by ducted thruster  300 , by reducing the peripheral speed of rotor blades  316 , by reducing the interference between rotor assembly  310  and stator assembly  312  and sleeve  390  by virtue of a specific configuration and arrangement of these elements within duct  304 , with a suitable separation from rotor assembly  310 . 
     For a rotor assembly  310  comprising ten rotor blades  316 , an example of uneven phase or azimuth modulation is represented in  FIG. 11 . The object of this phase modulation is to disrupt the conventional angular symmetry or conventional equi-angular distribution of rotor blades  316 , in order not to reduce the acoustic energy emitted but to distribute it more favorably over the frequency spectrum, contrary to that which is obtained in the absence of modulation (equally distributed blades), namely a concentration of the energy over specific frequencies (such as bΩ, 2bΩ, 3bΩ, etc.). 
     A phase modulation law for rotor blades  316  is a sinusoidal law or close to a sinusoidal law of type: 
       Θ n=n×   b   360° +ΔΘsin ( m×n×   b   360 ° )
 
     where Θn is the angular position of the nth rotor blade  316  counted successively from an arbitrary angular origin, b being the number of rotor blades  316 , and m and ΔΘ are the parameters of the sinusoidal law corresponding, in the case of m, to a whole number which is not prime with the number b of rotor blades  316  whereas ΔΘ is chosen to be greater than or equal to a minimum value ΔΘ min chosen as a function of the number b of rotor blades  316  and which decreases as b increases. 
     It should be understood that 
     
       
         
           
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                 × 
                 n 
                 × 
                 
                   
                     3 
                      
                     6 
                      
                     
                       0 
                       ∘ 
                     
                   
                   b 
                 
               
               ) 
             
           
         
       
     
     corresponds to the azimuth modulation term with respect to the equally distributed configuration. The parameters m and ΔΘ are chosen as a function of the number b of rotor blades  316  in order, at the same time, to provide dynamic balancing of rotor assembly  310 , optimum distribution of the energy over the frequency spectrum, and guarantee a minimal inter-blade angular separation imposed by the conditions of angular excursions of the blades in terms of pitch and structural adherence of rotor blades  316  to rotor hub  314 . The whole number m is chosen in the following fashion: it is first of all chosen to respect dynamic balancing of rotor assembly  310 . By writing this balance, the following two equations which have to be satisfied are obtained: 
       ΣcosΘ n =0 and ΣsinΘ n= 0
 
     For the sinusoidal modulation law Θn given hereinabove, these two equations are satisfied if m and b are not prime with each other. The possible choices for m as a function of the number b of rotor blades  316  varying from 6 to 12 are given by crosses in Table 1 below. 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 b 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 m 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
               
               
                   
                   
               
               
                   
                 2 
                 X 
                   
                 X 
                   
                 X 
                   
                 X 
               
               
                   
                 3 
                 X 
                   
                   
                 X 
                   
                   
                 X 
               
               
                   
                 4 
                 X 
                   
                 X 
                   
                 X 
                   
                 X 
               
               
                   
                   
               
            
           
         
       
     
     As a function of the possibilities offered in Table 1, the whole number m is as small as possible and preferably fixed to 2 or 3 in order to obtain the densest possible spectrum, and therefore, a better distribution of energy per third of an octave. The parameter m may, just about, be equal to 4, but the value of 1 is to be avoided. 
     The parameter ΔΘ must be chosen in the following fashion: it is greater than or equal to a minimum value ΔΘ min given by an acoustic criterion for a given number of rotor blades  316 , as indicated in Table 2 hereinbelow. 
     
       
         
           
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 b 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 6 
                 8 
                 9 
                 10 
                 12 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 ΔΘ min 
                 14.34° 
                 10.75° 
                 9.55° 
                 8.60° 
                 7.17° 
               
               
                   
                   
               
            
           
         
       
