Kurt F.J. Kirsten: Prolate Cycloidal propeller -- hovering flight, wingless; articles, patents ![](0logo.gif) **[rexresearch.com](../index.htm)** --- **Kurt F.J. KIRSTEN** **Prolate Cycloid Propeller** --- --- ***Modern Mechanics* ( October 1934 )** ![](mmx10-34.jpg) --- ![](psnov34.jpg) [**http://blog.modernmechanix.com/2007/09/04/flying-without-wings-or-motors/**](http://blog.modernmechanix.com/2007/09/04/flying-without-wings-or-motors/) ***Popular Science* ( November 1934 )** **Flying Without Wings or Motors** *Airplane design faces radical change. Prof. Kirsten's cycloidal propeller is ready to emerge from the experimental stage into a safe, wingless craft. In Europe ships are being developed eliminating not only wings, but motors also. An Interview with F. K. KIRSTEN, Professor of Aeronautical Engineering University of Washington* **by** **James Bowles** Picture yourself soaring over the Rockies in an airplane without fixed wings, with no propeller as you know the air screw today, yet climbing, diving, dashing ahead in level flight or actually stopping after the manner of a giant insect. There you have a preview of tomorrow's flight possibilities in heavier-than-air machines. Recently developed devices known as cycloidal propellers, projecting outward from the fuselage in the places where wings now are attached, serve not only to pull the cyclo-copter, the name given this machine, forward and up, but also to serve as both wings and air brakes when coming down to a safe three-point landing. This machine may be equipped with a standard propeller in the nose. It then is called a cyclo-gyro.

For 15 years Prof. F. K. Kirsten of the University of Washington has investigated the possibilities of cyloidal propulsion and sustentation. It suggested itself to him while he was engaged in an attempt to analyze the flight of birds. Speculation as to the characteristics of the actual path traced in the air by the tip of the bird's wing led him to conclude that this path might resemble the path of a cycloid, which finds expression in the cycloidal propeller, in which several flat surfaces, or wings, are rotated about a center. Birds, we know, possess the powers of sustentation --- the lift of an airplane wing --- and propulsion --- speed from the propeller --- in the same mechanism, the wings. Too, birds are far more versatile than airplanes in their ability to take off and land and to engage in rapid flight. Here is another important point, which in the past has not been even remotely approached in fixed-wing airplanes; birds have neither rudder nor ailerons, although they do possess a horizontal stabilizing fin in the form of tails. They accomplish every manner of control, including pitch, roll and yaw so familiar to airplane pilots, by moving the wing system. "Thus the new cyclo-copter," Professor Kirsten told me, with which we are now experimenting at the Guggenheim Aeronautical Laboratory, University of Washington, possesses a rotating wing-propeller system as in birds and gives us the advantages of free flight enjoyed by those inhabitants of the air. Its interconnected plane surfaces, representing a bird wing, by their interrelated motions as they revolve, react upon the air in such a way as to derive effects of lift and propulsion quite like those achieved by a bird's wings. When fitted as a cyclo-gyro, the air screw and the cycloidal propellers are turned independently. In this case the air blast from the propeller starts the blades turning. Whereas the screw may turn up to 2,000 r.p.m., the cycloidal propeller will deliver adequate thrust and lift while revolving only 350 r.p.m. Blades of the cycloidal propeller on this astounding new craft are so arranged mechanically that each makes a half turn for every revolution of the entire propeller. In level flight, for instance, the blade at the bottom of the circle stands on edge, presenting a flat surface to the air stream. This enables it to deliver maximum thrust in pushing the machine forward. If that blade is moving backward at a rate of 100 miles an hour, the top blade, which is now lying horizontal in the air stream, is moving forward 200 miles an hour with respect to the air --- speed of the propeller blades on their orbit plus the speed of the machine which supports it. This gives the top blades four times as great a lift per unit area than for a fixed wing. Together, these tiny wings operate with superior efficiency in propulsions and furnish the required lift at the same time. "It will not be necessary to fit these machines with propellers", Professor Kirsten told me, over the whir of the air-screw spinning on the model. "Experiments indicate the rotors alone will give them positive control, greater stability than theretofore has been possible, and an ability to land almost vertically even should the power plant fail. The cyclo-gyro model already built represents a one-sixth scale replicum of a 10-passenger transport plane. Later a full-size craft will be constructed. An entirely new flying technique will be used by pilots." **Cyclo-Gyro Has No Rudder** Since it does not employ a rudder, the pilot merely turns the wheel right and left for turns and banks, moves it forward and backward to glide or climb, stated Prof. Kirsten. When he turns the wheel left, for instance, control wires cause the angles of the blades in the propellers to be changed in opposite directions, raising the right side and lowering the left. Meantime the tail propellers serve to align the body of the machine in straight flight. Such is the accuracy and positiveness of control that a stabilizing vertical fin becomes unnecessary. Merely by turning a small wheel the pilot can change the thrust on the blades, now driving forward in level flight, again hovering over a single spot like a bird. By making adequate changes in the propeller system to achieve high pitch," said Prof. Kirsten, "there seems to be no limit to speed attainable. I am sure we can reach speeds and altitudes exceeding those so far attained by fixed-wing airplanes, at the same time retaining the safety and controllability so necessary at low speeds. Whereas the airliner of today lands at a speed exceeding in most cases a mile a minute, the cycloidal craft may be brought to earth with little if any forward momentum, much as the autogyro lands." **Possible Wartime Uses** Too, the cycloidal machine promises valuable military possibilities. Most of the noise of present airplanes comes from rhythmic impulses imparted by propellers to the air. The frequency of the sound made by the cycloidal propeller is too low to be heard. The cycloidal machine may hover over an enemy, silent as the night, while observers take note of movements on the ground. Its mission accomplished, it can speed away to safety faster than any airplanes yet constructed. Further, for fighting purposes, since the vision from the pilot's cockpit is unobstructed by wings, due to the rapid motion of the cycloidal propellers, and since there is no propeller in front of the cockpit to interfere, machine guns of adjustable sweep may be installed. --- ![](mmx1.jpg) ![](mmx2.jpg) ![](mmx3.jpg) --- **US Patent # 2,045,233** **Propeller for Aircraft** **Kurt F.J. KIRSTEN & Herbert M. HEUVER** **( Cl. 170-148 )** This invention relates to aircraft propulsion and more particularly to aircraft propellers of that class known in the art as cycloidal propellers wherein a plurality of propeller blades extend normal to the surface of a rotor, and wherein any point in the axis of any blade will describe the path of a prolate cycloid, when the slip of the propeller is zero, and wherein the blades rotate in their mountings in accordance with the rotation of the rotor to so align themselves that the planes of their median chords remain tangent to the prolate cycloid. Explanatory to the invention it will here be stated that the most important consideration in the design of a cycloidal propeller is the required pitch. The pitch ratio of a screw propeller has been defined as the advance per revolution in propeller diameters of the screw as a whole at zero slip. Applying the same definition to cycloidal propellers, the pitch ratio of a pure cycloidal propeller is pi, since the length of a cycloid period is equal to pi times the diameter of the generating circle. A cycloidal path is described by a point on the periphery of a wheel which rolls on a plane. The distance covered by the center of the wheel, or the wheel as a whole, per revolution is pi times the diameter; hence the pitch ratio of a cycloidal propeller representing the blade orbit as the rim of a wheel and rolling on a plane tangent to the blade orbit is pi or the advance per revolution of the propeller as a whole in orbit diameters. The curve generated by a point on the periphery of a wheel rolling on a plane is the path of a pure cycloidal curve. If, however, this wheel were attached concentrically to a larger wheel rolling on a plane, a point on the periphery of the smaller wheel will generate a prolate cycloidal path. Hence cycloidal propellers may be regrouped into three classes, viz., the pure, the prolate, and the curtate. In the cycloidal propeller the alignment of blades at all points along the cycloidal path for zero slip must be such that no force reaction normal to the path can result. This naturally requires a different blade movement for the curtate cycloid than for the pure cycloid pr prolate cycloid. For the prolate cycloid propeller, to which the present invention applies, the blades must rotate about their own axes at the same speed as the propeller rotor, or while the propeller rotor makes one revolution the blade must also make a full revolution. However, a uniform blade rotation is feasible only for the pure cycloidal propeller, for the prolate cycloidal propeller modifications must be applied to the blade actuating mechanism so that the blade alignment is correct for all point on the cycloidal path. It must have a blade rotational speed equal to that of the rotor, but this rotational speed must be retarded until the cycloid interests a plane parallel to the plane on which the generating circle rolls and located at a definite distance above that