Patent Publication Number: US-11649043-B2

Title: Tilted propellers for enhanced distributed propulsion control authority

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation patent application of and claims priority to U.S. patent application Ser. No. 16/013,201, filed on Jun. 20, 2018 entitled “Tilted Propellers for Enhanced Distributed Propulsion Control Authority”, the entire contents of which are incorporated herein by reference. 
    
    
     STATEMENT OF FEDERALLY FUNDED RESEARCH 
     Not applicable. 
     TECHNICAL FIELD OF THE INVENTION 
     The present invention relates in general to the field of aircraft flight control and propulsion. In particular, the present invention relates to vertical-takeoff-and-landing (VTOL) aircraft with distributed propulsion. 
     BACKGROUND OF THE INVENTION 
     Without limiting the scope of the invention, its background is described in connection with aircraft with distributed propulsion. 
     One example of an aircraft is a vertical-takeoff-and-landing (VTOL) aircraft. Some VTOL aircraft have distributed propulsion, in which thrust is spread around the aircraft by using three or more propellers and primarily using speed control to vary thrust for flight control. In such aircraft, the elimination of complex cyclic and collective controls plus the inherent redundancy provide coast, weight, and safety benefits. On small VTOL aircraft, distributed propulsion works very effectively to provide acceptable flight control authority. However, when used on medium and large VTOL aircraft, the higher aircraft weight and rotational inertia result in unacceptable flight control authority for safe flight. While it is feasible to add excessive power margin and cyclic and collective control to distributed propulsion systems, to enhance control authority, doing so eliminates the benefit of the distributed propulsion system. 
     The conventional practice of mounting all of the propellers in a distributed propulsion system in the same plane or in parallel planes results in all thrust vectors on a vertical direction for lift. For an aircraft with this configuration to move laterally (left or right) or longitudinally (forward or aft), the aircraft must first roll for lateral motion of pitch for longitudinal motion. To roll or pitch that aircraft must overcome the aircraft&#39;s rotational inertia about the roll or pitch axes before any lateral or longitudinal motion can occur. This results either in an unacceptable lag in the aircraft response to control commands or a requirement to incorporate an excessive power margin into the aircraft. 
     Existing methods and apparatuses for flight control with a distributed propulsion system are inadequate for safe flight or undercut the use of distributed propulsion system. Methods and apparatuses for flight control with a distributed propulsion system without an excessive power margin and without cyclic and collective controls are desirable. 
     SUMMARY OF THE INVENTION 
     One embodiment of the present invention provides an aircraft having a distributed propulsion system comprising a fuselage, one or more support structures connected to the fuselage, and one or more engines or motors disposed within or attached to the one or more support structures or the fuselage. The distributed propulsion system comprises two or more propellers symmetrically distributed in an array along the one or more support structures with respect to a center of gravity of the aircraft and operably connected to the one or more engines or motors, wherein each propeller has a rotation direction within a tilted plane of rotation, and a summation of horizontal force vectors created by the tilted plane of rotation of all the propellers is substantially zero when all the propellers are creating a substantially equal thrust magnitude. Movement of the aircraft is controlled by selectively increasing or decreasing a thrust of at least one of the two or more propellers. In one aspect, a summation of horizontal torque vectors created by the rotation direction of all the propellers is substantially zero when all the propellers are creating the substantially equal thrust magnitude. In another aspect, the movement comprises a lateral motion, a longitudinal motion or a combination thereof without rolling and/or pitching the aircraft. In another aspect, the movement comprises a pitch, a roll, a yaw, a translation or a combination thereof. 
     Another embodiment of the present invention provides a method of controlling an aircraft using a distributed propulsion system comprising providing one or more engines or motors disposed within or attached to one or more support structures or a fuselage of the aircraft, providing the distributed propulsion system comprising two or more propellers symmetrically distributed in an array along the one or more support structures with respect to a center of gravity of the aircraft and operably connected to the one or more engines or motors, wherein each propeller has a rotation direction within a tilted plane of rotation, creating a summation of horizontal force vectors by the tilted plane of rotation of all the propellers that is substantially zero when all the propellers are creating a substantially equal thrust magnitude, and controlling a movement of the aircraft by selectively increasing or decreasing a thrust of at least one of the two or more propellers. In one aspect, the method further comprises providing a control authority that is greater than that of a non-tilted distributed propulsion system. In another aspect, the method further comprises controlling the movement with a control lag that is less than that of a non-tilted distributed propulsion system. In another aspect, controlling the movement of the aircraft comprises producing a lateral motion, a longitudinal motion or a combination thereof without rolling and/or pitching the aircraft. In another aspect, controlling the movement of the aircraft comprises creating a pitch, a roll, a yaw, a translation or a combination thereof. In another aspect, the method further comprises creating a summation of horizontal torque vectors by the rotation direction of all the propellers that is substantially zero when all the propellers are creating the substantially equal thrust magnitude. 
     The following aspects correspond to both the aircraft and the method of controlling the aircraft. In one aspect, the two or more propellers are configured in one or more pairs of propellers, each pair of propellers comprising a first propeller creating a first thrust having a first horizontal force vector and a second propeller creating a second thrust having a second horizontal force vector, wherein a summation of the first horizontal force vector and the second horizontal force vector is substantially zero when the first thrust is substantially equal in magnitude to the second thrust. In another aspect, the two or more propellers are configured in one or more pairs of propellers, each pair of propellers comprising a first propeller having a first rotational axis within a first tangential plane, and a second propeller having a second rotational axis within a second tangential plane, wherein the first tangential plane and the second tangential plane are substantially parallel, the first propeller creates a clockwise thrust, and the second propeller creates a counterclockwise thrust. In another aspect, the two or more propellers are configured in one or more pairs of propellers, each pair of propellers comprising a first propeller having a first rotational axis, a second propeller having a second rotational axis, and a vertical axis disposed between the first propeller and the second propeller, wherein the first rotational axis and the second rotational axis are substantially coplanar with respect to the vertical axis, the first rotational axis has a negative tilt angle with respect to the vertical axis, the second rotational axis has a positive tilt angle with respect to the vertical axis, and the positive tilt angle and the negative tilt angle have a substantially equal magnitude. In another aspect, the rotation direction is clockwise for 50% of the two or more propellers and the rotation direction is counterclockwise for 50% of the two or more propellers. In another aspect, the tilted plane of rotation is tilted towards the center of gravity of the aircraft for all of the two or more propellers. In another aspect, the tilted plane of rotation is tilted towards the center of gravity of the aircraft for 50% of the two or more propellers and the tilted plane of rotation is tilted away from the center of gravity of the aircraft for 50% of the two or more propellers. In another aspect, the tilted plane of rotation is titled tangentially with respect to the center of gravity of the aircraft such that 50% of the two or more propellers create a clockwise thrust with respect to the center of gravity and 50% of the two or more propellers create a counterclockwise thrust with respect to the center of gravity. In another aspect, the one or more support structures comprise one or more booms, spokes, struts, supports or wings. In another aspect, the one or more support structures comprise a ring wing connected to the fuselage with one or more spokes, and the two or more propellers are equally spaced along the ring wing. In another aspect, the ring wing is circular shaped, oval shaped or ellipsoid shaped. In another aspect, the rotation direction of the two or more propellers disposed along the ring wing alternate between a clockwise direction and a counterclockwise direction. In another aspect, the tilted plane of rotation of the two or more propellers disposed along the ring wing alternate between tilted towards the center of gravity of the aircraft and tilted away from the center of gravity of the aircraft. In another aspect, the two or more propellers are configured in four or more pairs of propellers along the ring wing comprising: a first pair of propellers disposed along the ring wing, a second pair of propellers disposed along the ring wing, a third pair of propellers disposed along the ring wing, a fourth pair of propellers disposed along the ring wing, the rotation direction of the first pair and the third pair of propellers is counterclockwise, and the rotation direction of the second pair and the fourth pair of propellers is clockwise. In another aspect, the two or more propellers are fixed pitch propellers. 