     
     These values correspond to one and the same angular phase shift ΔΦ=bΔΘ, which comes into play as a parameter of Bessel functions characterizing the levels of the spectral lines of a sinusoidal modulation, with respect to the fundamental line, as explained in an article entitled “Noise Reduction by Applying Modulation Principles” by Donald Ewald et al., published in “The Journal of the Acoustical Society of America”, volume 49, Number 5 (part 1) 1971, pages 1381 to 1385, which is incorporated herein by reference in its entirety. The angular phase shift ΔΦ=1.5 radian corresponds to the value above which the Bessel function Jo (ΔΦ) is less than or equal to the Bessel functions Jn (ΔΦ) where n is other than 0 (see  FIG. 2  of the abovementioned article). This makes it possible to minimize the emergence of the fundamental in b S 2  with regard to the adjacent lines, because Jo (ΔΦ) represents the weighting coefficient on the fundamental line, whereas J 1  (ΔΦ) represents that of the adjacent lines (b-1)Ω and (b+1 Ω, which exist if there is modulation. The angular phase shift ΔΦ=bΔΘ=1.5 radian is the ideal point, because the noise level on the three adjacent lines bΩ, (b-1)Ω, and (b+1)Ω is identical, the energy concentrated on the line bΩ for a rotor with equally distributed rotor blades is thus distributed over the three lines. Table 2 thus gives the values of ΔΘ min as a function of b, so that bΔΘ8 min=1.5 radian. 
     This result corresponds to an ideal case, for which the pressure disturbance function is quite uniform, that is to say for a rotor with a large number of rotor blades (greater than 20). In the case of rotor assembly  310 , the relatively lower number of rotor blades  316  renders the pressure disturbance function more impulsive. Also, the above rule may be slightly adapted, which requires variation limits to be defined in order to match the sinusoidal modulation rule to the specific case of ducted thruster  300 . In addition, the minimal allowable inter-blade angular separation for enabling the blade angular excursion in terms of pitch without interfering with each other, as well as suitable structural adherence of rotor blades  316  to rotor hub  314  may necessitate a choice of ΔΘ less than ΔΘ min recommended by the acoustic criteria (Table 2). For example, if rotor assembly  310  has ten rotor blades  316 , the minimum inter-blade angular separation is 24 degrees. 
     A phase modulation law may therefore be adopted, based on a distorted sinusoidal law, for which bΔΘ may be chosen within the range of values extending from 1.5 radian to 1 radian and/or a variation of ±5 degrees about the angular position given initially by the sinusoidal distribution law for each rotor blade  316  may be adopted in order to cover the constraint of minimal inter-blade angular separation, while retaining good acoustic efficiency due to phase modulation. It should be noted that for bΔΘ=1 radian, the weighting coefficient for the fundamental line bΩ is 0.8 and falls to 0.45 for the adjacent lines (b±1)Ω. 
     Stator vanes  320  are evenly distributed about central longitudinal axis  306  in order to limit the interference between rotor assembly  310  and stator assembly  312 , and in particular in order to avoid any surge phenomenon (dynamic excitation) between rotor assembly  310  and stator assembly  312 . The phase modulation of rotor blades  316  is such that any angular separation between two rotor blades  316  which are not necessarily consecutive, is different from any angular separation between any two not necessarily consecutive stator vanes  320 . Mathematically, this condition may translate as follows: if Θij represents the angular separation between rotor blades  316  of order i and j, counted successively from an arbitrary angular origin, that is to say the angle defined between the pitch change axes of blades i and j, and if Θkl represents the angular separation between stator vanes  320  of order k and l, then regardless of the values of i, j, k,l, Θij is different from Θkl. This condition is considered to be respected if the differences between the respective angular separations of various rotor blades  316  and of various stator vanes  320  are greater than 1 degree in absolute values, for at least half of stator vanes  320 , not counting sleeve  390 . 
     If this angular condition, which prevents two rotor blades  316  from passing simultaneously opposite two stator vanes  320 , is not verified by the choice of phase modulation of sinusoidal type of the most advantageous type mentioned above, the angular positions of some rotor blades  316  must be modified by moving away from the sinusoidal law, and adopting a distorted sinusoidal law as mentioned above, that is, since ΔΘ cannot then be chosen such that bΔΘ=1.5 radian, then bΔΘ is decreased progressively from 1.5 to 1 radian until a suitable value of ΔΘ is obtained to respect the above-mentioned geometric condition Θij which is different from Θkl, without dropping below 1 radian, and cumulatively or alternatively a maximum variation of ±5 degrees about the angular position given initially by the sinusoidal distribution law for each rotor blade  316  is permitted. 
     If a decrease in sound nuisance is sought, avoiding simultaneous interactions between two rotor blades  316  and two stator vanes  320 , when rotor blades  316  are equally distributed, it is sufficient to choose a number b of rotor blades  316  which is prime with the number of stator vanes  320 , so as not to find an arbitrary angular separation between two not necessarily consecutive rotor blades  316  which is equal to an arbitrary angular separation between two not necessarily consecutive stator vanes  320 . 
     A decrease in acoustic nuisance from the interactions between rotor assembly  310  and stator assembly  312  is also obtained by decreasing the level of acoustic energy emitted by these interactions, independently of the frequencies on which it is concentrated or distributed. As represented in  FIG. 13 , in order to avoid the interaction between a rotor blade  316  and a stator vane  320  from arising simultaneously over the whole span of the stator vane  320 , stator vanes  320  are arranged in a non-radial fashion, and instead are each inclined by an angle V, lying between approximately 5 degrees and approximately 25 degrees to the radial direction, in the opposite direction from the direction of rotation of rotor blades  316  when considering stator vane  320  from central longitudinal axis  306  towards a periphery of duct  304 . This direction of inclination makes it possible not only to reduce the noise of interaction between rotor blades  316  and stator vanes  320 , but also to ensure better take up of the loadings withstood by the gearbox in stator hub  318 , stator vanes  320  operating in compression. In effect, since one of the functions of stator assembly  312  is to support the gearbox, stator vanes  320  may thus best take up the reactive torque to the torque transmitted to rotor assembly  310 . In addition, the relative thickness of the aerodynamic profiles of stator vanes  320  is chosen to best reduce the overall size in duct  304 , while ensuring sufficient mechanical strength for the function of supporting stator hub  318 . The relative thickness of the profiles of stator vanes  320  lies between approximately 8% and approximately 12%. 
     This choice of relative thickness is compatible with the use, for stator vanes  320 , of an aerodynamic profile of NACA 65 type, exhibiting an angle of attack setting to central longitudinal axis  306 , which is negative and lies between approximately 2 degrees and approximately 2.5 degrees, and a camber lying between approximately 20 degrees and approximately 28 degrees, these profile characteristics give stator assembly  312  good efficiency. 
     Furthermore, the reduction in the noise of interaction between rotor assembly  310  and stator assembly  312  becomes significant beyond a minimal axial separation between leading edges of stator vanes  320  and plane of rotation  342  of rotor assembly  310 , defined by pitch change axes  340  of rotor blades  316 , at approximately 40% of their chord length  360 , this minimum separation being at least equal to 1.5 times chord length  360 . However, since the support for the gearbox and stator hub  318  in duct  304  is provided by stator vanes  320 , in order to give good tolerance on the position of plane of rotation  342  of rotor assembly  310  within duct  304 , it is necessary to fix stator assembly  312  as close as possible to plane  342  of rotor assembly  310 . 
     A good compromise between these two contradictory requirements, between noise reduction and good tolerance on the position of plane  342 , is obtained by inclining stator vanes  320  at an angle Ψ, of approximately 2 degrees to approximately 6 degrees, as represented in an exaggerated manner in  FIG. 14 . This inclination of each stator vane  320  at a slant, from central longitudinal axis  306  towards interior surface  322  of duct  304  and from upstream to downstream, makes it possible to keep the leading edge of each stator vane  320  as far away as possible from plane  342 , while preserving correct positioning of the gearbox and stator hub  318 , and therefore of plane  342  in duct  304 . Taking account of the progressive nature of the aerodynamic loading between the roots of stator vanes  320 , coupled to stator hub  318 , and their more loaded ends coupled to interior surface  322  of duct  304 , the influence on noise remains negligible, despite the leading edges of stator vanes  320  coming close behind the roots of rotor blades  316 . For these reasons, the axial spacing between plane of rotation  342  and the leading edges of stator vanes  320 , at interior surface  322  of duct  304 , is a distance  392  lying between approximately 1.5 times chord length  360  and approximately 2.5 times chord length  360 . 
     As stated above, sleeve  390  is likened to a stator vane  320  in order to determine the angular positions of stator vanes  320  and of rotor blades  316 , but it is not profiled, and the number of profiled stator vanes  320  is chosen to be greater than or equal to the number of rotor blades  316 , less one. 
     Rotor blades  316  have an aerodynamic profile of the OAF type, with relative thickness and camber which progress along a span, the relative thickness decreasing for example from 13.9% to 9.5% between 40% and 100% of a radius of rotor assembly  310 . Likewise, a twist on the profile decreases moving away from central longitudinal axis  306 . 
     In a first example of ducted thruster  300 , rotor assembly  310  includes 8 rotor blades  316 , wherein the range of pitch of rotor blades  316  extends from −25 degrees to +41 degrees at 70% of the radius of rotor assembly  310 , and the profile of rotor blades  316  is a progressive OAF profile as mentioned above, with a twist decreasing from 17 degrees to 6.9 degrees from 40% to 100% of the radius of rotor assembly  310 . 
     When the first example of ducted thruster  300  is associated with a stator assembly  312  with ten profiled stator vanes  320 , to which is added sleeve  390  (ten inter-vane angular separations of 30.66 degrees and one angular separation of 53.4 degrees through which sleeve  390  passes), rotor assembly  310  with eight rotor blades  316  exhibits phase modulation of rotor blades  316  according to the optimal sinusoidal law (bΔΘ min=1.5 radian), of which the parameters are m =2 and ΔΘ=10.75 degrees, but in order to take account of stator assembly  312 , the optimal law is distorted by maximum angular variations of ±3.75 degrees, which leads to the following modulation of the eight rotor blades  316  of rotor assembly  310 : 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 n 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
             