plane. For the remainder of the half cycle the rotational speed of the blades must be increased. In view of the above it has been the principal object of this invention to provide a suitable and practical blade control mechanism for propellers of the prolate cycloid type whereby rotational speed of the blades may be controlled as above stated; thereby to change and control the pitch by an oscillating adjustment of the blades in their mountings effected automatically incident to rotation of the rotor. Another object of the invention reside in the combination and arrangement of parts whereby the change and control of pitch and axis of symmetry may be effected with the propeller in motion. Other objects of the invention reside in the details of construction and in the combination of parts and in their mode of operation, as will hereinafter be described. In accomplishing the various objects of the invention, we have provided the improved details of construction, the preferred forms of which are illustrated in the accompanying drawings wherein --- **Figure 1** is a side elevation of a portion of an airplane equipped with a cycloidal propeller embodying the present invention. ![](2045-1.jpg) **Figure 2** is a top, or plan, view of the parts, as seem in Figure 1. ![](2045-23.jpg) **Figure 3** is a diagram for purpose of explanation and illustration of operation of the present prolate cycloidal propeller. **Figure 4** is a cross sectional view in the axial planets of the rotor and a blade mounted thereby, particularly illustrating the means for changing and controlling the pitch of the propeller. ![](2045-45.jpg) **Figure 5** is an outside, or face view of a part of the propeller with the part of the housing broken away for better illustration of interior parts. Before going into a description of the mechanism, as disclosed in Figures 4 and 5, the invention will be explained with reference to the illustration of Figure 3. In this view, the dotted lie X represents the prolate cycloidal path penetrated by a point p on the periphery of an orbit A fixed concentric of a wheel C rolling on plane c-c. Applying the present construction to the diagram and assuming the orbit A to represent the circle in which the propeller blades of the rotor are mounted, all points in the axes of the blades b rotate for a given instant about the point of contact T of the imaginary wheel C rolling on plane c-c without slippage. The curtate cycloid will be normal to a line l between point of contact T and the axis of blade b. The plane f of the median chord of the blade will be tangent to the prolate chord and therefore normal to the said line l. The present invention takes into consideration the fact that the plane f of the median chord of the blade should be maintained normal to the line l except for a limited compromise whereby blade alignment is corrected for all points on the cycloidal curve thereby provided a very close approach to the pitch ration of pi. Referring more in detail to the drawings --- 1 designates a supporting frame structure for the propeller. This structure may be embodied in or may constitute a part of the fuselage 2 of the airplane, and fixed therein is a bearing sleeve 3 within which is rotatably mounted the spindle portion 4 of the propeller rotor designated in its entirety by numeral 5. The rotor is circular and concentric of the spindle 4 and it comprises, at its center, a hub housing 6 with which the spindle 4 is integrally formed. At the outer portion of the rotor a plurality of propeller blade mounting sleeves 7 are supported by brace bars 8; these bars being fixed at their inner ends to flanges 9 on the hub housing 6 and at their outer ends are fixed to the sleeves 7 thereby to rigidly maintain the latter equally spaced apart, also equally spaced from and axially parallel to the axis of the rotor. Keyed on the inner end of the spindle 4 is a beveled gear 10 and meshing therewith is a beveled gear10 and meshing therewith is a beveled driving pinion 11 fixed on the end of a driving shaft 12 that extends from the engine, or source of power, not herein shown; this shaft being rotatably supported adjacent the gear 11 in a bearing 13 that is fixed to frame structure 1. Rotatably fitted in the several sleeves 7 at the periphery of the rotor are the mounting journals 14 of the propeller blades 15, and at the inner end of each journal is a reduced shank 16 on which a beveled pinion 17, for rotating the blade, is fixed. Mounted radially of the rotor are blade control shafts 18 revolubly supported at their outer ends in bearings 19 formed integral with the inner end portions of the sleeves 7, and, at their inner ends, extending into the hub housing 6 through supporting bearings 20 integral with the housing. Fixed on the outer end of each shaft 18 is a beveled pinion gear 21 in mesh with the pinion gear 17 of the corresponding blade. Likewise, fixed on the inner ends of the shafts 18 are beveled pinion gears 22 meshing with beveled gears 24 that are located within housing 6 and keyed on supporting shafts 25; these supporting shafts being rotatably