Patent Publication Number: US-2021163103-A1

Title: Paddle wheel apparatus and method of use thereof

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 16/740,412 filed Jan. 11, 2020, which is a continuation-in-part of U.S. patent application Ser. No. 14/997,322 filed Jan. 15, 2016, which:
         is a continuation-in-part of U.S. patent application Ser. No. 14/821,682 filed Aug. 7, 2015, which
           claims benefit of U.S. provisional patent application No. 62/035,461 filed Aug. 10, 2014;   claims benefit of U.S. provisional patent application No. 62/038,116 filed Aug. 15, 2014; and   claims benefit of U.S. provisional patent application No. 62/038,133 filed Aug. 15, 2014; and   
           claims benefit of U.S. provisional patent application No. 62/793,845 filed Jan. 17, 2019,   all of which are incorporated herein in their entirety by this reference thereto.       

    
    
     TECHNICAL FIELD OF THE INVENTION 
     The present invention relates to the field of rotary engines. 
     BACKGROUND OF THE INVENTION 
     The controlled expansion of gases forms the basis for the majority of non-electrical rotational engines in use today. These engines include reciprocating, rotary, and turbine engines, which may be driven by heat, such as with heat engines, or other forms of energy. Heat engines optionally use combustion, solar, geothermal, nuclear, and/or forms of thermal energy. Further, combustion-based heat engines optionally utilize either an internal or an external combustion system, which are further described infra. 
     Internal Combustion Engines 
     Internal combustion engines derive power from the combustion of a fuel within the engine itself. Typical internal combustion engines include reciprocating engines, rotary engines, and turbine engines. 
     Internal combustion reciprocating engines convert the expansion of burning gases, such as an air-fuel mixture, into the linear movement of pistons within cylinders. This linear movement is subsequently converted into rotational movement through connecting rods and a crankshaft. Examples of internal combustion reciprocating engines are the common automotive gasoline and diesel engines. 
     Internal combustion rotary engines use rotors and chambers to more directly convert the expansion of burning gases into rotational movement. An example of an internal combustion rotary engine is a Wankel engine, which utilizes a triangular rotor that revolves in a chamber, instead of pistons within cylinders. The Wankel engine has fewer moving parts and is generally smaller and lighter, for a given power output, than an equivalent internal combustion reciprocating engine. 
     Internal combustion turbine engines direct the expansion of burning gases against a turbine, which subsequently rotates. An example of an internal combustion turbine engine is a turboprop aircraft engine, in which the turbine is coupled to a propeller to provide motive power for the aircraft. 
     Internal combustion turbine engines are often used as thrust engines, where the expansion of the burning gases exit the engine in a controlled manner to produce thrust. An example of an internal combustion turbine/thrust engine is the turbofan aircraft engine, in which the rotation of the turbine is typically coupled back to a compressor, which increases the pressure of the air in the air-fuel mixture and increases the resultant thrust. 
     All internal combustion engines suffer from poor efficiency; only a small percentage of the potential energy is released during combustion as the combustion is invariably incomplete. Of energy released in combustion, only a small percentage is converted into rotational energy while the rest is dissipated as heat. 
     If the fuel used in an internal combustion engine is a typical hydrocarbon or hydrocarbon-based compound, such as gasoline, diesel oil, and/or jet fuel, then the partial combustion characteristic of internal combustion engines causes the release of a range of combustion by-products pollutants into the atmosphere via an engine exhaust. To reduce the quantity of pollutants, a support system including a catalytic converter and other apparatus is typically necessitated. Even with the support system, a significant quantity of pollutants is released into the atmosphere as a result of incomplete combustion when using an internal combustion engine. 
     Because internal combustion engines depend upon the rapid and explosive combustion of fuel within the engine itself, the engine must be engineered to withstand a considerable amount of heat and pressure. These are drawbacks that require a more robust and more complex engine over external combustion engines of similar power output. 
     External Combustion Engines 
     External combustion engines derive power from the combustion of a fuel in a combustion chamber separate from the engine. A Rankine-cycle engine typifies a modern external combustion engine. In a Rankine-cycle engine, fuel is burned in the combustion chamber and used to heat a liquid at substantially constant pressure. The liquid is vaporized to a gas, which is passed into the engine where it expands. The desired rotational energy and/or power is derived from the expansion energy of the gas. Typical external combustion engines also include reciprocating engines, rotary engines, and turbine engines, described infra. 
     External combustion reciprocating engines convert the expansion of heated gases into the linear movement of pistons within cylinders and the linear movement is subsequently converted into rotational movement through linkages. A conventional steam locomotive engine is used to illustrate functionality of an external combustion open-loop Rankine-cycle reciprocating engine. Fuel, such as wood, coal, or oil, is burned in a combustion chamber or firebox of the locomotive and is used to heat water at a substantially constant pressure. The water is vaporized to a gas or steam form and is passed into the cylinders. The expansion of the gas in the cylinders drives the pistons. Linkages or drive rods transform the piston movement into rotary power that is coupled to the wheels of the locomotive and is used to propel the locomotive down the track. The expanded gas is released into the atmosphere in the form of steam. 
     External combustion rotary engines use rotors and chambers instead of pistons, cylinders, and linkages to more directly convert the expansion of heated gases into rotational movement. 
     External combustion turbine engines direct the expansion of heated gases against a turbine, which then rotates. A modern nuclear power plant is an example of an external-combustion closed-loop Rankine-cycle turbine engine. Nuclear fuel is consumed in a combustion chamber known as a reactor and the resultant energy release is used to heat water. The water is vaporized to a gas, such as steam, which is directed against a turbine forcing rotation. The rotation of the turbine drives a generator to produce electricity. The expanded steam is then condensed back into water and is typically made available for reheating. 
     With proper design, external combustion engines are more efficient than corresponding internal combustion engines. Through the use of a combustion chamber, the fuel is more thoroughly consumed, releasing a greater percentage of the potential energy. Further, more thorough consumption means fewer combustion by-products and a corresponding reduction in pollutants. 
     Because external combustion engines do not themselves encompass the combustion of fuel, they are optionally engineered to operate at a lower pressure and a lower temperature than comparable internal combustion engines, which allows the use of less complex support systems, such as cooling and exhaust systems. The result is external combustion engines that are simpler and lighter for a given power output compared with internal combustion engines. 
     External Combustion Engine Types 
     Turbine Engines 
     Typical turbine engines operate at high rotational speeds. The high rotational speeds present several engineering challenges that typically result in specialized designs and materials, which adds to system complexity and cost. Further, to operate at low-to-moderate rotational speeds, turbine engines typically utilize a step-down transmission of some sort, which again adds to system complexity and cost. 
     Reciprocating Engines 
     Similarly, reciprocating engines require linkages to convert linear motion to rotary motion resulting in complex designs with many moving parts. In addition, the linear motion of the pistons and the motions of the linkages produce significant vibration, which results in a loss of efficiency and a decrease in engine life. To compensate, components are typically counterbalanced to reduce vibration, which again increases both design complexity and cost. 
     Heat Engines 
     Typical heat engines depend upon the adiabatic expansion of the gas. That is, as the gas expands, it loses heat. This adiabatic expansion represents a loss of energy. 
     Problem 
     What is needed is a rotary engine operable in water. 
     SUMMARY OF THE INVENTION 
     The invention comprises a human powered rotary engine apparatus and method of use thereof. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete understanding of the present invention is derived by referring to the detailed description and claims when considered in connection with the figures, wherein like reference numbers refer to similar items throughout the figures. 
         FIG. 1  provides a block diagram of a rotary engine system; 
         FIG. 2  illustrates a perspective view of a rotary engine housing; 
         FIG. 3  illustrates a cross-sectional view of a single offset rotary engine; 
         FIG. 4  illustrates a sectional view of a double offset rotary engine; 
         FIG. 5  illustrates housing cut-outs; 
         FIG. 6  illustrates a housing build-up; 
         FIG. 7  provides a block diagram of a method of use of the rotary engine system; 
         FIG. 8  illustrates changes in expansion chamber volume with rotor rotation; 
         FIG. 9  illustrates an expanding concave expansion chamber with rotor rotation; 
         FIG. 10A  illustrates a vane having valved flow pathways and  FIG. 10B  illustrates a vane having seals functioning as valves; 
         FIG. 11A  illustrates a cross-section of a rotor having valving and  FIG. 11B  illustrates distances between vane valves; 
         FIG. 12  illustrates a rotor and vanes having fuel paths; 
         FIG. 13  illustrates a flow booster; 
         FIG. 14A  and  FIG. 14B  illustrate a vane having multiple fuel paths and a vane/rotor rod, respectively; 
         FIG. 15A  and  FIG. 15B  illustrate a fuel path running through a shaft and into a vane, respectively; 
         FIG. 16A  and  FIG. 16B  respectively illustrate a sliding vane in a cross-sectional view and in a perspective view and  FIG. 16C  illustrates a vane with a flexible vane head; 
         FIG. 17  illustrates a perspective view of a vane tip; 
         FIG. 18  illustrates a vane wing; 
         FIG. 19A  and  FIG. 19B  illustrate a first pressure relief cut and a second pressure relief cut in a vane wing, respectively; 
         FIG. 20  illustrates a vane wing booster; 
         FIG. 21A  and  FIG. 21B  illustrate a swing vane and a set of swing vanes, respectively, in a rotary engine; 
         FIG. 22  illustrates a perspective view of a vane having a cap; 
         FIG. 23A  and  FIG. 23B  illustrate a dynamic vane cap in a high potential energy state for vane cap actuation and in a relaxed vane cap actuated state, respectively; 
         FIG. 24A  and  FIG. 24B  illustrate a cap bearing relative to a vane cap in an un-actuated state and actuated state, respectively; 
         FIG. 25  illustrates multiple axes vane caps; 
         FIG. 26  illustrates rotor caps; 
         FIG. 27  provides an illustrated perspective view of a vane having lip seals; 
         FIG. 28  provides an illustrated perspective view of a cap having a lip seal; 
         FIG. 29A  and  FIG. 29B  provide a perspective view of lip seals in a natural state and in a deformed state, respectively; 
         FIG. 30  provides an illustrated a cross-sectional view of a rotor having lip seals; 
         FIG. 31  provides an illustrated cross-sectional view of a rotary engine having an exhaust cut; 
         FIG. 32A  and  FIG. 32B  illustrates a perspective view and an end view, respectively, of exhaust cuts and exhaust ridges; 
         FIG. 33  illustrates an exhaust cut and an exhaust booster combination; 
         FIG. 34  illustrates a low friction rolling bearing at two time points; 
         FIG. 35A  and  FIG. 35B  provide an illustrated perspective view of a rotor vane insert and a spooling sheet thereof, respectively; 
         FIG. 36  A-D illustrate a spooling spring with a left of center cut-out,  FIG. 36A ; a right of center cut-out,  FIG. 36B ; a Fibonacci cut-out,  FIG. 36C , and a non-rectangular perimeter,  FIG. 36D ; 
         FIG. 37  illustrates an extending vane insert; 
         FIG. 38  illustrates vane channels relative to a vane insert; 
         FIG. 39  illustrates a non-linear spring vane insert; 
         FIG. 40  illustrates a human powered water propulsion unit; 
         FIG. 41  illustrates a paddle wheel; 
         FIG. 42  illustrates a guided paddle wheel blade; 
         FIG. 43  illustrates a co-rotatable expansion chamber and paddle wheel; and 
         FIG. 44  illustrates hinged paddle wheel blades. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The invention comprises a paddle board apparatus and method of use thereof, comprising: a manual crank connected to a drive shaft, a rotatable housing, and a set of paddle wheels connected to an outer surface of the rotatable housing, where a child manually turning the crank simultaneously propels the paddle board forward in water through use of the paddle wheels and drives an air pump in the rotatable housing to blow bubbles about the paddle board for enjoyment of the child riding the paddle board. 
     In one embodiment, the rotary engine includes one or more optional injection ports, such as a first injection port in an expansion chamber, a second injection port in the expansion chamber after a first rotation of the rotor, a third injection port into the expansion chamber after a second rotation of the rotor, a fourth injection port from a fuel path through a shaft of the rotary engine, and/or a fifth injection port into a rotor-vane slot between the rotor and a vane. Optionally, one or more of the injection ports are controlled through mechanical valving and/or through computer control. Optionally, the first, second, and/or third injection ports are through a first endplate of the rotary engine separating the rotor from the circumferential housing, through a second endplate parallel to the first endplate, and/or through the circumferential housing. 
     In another embodiment, the rotary engine uses a vane actuation system having a stressed band wound at least partially around two or more rollers in an enclosure to alternatingly extend or retract a vane toward a housing, thereby aiding in seal formation of the vane to the housing. 
     In still another embodiment, a rotary engine method and apparatus is configured with an exhaust system. The exhaust system includes an exhaust cut or exhaust channel into one or more of a housing or an endplate of the rotary engine, which interrupts the seal surface of the expansion chamber housing. The exhaust cut directs spent fuel from the rotary engine fuel expansion/compression chamber out of the rotary engine either directly or via an optional exhaust port and/or exhaust booster. The exhaust system vents fuel to atmosphere or into a condenser for recirculation of fuel in a closed-loop circulating rotary engine system. Exhausting the engine reduces back pressure on the rotary engine thereby enhancing rotary engine efficiency. 
     In another embodiment, a rotary engine method and apparatus is configured with at least one lip seal. A lip seal restricts fuel flow from a fuel compartment to a non-fuel compartment and/or fuel flow between fuel compartments, such as between a reference expansion chamber and any of an engine: rotor, vane, housing, a leading expansion chamber, and/or a trailing expansion chamber. Types of lip seals include: vane lip seals, rotor lip seals, and rotor-vane slot lip seals. Generally, lip seals dynamically move or deform as a result of fuel movement or pressure to seal a junction between a sealing surface of the lip seal and a rotary engine component. For example, a vane lip seal sealing to the inner housing dynamically moves along the y-axis until an outer surface of the lip seal seals to the housing. 
     In another embodiment, a rotary engine is configured with elements having cap seals. A cap seal restricts fuel flow from a fuel compartment to a non-fuel compartment and/or fuel flow between fuel compartments, such as between a reference expansion chamber and any of an engine: rotor, vane, housing, leading expansion chamber, and/or trailing expansion chamber. Types of caps include vane caps, rotor caps, and rotor-vane slot caps. For a given type of cap, optional sub-cap types exist. For example, types of vane caps include: vane-housing caps, vane-rotor-rotor caps, and vane-endplate caps. Generally, caps dynamically move or float to seal a junction between a sealing surface of the cap and a rotary engine component. For example, a vane cap sealing to the inner housing dynamically moves along the y-axis until an outer surface of the cap seals to the housing. Means for providing cap sealing force to seal the cap against a rotary engine housing element comprise one or more of: a spring force, a magnetic force, a deformable seal force, and a fuel force. The dynamic caps ability to trace a noncircular path is particularly beneficial for use in a rotary engine having an offset rotor and a non-circular inner rotary engine compartment having engine wall cut-outs and/or build-ups. Further, the dynamic sealing forces provide cap sealing forces over a range of temperatures and operating rotational engine speeds. 
     In yet another embodiment, preferably three or more swing vanes are used in the rotary engine to separate expansion chambers of the rotary engine. A swing vane pivots about a pivot point on the rotor. Since, the swing vane pivots with rotation of the rotor in the rotary engine, the reach of the swing vane between the rotor and housing ranges from a narrow thickness or width of the swing vane to the longer length of the swing vane. The dynamic pivoting of the swing vane yields an expansion chamber separator ranging from the short width of the vane to the longer length of the vane, which allows use of an offset rotor in the rotary engine. Optionally, and in addition, the swing vane dynamically extends to reach the inner housing of the rotary engine. For example, an outer sliding swing vane portion of the swing vane slides along the inner pivoting portion of the swing vane to dynamically lengthen or shorten the length of the swing vane. The combination of the pivoting and the sliding of the vane allows for use with a double offset rotary engine having housing wall cut-outs and/or buildups, which allows greater volume of the expansion chamber during the power stroke or power stroke phase of the rotary engine and corresponding increases in power and/or efficiency. 
     In still yet another embodiment, the vane reduces chatter or vibration of the vane-tips against the inner wall of the housing of the rotary engine during operation of the engine, where chatter leads to unwanted opening and closing of the seal between an expansion chamber and a leading chamber. For example, an actuator force forces the vane against the inner wall of the rotary engine housing, thereby providing a seal between the leading chamber and the expansion chamber of the rotary engine. The reduction of engine chatter increases engine power and/or efficiency. Further, the pressure relief aids in uninterrupted contact of the seals between the vane and inner housing of the rotary engine, which yields enhanced rotary engine efficiency. 
     In yet still another embodiment, a rotary engine is described having fuel paths that run through a portion of a rotor of the rotary engine and/or through a vane of the rotary engine. The fuel paths are optionally opened and shut as a function of rotation of the rotor to enhance power provided by the engine. The valving that opens and/or shuts a fuel path operates: (1) to equalize pressure between an expansion chamber and a rotor-vane chamber and/or (2) to control a booster, which creates a pressure differential resulting in enhanced flow of fuel. The fuel paths, valves, seals, and boosters are further described, infra. 
     In still another embodiment, a rotary engine is provided for operation on a re-circulating fuel expanding about adiabatically during a power stroke or during an expansion mode of the rotary engine. To aid the power stroke efficiency, the rotary engine preferably contains one or more of:
         a double offset rotor geometry relative to a housing;   use of a first cut-out in the engine housing at the initiation of the power stroke;   use of a build-up in the housing at the end of the power stroke; and/or   use of a second cut-out in the housing at the completion of rotation of the rotor in the engine.       