            
               
                 Θn 
                 55° 
                 92° 
                 128° 
                 180° 
                 235° 
                 272° 
                 308° 
                 360° 
               
               
                   
               
            
           
         
       
     
     In contrast, when the first example of ducted thruster  300  is associated with a stator assembly  312  with seven profiled stator vanes  320  plus sleeve  390 , rotor assembly  310  with eight rotor blades  316  exhibits phase modulation according to a distorted sinusoidal law (bΔΘ=1.25 radian) of which the parameters are m=2 and ΔΘ=8.96 degrees with maximum angular variations of ±5 degrees, which gives the following modulation: 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 n 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
             
            
               
                 Θn 
                 56° 
                 93° 
                 131° 
                 180° 
                 236° 
                 273° 
                 311° 
                 360° 
               
               
                   
               
            
           
         
       
     
     The inclination V of stator vanes  320  to the radial direction passing through the base of each of them is about 10 degrees and their angle of slant Ψ towards interior surface  322 , and the outlet, of duct  304  is about 4 degrees. The distance  392  separating plane of rotation  342  from the leading edges of stator vanes  320  is approximately 1.53 to 1.66 times chord length  360  of rotor blades  316 . Profiled stator vanes  320  have a profile of NACA 65 type with a relative thickness of about 10%, a camber of a mid-line of the profile of about 27 degrees, and an angle of attack setting to central longitudinal axis  306  which is negative and equal to about 2.5 degrees. 
     In a second example of a ducted thruster  300 , rotor assembly  310  includes 10 rotor blades  316 . The profile of rotor blades  316  is an OAF profile similar to that of the preceding example, and the range of pitch extends from −25 degrees to +35 degrees at 70% of the radius of rotor assembly  310 . Rotor blades  316  exhibit phase or azimuth modulation given by the aforementioned sinusoidal law but distorted (bΔΘ=1 radian) of which the parameters are m=2 and ΔΘ=5.73 degrees with maximum angular variations of ±3.4 degrees. Stator assembly  312  includes ten profiled stator vanes  320 , to which sleeve  390  is added. This leads to the following modulation: 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 n 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
               
               
                   
               
             
            
               
                 Θn 
                 44.9° 
                 77.5° 
                 102.5° 
                 135.1° 
                 180° 
                 224.9° 
                 257.5° 
                 282.5° 
                 315.1° 
                 360° 
               
               
                   
               
            
           
         
       
     
     Angle of slant Ψ of profiled stator vanes  320  is 4 degrees and their inclination V to the radial direction is 7.8 degrees. The distance  392  between plane  342  of rotor assembly  310  and profiled stator vanes  320  is approximately 1.96 times chord length  360  of rotor blades  316 . Stator vanes  320  have a profile of NACA 65 type with about 10% relative thickness, with a camber of about 21 degrees for the mid-line of the profile, and an angle of attack setting which is negative and equal to about 2.5 degrees. 
     In a third example of ducted thruster  300 , rotor assembly  310  includes ten rotor blades  316 . As in the preceding examples, pitch change axes  340  for rotor blades  316  is at 40% of their chord length  360 , and their profile is a progressive OAF profile with the same law of variation in relative thickness, but a twist law which decreases from 7.25 degrees to −1.2 degrees between 40% and 100% of the radius of rotor assembly  310 . Stator assembly  312  includes either 13 stator vanes  320 , namely 12 profiled stator vanes  320  and sleeve  390 , or 17 stator vanes  320 , namely 16 profiled stator vanes  320  and sleeve  390 . The profile of profiled stator vanes  320  is a profile of NACA 65 type with about 10% relative thickness, a camber of about 23 degrees and an angle of attack setting which is negative and equal to about 2.2 degrees. Angle of slant Ψ of profiled stator vanes  320  is about 3 degrees and their angle V of inclination to the radial direction is about 11.2 degrees. Distance  392  between plane of rotation  342  of rotor assembly  310  and the leading edges of stator vanes  320  is from 1.65 times chord length  360  to 1.7 times chord length  360  and the application of the distorted sinusoidal law mentioned above in order to obtain phase modulation leading to no angle between two arbitrary rotor blades  316  being equal to any angle between two arbitrary stator vanes  320 , leads to the angular distribution of rotor blades  316  shown in Table 3 below, depending on whether stator assembly  312  comprises 13 or 17 stator vanes  320 . 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 n 
                 Θn stator: 13 
                 Θn stator: 17 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                   45.7° 
                   33.5° 
               
               
                 2 
                  77° 
                  77° 
               
               
                 3 
                 103° 
                   120.5° 
               
               
                 4 
                   134.3° 
                 154° 
               
               
                 5 
                 180° 
                 180° 
               
               
                 6 
                   225.7° 
                   213.5° 
               
               
                 7 
                 257° 
                 257° 
               
               
                 8 
                 283° 
                   300.5° 
               
               
                 9 
                   314.3° 
                 334° 
               
               
                 10 
                 360° 
                 360° 
               
               
                   
               
            
           
         
       
     