supported at their opposite ends respectively in the inner and outer walls 6a and 6b of the hub housing 6, and are equally spaced apart about the rotor axis and equally spaced from the axis. Coaxial of the spindle 4 is a tubular shaft 28 revolubly supported in bushings 29 and 30 applied to the spindle ends. At the inner end of the shaft 28 and fixed thereto is a gear 31. At the outer end of the shaft is an adjusting gear 32 in mesh with and normally held against rotation by an intermeshing worm gear 33 on a shaft 34 which provides, as presently understood, for adjustment of the axes of symmetry of the propeller. Rotatably mounted on each of the several shafts 25 is a gear 35. All of these are of the same diameter and all mesh with the gear 31 to provide a planetary motion thereof about the gear 31, and the relation of diameters of the gears 35 to that of gear 31 is such that, with the gear 31 held against rotation, the gears 35 will be caused to rotate exactly once about their supporting shafts 25 for each rotation of the rotor about its axis. Each gear 35 has a bevel gear 38 fixed relative thereto at the outer end of its hub portion and this gear is in mesh with spider gears 39 revoluble on spindles 40 that extend radially from the shaft 25 about which the gears 35 and 38 rotate. The spider gears also are in mesh with bevel gears 42 integral with the inner end portions of guide blocks 43 mounted on the outer end portions of the shafts 25. The gearing arrangement above described provides that with the gears 42 held relatively stationary, for each rotation of the rotor about its axis, the shafts 25, through the mediacy of the spider gears 39 and gears 31, 35,and 38 will be rotated once about their axes for each two rotations of the propeller. Also, the relationship of the gears connecting the shafts 25 and propeller blades is such that the propeller blades will be rotated once with uniform motion about their axes for each rotation of the shaft 25 and therefore once for each rotation of the propeller. Superimposed upon their uniform relative motion provided in the gearing above described is an oscillating motion transmitted to the blades by a mechanism embodying the present invention whereby change in pitch of the propeller is effected. This mechanism, as shown in Figures 4 and 5, comprises a forked bar 48 for each blade mechanism; the forked outer ends of the bars being slidable through their corresponding guide blacks 43 and their inner ends being pivotally mounted on a stud 49 eccentric of the rotor and integral with a cross head 50 that is slidably movable in a quideway 51 in a direction diametrically of the rotor; the guideway 51 being integral with the gear 31 and held against rotation thereby. This means of connection provides that, with the stud 49 relatively stationary, and the rotor rotating on its axis, the forked guide bars 48 will cause oscillation of their respective guide blocks 43 both in a clockwise and a counter-clockwise direction for each rotation of the rotor. The spider gears 39 associated with the gears 42 on the blacks cause the shafts 25 to oscillate with half the angular velocity of the oscillating guide blocks, and the relationship of gearing that is intermediate the shafts 25 and their corresponding blades causes the blades, while rotating once about their axes with each rotation of the propeller, to be subjected to oscillations of the same angular velocity of their respective guide blacks 43; the extent of oscillation being determined by the distance of spacing or eccentricity of the stud 49 from the axis of rotation of the rotor and decreases and increases in accordance with the movement of the stud towards and from the axis. The means for shifting the cross head in its guideway, thereby to shift the eccentric stud, comprises a shaft 60 coaxial of tubular shaft 28 and rotatable in bushings 61 and 62 fitted in opposite ends of shaft 28. At its inner end, shaft 60 has a pinion gear 63 fixed thereon in mesh with a rack 64 on the cross head, At its outer end the shaft 60 is equipped with a worm gear 65 which is held normally against rotation by an intermeshing worm gear 66 on a shaft 67. Rotation of shaft 66 effects rotation of gear 63 and this, through the mediacy of the rack 64, raises or lowers the cross head accordingly and thereby shifts the stud 49 toward or away from the axis of the rotor thereby to regulate the extent of the oscillating action of the blades. It is apparent that this arrangement of mechanism, as applied to the diagram of Figure 3 provides for changing the diameter of the imaginary wheel C and therefore controls the pitch of the propeller. Also, since the axis of symmetry is defined as a line drawn through the center of the propeller through the point of contact T, this is controlled by the worm 33, worm gear 32, shaft 28 and gear 31, which mounts the cross head guide 51. Thus by revolving the parts 31, 51, 50 and 49, the axis of symmetry is controlled. Having thus described our invention, what we claim as new therein and desire to secure by Letters Patent is --- [ Not included here ] --- **US Patent # 2,090,052** **Aircraft** **K. Kirsten** **( Cl. 244-20 )** **17 August 1937** This invention relates to aircraft, and more, particularly to aircraft of the heavier than air types employing cycloidal propulsion devices; the objects of the invention residing in the design, relationship and use of cooperatively arranged cycloidal propellers for propulsion stabilization and control of aircraft in flight. It is recognized that propellers of that type known as cycloidal propellers have heretofore been applied to aircraft and it is not the intention of this application to seek patent protection on that type of propeller, per se, but rather on the novel use of cycloidal propellers, as applied in a certain relationship to each other and to the fuselage of the craft in which they are used, thereby to obtain maximum efficiency for propulsion and sustentation as well as to make possible perfect control of the craft in taking off, while in flight, and in landing. In order to impart a better understanding of the present invention it will here be stated that during the past year much publicity has been given to cycloidal propulsion projects of heavier than air craft. One of the first to appear in various publications was a development of the Rohrbach machine in Germany. Another was a machine built and tested in France by Standgren. A third, which has appeared in the technical press. Is the Platt machine developed in the United States. Also, much prominence has been given recently to cycloidal propulsion in articles appearing in journals of the American Society of mechanical Engineers under the heading of Engineering Progress. However, no machine, to my knowledge, has used cycloidal propellers in the present cooperative relationship for purpose of stabilization, propulsion, and flight control. In the known machines, above mentioned, there are certain inherent defects which have been eliminated in the present construction. For instance, in the Rohrbach and Strandgran machines, the propellers are set out from and entirely cleat of the body structure, or fuselage, and there are long cylindrical propeller shafts extending into the slip stream, adding much resistance to flight. In the Rohrbach machine in particular there are a great many strut supports for the propeller blades and this is contrary to modern aircraft practice which seeks to eliminate all parts from the slip stream which do not contribute to propulsion and sustentation. The Strandgren machine employs two propellers with short blades and of large rotor diameter which design has also proven to be faulty, particularly because of end losses of its many short blades and its dependence on slip stream momentum for both propulsion and sustentation. In view of the objectionable and impractical features proven to exist in cycloidal propellers of prior machines, it has been the principal object of this invention to overcome them to a maximum extent by use of cycloidal propellers at opposite sides of the body or fuselage of the craft, each comprising a rotor set flush with the surface of the craft to avoid any possible interference or resistance to flight, and equipped with propeller blades of the cantilever type wherein each blade projects from the fuselage as a monoplane wing. The invention also provides both front and rear sets of propellers, with those of the rear set coupled with those of the front or forward set, in such manner that the blade speed of all propellers is of the same magnitude and both sets operate to produce a lift in normal flight. Also, the invention provides for differentially controlling the blade angle of the propellers so that they may additionally function both as ailerons and rudder. Other objects of the invention reside in the details of construction and in the combination of parts and mode of use, as will hereinafter be described. In accomplishing these and other objects of the invention, I have provided the improved details of construction, the preferred forms of which are illustrated in the accompanying drawings, wherein --- **Figure 1** is a plan, or top view of an airplane equipped with a font and a rear set of cycloidal propellers in accordance with the present invention. ![](2090-1.jpg) **Figure 2** is a side view of the same. ![](2090-2.jpg) **Figure 3** is a front end elevation of the airplane. ![](2090-3.jpg) **Figure 4** is a horizontal section, as on line 4-4 in Figure 2, illustrating the propeller driving means. ![](2090-4.jpg) **Figure 5** is a cross-section, as on line 5-5 in Figure 4, showing the dihedral of the front set of propellers. ![](2090-5.jpg) **Figure 6** is a detail of the control device for differentially controlling the blade angle of paired propellers and for control of the axis of symmetry. ![](2090-6.jpg) Referring more in detail to the drawings --- 1 designates the fuselage, or body, of an airplane which may be similar to or one of those of present day design and 2 designates its engine, or power plant, with drive shaft 3 extended in the central longitudinal plane of the craft for operative connection with the forward