     Further, fuels described maintain about adiabatic expansion even with a high gas-to-liquid ratio when maintained at a relatively constant temperature via use of a temperature controller for the expansion chambers. Expansive forces of the fuel acting on the rotor are aided by hydraulic forces, vortical forces, an about Fibonacci-ratio increase in volume of an expansion chamber as a function of rotor rotation during the power stroke, sliding vanes, and/or swinging vanes between the rotor and housing. 
     In yet still another embodiment, permutations and/or combinations of any of the rotary engine elements described herein are used to increase rotary engine efficiency. 
     Rotary Engine 
     A rotary engine system uses power from an expansive force, such as from an internal or external combustion process, to produce an output energy, such as a rotational or electric force. 
     Referring now to  FIG. 1 , a rotary engine  110  is preferably a component of an engine system  100 . In the engine system  100 , fuel/gas/liquid in various states or phases is circulated in a circulation system  180 , illustrated figuratively. In the illustrated example, gas output from the rotary engine  110  is transferred to and/or through a condenser  120  to form a liquid; then through an optional reservoir  130  to a fluid heater  140  where the liquid is heated to a temperature and pressure sufficient to result in state change of the liquid to gas form when passed through an injector  160  and back into the rotary engine  110 . In one case, the fluid heater  140  optionally uses an external energy source  150 , such as radiation, vibration, and/or heat to heat the circulating fluid in an energy exchanger  142 . In a second case, the fluid heater  140  optionally uses fuel in an external combustion chamber  154  to heat the circulating fluid in the energy exchanger  142 . Optionally, the rotary engine comprises multiple rotors, where one of the rotors, such as a center rotor, is an element of an internal combustion engine. The rotary engine  110 , is further described infra. 
     Still referring to  FIG. 1 , the rotary engine  110  is optionally connected to and/or controlled by a main controller  170 , where the main controller is optionally any form of computer, software interface, and/or user interface. In one example, the main controller  170  controls sub-elements of the rotary engine  110 , such as rotation speed, one or more inlet ports, an injector  160 , one or more valves or gates, temperature, input fuel rate, and/or electromagnetic generation. The main controller  170  is additionally optionally linked to any outside system, such as the condenser  120 , the reservoir  130 , the fluid heater  140 , the external source  150 , one or more sensors  190 , and/or a temperature controller  172 . 
     Still referring to  FIG. 1 , maintenance of the rotary engine  110  at a set operating temperature enhances precision and/or efficiency of operation of the engine system  100 . Hence, the rotary engine  110  is optionally coupled to a temperature controller  172  and/or a block heater  175 . Preferably, the temperature controller senses with one or more sensors the temperature of the rotary engine  110  and controls a heat exchange element attached and/or indirectly attached to the rotary engine  110 , which maintains the rotary engine  110  at about a set point operational temperature. In a first scenario, the block heater  174  heats expansion chambers, described infra, to a desired operating temperature. The block heater  175  is optionally configured to extract excess heat from the fluid heater  140  to heat one or more elements of the rotary engine  110 , such as the rotor  320 , vanes, an inner wall of the housing, an inner wall of the first endplate  212 , and/or an inner wall of the second endplate  214 . 
     Referring now to  FIG. 2 , the rotary engine  110  includes a housing  210  on an outer side of a series of expansion chambers, a first endplate  212  affixed to a first side of the housing, and a second endplate  214  affixed to a second side of the housing. Combined, the housing  210 , first endplate  212 , second endplate  214 , and a rotor, described infra, contain a series of expansion chambers in the rotary engine  110 . An offset shaft preferably runs into and/or runs through the first endplate  212 , inside the housing  210 , and into and/or through the second endplate  214 . The offset shaft  220  is centered to the rotor  440  and is offset relative to the center of the rotary engine  110 . Preferably, the rotary engine operates at greater than about 100, 1,000, 5,000, 10,000, 15,000, or 20,000 revolutions per minute. 
     Still referring to  FIG. 2 , the rotary engine  110  is illustrated with an optional set of inlet ports  3910 , where fuel is injected into expansion chambers in a power stroke of the rotary engine  110 . The set of inlet ports  3910  are further described, infra. 
     Rotors 
     For rotor description, an x-, y-, z-axis system is used for description, where the z-axis runs parallel to the rotary engine shaft  220  and the x/y plane is perpendicular to the z-axis. For vane description, the x-, y-, z-axis system is redefined relative to a vane  450 , as described infra. 
     Rotors of various configurations are optionally used in the rotary engine  110 . The rotors are optionally offset in the x- and/or y-axes relative to a z-axis running along the length of the shaft  220 . The shaft  220  is optionally double walled or multi-walled. The outer edge or face  442  of the rotor forming an inner wall of the expansion chambers is of varying geometry. Examples of rotor configurations in terms of offsets and shapes are further described, infra. The examples are illustrative in nature and each element is optional and may be used in various permutations and/or combinations. 
     Vanes 
     A vane or blade separates two chambers of a rotary engine. The vane optionally functions as a seal and/or valve. The vane itself optionally functions as a lever, propeller, an impeller, and/or a turbine blade. 
     Engines are illustratively represented herein with clock positions, with 12 o&#39;clock being a top of a cross-sectional view of the engine with an axis normal to the view running along the length of the shaft  220  of the engine. The 12 o&#39;clock position is alternatively referred to as a zero degree position. Similarly 12 o&#39;clock to 3 o&#39;clock is alternatively referred to as zero degrees to ninety degrees and a full rotation around the clock covers three hundred sixty degrees. Those skilled in the art will immediately understand that any multi-axes illustration system is alternatively used to describe the engine and that rotating engine elements in this coordination system alters only the description of the elements without altering the function of the elements. 
     Referring now to  FIG. 3 , vanes relative to an inner wall  432  of the housing  210  and relative to a rotor  320  are described. As illustrated, the length of the shaft  220  runs normal to the illustrated cross-sectional view and the rotor  320  rotates around the shaft  220 . Vanes extend between the rotor  320  and the inner wall  432  of the housing  210 . As illustrated, the single offset rotor system  300  includes six vanes, with: a first vane  330  at a 12 o&#39;clock position, a second vane  340  at a 2 o&#39;clock position, a third vane  350  at a 4 o&#39;clock position, a fourth vane  360  at a 6 o&#39;clock position, a fifth vane  370  at a 8 o&#39;clock position, and a sixth vane  380  at a 10 o&#39;clock position. Any number of vanes are optionally used, such as about 2, 3, 4, 5, 6, 8, or more vanes. Preferably, an even number of vanes are used in the rotor system  300 . 
     Still referring to  FIG. 3 , the vanes extend outward from the single offset rotor  320  through vane slots. As illustrated, the first vane  330  extends from a first vane slot  332 , the second vane  340  extends from a second vane slot  342 , the third vane  350  extends from a third vane slot  352 , the fourth vane  360  extends from a fourth vane slot  362 , the fifth vane  370  extends from a fifth vane slot  372 , and the sixth vane  380  extends from a sixth vane slot  382 . Each of the vanes is slidingly coupled and/or coupled with a hinge to the single offset rotor  320  and the single offset rotor  320  is fixed and/or coupled to the shaft  220 . When the rotary engine is in operation, the single offset rotor  320 , vanes, and vane slots rotate about the shaft  220 . Hence, the first vane  330  rotates from the 12 o&#39;clock position sequentially through each of the 2, 4, 6, 8, and 10 o&#39;clock positions and ends up back at the 12 o&#39;clock position. When the rotary engine  210  is in operation, pressure upon the vanes causes the single offset rotor  320  to rotate relative to the non-rotating inner wall of the housing  432 , which causes rotation of shaft  220 . As the rotor  210  rotates, each vane slides outward to maintain contact with the inner wall of the housing  432 . 
     Still referring to  FIG. 3 , expansion chambers or sealed expansion chambers relative to an inner wall  432  of the housing  210 , vanes, and single offset rotor  320  are described. Generally, an expansion chamber  333  rotates about the shaft  220  during use. The expansion chamber  333  has a radial cross-sectional area and volume that changes as a function of rotation of the single offset rotor  320  about the shaft  220 . In the illustrated example, the rotary system is configured with six expansion chambers. Each of the expansion chambers reside in the rotary engine  110  along an axis between the first endplate  212  and the second endplate  214 . Further, each of the expansion chambers reside between the single offset rotor  320  and inner wall of the housing  432 . Still further, the expansion chambers are contained between the vanes. As illustrated, a first expansion chamber  335  is in a first volume between the first vane  330  and the second vane  340 , a second expansion chamber  345  is in a second volume between the second vane  340  and the third vane  350 , a third expansion chamber  355  is in a third volume between the third vane  350  and the fourth vane  360 , a fourth expansion chamber or first reduction chamber  365  is in a fourth volume between the fourth vane  360  and the fifth vane  370 , a fifth expansion chamber or second reduction chamber  375  is in a fifth volume between the fifth vane  370  and the sixth vane  380 , and a sixth expansion chamber or third reduction chamber  385  is in a sixth volume between the sixth vane  380  and the first vane  330 . As illustrated, the volume of the second expansion chamber  345  is greater than the volume of the first expansion chamber and the volume of the third expansion chamber is greater than the volume of the second expansion chamber. The increasing volume of the expansion chambers in the first half of a rotation of the single offset rotor  320  about the shaft  220  results in greater efficiency, power, and/or torque, as described infra. 
     Single Offset Rotor 