       FIG. 11  represents rotor assembly  310  having the angular distribution indicated in Table 3 above for a stator assembly  312  with 13 stator vanes  320 . 
       FIGS. 16-20 and 35-37  illustrate components and configurations of a ducted thruster  400  for providing forward thrust to an aircraft. Ducted thruster  400 , shown in  FIG. 16  rotatably coupled to a wing  402 , comprises a duct  404  having a central longitudinal axis  406  and a thruster assembly  408  supported within duct  404 . Thruster assembly  408  comprises a rotor assembly  410  rotatably coupled about central longitudinal axis  406  within duct  404  and a stator assembly  412  coupled within duct  404  downstream of rotor assembly  410  with respect to a direction of the airflow through duct  404 . Rotor assembly  410  comprises a rotor hub  414  and a plurality of variable-pitch rotor blades  416  extending from rotor hub  414 . Rotor assembly  410  may include any suitable number of rotor blades  416 , e.g., nine rotor blades  416  as shown in the figures. Stator assembly  412  comprises a stator hub  418  and a plurality of stator vanes  420  extending from stator hub  418  to an interior surface  422  of duct  404 . Stator assembly  412  may include any suitable number of stator vanes  420 , e.g., equal to or unequal to the number of rotor blades  416 . 
     As shown in  FIGS. 17-19 , rotor blades  416  are modulated around central longitudinal axis  406  such that angles between adjacent rotor blades  416  are varied to create a balanced rotor assembly  410  while decreasing noise.  FIGS. 17 and 18  illustrate a rotor assembly  410  with modulation factor m, as discussed below, of m=1, with  FIG. 18  illustrating the optimized angle in degrees between each rotor blade  416 .  FIG. 20  provides a list of the angular spacing between each rotor blade  416  in  FIGS. 17 and 18  under the column labeled “m=1.”  FIG. 19  illustrates a rotor assembly  411  with modulation factor m, as discussed below, of m=2, illustrating the optimized angle in degrees between each rotor blade  416 .  FIG. 20  provides a list of the angular spacing between each rotor blade  416  shown in  FIG. 19  under the column labeled “m=2.” 
     Modulated rotor blade spacing reduces the amplitude of the fundamental frequency of a rotor and harmonics of that frequency and shifts the energy to other frequencies normally not substantially present. These new tones that are generated tend to be masked by other noise sources and make the resulting sound more broadband, rather than tonal, in quality. Furthermore, the blade spacing method of this disclosure can enable a dynamically balanced rotor to be developed without a modulation factor being a prime with respect to the number of rotor blades. That is, the blade modulation factor and the number of rotor blades can be such that the two numbers have no common divisor except unity. In other words, the blade modulation does not have to divide evenly into the number of rotor blades. A lower modulation factor results in a more random, or broadband, sound. The use of a non-prime modulation factor can lead to blade spacing angles that are difficult to manufacture, so an optimization technique is used to slightly change the blade angles to that which can be manufactured while keeping the rotor system balanced. Thus, the blade modulation reduces the amplitude of the fundamental tone of the rotor assembly and increases the broadband randomness of the sound, while at the same time enables dynamic balancing of the rotor assembly. 
     An embodiment of this disclosure includes a method of achieving a balanced rotor assembly with modulated rotor blades regardless of whether the modulation factor m is prime with the number of rotor blades and including when the modulation factor m is prime with the number of rotor blades. Additionally, the method of the subject application permits the use of low modulation factors, such as modulation factor m=1 and modulation factor m=2, since a lower modulation factor m can result in a more random, or broadband sound. 
     For an embodiment of this disclosure, the angular spacing of rotor blades  416  is determined by using the sinusoidal law: 
       Θ i ′=Θ i+ ΔΘ i sin(mΘ i )
 
     where Θ i ′ is the modulated blade angle for the ith rotor blade  416 ; Θ i  is the nominal blade angle for the ith rotor blade  416 ; ΔΘ  i  is the maximum modulation amplitude or the maximum blade angle change; and m is the modulation factor (1, 2, 3, . . . , where 1=1 cycle of modulation from 0 to 2π, 2=2 cycles of modulation from 0 to 2π, etc.). Additionally, the subject embodiment utilizes the equation: 
       ΔΘ i =ΔΦ/I
 