     The foregoing is a summary and thus contains, by necessity, simplifications, generalizations, and omissions of detail. Consequently, those skilled in the art will appreciate that this summary is illustrative only and is not intended to be in any way limiting. Various other aspects, features and advantages of the aircraft and method of controlling the aircraft are set forth in the teachings of the present disclosure, such as the claims, text, and drawings set forth herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the features and advantages of the present invention, reference is now made to the detailed description of the invention along with the accompanying figures, in which: 
         FIG.  1    depicts a flowchart of a method according to a particular embodiment of the present invention. 
         FIG.  2 A  depicts a plan view of an aircraft with distributed propulsion in hover mode according to a particular embodiment of the present invention; 
         FIG.  2 B  depicts a plan view of an aircraft with distributed propulsion in a left yaw according to a particular embodiment of the present invention; 
         FIG.  2 C  depicts a plan view of an aircraft with distributed propulsion in a right yaw according to a particular embodiment of the present invention; 
         FIG.  2 D  depicts a plan view of an aircraft with distributed propulsion in forward pitch and translation mode according to a particular embodiment of the present invention; 
         FIG.  2 E  depicts a plan view of an aircraft with distributed propulsion in aft pitch and translation mode according to a particular embodiment of the present invention; 
         FIG.  2 F  depicts a plan view of an aircraft with distributed propulsion in left roll and translation mode according to a particular embodiment of the present invention; 
         FIG.  2 G  depicts a plan view of an aircraft with distributed propulsion in right roll and translation mode according to a particular embodiment of the present invention; 
         FIG.  2 H  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting inwards according to a particular embodiment of the present invention; 
         FIG.  2 I  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting outwards according to a particular embodiment of the present invention; 
         FIG.  3 A  depicts a plan view of an aircraft with distributed propulsion in hover mode according to a second embodiment of the present invention; 
         FIG.  3 B  depicts a plan view of an aircraft with distributed propulsion in a left yaw according to a second embodiment of the present invention; 
         FIG.  3 C  depicts a plan view of an aircraft with distributed propulsion in a right yaw according to a second embodiment of the present invention; 
         FIG.  3 D  depicts a plan view of an aircraft with distributed propulsion pitching forward and translating forward according to a second embodiment of the present invention; 
         FIG.  3 E  depicts a plan view of an aircraft with distributed propulsion pitching aft and translating aft according to a second embodiment of the present invention; 
         FIG.  3 F  depicts a plan view of an aircraft with distributed propulsion rolling left and translating left according to a second embodiment of the present invention; 
         FIG.  3 G  depicts a plan view of an aircraft with distributed propulsion rolling right and translating right according to a second embodiment of the present invention; 
         FIG.  3 H  depicts a plan view of an aircraft with distributed propulsion translating forward according to a third embodiment of the present invention; 
         FIG.  3 I  depicts a plan view of an aircraft with distributed propulsion translating aft according to a second embodiment of the present invention; 
         FIG.  3 J  depicts a plan view of an aircraft with distributed propulsion translating left according to a second embodiment of the present invention; 
         FIG.  3 K  depicts a plan view of an aircraft with distributed propulsion translating right according to a second embodiment of the present invention. 
         FIG.  3 L  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting inwards according to a second embodiment of the present invention; 
         FIG.  3 M  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting outwards according to a second embodiment of the present invention; 
         FIG.  4 A  depicts a plan view of an aircraft with distributed propulsion in hover mode according to a third embodiment of the present invention; 
         FIG.  4 B  depicts a plan view of an aircraft with distributed propulsion in a left yaw according to a third embodiment of the present invention; 
         FIG.  4 C  depicts a plan view of an aircraft with distributed propulsion in a right yaw according to a third embodiment of the present invention; 
         FIG.  4 D  depicts a plan view of an aircraft with distributed propulsion pitching forward according to a third embodiment of the present invention; 
         FIG.  4 E  depicts a plan view of an aircraft with distributed propulsion pitching aft according to a third embodiment of the present invention; 
         FIG.  4 F  depicts a plan view of an aircraft with distributed propulsion rolling left according to a third embodiment of the present invention; 
         FIG.  4 G  depicts a plan view of an aircraft with distributed propulsion rolling right according to a third embodiment of the present invention; 
         FIG.  4 H  depicts a plan view of an aircraft with distributed propulsion translating forward according to a third embodiment of the present invention; 
         FIG.  4 I  depicts a plan view an aircraft with distributed propulsion translating aft according to a third embodiment of the present invention; 
         FIG.  4 J  depicts a plan view of an aircraft with distributed propulsion translating left according to a third embodiment of the present invention; 
         FIG.  4 K  depicts a plan view of an aircraft with distributed propulsion translating right according to a third embodiment of the present invention; 
         FIG.  4 L  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting tangentially clockwise according to a third embodiment of the present invention; 
         FIG.  4 M  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting tangentially counterclockwise according to a third embodiment of the present invention; 
         FIG.  5 A  depicts a plan view of a distributed propulsion system in a left yaw according to a fourth embodiment of the present invention; and 
         FIG.  5 B  depicts a tilted rotational axis and tilted plane of rotation of a pair of propellers tilting at a negative and positive tilt angle with respect to a vertical axis. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Illustrative embodiments of the system of the present application are described below. In the interest of clarity, not all features of an actual implementation are described in this specification. 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. Moreover, it will be appreciated that such a development effort might be complex and time-consuming but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. 
       FIG.  1    depicts a flowchart of a method  100  of controlling an aircraft using a distributed propulsion system in accordance with a particular embodiment of the present invention. One or more engines or motors disposed within or attached to one or more support structures or a fuselage of the aircraft in block  102 . The distributed propulsion system is provided in block  104  comprising two or more propellers symmetrically distributed in an array along the one or more support structures with respect to a center of gravity of the aircraft and operably connected to the one or more engines or motors, wherein each propeller has a rotation direction within a tilted plane of rotation. A summation of horizontal force vectors created by the tilted plane of rotation of all the propellers is substantially zero when all the propellers are creating a substantially equal thrust magnitude in block  106 . A movement of the aircraft is controlled in block  108  by selectively increasing or decreasing a thrust of at least one of the two or more propellers. 
     As will be explained in more detail below in reference to various non-limiting examples of distributed propulsion systems described herein, the method provides a control authority that is greater than that of a non-tilted distributed propulsion system. In another aspect, the method controls the movement with a control lag that is less than that of a non-tilted distributed propulsion system. In another aspect, controlling the movement of the aircraft includes producing a lateral motion, a longitudinal motion or a combination thereof without rolling and/or pitching the aircraft. In another aspect, controlling the movement of the aircraft includes creating a pitch, a roll, a yaw, a translation or a combination thereof. In another aspect, the method creates a summation of horizontal torque vectors by the rotation direction of all the propellers that is substantially zero when all the propellers are creating the substantially equal thrust magnitude. 
       FIGS.  2 A- 2 G,  3 A- 3 K and  4 A- 4 K  depict aircraft  200 ,  300  and  400  with different distributed propulsion systems. These distributed propulsion systems are provided as examples and the scope of the present invention is not limited to these specific examples. Each aircraft in these figures includes a fuselage, one or more support structures connected to the fuselage, and one or more engines or motors disposed within or attached to the one or more support structures or the fuselage. The support structures can be any combination of booms, spokes, struts, supports or wings, and are not limited to the examples shown and described herein. Note that the closed or ring wing can be circular shaped as shown, oval shaped, ellipsoid shaped, or other suitable shape. Moreover, the number of spokes can be one, two, three (as shown), or four or more. Note that aircraft can be manned as shown, or unmanned. The distributed propulsion system includes two or more propellers symmetrically distributed in an array along the one or more support structures with respect to a center of gravity of the aircraft and operably connected to the one or more engines or motors. The location and number of propellers are not limited to the examples shown herein. The engine(s) or motor(s) can provide mechanical, electric or hydraulic power to the two or more propellers. Moreover, the engine(s) or motor(s) can be configured with respect to the propellers in a one-to-one or one-to-many arrangement. 