     Still referring to  FIG. 3 , a single offset rotor  320  is illustrated. The housing  210  has a center position. In a single offset rotor system, the shaft  220  running along the z-axis is offset along one of the illustrated x- or y-axes. For clarity of presentation, expansion chambers are referred to herein as residing in static positions and having static volumes, though they rotate about the shaft  220  and change in both volume and position with rotation of the single offset rotor  320  about the shaft  220 . As illustrated, the shaft  220  is offset along the y-axis, though the offset could be along any x-, y-vector. Without the offset along the y-axis, each of the expansion chambers is uniform in volume. With the offset, the second expansion chamber  345 , at the position illustrated, has a volume greater than the first expansion chamber  335  and the third expansion chamber  355  has a volume greater than that of the second expansion chamber  345 . The fuel mixture from the fluid heater or vapor generator  140  is injected via the injector  160  into the first expansion chamber  335 . As the rotor rotates, the volume of the expansion chambers increases, as illustrated in the static position of the second expansion chamber  345  and third expansion chamber  355 . The increasing volume allows an expansion of the fuel, such as a gas, liquid, vapor, and/or plasma, which preferably occurs adiabatically or about adiabatically. The expansion of the fuel releases energy that is forced against the vane and/or vanes, which results in rotation of the rotor. 
     Double Offset Rotor 
     Referring now to  FIG. 4 , the increasing volume of a given expansion chamber through the first half of a rotation of the rotor  440 , such as in the power stroke described infra, about the shaft  220  combined with the extension of the vane from the rotor shaft to the inner wall of the housing  432  results in a greater surface area for the expanding gas to exert force against resulting in rotation of the rotor  320 . The increasing surface area to push against in the first half of the rotation increases efficiency of the rotary engine  110 . For reference, relative to double offset rotary engines and rotary engines including build-ups and cutouts, described infra, the single offset rotary engine has a first distance, d 1 , at the 2 o&#39;clock position and a fourth distance, d 4 , between the rotor  440  and an inner wall  432  of the housing  420 . 
     Still referring to  FIG. 4 , a double offset rotary engine  400  is illustrated. To demonstrate the offset of the housing, three housing  210  positions are illustrated. Herein a specific version of a rotor  440  is the single offset rotor  320 . Preferably, the rotor  440  is a double offset rotor. The rotor  440  and vanes  450  are illustrated only for the double offset housing position  430 . In the first zero offset position, the first housing position  410  is denoted by a dotted line and the housing  210  is equidistant from the rotor  440  in the x-,y-plane. Stated again, in the first housing position, the rotor  440  is centered relative to the first housing position  410  about point CA. The centered first housing position  410  is non-functional. The single offset rotor position was described, supra, and illustrated in  FIG. 3 . The single offset housing position  420  is repeated and still illustrated as a dashed line in  FIG. 4 . The second housing position is a single offset housing position  420  centered at point CB′, which has an offset in only the y-axis versus the zero offset housing position  410 . A third preferred housing position is a double offset rotor position  430  centered at position ‘C’. The double offset housing position  430  is offset in both the x- and y-axes versus the zero offset housing position. The offset of the housing  430  in two axes relative to the longitudinal axis of the shaft  220  results in efficiency gains of the double offset rotary engine, as described supra. Generally, the use of a double offset rotor increases the volume capacity of the expansion side of the engine and increases the vane length resulting in greater power output without increase in the housing size of the rotary engine. 
     Rotors  440  and vanes  450  are illustrated in the rest of this document relative to the double offset housing position  430 , where the shaft  220  is offset from center in both the x- and y-axes relative to the housing  210 . 
     Still referring to  FIG. 4 , the rotor  440  optionally includes a plurality of rotor vane slots with a corresponding set of rotor vane bases  448 , one vane base for each vane. In the design of the double offset rotor position  430 , the plurality of rotor vane bases  448  are optionally within 10, 5, 2, or 1 percent of equidistant from an axial center position of the shaft  220 , which has multiple benefits including a balanced rotor, the ability to combine with housing build ups and cut-outs, described infra, and ease of manufacture. Further, in the design of the double offset rotor position  430 , each of the plurality of rotor vane bases  448  optionally vary in distance to the housing along respective central lines running up the rotor vane slots by greater than 10, 20, or 30 percent as a function of rotation of the rotor  440  about the shaft  200 . 
     Still referring to  FIG. 4 , the extended 2 o&#39;clock vane position  340  for the single offset rotor illustrated in  FIG. 3  is re-illustrated in the same position in  FIG. 4  as a dashed line with a first distance, d 1 , between the vane wing tip and the outer edge of the rotor  440 . It is observed that the extended 2 o&#39;clock vane position  450  for the double offset rotor has a longer distance, d 2 , between the vane wing tip and the outer edge of the rotor  440  compared with the first distance, d 1 , of the extended position of the vane in the single offset rotor. The larger extension, d 2 , yields a larger cross-sectional area for the expansive forces in the first expansion chamber  335  to act on, thereby resulting in larger turning forces from the expanding gas pushing on the rotor  440  and/or a greater torque against the vane due to the extension of vane  450  from the first distance, d 1 , to the longer distance, d 2 . Note that the illustrated rotor  440  in  FIG. 4  is illustrated with a curved surface  442  running from near a vane wing tip toward the shaft in the expansion chamber to increases expansion chamber volume and to allow a greater surface area for the expanding gases to operate on with a force vector, F. The curved surface  442  is of any specified geometry to set the volume of the expansion chamber  335 . Similar force and/or power gains are observed from the 12 o&#39;clock to 6 o&#39;clock position using the double offset rotary engine  400  compared to the single offset rotary engine  300 . 
     Still referring to  FIG. 4 , The fully extended 8 o&#39;clock vane  370  of the single offset rotor is re-illustrated in the same position in  FIG. 4  as a dashed image with distance, d 4 , between the vane wing tip and the outer edge of the rotor  440 . It is noted that the double offset housing  430  forces full extension of the vane to a smaller distance, d 5 , at the 8 o&#39;clock position between the vane wing tip and the outer edge of the rotor  440 . However, rotational forces are not lost with the decrease in vane extension at the 8 o&#39;clock position as the expansive forces of the gas fuel are expended by the 6 o&#39;clock position and the gases are vented before the 8 o&#39;clock position, as described supra. The detailed 8 o&#39;clock position is exemplary of the 6 o&#39;clock to 12 o&#39;clock positions. 
     The net effect of using a double offset rotary engine  400  is increased efficiency and power in the power stroke, such as from the 12 o&#39;clock to 6 o&#39;clock position or through about 180 degrees, using the double offset rotary engine  400  compared to the single offset rotary engine  300  without loss of efficiency or power from the 6 o&#39;clock to 12 o&#39;clock positions. 
     Cutouts, Build-ups, and Vane Extension 
       FIG. 3  and  FIG. 4  illustrate inner walls of housings  410 ,  420 , and  430  that are circular. However, an added power and/or efficiency advantage results from cutouts and/or buildups in the inner surface of the housing. For example, an x-, y-axes cross-section of the inner wall shape of the housing  210  is optionally non-circular, oval, egg shaped, cutout relative to a circle, and/or built up relative to a circle. For example, the inner wall has a shape correlated a rotating cam. 
     Referring now to  FIG. 5 , optional cutouts in the housing  210  are described. A cutout is readily understood as a removal of material from a circular inner wall of the housing; however, the material is not necessarily removed by machining the inner wall, but rather is optionally cast or formed in final form or is defined by the shape of an insert piece that fits along the inner wall  420  of the housing. For clarity, cutouts are described relative to the inner wall  432  of the double offset rotor housing  430 ; however, cutouts are optionally used with any housing  210 . The optional cutouts and build-ups described herein are optionally used independently or in combination. 
     Still referring to  FIG. 5 , a first optional cutout  510  is illustrated at about the 1 o&#39;clock to 3 o&#39;clock position of the housing  430 . To further clarify, a cut-out or lobe or vane extension limiter is optionally: (1) a machined away portion of an inner wall of the circular housing  430 ; (2) an inner wall housing  430  section having a greater radius from the center of the shaft  220  to the inner wall of the housing  430  compared with a non-cutout section of the inner wall housing  430 ; or is a section molded, cast, and/or machined to have a further distance for the vane  450  to slide to reach compared to a nominal circular housing. For clarity, only the 10 o&#39;clock to 2 o&#39;clock position of the double offset rotary engine  400  is illustrated. The first cutout  510  in the housing  430  is present in about the 12 o&#39;clock to 3 o&#39;clock position and preferably at about the 2 o&#39;clock position. Generally, the first cutout allows a longer vane  450  extension at the cutout position compared to the circular x-, y-cross-section of the housing  430 . To illustrate, still referring to  FIG. 5 , the extended 2 o&#39;clock vane position  340  for the double offset rotor illustrated in  FIG. 4  is re-illustrated in the same position in  FIG. 5  as a solid line image with distance, d 2 , between the vane wing tip and the outer edge of the rotor  440 . It is observed that the extended 2 o&#39;clock vane position  450  for the double offset rotor having cutout  510  has a longer distance, d 3 , between the vane wing tip and the outer edge of the rotor  440  compared with the extended position vane in the double offset rotor. The larger extension, d 3 , yields a larger cross-sectional area for the expansive forces in the first expansion chamber  335  to act on and a longer torque distance from the shaft, thereby resulting in larger turning forces from the expanding gas pushing on the rotor  440 . To summarize, the vane extension distance, d 1 , using a single offset rotary engine  300  is less than the vane extension distance, d 2 , using a double offset rotary engine  400 , which is less than vane extension distance, d 3 , using a double offset rotary engine with a first cutout as is observed in equation 1. 
         d   1   &lt;d   2   &lt;d   3   (eq. 1)
 