     wherein I is number of rotor blades  416 . 
     Further, ΔΘ i  and, thus, ΔΦ are not constant in the sinusoidal law used in the subject embodiment. In the subject embodiment the disclosed method is utilized for balancing a modulated rotor assembly with a modulation factor m that is prime with the number of rotor blades  416 . That is, one embodiment of this disclosure includes balancing a nine rotor-blade rotor assembly with a modulation factor m of m=1. Another embodiment of this disclosure includes balancing a nine rotor-blade rotor assembly with a modulation factor m of m=2. 
     To accomplish modulating rotor assemblies  410  and  411  with odd numbers of rotor blades  416  and with the desired modulation factors of m=1 and m=2 to form balanced rotor assemblies  410  and  411 , ΔΦ is varied so that more harmonics (J 2,  J 3,  etc.) will be more even in amplitude, and near perfect balance is attainted. Thus, an iterative optimization is used with the sinusoidal law. That is, the sinusoidal law is modified such that ΔΘ is replaced with ΔΘ i  for each harmonic and an additional restriction of balance given by the sum of sin Θ and cos Θ is added to an objective function. The objective function for determining the modulation factor m=1 for rotor assembly  410  minimizes the following sum: (blade weighting)×(blade balance sum)+(Bessel weighting)×(Bessel values) subject to the minimum blade angle between rotor blades  416 . In the illustrated embodiment, the blade weighting was arbitrarily chosen to be 100 and the Bessel weighting was arbitrarily chosen to be 20. The minimum angle was arbitrarily chosen at 10 degrees but was later changed to 30, and then to 29. The exact values of ΔΦ can be approximated graphically from a plot of the Bessel functions. The values of Δ 101   typically varied from 0 to 13. One constraint placed on the optimization routine was that a rotor blade  416  was not modulated so that the rotor blade  416  switches order. Also, increasing the revolutions per minute (RPM) of rotor assembly  410  improved the balance of rotor assembly  410 . As an end result, the methodology of this embodiment of this disclosure, that is, a modified sinusoidal law, leads to a substantially balanced rotor assembly  410  regardless of whether the modulation factor is prime with the number of rotor blades  416 . 
     To accomplish the modulating of rotor assembly  411  with a modulation factor of m=2, a process similar to that used for determining the modulation of rotor assembly  410  for modulation factor m=1 is used, but for modulating rotor assembly  411  with a modulation factor of m=2 the evenness of the Bessel functions was not weighed into the equation. 
     For both cases of modulation factors m=1 and m=2, rotor assemblies  410  and  411  were not perfectly balanced using the sinusoidal law. It is necessary to further vary the modulated angles to achieve a theoretical balance more perfect than manufacturing error. It is not preferable to manufacture rotor hub  414  to a greater tolerance than two decimal places, so in a spreadsheet numerical routine (any numerical method can be used, with the objective function to minimize balance error minus the sum of the sines and cosines as discussed in column 11 of U.S. Pat. No. 5,588,618) each iteration was rounded off to two decimal places so that the balanced rotor is within manufacturing tolerances, that is, the manufacturing tolerance errors are greater than the theoretically balanced error for the two decimal places specified. 
     Thus, through the above-described methodology, in the illustrated embodiment, a nine bladed modulated rotor assembly  410  and  411  can be essentially balanced with a modulation factor m=1 and with a modulation factor of m=2. 
     Although the illustrated embodiment addresses the balancing of rotor assemblies  410  and  411  with nine rotor blades  416 , it should be understood that rotor assemblies  410  and  411  having any desired number of rotor blades can be balanced using the methodology of this disclosure, including a prime number of rotor blades  416 . For example, a rotor assembly  410  with seven rotor blades  416  or with eleven rotor blades  416  can be balanced. 
     One preferred modulated spacing of rotor blades  416  for rotor assembly  410  (m=1) is determined as set forth above and illustrated in  FIGS. 17 and 18  and listed in  FIG. 20  under the column “m=1.” One preferred modulated spacing of rotor blades  416  for rotor assembly  411  (m=2) is determined as set forth above and illustrated in  FIG. 19  and listed in  FIG. 20  under the column “m=2.” 
       FIGS. 21-28, 33, and 34  illustrate components and configurations of a ducted thruster  500  for providing forward thrust to an aircraft. Ducted thruster  500 , comprises a duct  504  having a central longitudinal axis  506  and a thruster assembly  508  supported within duct  504 . Thruster assembly  508  comprises a rotor assembly  510  rotatably coupled about central longitudinal axis  506  within duct  504  and a stator assembly  512  coupled within duct  504  downstream of rotor assembly  510  with respect to a direction of the airflow through duct  504 . Rotor assembly  510  comprises a rotor hub  514  and a plurality of variable-pitch rotor blades  516  extending from rotor hub  514 . Rotor assembly  510  may include any suitable number of rotor blades  516 , e.g., eight rotor blades  516  as shown in the figures. Stator assembly  512  comprises a stator hub  518  and a plurality of stator vanes  520  extending from stator hub  518  to an interior surface  522  of duct  504 . Stator assembly  512  may include any suitable number of stator vanes  520 , e.g., equal to or unequal to the number of rotor blades  516 . 
     To reduce the perceived noise of ducted thruster  500  during operation and to improve performance of ducted thruster  500 , stator vanes  520  of stator assembly  512  are angularly modulated around stator hub  518 . That is, the angular separation between each of stator vanes  520  is not constant, but instead is varied. Stator vanes  520  are modulated such that only a portion of a rotor blade  516  intersects a portion of a stator vane  520  at any given time when a rotor blade  516  rotates around central longitudinal axis  506  and moves past each stator vane  520 . That is, a full rotor blade  516  does not overlap a full stator vane  520  at any given time. Moreover, the intersection points between rotor blades  520  and the respective stator vanes  520  at any given time each have a different radial length from central longitudinal axis  506 . Thus, the angular modulation of stator vanes  520  ensures that no two rotor blades  516  pass over the same portion of a stator vane  520  at the same time. By varying the points at which rotor blades  516  intersect respective stator vanes  520  at any given time, the noise generated at each of the intersections is diversified so as to reduce the perceived noise level of ducted thruster  500 . Modulated stator vanes  520  may be integrated into any suitable ducted thruster. 
       FIGS. 21, 22, and 24-28  show schematic representations of rotor blades  516  and stator vanes  520  to illustrate the relative relationships between rotor blades  516  and stator vanes  520 .  FIGS. 21, 22, and 24-28  show representations of rotor blades  516  and stator vanes  520  as seen from the stator-side of ducted thruster  500 . That is,  FIGS. 21, 22, and 24-28  illustrate rotor blades  516  and stator vanes  520  from the downstream side of duct  504  looking upstream.  FIG. 23  is an isolated view of stator vanes  520  from the rotor-side of ducted thruster  500 . 
       FIGS. 21 and 22  schematically illustrate rotor blades  516  intersecting stator vanes  520 . Specifically,  FIGS. 21 and 22  illustrate rotor blade centerlines of rotor blades  516  intersecting with stator vane centerlines of modulated stator vanes  520  ( FIG. 21  illustrates the rotor blade centerlines in solid lines and the stator vane centerlines in dashed lines, whereas  FIG. 22  illustrates the stator vane centerlines in solid lines and the rotor blade centerlines in dashed lines). As best shown in  FIG. 21 , rotor assembly  510  includes eight rotor blades  516 , hence eight rotor blade centerlines are successively labeled as B 1  to B 8 . However, rotor assembly  510  may include any other suitable number of rotor blades  516 , e.g., nine rotor blades  516 . Also, in the illustrated embodiment, rotor blades  516  are modulated about rotor hub  514 . That is, the intersection angle between adjacent rotor blade centerlines B 1  to B 8  is varied or non-uniform. However, rotor assembly  510  may include rotor blades  516  that are un-modulated (equally or uniformly distributed) around rotor hub  514 . Moreover, as shown in  FIG. 24 , rotor blades  516  extend radially. That is, each of rotor blade centerlines B 1  to B 8  are radial and pass through central longitudinal axis  506 . However, rotor assembly  510  may include rotor blades  516  that are non-radial. When operated, rotor blades  516  rotate clockwise in the direction of arrow A (as viewed in  FIGS. 21 and 22 ). 