       FIGS.  2 A- 2 G  depict a plan view of a VTOL aircraft  200  with distributed propulsion in various flight modes according to a particular embodiment of the present invention. Aircraft  200  includes a fuselage  205 , one or more support structures (e.g., spokes  210   a ,  210   b ,  210   c , and closed or ring wing  215 ) connected to the fuselage  205 , and one or more engines or motors (not shown) disposed within or attached to the one or more support structures (e.g., spokes  210   a ,  210   b ,  210   c , and closed or ring wing  215 ) or the fuselage  205 . The distributed propulsion system includes two or more propellers (e.g., propellers  220   a  through  220   l ) symmetrically distributed in an array along the one or more support structures (e.g., closed or ring wing  215 ) with respect to a center of gravity of the aircraft  200  and operably connected to the one or more engines or motors. 
     Now also referring to  FIG.  2 H , each propeller  220   a  through  220   l  has a rotation direction  225   a  through  225   l  indicated by curved arrows (e.g., clockwise or counterclockwise) within a tilted plane of rotation  235   a  through  235   l  based on tilt angle γ. The rotation direction  225   a ,  225   c ,  225   e ,  225   g ,  225   i ,  225   k  is clockwise for 50% of the propellers  220   a ,  220   c ,  220   e ,  220   g ,  220   i ,  220   k  and the rotation direction  225   b ,  225   d ,  225   f ,  225   h ,  225   j ,  225   l  is counterclockwise for 50% of the propellers  220   b ,  220   d ,  220   f ,  220   h ,  220   j ,  220   l . As shown, the rotation direction  225   a  through    225 l o f the propellers  220   a  through  220   l  disposed along the ring wing  215  alternate between a clockwise direction  225   a ,  225   c ,  225   e ,  225   g ,  225   i ,  225   k  and a counterclockwise direction  225   b ,  225   d ,  225   f ,  225   h ,  225   j ,  225   l . The tilted plane of rotation  235   a  through  235   l  is tilted towards the center of gravity of the aircraft  200  for all of the two or more propellers  220   a  through  220   l  (i.e., all tilted inward) such that the X-axis intersects the center  250  of the ring wing  215 . Alternatively and as shown in  FIG.  2 I , all of the propellers  220   a  through  220   l  could be tilted outward away from the center of gravity of the aircraft  200  such that the X-axis intersects the center  250  of the ring wing  215 . Moreover, a summation of horizontal force vectors  230   a  through  230   l  created by the tilted plane of rotation  235   a  through  235   l  of all the propellers  220   a  through  220   l  is substantially zero when all the propellers  220   a  through  220   l  are creating a substantially equal thrust magnitude. The propellers  220   a  through  220   l  can be configured in pairs ( 220   a  and  220   g ,  220   b  and  220   h ,  220   c  and  220   i ,  220   d  and  220   j ,  220   e  and  220   k  and  220   f  and  220   l ), each pair of propellers comprising a first propeller  220   a  through  220   f  creating a first thrust having a first horizontal force vector  230   a  through  230   f  and a second propeller  220   g  through  220   l  creating a second thrust having a second horizontal force vector  230   g  through  230   l , wherein a summation of the first horizontal force vector  230   a  through  230   f  and the second horizontal force vector  230   g  through  230   l  is substantially zero when the first thrust is substantially equal in magnitude to the second thrust. In one aspect, a summation of horizontal torque vectors (not shown) created by the rotation direction  225   a  through  225   l  of all the propellers  220   a  through  220   l  is substantially zero when all the propellers  220   a  through  220   l  are creating a substantially equal thrust magnitude. The tilt angle γ can be selected from about 1 degree to about 15 degrees depending on the aircraft size, weight and engine/motor distribution. Note that sufficient clearance should be maintained between the propellers  220   a  through  220   l  and the support structures  210   a ,  210   b ,  210   c ,  215  and fuselage  205 . The first rotational axis  240   a  through  240   f  of the first propellers  220   a  through  220   f  and the second rotational axis  240   g  through  240   l  of the second propellers  220   g  through  220   l  are substantially coplanar with respect to a vertical axis  245  disposed between the first propellers  220   a  through  220   f  and the second propellers  220   g  through  220   l , which in this example is the center  250  of the ring wing  215 . In order to minimize weight and complexity, the propellers  220   a  through  220   l  are preferably fixed pitch propellers and the nacelles are preferably fixed. But in some embodiments, it may be desirable to use variable pitch propellers and/or moveable nacelles. 
       FIG.  2 A  depicts the aircraft  200  in hover mode in which all the propellers  220   a  through  220   l  are operated at a low RPM, which creates low horizontal thrust  230   a  through  230   l . Positioning the propellers  220   a  through  220   l  symmetrically around the center of gravity of the aircraft  200  results in the effective cancellation of all horizontal thrust vectors  230   a  through  230   l  for a stable hover. Having the horizontal thrust vectors pass radially through the aircraft center of gravity minimizes undesirable coupling of aircraft roll, pitch, and yaw commands. The aircraft  200  can be moved in a vertical direction by increasing or decreasing a thrust of all of the propellers  220   a  through  220   l.    
     As shown in  FIGS.  2 B- 2 G , movement of the aircraft  200  is controlled by selectively increasing or decreasing a thrust of at least one of the propellers  220   a  through  220   l . The movement can be a lateral motion, a longitudinal motion or a combination thereof without rolling and/or pitching the aircraft  200 . The movement may also be a pitch, a roll, a yaw, a translation or a combination thereof. The tilted distributed propulsion system moves the aircraft with a control lag that is less than that of a non-tilted distributed propulsion system. As a result, the present invention provides a control authority that is greater than that of a non-tilted distributed propulsion system. This is achieved without the need to add excessive power margin. Those skilled in the art will understand and appreciate that the differences in control lag and control authority between tilted distributed propulsion systems and non-tilted distributed propulsion systems will vary depending to the aircraft design and distributed propulsion system, but that such terms are understandable and not indefinite based on the teachings herein. 
       FIG.  2 B  depicts the aircraft  200  in a left yaw  255 . The rotational speeds of all of the propellers  220   a ,  220   c ,  220   e ,  220   g ,  220   i ,  220   k  that rotate in a clockwise direction  225   a ,  225   c ,  225   e ,  225   g ,  225   i ,  225   k  are increased. A summation of horizontal force vectors  230   a  through  230   l  created by the tilted plane of rotation  235   a  through  235   l  of all the propellers  220   a  through  220   l  is substantially zero even though all the propellers  220   a  through  220   l  are not creating a substantially equal thrust magnitude. The thrust for each pair ( 220   a  and  220   g ,  220   b  and  220   h ,  220   c  and  220   i ,  220   d  and  220   j ,  220   e  and  220   k  and  220   f  and  220   l ) is substantially equal in magnitude and opposite in direction such that they cancel each other out. But, operating the clockwise rotating propellers  220   a ,  220   c ,  220   e ,  220   g ,  220   i ,  220   k  at a faster RPM than the counterclockwise rotating propellers  220   b ,  220   d ,  220   f ,  220   h ,  220   j ,  220   l  creates a differential torque to yaw the aircraft  200  counterclockwise, or left  255 . 