     Still referring to  FIG. 5 , a second optional cutout  520  is illustrated at about the 11 o&#39;clock position of the housing  430 . The second cutout  520  is present at about the 10 o&#39;clock to 12 o&#39;clock position and preferably at about the 11 o&#39;clock to 12 o&#39;clock position. Generally, the second cutout allows a vane having a wingtip, described supra, to physically fit between the rotor  440  and housing  430  in a double offset rotary engine  500 . The second cutout  520  also adds to the magnitude of the offset possible in the single offset engine  300  and in the double offset engine  400 , which increases distances d 2  and d 3 , as described supra. 
     Referring now to  FIG. 6 , an optional build-up  610  on the interior wall of the housing  430  is illustrated from an about 5 o&#39;clock to an about 7 o&#39;clock position of the engine rotation. The build-up  610  allows a greater offset of the rotor  440  along the y-axis. Without the build-up, a smaller y-axis offset of the rotor  440  relative to the housing  430  is needed as the vane  450  at the 6 o&#39;clock position would not reach the inner wall of the housing  430  without the build-up  610 . As illustrated, the build-up  610  reduces the vane extension distance required for the vane  450  to reach from the rotor  440  to the housing  430  from a sixth distance, d 6 , to a seventh distance, d 7 . As described, supra, the greater offset in the x- and y-axes of the rotor  440  relative to an inner wall of the housing  432  yields enhanced rotary engine  110  output power and/or efficiency by increasing the volume of the first expansion chamber  335 , second expansion chamber  345 , and/or third expansion chamber  345 . Herein, the inner wall of the housing  432  refers to the inner wall of housing  210 , regardless of rotor offset position, use of housing cut-outs, and/or use of a housing build-up. 
     Method of Operation 
     For the purposes of this discussion, any of the single offset-rotary engine  300 , double offset rotary engine  400 , rotary engine having a cutout  500 , rotary engine having a build-up  600 , or a rotary engine having one or more elements described herein is applicable to use as the rotary engine  110  used in this example. Further, any housing  210 , rotor  440 , and vane  450  dividing the rotary engine  110  into expansion chambers is optionally used as in this example. For clarity, a reference expansion chamber  333  is used to describe a current position of the expansion chambers. For example, the reference chamber  333  rotates in a single rotation from the 12 o&#39;clock position and sequentially through the 1 o&#39;clock position, 3 o&#39;clock position, 5 o&#39;clock position, 7 o&#39;clock position, 9 o&#39;clock position, and 11 o&#39;clock position before returning to the 12 o&#39;clock position. 
     Referring now to  FIG. 7 , a flow chart of an operation process  700  of the rotary engine system  100  in accordance with a preferred embodiment is described. Process  700  describes the operation of rotary engine  110 . 
     Initially, a fuel and/or energy source is provided  710 . The fuel is optionally from the external energy source  150 . The energy source  150  is a source of: radiation, such as solar; vibration, such as an acoustical energy; and/or heat, such as convection. Optionally the fuel is from an external combustion chamber  154 . 
     Throughout operation process  700 , a first parent task circulates the fuel  760  through a closed loop. The closed loop cycles sequentially through: heating the fuel  720 ; injecting the fuel  730  into the rotary engine  110 ; expanding the fuel  742  in the reference expansion chamber; one or both of exerting an expansive force  743  on the rotor  440  and exerting a vortical force  744  on the rotor  440 ; rotating the rotor  746  to drive an external process, described infra; exhausting the fuel  748 ; condensing the fuel  750 , and repeating the process of circulating the fuel  760 . Preferably, the external energy source  150  provides the energy necessary in the heating the fuel step  720 . Individual steps in the operation process are further described, infra. 
     Throughout the operation process  700 , an optional second parent task maintains temperature  770  of at least one component of the rotary engine  110 . For example, a sensor senses engine temperature  772  and provides the temperature input to a controller of engine temperature  774 . The controller directs or controls a heater  776  to heat the engine component. Preferably, the temperature controller  770  heats at least the first expansion chamber  335  to an operating temperature in excess of the vapor-point temperature of the fuel. Preferably, at least the first three expansion chambers  335 ,  345 ,  355  are maintained at an operating temperature exceeding the vapor-point of the fuel throughout operation of the rotary engine system  100 . Preferably, the fluid heater  140  is simultaneously heating the fuel to a temperature about proximate or less than the vapor-point temperature of fluid. Hence, when the fuel is injected through the injector  160  into the first expansion chamber  335 , the fuel flash vaporizes exerting expansive force  743 , causing the rotor  440  to rotate and/or starts to rotate within the reference chamber due to reference chamber geometry and rotation of the rotor to form the vortical force  744  forces the rotor  440  to rotate. 
     The fuel is optionally any fuel that expands into a vapor, gas, and/or gas-vapor mix where the expansion of the fuel releases energy used to drive the rotor  440 . The fuel is preferably a liquid component and/or a fluid that phase changes to a vapor phase at a very low temperature and has a significant vapor expansion characteristic. Fuels and energy sources are further described, infra. 
     In task  720 , the fluid heater  140  preferably superheats the fuel to a temperature greater than or equal to a vapor-point temperature of the fuel. For example, if a plasmatic fluid is used as the fuel, the fluid heater  140  heats the plasmatic fluid to a temperature greater than or equal to a vapor-point temperature of plasmatic fluid. 
     In a task  730 , the injector  160  injects the heated fuel, via a first inlet port  162 , also referred to herein as the first fuel inlet port, into the reference cell  333 , which is the first expansion chamber  335  at time of fuel injection into the rotary engine  110 . The first inlet port  162  is optionally a port through one or more of: (1) the housing  210 , (2) the first endplate  212 , and (3) the second endplate  214  into the reference cell  333 . Because the fuel is superheated, or in the case of a cryogenic fuel super-cooled, the fuel flash-vaporizes and expands  742 , which exerts one of more forces on the rotor  440 . A first force is an expansive force  743  resultant from the phase change of the fuel from predominantly a liquid phase to substantially a vapor and/or gas phase. The expansive force acts on the rotor  440  as described, supra, and is represented by force, F, in  FIG. 4  and is illustratively represented as expansive force vectors  620  in  FIG. 6 . A second force is a vortical force  744  exerted on the rotor  440 . The vortical force  744  is resultant of geometry of the reference cell, which causes a vortex or rotational movement of the fuel in the chamber based on the geometry of the inlet port and/or injection port, rotor outer wall  442  of the rotor  440 , inner wall  432  of the housing  210 , first endplate  212 , second endplate  214 , and the extended vane  450  and is illustratively represented as vortex force vectors  625  in  FIG. 6 . A third force is a hydraulic force of the fuel pushing against the leading vane as the inlet preferably forces the fuel into the leading vane upon injection of the fuel  730 . The hydraulic force exists early in the power stroke before the fluid is flash-vaporized. All of the hydraulic force, the expansive force vectors  620 , and vortex force vectors  625  optionally exist simultaneously in the reference cell  333 , in the first expansion chamber  335 , second expansion chamber  345 , and third expansion chamber  355 . Hydraulic forces are optionally achieved in the second and/or third expansion chambers  335 ,  345  through use of second and third fuel inlet ports to the second and third expansion chambers  335 ,  345 , respectively. 
     When the fuel is introduced into the reference cell  333  of the rotary engine  110 , the fuel begins to expand hydraulically and/or about adiabatically in a task  740 . The expansion in the reference cell begins the power stroke or power cycle of engine, described infra. In a task  746 , the hydraulic and about adiabatic expansion of fuel exerts the expansive force  743  upon a leading vane  450  or upon the surface of the vane  450  bordering the reference cell  333  in the direction of rotation  390  of the rotor  440 . Simultaneously, in a task  744 , a vortex generator, generates a vortex  625  within the reference cell, which exerts a vortical force  744  upon the leading vane  450 , which exceed the vortical force applied to the trailing chamber due to the larger surface area of the leading vane. The vortical force  744  adds to the expansive force  743  and contributes to rotation  390  of rotor  450  and shaft  220 . Alternatively, either the expansive force  743  or vortical force  744  causes the leading vane  450  to move in the direction of rotation  390  and results in rotation of the rotor  746  and shaft  220 . Examples of a vortex generator include: an aerodynamic fin, a vapor booster, a vane wingtip, expansion chamber geometry, valving, first inlet port  162  orientation, an exhaust port booster, and/or power shaft injector inlet. 
     The about adiabatic expansion resulting in the expansive force  743  and the generation of a vortex resulting in the vortical force  744  continue throughout the power cycle of the rotary engine, which is nominally complete at about the 6 o&#39;clock position of the reference cell. Thereafter, the reference cell progressively decreases in volume, as in the first reduction chamber  365 , second reduction chamber  375 , and third reduction chamber  385 . In a task  748 , the fuel is exhausted or released  748  from the reference cell, such as through exhaust grooves cut through the housing  210 , the first endplate  212 , and/or the second endplate  214  at or about the 6 o&#39;clock to 8 o&#39;clock position. The exhausted fuel is optionally discarded in a non-circulating system. Preferably, the exhausted fuel is condensed  750  to liquid form in the condenser  120 , optionally stored in the reservoir  130 , and re-circulated  760 , as described supra. 
     Still referring to  FIG. 7 , the main controller  170  optionally controls any of the steps of providing fuel  710 , heating the fuel  720 , injecting the fuel  730 , operating the rotary engine, condensing the fuel  750 , circulating the fuel  760 , controlling temperature  770 , and/or controlling electrical output. 
     Fuel 
     Fuel is optionally any liquid or liquid/solid mixture that expands into a vapor, vapor-solid, gas, compressed gas, gas-solid, gas-vapor, gas-liquid, gas-vapor-solid mix where the expansion of the fuel releases energy used to drive the rotor  440 . The fuel is preferably substantially a liquid component and/or a fluid that phase changes to a vapor phase at a very low temperature and has a significant vapor expansion characteristic. Additives, such as deuterium or deuterium oxide, into the fuel and/or mixtures of fuels include any permutation and/or combination of fuel elements described herein. A first example of a fuel is any fuel that both phase changes to a vapor at a very low temperature and has a significant vapor expansion characteristic for aid in driving the rotor  440 , such as a nitrogen and/or an ammonia-based fuel. A second example of a fuel is a diamagnetic liquid fuel. A third example of a fuel is a liquid having a permeability of less than that of a vacuum and that has an induced magnetism in a direction opposite that of a ferromagnetic material. A fourth example of a fuel is a fluorocarbon, such as Fluorinert liquid FC-77® ( 3 M, St. Paul, Minn.), 1,1,1,3,3-pentafluoropropane, and/or Genetron® 245fa (Honeywell, Morristown, N.J.). A fifth example of a fuel is a plasmatic fluid composed of a non-reactive liquid component to which a solid component is added. The solid component is optionally a particulate held in suspension within the liquid component. Preferably the liquid and solid components of the fuel have a low coefficient of vaporization and a high heat transfer characteristic making the plasmatic fluid suitable for use in a closed-loop engine with moderate operating temperatures, such as below about 400° C. (750° F.) at moderate pressures. The solid component is preferably a particulate paramagnetic substance having non-aligned magnetic moments of the atoms when placed in a magnetic field and that possess magnetization in direct proportion to the field strength. An example of a paramagnetic solid additive is powdered magnetite (Fe 3 O 4 ) or a variation thereof. The plasmatic fluid optionally contains other components, such as an ester-based fuel lubricant, a seal lubricant, and/or an ionic salt. The plasmatic fluid preferably comprises a diamagnetic liquid in which a particulate paramagnetic solid is suspended, such as when the plasmatic fluid is vaporized the resulting vapor carries a paramagnetic charge, which sustains an ability to be affected by an electromagnetic field. That is, the gaseous form of the plasmatic fluid is a current-carrying plasma and/or an electromagnetically responsive vapor fluid. The exothermic release of chemical energy of the fuel is optionally used as a source of power. 
     The fuel is optionally an electromagnetically responsive fluid and/or vapor. For example, the electromagnetically responsive fuel contains one or more of: a salt and a paramagnetic material. 
     The engine system  100  is optionally run in either an open loop configuration or a closed loop configuration. In the open loop configuration, the fuel is consumed and/or wasted. In the closed loop, the fuel is consumed and/or re-circulated. 
     Power Stroke 
     The power stroke of the rotary engine  110  occurs when the fuel is expanding exerting the expansive force  743  and/or is exerting the vortical force  744 . In a first example, the power stroke occurs from through about the first 180 degrees of rotation, such as from about the 12 o&#39;clock position to the about 6 o&#39;clock position. In a second example, the power stroke or a power cycle occurs through about 360 degrees of rotation. In a third example, the power stroke occurs from when the reference cell is in approximately the 1 o&#39;clock position until when the reference cell is in approximately the 6 o&#39;clock position. From the 1 o&#39;clock to 6 o&#39;clock position, the reference chamber  333  preferably increases continuously in volume, in a cross-sectional solid angle from the shaft  220  to the housing  210 . 
     The increase in volume allows energy to be obtained from the combination of vapor hydraulics, adiabatic expansion forces  743 , and/or the vortical forces  744  as greater surface areas on the leading vane are available for application of the applied force backed by simultaneously increasing volume of the reference chamber  333 . To maximize use of energy released by the vaporizing fuel, preferably the curvature of housing  210  relative to the rotor  450  results in a radial cross-sectional distance or a radial cross-sectional area that has a volume of space within the reference cell that increases at about a golden ratio, ϕ, as a function of radial angle. The golden ratio is defined as a ratio where the lesser is to the greater as the greater is to the sum of the lesser plus the greater, equation 2. 
     