     As best shown in  FIGS. 22 and 23 , stator assembly  512  includes eight stator vanes  520 , hence eight stator vane centerlines successively labeled as V 1  to V 8 . However, stator assembly  512  may include any other suitable number of stator vanes  520 . A driveshaft  590  powering rotor assembly  510  extends from interior surface  522  of duct  504  to stator hub  518  between stator vanes V 1  and V 8 . Driveshaft  590  is drivingly engaged with rotor assembly  510  to operate the same. Driveshaft  590  extends from the aircraft toward central longitudinal axis  506  to drive rotor assembly  510 . 
     As best shown in  FIGS. 22 and 23 , stator vanes  520  are modulated in the same direction about stator hub  518 . Specifically, stator vanes  520  are inclined with respect to rotor blades  516  in the clockwise direction, in the direction of rotation A of rotor assembly  510 . Thus, stator vane centerlines V 1  to V 8  are inclined relative to rotor blade centerlines B 1  to B 8 , and a full stator vane centerline V 1 -V 8  will not overlap a full rotor blade centerline B 1 -B 8  at any given time. Moreover, the modulation angle between adjacent stator vane centerlines V 1 -V 8  is varied or non-uniform. For example, as shown in  FIG. 25 , the angle Θ between V 3  and V 4  is different than the angle β between V 4  and V 5 . 
     Additionally, stator vanes  520  are non-radial. As shown in  FIG. 25 , each of stator vane centerlines V 1 -V 8  passes through circular stator hub  518 , but not through central longitudinal axis  506 . Specifically, each stator vane centerline V 1 -V 8  is tangent to a respective circle having central longitudinal axis  506  as its axis. Thus, the modulation angles between stator vane centerlines V 1 -V 8  are continuously varied so that stator vane centerlines V 1 -V 8  do not have a radial configuration about central longitudinal axis  506  as do rotor blade centerlines B 1 -B 8 . 
     The modulation angles are a function of the circumferential position of each stator vane  520 , which is a function of rotor blade  516  distribution. That is, the orientation of each stator vane  520  is based on rotor blade  516  distribution. To determine stator vane  520  modulation, a point is selected along each of rotor blade centerlines B 1 -B 8 , as shown in  FIG. 26 . Thus, eight points are selected and successively labeled as P 1  to P 8 . Points P 1 -P 8  are selected such that a line connecting the points forms an imaginary helix H. This arrangement positions eight points P 1 -P 8  such that each of eight points P 1 -P 8  has a different radial length from central longitudinal axis  506 . For example, P 5  is closer to central longitudinal axis  506  than P 6 , and P 6  is closer to central longitudinal axis  506  than P 7 , etc. The positioning of eight points P 1 -P 8  may be determined in any suitable manner, e.g., mathematical modeling, experimenting, etc. 
     Then, as shown in  FIG. 27 , an inclined line is passed through each of points P 1 -P 8  on rotor blade centerlines B 1 -B 8 . The lines are inclined in the same direction, i.e., in the direction of rotation A of rotor assembly 510. These lines define stator vane centerlines V 1 -V 8  of stator vanes  520 . As illustrated, intersection angles a between stator vane centerlines V 1 -V 8  and respective rotor blade centerlines B 1 -B 8  are equal. The angle a is approximately 17 degrees. However, the angle may have any suitable and appropriate magnitude, and the magnitude may be determined in any suitable manner, e.g., mathematical modeling, experimenting, etc. 
     Thus, when rotor assembly  510  is operated, rotor blades  516  intersect with respective stator vanes  520  at about a 17-degree angle, but the point of intersection between each rotor blade  516  and respective stator vane  520  is at a different radial length from central longitudinal axis  506 . By changing how each rotor blade  516  crosses a respective stator blade  520 , the sound generated from the crossing is diversified and not symmetric. For example, the sound generated when B 1  crosses V 1  will be different from the sound generated when B 2  crosses V 2 , and the sound generated when B 2  crosses V 2  will be different from the sound generated when B 3  crosses V 3 . The range of sounds reduces the perceived noise generated by ducted thruster  500  during operation. 
     The arrangement of stator assembly  512  described above places each of stator vanes  520  in tension when rotor assembly  510  is operating due to the torque created by the rotation of rotor assembly  510  wherein the torque is in the direction opposite to the direction of rotation of rotor assembly  510 . 
       FIG. 28  illustrates possible dimensions of the elements discussed with respect to  FIGS. 21-27 . It should be understood that the dimensions in  FIG. 28  are only one example of the dimensions and proportions of the various elements illustrated. 
       FIGS. 29 and 30  illustrate configurations of a ducted thruster  600  for providing forward thrust. Ducted thruster  600  comprises a duct having a central longitudinal axis  606  and a thruster assembly supported within the duct. The thruster assembly comprises a rotor assembly  610  rotatably coupled about central longitudinal axis  606  within the duct and a stator assembly  612  coupled within the duct downstream of rotor assembly  610  with respect to a direction of the airflow through the duct. Rotor assembly  610  comprises a rotor hub  614  and a plurality of variable-pitch rotor blades  616  extending from rotor hub  614 . Rotor assembly  610  may include any suitable number of rotor blades  616 , e.g., eight rotor blades  616  as shown in the figures. Stator assembly  612  comprises a stator hub  618  and a plurality of stator vanes  620  extending from stator hub  618  to an interior surface of the duct. Stator assembly  612  may include any suitable number of stator vanes  620 , e.g., equal to or unequal to the number of rotor blades  616 . 
       FIGS. 29 and 30  schematically illustrate modulated stator vanes  620 . In this embodiment, one of stator vanes  620  (each stator vane  620  and rotor blade  616  being represented by a center line) near a driveshaft  690 , e.g., V 8 , is oppositely inclined with respect to remaining stator vanes V 1 -V 7 . Specifically, V 8  is inclined with respect to rotor blades B 1 -B 8  in the opposite direction of rotation A of rotor assembly  610 . 
     This arrangement of stator assembly  612  places one stator vane V 8  in compression and the remaining stator vanes V 1 -V 7  in tension when rotor assembly  610  is operating. Moreover, this arrangement enables the two stator vanes V 1  and V 8  closest to driveshaft  690  to be mounted close to areas of high stress, which leads to better stress flow, reduced weight, and improved structural integrity. Additionally, more than one of stator vanes V 1 -V 8  may be oppositely inclined. 
     It should be understood that illustrated stator assemblies  512  and  612  are only exemplary, and stator assemblies  512  and  612  may include stator vanes  520  and  620  modulated in any suitable manner to reduce the perceived sound of ducted thrusters  500  and  600 , respectively, and to improve structural integrity. Moreover, it should be understood that the determination of the stator vane modulation described above is only exemplary, and the stator vane modulation may be determined in any other suitable manner. 
     Modulated stator vanes may be utilized with any suitable rotor assembly, including a rotor assembly with modulated rotor blades or a rotor assembly with un-modulated rotor blades. A rotor assembly with un-modulated rotor blades refers to a rotor assembly in which the angular spacing between adjacent rotor blades is constant. That is, the rotor blades are evenly spaced around the rotor hub such that the angle between every pair of adjacent rotor blades is the same. For example,  FIG. 31  illustrates a ducted thruster  700 , wherein rotor blades  716  of a rotor assembly  710  are un-modulated and stator vanes  720  of a stator assembly  712  are modulated similar to  FIGS. 22 and 23  and are substantially identical to the stator vanes discussed above with respect to similar to  FIGS. 22 and 23 .  FIG. 32  illustrates a ducted thruster  800 , wherein rotor blades  816  of a rotor assembly  810  are un-modulated and stator vanes  820  of a stator assembly  812  are modulated similar to  FIG. 30  and are substantially identical to stator vanes  620  discussed above with respect to  FIG. 30 . 