       FIG.  2 C  depicts the aircraft  200  in a right yaw  260 . The rotational speeds of all of the propellers  220   b ,  220   d ,  220   f ,  220   h ,  220   j ,  220   l  that rotate in a counterclockwise direction  225   b ,  225   d ,  225   f ,  225   h ,  225   j ,  225   l  are increased. A summation of horizontal force vectors  230   a  through  230   l  created by the tilted plane of rotation  235   a  through  235   l  of all the propellers  220   a  through  220   l  is substantially zero even though all the propellers  220   a  through  220   l  are not creating a substantially equal thrust magnitude. The thrust for each pair ( 220   a  and  220   g ,  220   b  and  220   h ,  220   c  and  220   i ,  220   d  and  220   j ,  220   e  and  220   k  and  220   f  and  220   l ) is substantially equal in magnitude and opposite in direction such that they cancel each other out. But, operating the counterclockwise rotating propellers  220   b ,  220   d ,  220   f ,  220   h ,  220   j ,  220   l  at a faster RPM than the clockwise rotating propellers  220   a ,  220   c ,  220   e ,  220   g ,  220   i ,  220   k  creates a differential torque to yaw the aircraft  200  clockwise, or right  260 . 
       FIG.  2 D  depicts the aircraft  200  pitching forward and translating forward  265 . The rotational speeds of propellers  220   e ,  220   f ,  220   g ,  220   h ,  220   i  aft of center of gravity centerline  252  are increased. Operating propellers  220   e ,  220   f ,  220   g ,  220   h ,  220   i  aft of center of gravity centerline  252  at a faster RPM than propellers  220   a ,  220   b ,  220   c ,  220   d ,  220   j ,  220   k ,  220   l  creates an immediate forward differential thrust to pitch and translate the aircraft  200  forward  265 , which minimizes control lag. 
       FIG.  2 E  depicts the aircraft  200  pitching aft and translating aft  270 . The rotational speeds of propellers  220   a ,  220   b ,  220   c ,  220   k ,  220   l  forward of center of gravity centerline  252  are increased. Operating propellers  220   a ,  220   b ,  220   c ,  220   k ,  220   l  forward of center of gravity centerline  252  at a faster RPM than propellers  220   d ,  220   e ,  220   f ,  220   g ,  220   h ,  220   i ,  220   j  creates an immediate aft differential thrust to pitch and translate the aircraft  200  aft  270 , which minimizes control lag. 
       FIG.  2 F  depicts the aircraft  200  rolling left and translating left  275 . The rotational speeds of propellers  220   b ,  220   c ,  220   d ,  220   e ,  220   f  to the right of center of gravity centerline  254  are increased. Operating propellers  220   b ,  220   c ,  220   d ,  220   e ,  220   f  to the right of center of gravity centerline  254  at a faster RPM than  220   a ,  220   g ,  220   h ,  220   i ,  220   j ,  220   k ,  220   l  creates an immediate left lateral differential thrust to roll and translate the aircraft  200  left  275 , which minimizes control lag. 
       FIG.  2 G  depicts the aircraft  200  rolling right and translating right  280 . The rotational speeds of propellers  220   h ,  220   i ,  220   j ,  220   k ,  220   l  to the left of center of gravity centerline  254  are increased. Operating propellers  220   h ,  220   i ,  220   j ,  220   k ,  220   l  to the left of center of gravity centerline  254  at a faster RPM than propellers  220   a ,  220   b ,  220   c ,  220   d ,  220   e ,  220   f ,  220   g  creates an immediate right lateral differential thrust to roll and translate the aircraft  200  right  280 , which minimizes control lag. 
       FIGS.  3 A- 3 K  depict a plan view of an aircraft  300  with distributed propulsion in various flight modes according to a second embodiment of the present invention. Aircraft  300  includes a fuselage  305 , one or more support structures (e.g., spokes  310   a ,  310   b ,  310   c , and closed or ring wing  315 ) connected to the fuselage  305 , and one or more engines or motors (not shown) disposed within or attached to the one or more support structures (e.g., spokes  310   a ,  310   b ,  310   c , and closed or ring wing  315 ) or the fuselage  305 . The distributed propulsion system includes two or more propellers (e.g., propellers  320   a  through  320   l ) symmetrically distributed in an array along the one or more support structures (e.g., closed or ring wing  315 ) with respect to a center of gravity of the aircraft  300  and operably connected to the one or more engines or motors. 
     Now also referring to  FIG.  3 L- 3 M , each propeller  320   a  through  320   l  has a rotation direction indicated by curved arrows  325   a  through  325   l  (e.g., clockwise or counterclockwise) within a tilted plane of rotation  335   a  through  335   l  based on tilt angle γ. The rotation direction  325   a ,  325   c ,  325   e ,  325   g ,  325   i ,  325   k  is clockwise for 50% of the propellers  320   a ,  320   c ,  320   e ,  320   g ,  320   i ,  320   k  and the rotation direction  325   b ,  325   d ,  325   f ,  325   h ,  325   j ,  325   l  is counterclockwise for 50% of the propellers  320   b ,  320   d ,  320   f ,  320   h ,  320   j ,  320   l . As shown, the rotation direction  325   a  through  325   l  of the propellers  320   a  through  320   l  disposed along the ring wing  315  alternate between a clockwise direction  325   a ,  325   c ,  325   e ,  325   g ,  325   i ,  325   k  and a counterclockwise direction  325   b ,  325   d ,  325   f ,  325   h ,  325   j ,  325   l . The tilted plane of rotation  335   b ,  335   d ,  335   f ,  335   h ,  335   j ,  335   l  is tilted towards the center of gravity of the aircraft  300  for 50% of the two or more propellers  320   b ,  320   d ,  320   f ,  320   h ,  320   j ,  320   l  (i.e., all tilted inward) such that the X-axis intersects the center  350  of the ring wing  315 , and the tilted plane of rotation  335   a ,  335   c ,  335   e ,  335   g ,  335   i ,  335   k  is tilted outwards away from the center of gravity of the aircraft  300  for 50% of the two or more propellers  320   a ,  320   c ,  320   e ,  320   g ,  320   i ,  320   k  (i.e., all tilted outward) such that the X-axis intersects the center  350  of the ring wing  315 . The direction of tilting of the propellers  320   a  through  320   l  disposed along the ring wing  315  alternate between tilting inwards and tilting outwards. Moreover, a summation of horizontal force vectors  330   a  through  330   l  created by the tilted plane of rotation  335   a  through  335   l  of all the propellers  320   a  through  320   l  is substantially zero when all the propellers  320   a  through  320   l  are creating a substantially equal thrust magnitude. The propellers  320   a  through  320   l  can be configured in pairs ( 320   a  and  320   g ,  320   b  and  320   h ,  320   c  and  320   i ,  320   d  and  320   j ,  320   e  and  320   k  and  320   f  and  320   l ), each pair of propellers comprising a first propeller  320   a  through  320   f  creating a first thrust having a first horizontal force vector  330   a  through  330   f  and a second propeller  320   g  through  320   l  creating a second thrust having a second horizontal force vector  330   g  through  330   l , wherein a summation of the first horizontal force vector  330   a  through  330   f  and the second horizontal force vector  330   g  through  330   l  is substantially zero when the first thrust is substantially equal in magnitude to the second thrust. In one aspect, a summation of horizontal torque vectors (not shown) created by the rotation direction  325   a  through  325   l  of all the propellers  320   a  through  320   l  is substantially zero when all the propellers  320   a  through  320   l  are creating a substantially equal thrust magnitude. The tilt angle γ can be selected from about 1 degree to about 15 degrees depending on the aircraft size, weight and engine/motor distribution. Note that sufficient clearance should be maintained between the propellers  320   a  through  320   l  and the support structures  310   a ,  310   b ,  310   c ,  315  and fuselage  305 . As shown in  FIG.  3 L  for the inboard tilted propellers, the first rotational axis  340   b ,  340   d ,  340   f  of the first propellers  320   b ,  320   d ,  320   f  and the second rotational axis  340   h ,  340   j ,  340   lf  of the second propellers  320   h ,  320   j ,  320   f  are substantially coplanar with respect to a vertical axis  345  disposed between the first propellers  320   b ,  320   d ,  320   f  and the second propellers  310   h ,  310   j ,  310   f , which in this example is the center  350  of the ring wing  315 . As shown in  FIG.  3 M  for the outward tilted propellers, the first rotational axis  340   a ,  340   c ,  340   e  of the first propellers  320   a ,  320   c ,  320   e  and the second rotational axis  340   g ,  340   i ,  340   k  of the second propellers  320   g ,  320   i ,  320   k  are substantially coplanar with respect to a vertical axis  345  disposed between the first propellers  320   a ,  320   c ,  320   e  and the second propellers  320   g ,  320   i ,  320   k , which in this example is the center  350  of the ring wing  315 . In order to minimize weight and complexity, the propellers  320   a  through  320   l  are preferably fixed pitch propellers and the nacelles are preferably fixed. But in some embodiments, it may be desirable to use variable pitch propellers and/or moveable nacelles. 