       
         
           
             
               
                 
                   
                     a 
                     b 
                   
                   = 
                   
                     b 
                     
                       a 
                       + 
                       b 
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                     . 
                     
                         
                     
                      
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Assuming the lesser, a, to be unity, then the greater, b, becomes ϕ, as calculated in equations 3 to 5. 
     
       
         
           
             
               
                 
                   
                     1 
                     φ 
                   
                   = 
                   
                     φ 
                     
                       1 
                       + 
                       φ 
                     
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                     . 
                     
                         
                     
                      
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     φ 
                     2 
                   
                   = 
                   
                     φ 
                     + 
                     1 
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                     . 
                     
                         
                     
                      
                     4 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       φ 
                       2 
                     
                     - 
                     φ 
                     - 
                     1 
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   
                     eq 
                     . 
                     
                         
                     
                      
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
     Using the quadratic formula, limited to the positive result, the golden ratio is about 1.618, which is the Fibonacci ratio, equation 6. 
     
       
         
           
             
               
                 
                   φ 
                   = 
                   
                     
                       
                         1 
                         + 
                         
                           5 
                         
                       
                       2 
                     
                     ≅ 
                     1.618033989 
                   
                 
               
               
                 
                   ( 
                   
                     eq 
                     . 
                     
                         
                     
                      
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     Hence, the cross-sectional area of the reference chamber  333  as a function of rotation or the surface area of the leading vane  450  as a function of rotation is preferably controlled by geometry of the rotary engine  110  to increase at a ratio of about 1.4 to 1.8 and more preferably to increase with a ratio of about 1.5 to 1.7, and still more preferably to increase at a ratio of about 1.618 through any of the power stroke from the about 1 o&#39;clock to about the 6 o&#39;clock position. More generally, at any position within the power stroke of the rotary engine, the radial cross-sectional area of a plane swept by the vane  450  between the center of the shaft  220  and the housing  210  increases from a first area to a second area by within 10, 5, 2, and/or 1 percent of 1.618 as a function of rotation of 1, 2, 3, 5, 10, 15, 30, 45, 60, and/or 90 degrees. 
     The ratio is controlled by a combination of one or more of use of: the double offset rotor geometry  400 , use of the first cut-out  510  in the housing  210 , use of the build-up  610  in the housing  210 , and/or use of the second cut-out  520  in the housing. Further, the fuels described maintain about adiabatic expansion to a high ratio of gas/liquid when maintained at a relatively constant temperature by the temperature controller  172 . 
     Expansion Volume 
     Referring now to  FIG. 8 , an expansion volume of a chamber  800  preferably increases as a function of radial angle through the power stroke/expansion phase of the expansion chamber of the rotary engine, such as from about the 12 o&#39;clock position through about the 6 o&#39;clock position, where the radial angle, e, is defined by two hands of a clock having a center. Illustrative of a chamber volume, the expansion chamber  333  is illustrated between: an outer rotor surface  442  of the rotor  440 , the inner wall of the housing  410 , a trailing vane  451 , and a leading vane  453 . The trailing vane  451  has a trailing vane chamber side  455  and the leading vane  453  has a leading vane chamber side  454 . It is observed that the expansion chamber  333  has a smaller interface area  810 , A 1 , with the trailing vane chamber side  455  and a larger interface area  812 , A 2 , with the leading vane chamber side  454 . Fuel expansion forces applied to the rotating vanes  451 ,  453  are proportional to the interface area. Thus, the trailing vane interface area  810 , A 1 , experiences expansion force 1, F 1 , and the leading vane interface area  812 , A 2 , experience expansion force 2, F 2 . Hence, the net rotational force, F T , is about the difference in the forces, according to equation 7. 
         F   T   ≅F   2   −F   1   (eq. 7)
 