     Also, in an embodiment, one of the angles between adjacent rotor blades may be equal to one of the angles between adjacent stator vanes. In one example, one of the angles between adjacent rotor blades of an un-modulated rotor assembly may be equal to one of the angles between adjacent stator vanes of a modulated stator assembly. In another example, one of the angles between adjacent rotor blades of a modulated rotor assembly may be equal to one of the angles between adjacent stator vanes of a modulated stator assembly. 
       FIG. 33  illustrates rotor assembly  510  having substantially non-rectangular planform shaped rotor blades  516 . Rotor blades  516  disclosed may have a scimitar planform shape, or they may have a tapered planform shape (see rotor blades  516  in  FIG. 33 ). The rotor blades may be constructed from any suitable material and may be constructed in any suitable manner. 
     The scimitar planform shaped rotor blade is formed like a saber having a curved blade. Specifically, the scimitar planform shaped rotor blade has a leading edge that faces the direction of rotation of the rotor assembly, and a trailing edge. The leading edge has a generally convex configuration, and the trailing edge has a slightly concave configuration. However, the trailing edge may be generally parallel with a longitudinally extending centerline of the rotor blade or may have any other suitable configuration. Also, a proximal edge of the rotor blade, adjacent the rotor hub, and a distal edge of the rotor blade are both generally perpendicular to the rotor blade centerline. However, these edges may have any other suitable configuration, e.g., inclined, curved. Thus, the edges of the rotor blade cooperate to form a substantially non-rectangular planform shape. In use, this shape helps to reduce the Mach compressibility effects and perceived noise while maintaining performance. Specifically, this substantially non-rectangular planform shape of the rotor blade keeps a length of the rotor blade from crossing a length of a stator vane at any given time during operation. 
     Moreover, a cross-sectional configuration of the scimitar planform shaped rotor blade varies along the length thereof. The various cross-sections may have different configurations from one another, and the configurations may be solid, hollow, multiple-layered, etc. Also, the rotor blade has a twisted configuration. The twist of the rotor blade increases along a first portion of the length, then the twist slightly decreases along a second portion of the length. Also, a chord length of the rotor blade increases and then sharply decreases along length thereof. This variation in chord length gives the rotor blade its scimitar planform shape. 
       FIGS. 33 and 34  illustrate tapered rotor blade  516  having a tapered planform shape. Specifically, a trailing edge  517  of each of rotor blades  516  is inclined towards a pitch-change axis  540  of rotor blade  516 . As illustrated in  FIG. 34 , trailing edge  517  is inclined relative to a line  519  that is substantially parallel to pitch-change axis  540  by an angle A. A leading edge  521  is substantially parallel with respect to pitch-change axis  540 . However, leading edge  521  and trailing edge  517  may have other suitable configuration, e.g., inclining leading edge  521  relative to pitch-change axis  540  along with inclined trailing edge  517  or by itself instead of inclined trailing edge  517 . Also, a proximal edge  523  of rotor blade  516  and a distal edge  525  of rotor blade  516  are both generally perpendicular to pitch-change axis  540 . However, edges  523  and  525  may have any other suitable configuration, e.g., inclined. Thus, edges  517 ,  521 ,  523 , and  525  of rotor blade  516  cooperate to form a substantially non-rectangular planform shape. When rotor assembly  510  is operated, rotor blades  516  intersect with respective stator vanes  520  at an incline. By changing how each rotor blade  516  crosses a respective stator vane  520 , the perceived noise generated by ducted thruster  500  is reduced during operation. 
     It is contemplated that stator vanes  520  may have a substantially non-rectangular planform shape, e.g., scimitar, tapered. In such construction, rotor blades  516  of rotor assembly  510  may have a rectangular planform shape. In use, rotor blades  516  and stator vanes  520  would intersect one another at an incline to provide the noise reducing benefit. 
     It should be understood that illustrated rotor assembly  510  is only exemplary, and rotor assembly  510  may include rotor blades  516  with any other suitable substantially non-rectangular planform shape so as to reduce the perceived sound of ducted thruster  500  and to improve aerodynamic performance of ducted thruster  500 . 
       FIG. 35  schematically illustrates rotor blades  416  intersecting with modulated stator vanes  420 . Specifically,  FIG. 35  illustrates rotor blade centerlines of rotor blades  416  intersecting with stator vane centerlines of modulated stator vanes  520  ( FIGS. 35 and 36  illustrate the rotor blade centerlines in solid lines and the stator vane centerlines in dashed lines). Rotor assembly  510  includes eight rotor blades  416 , hence eight rotor blade centerlines are successively labeled as B 1  to B 8 . Rotor assembly  410  may include any other suitable number of rotor blades  416 , e.g., nine rotor blades  416 . Also, rotor blades  416  are modulated about rotor hub  414 . That is, the intersection angle between adjacent rotor blade centerlines B 1  to B 8  is varied, or non-uniform. Because the angles between each rotor blade centerline B 1 -B 8  varies, rotor blades  416  are angularly modulated. However, rotor assembly  410  may include rotor blades  416  that are equally or uniformly distributed around rotor hub  414 . Moreover, as shown in  FIGS. 18 and 19 , rotor blades  416  extend radially from central longitudinal axis  406 . That is, each of rotor blade centerlines B 1  to B 8  are radial and pass through central longitudinal axis  406 . However, rotor assembly  410  may include rotor blades  416  that are non-radial. When operated, rotor blades  416  rotate clockwise in the direction of arrow A (as viewed in  FIG. 35 ). 
     As shown in  FIGS. 35 and 37 , stator assembly  412  includes eight stator vanes  420 , hence eight stator vane centerlines successively labeled as V 1   m  to V 8   m . (The “m” indicates that stator vanes  420  are angularly modulated.) However, stator vanes  420  may include any other suitable number of stator vanes  420 . A driveshaft  490  powering rotor assembly  410  extends from interior surface  422  of duct  404  to stator hub  418  between stator vanes V 1   m  and V 8   m . Driveshaft  490  is drivingly engaged with rotor assembly  410  to operate the same. 
     Also shown in  FIGS. 35 and 37 , stator vanes  420  are modulated in the same direction about stator hub  418 . Specifically, stator vanes  420  are inclined with respect to rotor blades  416  in the clockwise direction, in the direction of rotation A of rotor assembly  410 . Thus, stator vane centerlines V 1   m  to V 8   m  are inclined relative to rotor blade centerlines B 1  to B 8 , and a full stator vane centerline V 1   m -V 8   m  will not overlap a full rotor blade centerline B 1 -B 8  at any given time. Moreover, the modulation angle between adjacent stator vane centerlines V 1   m -V 8   m  is varied or non-uniform. Additionally, stator vanes  420  are non-radial. As shown in  FIG. 35 , each of stator vane centerlines V 1   m -V 8   m  passes through stator hub  418 , but not through central longitudinal axis  406 . Specifically, each stator vane centerline V 1   m -V 8   m  is tangent to a respective circle having central longitudinal axis  406  as its axis. Thus, the modulation angles between stator vane centerlines V 1   m -V 8   m  are continuously varied so that stator vane centerlines V 1   m -V 8   m  do not have a radial configuration about central longitudinal axis  406  as do rotor blade centerlines B 1 -B 8 . 
     The modulation angles are a function of the circumferential position of each stator vane  420 , which is a function of rotor blade  416  distribution. That is, the orientation of each stator vane  420  is based on rotor blade  416  distribution. To determine stator vane  420  modulation, a point is selected along each of rotor blade centerlines B 1 -B 8 . Thus, eight points are selected. The points are selected such that a line connecting the points forms an imaginary helix. This arrangement positions the eight points such that each of the eight points has a different radial length from central longitudinal axis  406 . The positioning of the eight points may be determined in any suitable manner, e.g., mathematical modeling, experimenting, etc. 