       FIG.  3 A  depicts the aircraft  300  in hover mode in which all the propellers  320   a  through  320   l  are operated at a low RPM, which creates low horizontal thrust  330   a  through  330   l . Positioning the propellers  320   a  through  320   l  symmetrically around the center of gravity of the aircraft  300  results in the effective cancellation of all horizontal thrust vectors  330   a  through  330   l  for a stable hover. Alternating the inboard and outboard tilting of the propellers  320   a  through  320   l  provides for lateral and longitudinal directional control of the aircraft  300  completely independent of aircraft pitch and roll. Having the horizontal thrust vectors pass radially through the aircraft center of gravity minimizes undesirable coupling of aircraft roll, pitch, and yaw commands. This capability enhances aircraft directional control by eliminating the effect of the rotational inertia of aircraft  300  from lateral and longitudinal control. The aircraft  300  can be moved in a vertical direction by increasing or decreasing a thrust of all of the propellers  320   a  through  320   l.    
     As shown in  FIGS.  3 B- 3 K , movement of the aircraft  300  is controlled by selectively increasing or decreasing a thrust of at least one of the propellers  320   a  through  320   l . The movement can be a lateral motion, a longitudinal motion or a combination thereof without rolling and/or pitching the aircraft  300 . The movement may also be a pitch, a roll, a yaw, a translation or a combination thereof. The tilted distributed propulsion system moves the aircraft with a control lag that is less than that of a non-tilted distributed propulsion system. As a result, the present invention provides a control authority that is greater than that of a non-tilted distributed propulsion system. This is achieved without the need to add excessive power margin. Those skilled in the art will understand and appreciate that the differences in control lag and control authority between tilted distributed propulsion systems and non-tilted distributed propulsion systems will vary depending to the aircraft design and distributed propulsion system, but that such terms are understandable and not indefinite based on the teachings herein. 
       FIG.  3 B  depicts the aircraft  300  in a left yaw  355 . The rotational speeds of all of the propellers  320   a ,  320   c ,  320   e ,  320   g ,  320   i ,  320   k  that rotate in a clockwise direction  325   a ,  325   c ,  325   e ,  325   g ,  325   i ,  325   k  are increased. A summation of horizontal force vectors  330   a  through  330   l  created by the tilted plane of rotation  335   a  through  335   l  of all the propellers  320   a  through  320   l  is substantially zero even though all the propellers  320   a  through  320   l  are not creating a substantially equal thrust magnitude. The thrust for each pair ( 320   a  and  320   g ,  320   b  and  320   h ,  320   c  and  320   i ,  320   d  and  320   j ,  320   e  and  320   k  and  320   f  and  320   l ) is substantially equal in magnitude and opposite in direction such that they cancel each other out. But, operating the clockwise rotating propellers  320   a ,  320   c ,  320   e ,  320   g ,  320   i ,  320   k  at a faster RPM than the counterclockwise rotating propellers  320   b ,  320   d ,  320   f ,  320   h ,  320   j ,  320   l  creates a differential torque to yaw the aircraft  300  counterclockwise, or left  355 . 
       FIG.  3 C  depicts the aircraft  300  in a right yaw  360 . The rotational speeds of all of the propellers  320   b ,  320   d ,  320   f ,  320   h ,  320   j ,  320   l  that rotate in a counterclockwise direction  325   b ,  325   d ,  325   f ,  325   h ,  325   j ,  325   l  are increased. A summation of horizontal force vectors  330   a  through  330   l  created by the tilted plane of rotation  335   a  through  335   l  of all the propellers  320   a  through  320   l  is substantially zero even though all the propellers  320   a  through  320   l  are not creating a substantially equal thrust magnitude. The thrust for each pair ( 320   a  and  320   g ,  320   b  and  320   h ,  320   c  and  320   i ,  320   d  and  320   j ,  320   e  and  320   k  and  320   f  and  320   l ) is substantially equal in magnitude and opposite in direction such that they cancel each other out. But, operating the counterclockwise rotating propellers  320   b ,  320   d ,  320   f ,  320   h ,  320   j ,  320   l  at a faster RPM than the clockwise rotating propellers  320   a ,  320   c ,  320   e ,  320   g ,  320   i ,  320   k  creates a differential torque to yaw the aircraft  300  clockwise, or right  360 . 
       FIG.  3 D  depicts the aircraft  300  pitching forward  365 . The rotational speeds of propellers  320   e ,  320   f ,  320   g ,  320   h ,  320   i  aft of center of gravity centerline  252  are increased. Operating propellers  320   e ,  320   f ,  320   g ,  320   h ,  320   i  aft of center of gravity centerline  252  at a faster RPM than propellers  320   a ,  320   b ,  320   c ,  320   d ,  320   j ,  320   k ,  320   l  creates an immediate forward differential thrust that lifts the aft part of the aircraft  300  to pitch the aircraft  300  forward  365 , which minimizes control lag. The sum of the longitudinal thrust vectors can cancel any resulting forward motion. 
       FIG.  3 E  depicts the aircraft  300  pitching aft  370 . The rotational speeds of propellers  320   a ,  320   b ,  320   c ,  320   k ,  320   l  forward of center of gravity centerline  352  are increased. Operating propellers  320   a ,  320   b ,  320   c ,  320   k ,  320   l  forward of center of gravity centerline  352  at a faster RPM than propellers  320   d ,  320   e ,  320   f ,  320   g ,  320   h ,  320   i ,  320   j  creates an immediate aft differential thrust that lifts the forward part of the aircraft  300  to pitch the aircraft  300  aft  370 , which minimizes control lag. The sum of the longitudinal thrust vectors can cancel any resulting forward motion. 
       FIG.  3 F  depicts the aircraft  300  rolling left  375 . The rotational speeds of propellers  320   b ,  320   c ,  320   d ,  320   e ,  320   f  to the right of center of gravity centerline  354  are increased. Operating propellers  320   b ,  320   c ,  320   d ,  320   e ,  320   f  to the right of center of gravity centerline  354  at a faster RPM than propellers  320   a ,  320   g ,  320   h ,  320   i ,  320   j ,  320   k ,  320   l  creates an immediate left lateral differential thrust that lifts the right part of the aircraft  300  to roll the aircraft  300  left  375 , which minimizes control lag. The sum of the lateral thrust vectors can cancel any resulting left lateral motion. 
       FIG.  3 G  depicts the aircraft  300  rolling right  380 . The rotational speeds of propellers  320   h ,  320   i ,  320   j ,  320   k ,  320   l  to the left of center of gravity centerline  354  are increased. Operating propellers  320   h ,  320   i ,  320   j ,  320   k ,  320   l  to the right of center of gravity centerline  354  at a faster RPM than propellers  320   a ,  320   b ,  320   c ,  320   d ,  320   e ,  320   f ,  320   g  creates an immediate right lateral differential thrust that lifts the left part of the aircraft  300  to roll the aircraft  300  right  380 , which minimizes control lag. The sum of the lateral thrust vectors can cancel any resulting right lateral motion. 