     The force calculation according to equation 7 is an approximation and is illustrative in nature. However, it is readily observed that the net turning force in a given expansion chamber  333  is the difference in expansive force applied to the leading vane  453  and the trailing vane  451 . Hence, the use of the any of: the single offset rotary engine  300 , the double offset rotary engine  400 , the first cutout  510 , the build-up  610 , and/or the second cutout  520 , which allow a larger cross-section of the expansion chamber  333  as a function of radial angle yields more net turning forces on the rotor  440 . Referring now to  FIG. 9 , to further illustrate, the cross-sectional area of the expansion volume  333  described in  FIG. 8  is illustrated in  FIG. 9  at three radial positions. In the first radial position, the cross-sectional area of the expansion volume  333  is illustrated as the area defined by points B 1 , C 1 , F 1 , and E 1 . The cross-sectional area of the expansion chamber  333  is observed to expand at a second radial position as illustrated by points B 2 , C 2 , F 2 , and E 2 . The cross-sectional area of the expansion chamber  333  is observed to still further expand at a third radial position as illustrated by points B 3 , C 3 , F 3 , and E 3 . Hence, as described supra, the net rotational force turns the rotor  440  due to the increase in cross-sectional area of the expansion chamber  333  as a function of radial angle. 
     Referring still to  FIG. 9 , a rotor cutout expansion volume is described that yields a yet larger net turning force on the rotor  440 . As illustrated in  FIG. 3 , the outer surface of rotor  320  is circular. As illustrated in  FIG. 4 , the outer surface of the rotor  442  is optionally shaped to increase the distance between the outer surface of the rotor and the inner wall of the housing  432  as a function of radial angle through at least a portion of a expansion chamber  333 . Optionally, the rotor  440  has an outer surface proximate the expansion chamber  333  that is concave. Preferably, the outer wall of rotor  440  includes walls next to each of: the endplates  212 ,  214 , the trailing edge of the rotor, and the leading edge of the rotor. The concave rotor chamber is optionally described as a rotor wall cavity, a ‘dug-out’ chamber, or a chamber having several sides partially enclosing an expansion volume larger than an expansion chamber having an inner wall of a circular rotor. The ‘dug-out’ volume optionally increases as a function of radial angle within the reference expansion cell, illustrated as the expansion chamber or expansion cell  333 . Referring still to  FIG. 9 , the ‘dug-out’ rotor  444  area of the rotor  440  is observed to expand with radial angle theta and is illustrated at the same three radial angles as the expansion volume cross-sectional area. In the first radial position, the cross-section of the ‘dug-out’ rotor  444  area is illustrated as the area defined by points A 1 , B 1 , E 1 , and D 1 . The cross-sectional area of the ‘dug-out’ rotor  440  volume is observed to expand at the second radial position as illustrated by points A 2 , B 2 , E 2 , and D 2 . The cross-sectional area of the ‘dug-out’ rotor  444  is observed to still further expand at the third radial position as illustrated by points A 3 , B 3 , E 3 , and D 3 . Hence, as described supra, the rotational forces applied to the leading rotor surface exceed the forces applied to the trailing rotor edge yielding a net expansive force applied to the rotor  440 , which adds to the net expansive forces applied to the vane, F T , which turns the rotor  440 . The ‘dug-out’ rotor  444  volume is optionally machined or cast at time of rotor creation and the term ‘dug-out’ is descriptive in nature of shape, not of a manufacturing process of producing the dug-out rotor  444 . 
     The overall volume of the expansion chamber  333  is increased by removing a portion of the rotor  440  to form the dug-out rotor. The increase in the overall volume of the expansion chamber using a dug-out rotor enhances rotational force of the rotary engine  110  and/or efficiency of the rotary engine. 
     Vane Valves/Seals 
     Fuel Routing Valves/Seals 
     Referring now to  FIG. 10A ,  FIG. 10B , and  FIG. 14B , in another embodiment, gas, expanding gas, vapor, and/or fluid fuels are routed from an expansion chamber  333  through one or more rotor conduits  1020  leading from the expansion chamber  333  to the rotor-vane chamber  452  or rotor-vane slot on a shaft  220  side of the vane  450  in the rotor guide. The expanding fuel optionally runs through the rotor  440  to the rotor-vane chamber  452 ; into the vane  450  and/or into a tip of the vane  450 ; and into the expansion chamber  333 . Fuel routing paths additionally optionally run through the shaft  220  of the rotary engine  110 , through piping  1510 , which is optionally thorium coated, and into the rotor-vane chamber  452 . Any of the fuel routing paths are optionally controlled, such as a function of time, rotation, power demand, and/or load, using valves and/or seals as further described, infra. 
     Valves 
     Referring now to  FIG. 10A  and  FIG. 11 , one or more rotary engine valves  1010  are used to direct and/or time flow of the fuel through one or more elements of the rotary engine  110 . To illustrate, several non-limiting examples are provided. In a first example of a rotary engine valve  1010 , a rotor conduit valve  1012  is used to control timing of flow of fuel through a first rotor conduit  1022 , further described infra, into a rotor-vane chamber  452 , further described infra, and subsequently into any passageway leading therefrom. In a second example of a rotary engine valve  1010 , a shaft fuel conduit inlet port, referred to herein as a second inlet port  1014  or second fuel inlet port, is used to control flow of fuel anywhere through a passageway leading through the shaft  220  and subsequently through the vane  450 . In a third example, the rotary engine valves are optionally positioned in: (1) the rotor  440 , such as in a rotor conduit  1020 ; (2) in a vane  450 , such as in a vane conduit, a vane base, a vane head, a vane wing, a trailing vane side; and/or (3) in the shaft  220 , such as in a shaft passageway. Any of the rotary engine valves  1010  are optionally controlled by the main controller  170 . Optionally, the main controller  170  times/sequences opening and/or closing of one or more of the rotary engine valves as a function of: (1) provided power to the rotary engine; (2) rotational velocity of the rotor  440  about the shaft  220 ; (3) a sensed temperature from a temperature sensor or probe, such as a from one or more of: an auxiliary fuel temperature sensor, an inlet port temperature sensor, an expansion chamber temperature sensor, a rotor temperature sensor, a vane temperature sensor, a shaft temperature sensor, and/or an exhaust port temperature sensor; and/or (4) a power load demand. 
     Seals 
     Referring now to  FIG. 10B , an example of a vane  450  is provided. Preferably, the vane  450  includes a plurality of seals, such as: a lower trailing vane seal  1026 , a lower leading seal  1027 , an upper trailing seal  1028 , an upper leading seal  1029 , an inner seal, and/or an outer seal. The lower trailing seal  1026  and lower leading seal  1028  are preferably (1) attached to the vane  450  and (2) move or slide with the vane  450 . The upper trailing seal  1028  and upper leading seal  1029  are (1) preferably attached to the rotor  440  and (2) do not move relative to the rotor  440  as the vane  450  moves. Both the lower trailing seal  1026  and upper trailing seal  1028  optionally operate as valves, as described infra. Each of the seals  1026 ,  1027 ,  1028 ,  1029  restrict and/or stop expansion of the fuel between the rotor  440  and vane  450 . 
     Seals/Valves 
     One or more seals of the plurality of seals optionally/additionally function as valves. Particularly, as the seal translates along an axis, the seal functions as a valve by moving across a fuel and/or expansion fuel route. For example, as the vane  450  and lower trailing vane seal  1026  retracts into the rotor-vane chamber  452  the lower trailing vane seal  1026  optionally functions as a valve by closing a rotor passageway, such as the first rotor conduit  1022 , and subsequently again functions as a valve by opening the rotor passageway when the vane  450  moves outward away from the rotor vane base  448 . The use of one or more seals functioning as valves in the rotary engine  110  is further described, infra. 
     Referring again to  FIG. 11 , an example of a rotor  440  having fuel routing paths  1100  is provided. The fuel routing paths, valves, and seals are all optional. Upon expansion and/or flow, fuel in the expansion chamber  333  enters into a first rotor conduit, tunnel, or fuel pathway running from the expansion chamber  333  or rotor dug-out chamber  444  to the rotor-vane chamber  452 . The rotor-vane chamber  452 : (1) aids in guiding movement of the vane  450  and (2) optionally provides a partial containment chamber for fuel from the expansion chamber  333  as described herein and/or as a partial containment chamber from fuel routed through the shaft  220 , as described infra. 
     In an initial position of the rotor  440 , such as for the first expansion chamber at about the 2 o&#39;clock position, the first rotor conduit  1022  terminates at the lower trailing vane seal  1026 , which prevents further expansion and/or flow of the fuel through the first rotor conduit  1022 . Stated again, the lower trailing vane seal  1026  functions as a valve that is off or closed at about the 2 o&#39;clock position and is on or open at a later position in the power stroke of the rotary engine  110 , as described infra. The first rotor conduit  1022  optionally runs from any portion of the expansion chamber  333  to the rotor vane guide, but preferably runs from the expansion chamber dug-out volume  444  of the expansion chamber  333  to an entrance port sealed by either the vane body  1610  or lower trailing vane seal  1026 . When the entrance port is open, the fuel runs through the first rotor conduit  1022  into the rotor vane guide or rotor-vane chamber  452  on an inner radial side of the vane  450 , which is the side of the vane closest to the shaft  220 . The cross-sectional geometry of the first rotor conduit  1022  is preferably circular, but is optionally of any geometry. An optional second rotor conduit  1024  runs from the expansion chamber  333  to the first rotor conduit  1022 . Preferably, the first rotor conduit  1022  includes a cross-sectional area at least twice that of a cross-sectional area of the second rotor conduit  1024 . The intersection of the first rotor conduit  1022  and second rotor conduit  1024  is further described, infra. 
     As the rotor  440  rotates, such as to about the 4 o&#39;clock position, the vane  450  extends toward the housing  430 . As described supra, the lower trailing vane seal  1026  is preferably affixed to the vane  450  and hence moves, travels, translates, and/or slides with the vane  450 . The extension of the vane  450  results in outward radial movement of the lower vane seals  1026 ,  1027 . Outward radial movement of the lower trailing vane seal  1026  opens a pathway, such as opening of a valve, at the lower end of the first rotor conduit  1022  into the rotor-vane chamber  452  or the rotor guiding channel on the shaft  220  side of the vane  450 . Upon opening of the lower trailing vane seal or valve  1026 , the expanding fuel enters the rotor-vane chamber  452  behind the vane and the expansive forces of the fuel aid centrifugal forces in the extension of the vane  450  toward the inner wall of the housing  430 . The lower vane seals  1026 ,  1027  hinders and preferably stops flow of the expanding fuel about outer edges of the vane  450 . As described supra, the upper trailing vane seal  1028  is preferably affixed to the rotor  440 , which results in no movement of the upper vane seal  1028  with movement of the vane  450 . The optional upper vane seals  1028 ,  1029  hinders and preferably prevents direct fuel expansion from the expansion chamber  333  into a region between the vane  450  and rotor  440 . 
     As the rotor  440  continues to rotate, the vane  450  maintains an extended position keeping the lower trailing vane seal  1028  in an open position, which maintains an open aperture at the terminal end of the first rotor conduit  1022 . As the rotor  440  continues to rotate, the inner wall  432  of the housing  430  forces the vane  450  back into the rotor guide, which forces the lower trailing vane seal  1026  to close or seal the terminal aperture of the first rotor conduit  1022 . 
     During a rotation cycle of the rotor  440 , the first rotor conduit  1022  provides a pathway for the expanding fuel to push on the back of the vane  450  during the power stroke. The moving lower trailing vane seal  1026  functions as a valve opening the first rotor conduit  1022  near the beginning of the power stroke and further functions as a valve closing the rotor conduit  1022  pathway near the end of the power stroke. 
     Referring now to  FIG. 12 , concurrently, the upper trailing vane seal  1028  functions as a second valve. The upper trailing vane seal  1028  valves an end of the vane conduit  1025  proximate the expansion chamber  333 . For example, at about the 10 o&#39;clock and 12 o&#39;clock positions, the upper trailing vane seal  1028  functions as a closed valve to the vane conduit  1025 . Similarly, in the about 4 o&#39;clock and 6 o&#39;clock positions, the upper trailing vane seal functions as an open valve to the vane conduit  1025 . 
     In one embodiment, a distance between vanes seals periodically varies as a function of rotation of the rotor  440  about the shaft  220 . For example, the distance between the upper trailing vane seal  1028  and lower trailing vane seal  1026  is at a minimum distance when the vane  450  is fully extended and at a maximum distance, at least 200, 300, and/or 400 percent of the minimum distance, when the vane  450  is fully retracted. The distance similarly varies between the upper leading vane seal  1029  and lower leading vane seal  1027 . 
     Optionally, the expanding fuel is routed through at least a portion of the shaft  220  to the rotor-vane chamber  452  in the rotor guide on the inner radial side of the vane  450 , as discussed infra. 
     Referring now to  FIG. 11B , nonlinearity of size of the reference chamber  333  as a function of rotation is further described. As described, supra, the reference chamber  333  expands in cross-sectional area and/or in total volume as the rotor  440  turns through the power stroke. Here, vane extension or inter-vane seal distance is quantified by use of a distance between two seals, one affixed to the rotor  440  that does not move radially and one affixed to the vane  450 , that varies in radial position from the shaft  220  as a function of rotation of the rotor  440 . In this example, the relative distance between the lower trailing vane seal  1026  and upper trailing vane seal  1024  is plotted as a function of rotor clock position. Several features of the design of the rotary engine  110  are demonstrated. First, the greatest rate of expansion of the inter-vane seal distance as a function of rotation occurs in the power stroke, such as represented by slope m 1  in  FIG. 11B . Second, an intra-vane seal distance of greater than fifty percent of maximum is represented by greater than one-half of all clock positions. 
     Vane Conduits 