and rearward sets of cycloidal propellers, as presently described. The two propellers A and A, comprising the forward set, are located toward the forward end of the fuselage and at opposite sides thereof, as shown in Figure 1, and the propellers B and B, comprising the rearward set, are similarly located near the rear end or in the tail of the fuselage. Briefly, each propeller comprises a rotor 4 from which extend a plurality of propeller blades 5, arranged in a circle concentric of the rotor. These blades are of the cantilever type and diverge slightly and uniformly from the axis of rotation. Each blade 5 has a journal 6 at its inner end whereby it is rotatably mounted in a bearing sleeve 7 carried at the periphery of the rotor and each rotor has a tubular mounting spindle 8 coaxial thereof whereby it is revolubly supported in a frame structure 9 through the mediacy of antifriction bearings 10 and 11, as seen in Figure 5; the frame 9 constituting a part of or is fixed solidly within the fuselage. Fixed on the inner ends, the spindles 8 of paired rotors, respectively, are beveled gears 12 and 13 which mesh respectively with beveled driving gears 14 and 15 on the motor shaft 3; these intermeshing gears being so arranged and in such relative proportion that they will impart rotary motion to the rotors in the same direction and at the same speed. Rotatably contained coaxially within the spindles 8-8 of the forward pair of rotors are shafts 18-18 which, at their inner ends have worm gears 19-19 fixed thereon in mesh with worm gears 20-20 on adjusting shafts 21-21. At their outer ends are bevel gears 22, normally held against rotation by reason of the worm gears 20-20 but rotatably adjustable by rotative adjustment of shafts 21 and 21. Extending radially of the rotors from the center to each of the propeller blades, are blade adjusting shafts 25 rotatably supported in bearings 26 in the rotor structure. At the inner end of each shaft 25 is a bevel gear 27 meshing with the centrally located gear 22, and fixed on the outer end of each shaft 25 is a bevel gear 28 meshing with a bevel gear 29 fixed on the spindle 6 of the corresponding blade. The relationship and relative sizes of the several gears is such that, with the gears 22 held against rotation, the blades will be caused to rotate once on their axes for each rotation of the rotor and in a direction opposite thereto. Rotatable adjustment of the worm gears 20 and 20 will effect adjustment of the pitch of the blades, and the control device is such that the blades may be differentially or uniformly adjustable through geared connection with the shafts 21 and 21 . The outside of each rotor is covered by a smooth, flat disk 32 and this is flush with the side surface of the fuselage, as shown in Figure 5. Also the axes of paired rotors are similarly upwardly inclined from the vertical longitudinal plane of the fuselage to form a dihedral that is very desirable from the aerodynamic standpoint and at the same time creates a very convenient compartment due to the spread of the lower portion of the rotors which can be utilized for the variable fuel load and thus placing the variable load directly in line with the principal lift reactions. In all aircraft, freedom and control of motion about and along the three axes of space are required. Granting that the motion of the cycloidal aircraft in a horizontal plane, in a vertical place through the major axis of the craft and in a vertical plane through the propeller axes is as readily achieved as with the airplane, there still remains the problem of pitching, rolling, and yawing motions and their control. For the present use type of cycloidal aircraft, pitching is induced by the torque of the blades. This pitching moment is automatically stabilized by placing the center of gravity a sufficient distance below the horizontal axes of the propeller rotors. An increase in torque will tend to swing the mass of the vehicle about the axis of the propeller in a direction opposite to that of the direction of rotation of the rotor. If the topmost blades are made to move in the same direction as the vessel, an increase in torque will displace the center of gravity forward of the pitching axis. This displacement creates a gravitational restoring moment, making the system stoically stable. However, as the vessel swings through the displacement angle, the blades are also turned an angle with respect to their former position unless they can be automatically prevented from being influenced by the pitching of the vessel. This increased angle of attack increases the propeller torque still more, which again increases the propeller torque still more, which again increases the displacement of the center of gravity. Consequently, this arrangement appears to be dynamically unstable in pitching. The same results are obtained by an analysis of operation under negative slip propellers. Consequently, for cycloidal aircraft which depend only upon a favorable location of the center of gravity for pitching control, a horizontal tail surface must be provided. In the present instance