     Then, an inclined line is passed through each of the points on rotor blade centerlines B 1 -B 8 . The lines are inclined in the same direction, i.e., in the direction of rotation A of rotor assembly  410 . These lines define stator vane centerlines V 1   m -V 8   m  of stator vanes  420 . The intersection angles between stator vane centerlines V 1   m -V 8   m  and respective rotor blade centerlines B 1 -B 8  are equal. The angle is approximately 17 degrees. However, the angle may have any suitable and appropriate magnitude, and the magnitude may be determined in any suitable manner, e.g., mathematical modeling, experimenting, etc. 
     Thus, when rotor assembly  410  is operated, rotor blades  416  intersect with respective stator vanes  420  at about a 17-degree angle, but the point of intersection between each rotor blade  416  and respective stator vane  420  is at a different radial length from central longitudinal axis  406 . By changing how each rotor blade  416  crosses a respective stator vane  420 , the sound generated from the crossing is diversified and not symmetric. For example, the sound generated when B 1  crosses Vlm will be different from the sound generated when B 2  crosses V 2   m , and the sound generated when B 2  crosses V 2   m  will be different from the sound generated when B 3  crosses V 3   m . The range of sounds reduces the perceived noise generated by ducted thruster  400  during operation. The above modulation of rotor blades  416  can be accomplished with rotor blades  416  of any planform shape, including substantially rectangular and substantially nonrectangular, including tapered planforms and scimitar planforms. 
     However, since the rotor blade planform shapes in accordance with this disclosure are substantially nonrectangular, the same advantages described above using modulated stator vanes  420  can be accomplished with stators vanes  420  that are radial. That is, whereas stator vanes  420  of  FIG. 35  do not extend from central longitudinal axis  406 , stator vanes  420  of  FIG. 36  do extend from central longitudinal axis and are radial stator vanes. Stator vanes  420  in  FIG. 36  can be radial since the nonrectangular nature of rotor blades  416  achieves the same benefits outlined above. That is, the nonrectangular rotor blades  416  are designed and modulated so that no rotor blade  416  crosses over a stator vane  420  at the same point as another rotor blade  416  and no rotor blade  416  ever overlaps a full stator vane  420  due to the different shape of rotor blades  416  relative to stator vanes  420 . Stator vanes  420  are labeled in  FIG. 36  as V 1 R-V 8 R (the subscript “R” identifying the stator vanes as radial). Substantially nonrectangular rotor blades  416  may be of various planform shapes, including scimitar planforms and tapered planforms. Also, the benefits identified above may be further achieved by using substantially non-rectangular rotor blade planforms and using unmodulated stator vanes  420  that have a constant spacing where stator vanes  420  are either radial or non-radial. 
     Some rotorcraft include a ducted anti-torque device transversely mounted in a tail section to control rotation of the rotorcraft about an axis of rotation of a main rotor mast. The following patents, relating to transversely-mounted ducted anti-torque devices, include additional features which may be incorporated into the embodiments divulged in this disclosure: U.S. Pat. No. 5,454,691, issued on Oct. 3, 1995; U.S. Pat. No. 5,498,129, issued on Mar. 12, 1996; U.S. Pat. No. 5,566,907, issued on Oct. 22, 1996; U.S. Pat. No. 5,588,618, issued on Dec. 31, 1996; U.S. Pat. No. 5,634,611, issued on Jun. 3, 1997; and U.S. Pat. No. 8,286,908, issued on Oct. 16, 2012; all of which are incorporated herein by reference in their entireties. 
       FIGS. 38-40  illustrate another embodiment of a ducted thruster  900 . Ducted thruster  900  comprises a duct having a central longitudinal axis  906  and a thruster assembly supported within the duct  904 . The thruster assembly comprises a rotor assembly  910  rotatably coupled about central longitudinal axis  906  within the duct  904  and a stator assembly  912  coupled within the duct  904  downstream of rotor assembly  910  with respect to a direction of the airflow through the duct  904 . Rotor assembly  910  comprises a rotor hub  914  and a plurality of rotor blades  916  extending from rotor hub  914 . Rotor assembly  910  may include any suitable number of rotor blades  916 , e.g., five rotor blades  916  as shown in the figures. Stator assembly  912  comprises a stator hub  918  and a plurality of stator vanes  920  extending from stator hub  918  to an interior surface of the duct  904 . 
     In this embodiment, a first stator vane  920   a , a second stator vane  920   b , a third stator vane  920   c , and a fourth stator vane  920   d  extend longitudinally along longitudinal axes  921   a ,  921   b ,  921   c , and  921   d , respectively. In this embodiment, the first stator vane 920 a  extends between the stator hub  918  and the duct  904  and the longitudinal axis  921   a  is substantially tangential to a portion of the stator hub  918 . The second stator vane  920   b  extends between the stator hub  918  and the duct  904  and the longitudinal axis  921   b  is substantially perpendicular to the longitudinal axis  921   a . The third stator vane  920   c  extends between the stator hub  918  and the duct  904  and the longitudinal axis  921   c  extends substantially perpendicular to the longitudinal axis  921   a . The longitudinal axis  921   c  is offset from the second longitudinal axis  921   b . The fourth stator vane  920   d  extends between the stator hub  918  and the duct  904  and the longitudinal axis  921   d  is substantially parallel to the longitudinal axis  921   a . The longitudinal axis  921   d  offset from the first longitudinal axis  921   a.    
     The ducted thruster  900  increases thrust performance and abates undesired noise. Stators  920  mounted in this configuration create a scissor action between the stators  920  and rotor blades  916  that minimizes the amount of blade sweeping over any stator  920  at any given time, thus reducing noise created from the blade-stator interaction. In addition, the tangential stator attachment to the stator hub  918  resists motor torque more efficiently than radially attached stators, regardless of the rotor spin direction. In this embodiment, the stator hub  918  generally encircles or is a portion of a motor mount that holds a motor for turning the rotor blades  916 . 
     At least one embodiment is disclosed, and variations, combinations, and/or modifications of the embodiment(s) and/or features of the embodiment(s) made by a person having ordinary skill in the art are within the scope of the disclosure. Alternative embodiments that result from combining, integrating, and/or omitting features of the embodiment(s) are also within the scope of the disclosure. Where numerical ranges or limitations are expressly stated, such express ranges or limitations should be understood to include iterative ranges or limitations of like magnitude falling within the expressly stated ranges or limitations (e.g., from about 1 to about 10 includes, 2, 3, 4, etc.; greater than 0.10 includes 0.11, 0.12, 0.13, etc.). For example, whenever a numerical range with a lower limit, R l , and an upper limit, R u , is disclosed, any number falling within the range is specifically disclosed. In particular, the following numbers within the range are specifically disclosed: R=R 1 +k* (R u -R l ), wherein k is a variable ranging from 1 percent to 100 percent with a 1 percent increment, i.e., k is 1 percent, 2 percent, 3 percent, 4 percent, 5 percent, . . . 50 percent, 51 percent, 52 percent, . . . , 95 percent, 96 percent, 95 percent, 98 percent, 99 percent, or 100 percent. Moreover, any numerical range defined by two R numbers as defined in the above is also specifically disclosed. Use of the term “optionally” with respect to any element of a claim means that the element is required, or alternatively, the element is not required, both alternatives being within the scope of the claim. Use of broader terms such as comprises, includes, and having should be understood to provide support for narrower terms such as consisting of, consisting essentially of, and comprised substantially of. Accordingly, the scope of protection is not limited by the description set out above but is defined by the claims that follow, that scope including all equivalents of the subject matter of the claims. Each and every claim is incorporated as further disclosure into the specification and the claims are embodiment(s) of the present invention. Also, the phrases “at least one of A, B, and C” and “A and/or B and/or C” should each be interpreted to include only A, only B, only C, or any combination of A, B, and C.