     Referring again to  FIG. 12 , in yet another embodiment the vane  450  includes a fuel conduit  1200 . In this embodiment, expanding fuel moves from the rotor-vane chamber  452  in the rotor guide at the inner radial side of the vane  450  into one or more vane conduits. Preferably 2, 3, 4 or more vane conduits are used in the vane  450 . For clarity, a single vane conduit is used in this example. The single vane conduit, first vane conduit  1025 , flows about longitudinally along or through at least fifty percent of the length of the vane  450  and terminates along a trailing edge of the vane  450  into the expansion chamber  333 . Hence, fuel runs and/or expands sequentially: from the first inlet port  162 , through the expansion chamber  333 , through a rotor conduit  1020 , such as the first rotor conduit  1022  and/or second rotor conduit  1024 , to the rotor-vane chamber  452  at the inner radial side of the vane  450 , through a portion of the vane in the first vane conduit  1025 , and exits or returns into the same expansion chamber  333 . The exit of the first vane conduit  1025  from the vane  450  back to the expansion chamber  333 , which is additionally referred to as the trailing expansion chamber  333 , is optionally through a vane exit port on the trailing edge of the vane and/or through a trailing portion of the T-form vane head. The expanding fuel exiting the vane provides a rotational force aiding in rotation  390  of the rotor  450  about the shaft  220 . Either the rotor  440  body or the upper trailing vane seal  1028  controls timing of opening and closing of a pressure equalization path between the expansion chamber  333  and the rotor-vane chamber  452 . Preferably, the exit port from the vane conduit to the trailing expansion chamber  333  couples two vane conduits into a vane flow booster  1340 . The vane flow booster  1340  is a species of a flow booster  1300 , described infra. The vane flow booster  1340  uses fuel expanding and/or flowing in a first vane flow path in the vane to accelerate fuel expanding into the expansion chamber  333 . 
     Flow Booster 
     Referring now to  FIG. 13 , an optional flow booster  1300  or amplifier accelerates movement of the gas/fuel in the first rotor conduit  1022 . In this description, the flow booster is located at the junction of the first rotor conduit  1022  and second rotor conduit  1024 . However, the description applies equally to flow boosters located at one or more exit ports of the fuel flow path exiting the vane  450  into the trailing expansion chamber  333 . In this example, fuel in the first rotor conduit  1022  optionally flows from a region having a first cross-sectional distance  1310 , d 1 , through a region having a second cross-sectional distance  1320 , d 2 , where d 1 &gt;d 2 . At the same time, fuel and/or expanding fuel flows through the second rotor conduit  1024  and optionally circumferentially encompasses an about cylindrical barrier separating the first rotor conduit  1022  from the second rotor conduit  1024 . The fuel in the second rotor conduit  1024  passes through an exit port  1330  and mixes and/or forms a vortex with the fuel exiting out of the cylindrical barrier in the first rotor conduit  1022 , which accelerates the fuel traveling through the first rotor conduit  1022 . 
     Branching Vane Conduits 
     Referring now to  FIG. 14A , in yet another embodiment, expanding fuel moves from the rotor-vane chamber  452  in the rotor guide at the inner radial side of the vane  450  into a branching vane conduit. For example, the first vane conduit  1025  runs about longitudinally along or through at least fifty percent of the length of the vane  450  and branches into at least two branching vanes, where each of the branching vanes exit the vane  450  into the trailing expansion chamber  333 . For example, the first vane conduit  1025  branches into a first branching vane conduit  1410  and a second branching vane conduit  1420 , which each in turn exit to the trailing expansion chamber  333 . Alternatively, the expanding fuel passes through the first rotor conduit  1022  and applies an outward force on the base of the vane  450  toward the housing  210 . In all cases, the fuel/expanding gas flow is optionally controlled using valves controlled by the main controller  170  and/or is controlled through mechanical means, such as the lower trailing vane seal  1026  functioning as a valve, as described supra. 
     Referring now to  FIG. 14B , in still yet another embodiment, expanding fuel moves from the shaft  220  through a flow tube  1510 , passing through the rotor-vane chamber  452 , into a shaft-vane conduit  1520 , which leads to an outlet, such as (1) a trailing vane side port, which provides an additional rotational force applied to the vane  450 ; (2) through an inward side of a trailing vane wing to provide an outward sealing force pushing the vane  450  toward the housing  210 ; and/or (3) into the second rotor conduit  1024 , optionally via a telescoping second rotor conduit insert  1512 , to provide a booster flow to fuel expanding through the first rotor conduit  1022 . In all cases, the fuel/expanding gas flow is optionally controlled using one or more valves, positioned anywhere in the fuel expansion/flow path, controlled by the main controller  170 . For example, fuel flow from the shaft  220  is timed using the main controller  170  to: (1) provide an outward force on the vane toward the housing at zero or low rotational velocity, such as less 5, 10, 50, and/or 100 revolutions per minute; (2) to provide additional vane rotational forces when energy/load demand increases and/or is above a threshold; and/or (3) when provided energy to the rotary engine  110  is increasing and/or above a threshold. Fuel flow through the shaft  220  to move the vane  450  toward the housing  410  is useful to initiate a vane-housing seal at startup of the rotary engine  110  and/or to maintain proximate contact between the vane  450  and the housing  410  at low rotational speeds of the rotary engine  110  where centrifugal force is not sufficient to push the vane  450  radially outward to a sealing position. 
     Multiple Fuel Lines 
     Referring now to  FIG. 15A  and  FIG. 15B , in still yet an additional embodiment, fuel additionally enters into the rotor-vane chamber  452  through at least a portion of the shaft  220 . Referring now to  FIG. 15A , the shaft  220  is illustrated. The shaft  220  optionally includes an internal insert  224 . The insert  224  remains static while a wall  222  of the shaft  220  rotates about the insert  224  on one or more bearings  229 . Fuel, preferably under pressure, flows from the insert  224  through an optional valve  226 , which is optionally controlled by the main controller  170 , into a fuel shaft chamber  228 , which rotates with the shaft wall  222 . Referring now to  FIG. 15B , a flow tube  1510 , which rotates with the shaft wall  222  transports the fuel from the rotating fuel shaft chamber  228  and optionally through the rotor-vane chamber  452  where the fuel enters into a shaft-vane conduit  1520 , which terminates at the trailing expansion chamber  333 . The pressurized fuel in the static insert  224  expands before entering the expansion chamber  333  and the force of expansion and/or directional booster force of propulsion provides torsional forces against the rotor  440  to force the rotor to rotate. Optionally, a second vane conduit is used in combination with a flow booster to enhance movement of the fuel into the expansion chamber  333  adding additional expansion and directional booster forces. Upon entering the expansion chamber  333 , the fuel may proceed to expand through any of the rotor conduits  1020 , as described supra. 
     Vanes 
     Referring now to  FIG. 16A , a sliding vane  450  is illustrated relative to a rotor  440  and the inner wall  432  of the housing  210 . The inner wall  432  is exemplary of the inner wall of any rotary engine housing. Referring still to  FIG. 16A  and now referring to  FIG. 16B , the vane  450  is illustrated in a perspective view. The vane includes a vane body  1610  between a vane base  1612 , and vane-tip  1614 . The vane-tip  1614  is proximate the inner housing  432  during use. The vane  450  has a leading face  1616  proximate a leading chamber  334  and a trailing face  1618  proximate a trailing chamber or reference expansion chamber  333 . In one embodiment, the leading face  1616  and trailing face  1618  of the vane  450  extend as about parallel edges, sides, or faces from the vane base  1612  to the vane-tip  1614 . Optional wing tips are described, infra. Herein, the leading chamber  334  and reference expansion chamber  333  are both expansion chambers. The leading chamber  334  and reference expansion chamber  333  are chambers on opposite sides of a vane  450 . 
     Vane Axis 
     The vanes  450  rotate with the rotor  440  about a rotation point and/or about the shaft  220 . Hence, a localized axis system is optionally used to describe elements of the vane  450 . For a static position of a given vane, an x-axis runs through the vane body  1610  from the trailing chamber or  333  to the leading chamber  334 , a y-axis runs from the vane base  1612  to the vane-tip  1614 , and a z-axis is normal to the x/y-plane, such as defining a thickness of the vane. Hence, as the vane rotates, the axis system rotates and each vane has its own axis system at a given point in time. 
     Vane Head 
     Referring now to  FIG. 17 , the vane  450  optionally includes a replaceably attachable vane head  1611  attached to the vane body  1610 . The replaceable vane head  1611  allows for separate machining and ready replacement of the vane wings, such as the leading vane wing  1620  and/or the trailing vane wing  1630 , and vane tip  1614  elements. Optionally the vane head  1611  snaps or slides onto the vane body  1610 . 
     Vane Caps/Vane Seals 
     Preferably vane caps, not illustrated, cover the upper and lower surface of the vane  450 . For example, an upper vane cap covers the entirety of the upper z-axis surface of the vane  450  and a lower vane cap covers the entirety of the lower z-axis surface of the vane  450 . Optionally the vane caps function as seals or seals are added to the vane caps. 
     Vane Movement 
     Referring again to  FIG. 16A  and  FIG. 16B , the vane  450 , optionally, slidingly moves along and/or within the rotor-vane chamber  452  or rotor-vane slot. The edges of the rotor-vane chamber  452  function as guides to restrict movement of the vane along the x-axis. The vane movement moves the vane body, in a reciprocating manner, toward and then away from the housing inner wall  432 . The vane  450  is illustrated at a fully retracted position into the rotor-vane chamber  452  or rotor-vane channel at a first time, t 1 , and at a fully extended position at a second time, t 2 . 
     Vane Wing-Tips 
     Herein vane wings are defined, which extend away from the vane body  1610  along the x-axis. Certain elements are described for a leading vane wing  1620 , that extends into the leading chamber  334  and certain elements are described for a trailing vane wing  1630 , that extends into the expansion chamber  333 . Any element described with reference to the leading vane wing  1620  is optionally applied to the trailing vane wing  1630 . Similarly, any element described with reference to the trailing vane wing  1630  is optionally applied to the leading vane wing  1620 . Further, the rotary engine  110  optionally runs clockwise, counter-clockwise, and/or is reversible from clock-wise to counter-clockwise rotation. 
     Still referring to  FIG. 16A  and  FIG. 16B , optional vane-tips are illustrated. Optionally, one or more of a leading vane wing  1620 , also referred to as a leading vane wing-tip, and a trailing vane wing  1630 , also referred to as a trailing vane wing-tip, are added to the vane  450 . The leading vane wing  1620  extends from about the vane-tip  1614  into the leading chamber  334  and the trailing vane wing  1630  extends from about the vane-tip  1614  into the trailing chamber or reference expansion chamber  333 . The leading vane wing  1620  and trailing vane wing  1630  are optionally of any geometry. 
     Referring now to  FIG. 16C , another example of a vane  450  is described. In this example, the leading vane wing  1620  is a first flexible wing element  1682  and the trailing vane wing  1630  is a second flexible wing element  1684 , where there is an air gap between the leading vane wing  1620  and the trailing vane wing  1630 . As the rotor  440  rotates, the first and/or second flexible wing elements  1682 ,  1684  flex and follow the non-circular inner wall  432  of the housing. Optionally, the first flexible wing element  1682  terminates with a first terminal wing element  1692  and/or the second flexible wing element  1684  terminates with a second terminal wing element  1694  that are optionally seals and/or a magnetic seal attracted to the housing and/or a magnet therein or thereon. 
     Still referring to  FIG. 16C , the vane  450  is illustrated with an outward vane force system  1670 . As illustrated, the outward vane force system includes a rod within a rod, where the internal rod is a push rod with one or both longitudinal ends of the internal push rod connected to springs and/or a potential energy loaded accordion shaped metal, such as a shape memory alloy metal, a spring steel metal, and/or nitinol, which provides a radially outward force to a section of the vane that provides a sealing force between the vane  450  and the inner wall  432  of the housing. 
     The preferred geometry of the wing-tips reduces chatter or vibration of the vane-tips against the outer housing during operation of the engine. Chatter is unwanted opening and closing of the seal between expansion chamber  333  and leading chamber  334 . The unwanted opening and closing results in unwanted release of pressure from the expansion chamber  333 , because the vane tip  1614  is forced away from the inner wall  432  of the housing, with resulting loss of expansion chamber  333  pressure and rotary engine  110  power. For example, the outer edge of the leading vane wing  1620  and/or the trailing vane wing  1630 , proximate the inner wall  432 , is progressively further from the inner wall  432  as the wing-tip extends away from the vane-tip  1614  along the x-axis. In another example, a distance between the inner edge of the wing-tip bottom  1634  and the inner housing  432  decreases along a portion of the x-axis versus a central x-axis point of the vane body  1610 . Some optional wing-tip shape elements include:
         an about perpendicular wing-tip bottom  1634  adjoining the vane body  1610 ;   a curved wing-tip surface proximate the inner housing  432 ;   a pivotable concave wingtip, the concave portion facing the housing inner wall  432 ;   an outer vane wing-tip surface extending further from the housing inner wall  432  with increasing x-axis or rotational distance from a central point of the vane-tip  1614 ;   the inner vane wing-tip bottom  1634 , or radially inner portion of the wing-tip, having a decreasing y-axis distance to the housing inner wall  432  with increasing x-axis or rotational distance from a central point of the vane-tip  1614 ;   the outer vane wing-tip top, or radially outer portion of the wing-tip, having a decreasing y-axis distance to the housing inner wall  432  with increasing x-axis or rotational distance from a central point of the vane-tip  1614 ;   the outer vane wing-tip top, or radially outer portion of the wing-tip, having an increasing y-axis distance to the housing inner wall  432  with increasing x-axis or rotational distance from a central point of the vane-tip  1614 ; and   a 3, 4, 5, 6, or more sided polygon perimeter in an x-, y-cross-sectional plane of an individual wing tip, such as the leading vane wing  1620  or trailing vane wing  1630 .       