       FIG.  3 H  depicts the aircraft  300  translating forward  385 . The rotational speeds of the propellers  320   a ,  320   c ,  320   f ,  320   h ,  320   k  are increased. Operating the propellers  320   a ,  320   c ,  320   f ,  320   h ,  320   k  at a faster RPM than propellers  320   b ,  320   d ,  320   e ,  320   g ,  320   i ,  320   j ,  320   l  creates an immediate forward acting differential thrust that translates the aircraft  300  forward  385 , which minimizes control lag. The sum of the forward and aft pitch moments can cancel any resulting forward pitching motion. 
       FIG.  3 I  depicts the aircraft  300  translating aft  390 . The rotational speeds of the propellers  320   b ,  320   e ,  320   g ,  320   i ,  320   i  are increased. Operating the propellers  320   b ,  320   e ,  320   g ,  320   i ,  320   i  at a faster RPM than propellers  320   a ,  320   c ,  320   d ,  320   f ,  320   h ,  320   j ,  320   k  creates an immediate aft acting differential thrust that translates the aircraft  300  aft  390 , which minimizes control lag. The sum of the forward and aft pitch moments can cancel any resulting aft pitching motion. 
       FIG.  3 J  depicts the aircraft  300  translating left  394 . The rotational speeds of the propellers  320   b ,  320   d ,  320   f ,  320   i ,  320   k  are increased. Operating the propellers  320   b ,  320   d ,  320   f ,  320   i ,  320   k  at a faster RPM than propellers  320   a ,  320   c ,  320   e ,  320   g ,  320   h ,  320   j ,  320   l  creates an immediate left acting differential thrust that translates the aircraft  300  left  394 , which minimizes control lag. The sum of the left and right roll moments can cancel any resulting left rolling motion. 
       FIG.  3 K  depicts the aircraft  300  translating right  396 . The rotational speeds of the propellers  320   c ,  320   e ,  320   h ,  320   j ,  320   l  are increased. Operating the propellers  320   c ,  320   e ,  320   h ,  320   j ,  320   l  at a faster RPM than propellers  320   a ,  320   b ,  320   d ,  320   f ,  320   g ,  320   i ,  320   k  creates an immediate right acting differential thrust that translates the aircraft  300  right  396 , which minimizes control lag. The sum of the left and right roll moments can cancel any resulting right rolling motion. 
       FIGS.  4 A- 4 K  depict a plan view of an aircraft  400  with distributed propulsion in various flight modes according to a third embodiment of the present invention. Aircraft  400  includes a fuselage  405 , one or more support structures (e.g., spokes  410   a ,  410   b ,  410   c , and closed or ring wing  415 ) connected to the fuselage  405 , and one or more engines or motors (not shown) disposed within or attached to the one or more support structures (e.g., spokes  410   a ,  410   b ,  410   c , and closed or ring wing  415 ) or the fuselage  405 . The distributed propulsion system includes two or more propellers (e.g., propellers  420   a  through  420   l ) symmetrically distributed in an array along the one or more support structures (e.g., closed or ring wing  415 ) with respect to a center of gravity of the aircraft  400  and operably connected to the one or more engines or motors. 
     Now also referring to  FIG.  4 L- 4 M , each propeller  420   a  through  420   l  has a rotation direction indicated by curved arrows  425   a  through  425   l  (e.g., clockwise or counterclockwise) within a tilted plane of rotation  435   a  through  435   l  based on tilt angle γ. The rotation direction  425   a ,  425   c ,  425   e ,  425   g ,  425   i ,  425   k  is counterclockwise for 50% of the propellers  420   a ,  420   c ,  420   e ,  420   g ,  420   i ,  420   k  and the rotation direction  425   b ,  425   d ,  425   f ,  425   h ,  425   j ,  425   l  is clockwise for 50% of the propellers  420   b ,  420   d ,  420   f ,  420   h ,  420   j ,  420   l . As shown, the rotation direction  425   a  through  425   l  of the propellers  420   a  through  420   l  disposed along the ring wing  415  alternate between a counterclockwise direction  425   a ,  425   c ,  425   e ,  425   g ,  425   i ,  425   k  and a clockwise direction  425   b ,  425   d ,  425   f ,  425   h ,  425   j ,  425   l . The tilted plane of rotation  435   b ,  435   d ,  435   f ,  435   h ,  435   j ,  435   l  is tilted left along a tangential line intersecting the ring wing  415  at the propeller location for 50% of the two or more propellers  420   b ,  420   d ,  420   f ,  420   h ,  420   j ,  420   l  such that the X-axis is a tangential line intersecting the ring wing  415  at the propeller location. The tilted plane of rotation  435   a ,  435   c ,  435   e ,  435   g ,  435   i ,  435   k  is tilted right along a tangential line intersecting the ring wing  415  at the propeller location for 50% of the two or more propellers  420   a ,  420   c ,  420   e ,  420   g ,  420   i ,  420   k  such that the X-axis is a tangential line intersecting the ring wing  415  at the propeller location. The direction of tilting of the propellers  420   a  through  420   l  disposed along the ring wing  415  alternate between tilting right tangentially and tilting left tangentially. Moreover, a summation of horizontal force vectors  430   a  through  430   l  created by the tilted plane of rotation  435   a  through  435   l  of all the propellers  420   a  through  420   l  is substantially zero when all the propellers  420   a  through  420   l  are creating a substantially equal thrust magnitude. The propellers  420   a  through  420   l  can be configured in pairs ( 420   a  and  420   g ,  420   b  and  420   h ,  420   c  and  420   i ,  420   d  and  420   j ,  420   e  and  420   k  and  420   f  and  420   l ), each pair of propellers comprising a first propeller  420   a  through  420   f  creating a first thrust having a first horizontal force vector  430   a  through  430   f  and a second propeller  420   g  through  420   l  creating a second thrust having a second horizontal force vector  430   g  through  430   l , wherein a summation of the first horizontal force vector  430   a  through  430   f  and the second horizontal force vector  430   g  through  430   l  is substantially zero when the first thrust is substantially equal in magnitude to the second thrust. In one aspect, a summation of horizontal torque vectors (not shown) created by the rotation direction  425   a  through  425   l  of all the propellers  420   a  through  420   l  is substantially zero when all the propellers  420   a  through  420   l  are creating a substantially equal thrust magnitude. The tilt angle γ can be selected from about 1 degree to about 15 degrees depending on the aircraft size, weight and engine/motor distribution. Note that sufficient clearance should be maintained between the propellers  420   a  through  420   l  and the support structures  410   a ,  410   b ,  410   c ,  415  and fuselage  405 . As shown in  FIG.  4 L , the first rotational axis  440   a ,  440   c ,  440   e  of the first propellers  420   a ,  420   c ,  420   e  are tilted tangentially right (clockwise), and the second rotational axis  440   g ,  440   i ,  440   k  of the second propellers  420   g ,  410   i ,  410   k  are tilted tangentially left (counterclockwise). The tangential plane containing the first rotational axis  440   a ,  440   c ,  440   e  of the first propellers  420   a ,  420   c ,  420   e  is substantially parallel to the tangential plane containing the second rotational axis  440   g ,  440   i ,  440   k  of the second propellers  420   g ,  410   i ,  410   k . As shown in  FIG.  4 M , the first rotational axis  440   b ,  440   d ,  440   f  of the first propellers  420   b ,  420   d ,  420   f  are tilted tangentially left (counterclockwise) and the second rotational axis  440   h ,  440   j ,  440   lf  of the second propellers  420   h ,  420   j ,  420   f  are tilted tangentially right (clockwise). The tangential plane containing the first rotational axis  440   b ,  440   d ,  440   f  of the first propellers  420   b ,  420   d ,  420   f  is substantially parallel to the tangential plane containing the second rotational axis  440   h ,  440   j ,  440   l  of the second propellers  420   h ,  420   j ,  420   l . In order to minimize weight and complexity, the propellers  420   a  through  420   l  are preferably fixed pitch propellers and the nacelles are preferably fixed. But in some embodiments, it may be desirable to use variable pitch propellers and/or moveable nacelles. 