the rearward pair of cycloidal propellers B and B take the place of the horizontal tail surface, and is the means for controlling pitching. As shown in Figure 4, the rear pair of cycloidal propellers is coupled with the front pair and in such a way that the blade speeds of all propellers are of the same magnitude. An increase of torque in the front propellers automatically increases the torque of the rear propellers in the same proportion. The rear propellers are arranged to produce a lift in normal flight, that is; both pairs of propellers are lifting surfaces. The lift of the rear propellers multiplied by the distance between centers of front and rear propellers must be equal to the torque of the motor for static stability. Assuming now that the torque on the front propellers suddenly increases, the rear propellers receive a downward impulse but the slightest downward motion increase the angle of attack of the rear propeller blades. This increases the lift and thus the counter torque on the front propellers. Hence, this system is automatically stable. Since the blade setting of both sets of propellers is controlled by the pilot, the attitude of the craft in flight may be adjusted at will. Normally the tail propeller control will be coupled with the blade control of the main or forward propellers. However, linkage between the two controls may be made adjustable so as to simulate the adjustability of the airplane elevators. Rolling stability depends on the adjustment of the blade control for both the starboard and port propellers. Once this adjustment is perfected for operation on an even keel no further balancing mechanisms are required. The slight dihedral in the exes of each pair of propellers is of help in securing dynamic stability. But the most effective recovery movements are the forces dynamically acting on the blades due to a change in the inflow direction of air when a rolling movement takes place. These recovery movements are very large since the change of inflow direction effects mainly the upper blades, the velocities of which are usually more than twice the velocity of the vessel. Consequently, the present cycloidal aircraft is also statically and dynamically stable in rolling. An analysis for yawing movements of cycloidal aircraft is somewhat more involved than for the analysis for pitching and rolling. The lift at any slip increases in direct proportion to the angle of blade setting or the shift of the axis of symmetry of the blades from the plane normal to the inflow direction. Similarly, the thrust at all slips increases as the angle of blade setting increases from zero to about fifteen degrees, at which it reaches a maximum for a given blade speed. If the setting of this angle for cycloidal propellers is at values below fifteen degrees in normal flight, any small change in this angle in the positive direction increases both lift and thrust, and a change in the negative direction decreases both lift and thrust. Hence, if the controls of the propellers are differentially coupled; namely, so that the pilot can increase the angle of setting for the starboard propeller and decrease it the same amount for the port propeller, or vice versa, the yawing control is completely established, If he wishes to turn to port, the angle is increased for the starboard propeller and decreased for the port propeller. This increases the thrust on the starboard side and decreases the thrust on the port side, at the same time creating the starboard banking attitude of the vessel on its curved flight path. For this maneuver no rudder is required. This demonstrates that differentially controlled cycloidal propellers perform the function of both the ailerons and rudder of the airplane, and that the cycloidal ship is statically stable in yawing. In order to make it dynamically stable, a vertical fin, as designated at 40, is attached to the rear of the vessel. However, this fin may not be necessary of the ship is so built that it presents sufficient vertical surface in its body to accomplish the same results. For differentially controlling the blade angle adjustment of paired propellers, the shafts 18 and 18 are rotated in opposite directions from a neutral setting. To change the angle of symmetry for the propeller blades, the shafts 18 and 18 are rotatably adjusted in unison. For this latter adjustment, the shafts 21 and 21 are extended, as seen in Figure 6, and are equipped with bevel pinions 45 and 45 meshing with bevel gears 46 and 46 and has a gear 49 thereon in mesh with gears 46 and 46. Oscillation of the shaft effects a simultaneous rotation of the gears 45 and 45 and a similar rotative adjustment of the worm gears to thereby change the angle of symmetry of both propellers to the same extent. Rotation of the control shaft in opposite direction by means of the wheel 50 at its end effects an opposite rotative adjustment of the worm gears and a differential adjustment of the propeller blade angles. Having thus described my invention, what I claim as new therein and desire to secure by letters patent is --- [ Not included here ] ---