       FIG.  4 A  depicts the aircraft  400  in hover mode in which all the propellers  420   a  through  420   l  are operated at a low RPM, which creates low horizontal thrust  430   a  through  430   l . Positioning the propellers  420   a  through  420   l  symmetrically around the center of gravity of the aircraft  400  results in the effective cancellation of all horizontal thrust vectors  430   a  through  430   l  for a stable hover. Generally, the propellers  420   a  through  420   l  are alternately tilted to provide horizontal thrust vector components in a tangential direction perpendicular to a vector from the propeller to a center of gravity of the aircraft  400 . Alternating the right (clockwise) and left (counterclockwise) tangential tilting of the propellers  420   a  through  420   l  creates six symmetric thrust vector components directed to drive the aircraft  400  clockwise around the aircraft center of gravity and six symmetric thrust vector components directed to drive the aircraft  400  counterclockwise around the aircraft center of gravity. This provides improved aircraft yaw control using only the differential reaction torque from the propellers. While not having the thrust vector components pass through the center of gravity can generate undesirable coupling of roll, pitch, and yaw control moments, positioning the propellers symmetrically in the array allows for both cancellation of all thrust vector components for a stable hover and provides for mitigation of undesirable coupling. With alternating tangential tilting, the unacceptable lag in the aircraft control response to control commands is alleviated by the immediate lateral and longitudinal response provided by the tilted propeller tangential thrust vectors. This is achieved without the need to add excessive power margin. Additionally, alternating tangential tilting of the propellers provides for lateral and longitudinal directional control of the aircraft  400  completely independent of aircraft pitch and roll. This capability enhances directional control by eliminating the effect of the rotational inertia of the aircraft  400  from lateral and longitudinal control. The aircraft  400  can be moved in a vertical direction by increasing or decreasing a thrust of all of the propellers  420   a  through  420   l.    
     As shown in  FIGS.  4 B- 4 K , movement of the aircraft  400  is controlled by selectively increasing or decreasing a thrust of at least one of the propellers  420   a  through  420   l . The movement can be a lateral motion, a longitudinal motion or a combination thereof without rolling and/or pitching the aircraft  400 . The movement may also be a pitch, a roll, a yaw, a translation or a combination thereof. The tilted distributed propulsion system moves the aircraft with a control lag that is less than that of a non-tilted distributed propulsion system. As a result, the present invention provides a control authority that is greater than that of a non-tilted distributed propulsion system. This is achieved without the need to add excessive power margin. Those skilled in the art will understand and appreciate that the differences in control lag and control authority between tilted distributed propulsion systems and non-tilted distributed propulsion systems will vary depending to the aircraft design and distributed propulsion system, but that such terms are understandable and not indefinite based on the teachings herein. 
       FIG.  4 B  depicts the aircraft  400  in a left yaw  455 . The rotational speeds of all of the propellers  420   b ,  420   d ,  420   f ,  420   h ,  420   j ,  420   l  that rotate in a clockwise direction  425   b ,  425   d ,  425   f ,  425   h ,  425   j ,  425   l  are increased. Operating the clockwise rotating propellers  420   b ,  420   d ,  420   f ,  420   h ,  420   j ,  420   l  at a faster RPM than the counterclockwise rotating propellers  420   a ,  420   c ,  420   e ,  420   g ,  420   i ,  420   k  creates a differential thrust vector and a differential torque to yaw the aircraft  400  counterclockwise, or left  455 . 
       FIG.  4 C  depicts the aircraft  400  in a right yaw  460 . The rotational speeds of all of the propellers  420   a ,  420   c ,  420   e ,  420   g ,  420   i ,  420   k  that rotate in a counterclockwise direction  425   a ,  425   c ,  425   e ,  425   g ,  425   i ,  425   k  are increased. Operating the counterclockwise rotating propellers  425   a ,  425   c ,  425   e ,  425   g ,  425   i ,  425   k  at a faster RPM than the clockwise rotating propellers  420   b ,  420   d ,  420   f ,  420   h ,  420   j ,  420   l  creates a differential thrust vector and a differential torque to yaw the aircraft  400  clockwise, or right  460 . 
       FIG.  4 D  depicts the aircraft  400  pitching forward  465 . The rotational speeds of propellers  420   d ,  420   e ,  420   f ,  420   g ,  420   h ,  420   i  aft of center of gravity centerline  452  are increased. Operating propellers  420   d ,  420   e ,  420   f ,  420   g ,  420   h ,  420   i  aft of center of gravity centerline  452  at a faster RPM than propellers  420   a ,  420   b ,  420   c ,  420   j ,  420   k ,  420   l  creates an immediate forward differential thrust that lifts the aft part of the aircraft  400  to pitch the aircraft  400  forward  465 , which minimizes control lag. The sum of the longitudinal thrust vectors can cancel any resulting forward motion. 
       FIG.  4 E  depicts the aircraft  400  pitching aft  470 . The rotational speeds of propellers  420   a ,  420   b ,  420   c ,  420   j ,  420   k ,  420   l  forward of center of gravity centerline  452  are increased. Operating propellers  420   a ,  420   b ,  420   c ,  420   j ,  420   k ,  420   l  forward of center of gravity centerline  452  at a faster RPM than propellers  420   d ,  420   e ,  420   f ,  420   g ,  420   h ,  420   i  creates an immediate aft differential thrust that lifts the forward part of the aircraft  400  to pitch the aircraft  400  aft  470 , which minimizes control lag. The sum of the longitudinal thrust vectors can cancel any resulting forward motion. 
       FIG.  4 F  depicts the aircraft  400  rolling left  475 . The rotational speeds of propellers  420   a ,  420   b ,  420   c ,  420   d ,  420   e ,  420   f  to the right of center of gravity centerline  454  are increased. Operating propellers  420   a ,  420   b ,  420   c ,  420   d ,  420   e ,  420   f  to the right of center of gravity centerline  454  at a faster RPM than propellers  420   g ,  420   h ,  420   i ,  420   j ,  420   k ,  420   l  creates an immediate left lateral differential thrust that lifts the right part of the aircraft  400  to roll the aircraft  400  left  475 , which minimizes control lag. The sum of the lateral thrust vectors can cancel any resulting left lateral motion. 
       FIG.  4 G  depicts the aircraft  400  rolling right  480 . The rotational speeds of propellers  420   g ,  420   h ,  420   i ,  420   j ,  420   k ,  420   l  to the left of center of gravity centerline  454  are increased. Operating propellers  420   g ,  420   h ,  420   i ,  420   j ,  420   k ,  420   l  to the right of center of gravity centerline  454  at a faster RPM than propellers  420   a ,  420   b ,  420   c ,  420   d ,  420   e ,  420   f  creates an immediate right lateral differential thrust that lifts the left part of the aircraft  400  to roll the aircraft  400  right  480 , which minimizes control lag. The sum of the lateral thrust vectors can cancel any resulting right lateral motion. 
       FIG.  4 H  depicts the aircraft  400  translating forward  485 . The rotational speeds of the propellers  420   b ,  420   d ,  420   f ,  420   g ,  420   i ,  420   k  are increased. Operating the propellers  420   b ,  420   d ,  420   f ,  420   g ,  420   i ,  420   k  at a faster RPM than propellers  420   a ,  420   c ,  420   e ,  420   h ,  420   j ,  420   l  creates an immediate forward acting differential thrust that translates the aircraft  400  forward  485 , which minimizes control lag. The sum of the forward and aft pitch moments can cancel any resulting forward pitching motion. 
       FIG.  4 I  depicts the aircraft  400  translating aft  490 . The rotational speeds of propellers  420   a ,  420   c ,  420   f ,  420   e ,  420   h ,  420   j ,  420   l  are increased. Operating propellers  420   a ,  420   c ,  420   f ,  420   e ,  420   h ,  420   j ,  420   l  at a faster RPM than propellers  420   b ,  420   d ,  420   f ,  420   g ,  420   i ,  420   k  creates an immediate aft acting differential thrust that translates the aircraft  400  aft  490 , which minimizes control lag. The sum of the forward and aft pitch moments can cancel any resulting aft pitching motion. 
       FIG.  4 J  depicts the aircraft  400  translating left  494 . The rotational speeds of propellers  420   b ,  420   e ,  420   g ,  420   i ,  420   j ,  420   l  are increased. Operating propellers  420   b ,  420   e ,  420   g ,  420   i ,  420   j ,  420   l  at a faster RPM than propellers  420   a ,  420   c ,  420   d ,  420   f ,  420   h ,  420   k  creates an immediate left acting differential thrust that translates the aircraft  400  left  494 , which minimizes control lag. The sum of the left and right roll moments can cancel any resulting left rolling motion. 
       FIG.  4 K  depicts the aircraft  400  translating right  496 . The rotational speeds of propellers  420   a ,  420   c ,  420   d ,  420   f ,  420   h ,  420   k  are increased. Operating the propellers  420   a ,  420   c ,  420   d ,  420   f ,  420   h ,  420   k  at a faster RPM than propellers  420   b ,  420   e ,  420   g ,  420   i ,  420   j ,  420   l  creates an immediate right acting differential thrust that translates the aircraft  400  right  496 , which minimizes control lag. The sum of the left and right roll moments can cancel any resulting right rolling motion. 
       FIG.  5 A  depicts a plan view of a distributed propulsion system  500  in a left yaw  550  according to a fourth embodiment of the present invention. The two or more propellers are configured in four or more pairs of propellers along the ring wing: a first pair  502  of propellers  510   a ,  510   b  disposed along the ring wing, a second pair  504  of propellers  510   c ,  510   d  disposed along the ring wing, a third pair  506  of propellers  510   e ,  510   f  disposed along the ring wing, and a fourth pair  508  of propellers  510   g ,  510   h  disposed along the ring wing. Now also referring to  FIG.  5 B , each propeller  510   a  through  510   h  has a rotation direction  512   a  through  512   h  indicated by curved arrows (e.g., clockwise or counterclockwise) within a tilted plane of rotation  514   a  through  514   h  based on tilt angle γ. The rotation direction of the first pair  502  of propellers  510   a ,  510   b  and the third pair  506  of propellers of propellers  510   e ,  510   f  is counterclockwise. The rotation direction of the second pair  504  of propellers  510   c ,  510   d  and the fourth pair  508  of propellers  510   g ,  510   h  is clockwise. Each pair of propellers  502 ,  504 ,  506 ,  508  includes a first propeller  510   a ,  510   c ,  510   e ,  510   g  having a first rotational axis  516   a ,  516   c ,  516   e ,  516   g , a second propeller  510   b ,  510   d ,  510   f ,  510   h  having a second rotational axis  516   b ,  516   d ,  516   f ,  516   h , and a vertical axis  518  disposed between the first propeller  510   a ,  510   c ,  510   e ,  510   g  and the second propeller  510   b ,  510   d ,  510   f ,  510   h . The first rotational axis  516   a ,  516   c ,  516   e ,  516   g  and the second rotational axis  516   b ,  516   d ,  516   f ,  516   h  are substantially coplanar with respect to the vertical axis  518 . The first rotational axis  516   a ,  516   c ,  516   e ,  516   g  has a negative tilt angle −γ with respect to the vertical axis  518 , the second rotational axis  516   b ,  516   d ,  516   f ,  516   h  has a positive tilt angle +γ with respect to the vertical axis  518 , and the positive tilt angle +γ and the negative tilt angle −γ have a substantially equal magnitude. As shown, the vertical axis  518  is perpendicular to first center of gravity centerline  520  or a second center of gravity centerline  522 . The rotational speeds of propellers  510   a ,  510   c ,  510   e ,  510   g  are increased. Operating propellers  510   a ,  510   c ,  510   e ,  510   g  at a faster RPM than propellers  510   b ,  510   d ,  510   f ,  510   h  creates a differential thrust vector to yaw the aircraft counterclockwise, or left  550 . 
     The distributed propulsion system  500  can be applied to an aircraft as described above. Moreover, the distributed propulsion system  500  can be operated to move the aircraft in any of the directions described above. 
     It will be understood that particular embodiments described herein are shown by way of illustration and not as limitations of the invention. The principal features of this invention can be employed in various embodiments without departing from the scope of the invention. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, numerous equivalents to the specific procedures described herein. Such equivalents are considered to be within the scope of this invention and are covered by the claims. 
     All publications and patent applications mentioned in the specification are indicative of the level of skill of those skilled in the art to which this invention pertains. All publications and patent applications are herein incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference. 
     The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and/or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” The use of the term “or” in the claims is used to mean “and/or” unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and/or.” Throughout this application, the term “about” is used to indicate that a value includes the inherent variation of error for the device, the method being employed to determine the value, or the variation that exists among the study subjects. 
     As used in this specification and claim(s), the words “comprising” (and any form of comprising, such as “comprise” and “comprises”), “having” (and any form of having, such as “have” and “has”), “including” (and any form of including, such as “includes” and “include”) or “containing” (and any form of containing, such as “contains” and “contain”) are inclusive or open-ended and do not exclude additional, unrecited elements or method steps. In embodiments of any of the compositions and methods provided herein, “comprising” may be replaced with “consisting essentially of” or “consisting of.” As used herein, the phrase “consisting essentially of” requires the specified integer(s) or steps as well as those that do not materially affect the character or function of the claimed invention. As used herein, the term “consisting” is used to indicate the presence of the recited integer (e.g., a feature, an element, a characteristic, a property, a method/process step, or a limitation) or group of integers (e.g., feature(s), element(s), characteristic(s), property(ies), method/process(s) steps, or limitation(s)) only. 
     The term “or combinations thereof” as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof” is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context. 
     As used herein, words of approximation such as, without limitation, “about,” “substantial” or “substantially” refers to a condition that when so modified is understood to not necessarily be absolute or perfect but would be considered close enough to those of ordinary skill in the art to warrant designating the condition as being present. The extent to which the description may vary will depend on how great a change can be instituted and still have one of ordinary skill in the art recognize the modified feature as still having the required characteristics and capabilities of the unmodified feature. In general, but subject to the preceding discussion, a numerical value herein that is modified by a word of approximation such as “about” may vary from the stated value by at least ±1, 2, 3, 4, 5, 6, 7, 10, 12 or 15%. 
     All of the devices and/or methods disclosed and claimed herein can be made and executed without undue experimentation in light of the present disclosure. While the devices and/or methods of this invention have been described in terms of particular embodiments, it will be apparent to those of skill in the art that variations may be applied to the compositions and/or methods and in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit and scope of the invention. All such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope, and concept of the invention as defined by the appended claims. 
     In the specification, 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 the present application, 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. 
     Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the disclosure. Accordingly, the protection sought herein is as set forth in the claims below. 
     Modifications, additions, or omissions may be made to the systems and apparatuses described herein without departing from the scope of the invention. The components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses may be performed by more, fewer, or other components. The methods may include more, fewer, or other steps. Additionally, steps may be performed in any suitable order. 
     To aid the Patent Office, and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims to invoke 35 U.S.C. § 112(f) as it exists on the date of filing hereof unless the words “means for” or “step for” are explicitly used in the particular claim.