     Further examples of wing-tip shapes are illustrated in connection with optional wing-tip pressure elements and vane caps, described infra. 
     A t-shaped vane refers to a vane  450  having both a leading vane wing  1620  and trailing vane wing  1630 . 
     Vane-Tip Components 
     Referring now to  FIG. 17 , examples of optional vane-tip  1614  components are illustrated. Optional and preferable vane-tip  1614  components include:
         one or more bearings for bearing the force of the vane  450  applied to the inner housing  420 ;   one or more seals for providing a seal between the leading chamber  334  and expansion chamber  333 ;   one or more pressure relief cuts for reducing pressure build-up between the vane wings  1620 ,  1630  and the inner wall  432  of the housing; and   a booster enhancing pressure equalization above and below a vane wing.       

     Each of the bearings, seals, pressure relief cuts, and booster are further described herein. 
     Bearings 
     The vane-tip  1614  optionally includes a roller bearing  1740 . The roller bearing  1740  preferably takes a majority of the force of the vane  450  applied to the inner housing  432 , such as fuel expansion forces and/or centrifugal forces. The roller bearing  1740  is optionally an elongated bearing or a ball bearing. An elongated bearing is preferred as the elongated bearing distributes the force of the vane  450  across a larger portion of the inner housing  432  as the rotor  440  turns about the shaft  220 , which minimizes formation of a wear groove on the inner housing  432 . The roller bearing  1740  is optionally 1, 2, 3, or more bearings. Preferably, each roller bearing is spring loaded to apply an outward force of the roller bearing  1740  into the inner wall  432  of the housing. The roller bearing  1740  is optionally magnetic. 
     Seals 
     Still referring to  FIG. 17 , the vane-tip  1614  preferably includes one or more seals affixed to the vane  450 . The seals provide a barrier between the leading chamber  334  and expansion chamber  333 . A first vane-tip seal  1730  example comprises a seal affixed to the vane-tip  1614 , where the vane-seal includes a longitudinal seal running along the z-axis from about the top of the vane  1617  to about the bottom of the vane  1619 . The first-vane seal  1730  is illustrated as having an arched longitudinal surface. A second vane-tip seal  1732  example includes a flat edge proximately contacting the housing inner wall  432  during use. Optionally, for each vane  450 ,  1 ,  2 ,  3 , or more vane seals are configured to provide proximate contact between the vane-tip  1614  and housing inner wall  432 . Optionally, the vane-seals  1730 ,  1732  are fixedly and/or replaceably attached to the vane  450 , such as by sliding into a groove in the vane-tip running along the z-axis. Preferably, the vane-seal comprises a plastic, fluoropolymer, flexible, and/or rubber seal material. 
     Pressure Relief Cuts 
     As the vane  450  rotates, a resistance pressure builds up between the vane-tip  1614  and the housing inner wall  432 , which may result in chatter. For example, pressure builds up between the leading wing-tip surface  1710  and the housing inner wall  432 . Pressure between the vane-tip  1614  and housing inner wall  432  results in vane chatter and inefficiency of the engine. 
     The leading vane wing  1620  optionally includes a leading wing-tip surface  1710 . The leading wing-tip surface  1710 , which is preferably an edge running along the z-axis cuts, travels, and/or rotates through air and/or fuel in the leading chamber  334 . 
     The leading vane wing  1620  optionally includes: a cut, aperture, hole, fuel flow path, air flow path, and/or tunnel  1720  cut through the leading wing-tip along the y-axis. The cut  1720  is optionally 1, 2, 3, or more cuts. As air/fuel pressure builds between the leading wing-tip surface  1710  or vane-tip  1614  and the housing inner wall  432 , the cut  1720  provides a pressure relief flow path  1725 , which reduces chatter in the rotary engine  110 . Hence, the cut or tunnel  1720  reduces build-up of pressure, resultant from rotation of the engine vanes  450 , about the shaft  220 , proximate the vane-tip  1614 . The cut  1720  provides an air/fuel flow path  1725  from the leading chamber  334  to a volume above the leading wing-tip surface  1710 , through the cut  1720 , and back to the leading chamber  334 . Any geometric shape that reduces engine chatter and/or increases engine efficiency is included herein as possible wing-tip shapes. 
     Still referring to  FIG. 17 , the vane-tip  1614  optionally includes one or more trailing: cuts, apertures, holes, fuel flow paths, air flow paths, and/or tunnels  1750  cut through the trailing vane wing  1630  along the y-axis. The trailing cut  1750  is optionally 1, 2, 3, or more cuts. As fuel expansion pressure builds between the trailing edge tip  1750  or vane-tip  1614  and the housing inner wall  432 , the cut  1750  provides a pressure relief flow path  1755 , which reduces chatter in the rotary engine  110 . Hence, the cut or tunnel  1750  reduces build-up of pressure, resultant from fuel expansion in the trailing chamber during rotation of the engine vanes  450  about the shaft  220 , proximate the vane-tip  1614 . The cut  1750  provides an air/fuel flow path  1755  from the expansion chamber  333  to a volume above the trailing wing-tip surface  1760 , through the cut  1750 , and back to the trailing chamber or reference chamber  333 . Any geometric shape that reduces engine chatter and/or increases engine efficiency is included herein as possible wing-tip shapes. 
     Vane Wing 
     Referring now to  FIG. 18 , a cross-section of the vane  450  is illustrated having several optional features including: a curved outer surface, a curved inner surface, and a curved tunnel, each described infra. 
     The first optional feature is a curved outer surface  1622  of the leading vane wing  1620 . In a first case, the curved outer surface  1622  extends further from the inner wall of the housing  432  as a function of x-axis position relative to the vane body  1610 . For instance, at a first x-axis position, x 1 , there is a first distance, d 1 , between the outer surface  1622  of the leading vane wing  1620  and the inner housing  432 . At a second position, x 2 , further from the vane body  1610 , there is a second distance, d 2 , between the outer surface  1622  of the leading vane wing  1620  and the inner housing  432  and the second distance, d 2 , is greater than the first distance, d 1 . Preferably, there are positions on the outer surface  1622  of the leading vane wing  1620  where the second distance, d 2 , is about 2, 4, or 6 times as large as the first distance, d 1 . In a second case, the outer surface  1622  of the leading vane wing  1620  contains a negative curvature section  1623 . The negative curvature section  1623  is optionally described as a concave region. The negative curvature section  1623  on the outer surface  1622  of the leading vane wing  1620  allows the build-up  610  and the cut-outs  510 ,  520  in the housing as without the negative curvature  1623 , the vane  450  mechanically catches or physically interferes with the inner wall of the housing  432  with rotation of the vane  450  about the shaft  220  when using a double offset housing  430 . 
     The second optional feature is a curved inner surface  1624  of the leading vane wing  1620 . The curved inner surface  1624  extends further toward the inner wall of the housing  432  as a function of x-axis position relative to the vane body  1610 . Stated differently, the inner surface  1624  of the leading vane curves away from a reference line  1625  normal to the vane body at the point of intersection of the vane body  1610  and the leading vane wing  1620 . For instance, at a third x-axis position, x 3 , there is a third distance, d 3 , between the outer surface  1622  of the leading vane wing  1620  and the reference line  1625 . At a fourth position, x 4 , further from the vane body  1610 , there is a fourth distance, d 4 , between the outer surface  1622  of the leading vane wing  1620  and the reference line  1625  and the fourth distance, d 4 , is greater than the third distance, d 3 . Preferably, there are positions on the outer surface  1622  of the leading vane wing  1620  where the fourth distance, d 4 , is about 2, 4, or 6 times as large as the third distance, d 3 . 
     The third optional feature is a curved fuel flow path  2010  running through the leading vane wing  1620 , where the fuel flow path is optionally described as a hole, aperture, and/or tunnel. The curved fuel flow path  2010  includes an entrance opening  2012  and an exit opening  2014  of the fuel flow path  2010  in the leading vane wing  1620 . The edges of the fuel flow path are preferably curved, such as with a curvature approximating an aircraft wing. A distance from the vane wing-tip  1710  through the fuel flow path  2010  to the inner surface at the exit port  2014  of the leading wing  1624  is longer than a distance from the vane wing-tip  1710  to the exit port  2014  along the inner surface  1624  of the leading vane wing  1620 . Hence, the flow rate of the fuel through the fuel flow path  2010  maintains a higher velocity compared to the fuel flow velocity along the base  1624  of the leading vane wing  1620 , resulting in a negative pressure between the leading vane wing  1620  and the inner housing  432 . The negative pressure lifts the vane  450  toward the inner wall  432 , which lifts the vane tip  1614  along the y-axis to proximately contact the inner housing  432  during use of the rotary engine  110 . The fuel flow path  2010  additionally reduces unwanted pressure between the leading vane wing  1620  and inner housing  432 , where excess pressure results in detrimental engine chatter during intermittent release of the excess pressure via leakage between expansion chambers. 
     Generally, an aperture through the leading vane wing allows pressure relief before the pressure creates momentary forces between the vane  450  and the housing  210  results in chatter. For instance, as the vane rotates, forces build up at the intersection of the leading vane side and the housing, such as resultant from a diminishing cross-sectional area available for the expanding fuel as a function of rotation and/or more time for the fuel to expand. When the pressure exceeds a threshold and/or a small gap is present between a vane/housing seal, the pressure forces the vane inward until the pressure is relieved, which results in chatter. By placing an aperture through the leading wing vane at a point where the vane wing does not touch the housing, the pressure is relieved prior to the occurrence and/or initiation of chatter. Optionally, the aperture is elongated along the z-axis to allow uniform relief of the building pressure. For example, the z-axis opening size of the aperture is at least 200, 300, 400, and/or 500 percent of the x-axis opening size of the aperture. 
     Trailing Wing 
     Referring now to  FIG. 19A  and  FIG. 19B , an example of a trailing cut  1750  in a vane  450  trailing vane wing  1630  is illustrated. For clarity, only a portion of vane  450  is illustrated. The trailing vane wing  1630  is illustrated, but the elements described in the trailing vane wing  1630  are optionally used in the leading vane wing  1620 . The optional hole or aperture  1750  leads from an outer area  1920  of the wing-tip to an inner area  1930  of the wing-tip. Referring now to  FIG. 19A , a cross-section of a single hole  1940  having about parallel sides is illustrated. The aperture aids in equalization of pressure in an expansion chamber between an inner side of the wing-tip and an outer side of the wing-tip. 
     Still referring to  FIG. 19A , a single aperture  1750  is illustrated. Optionally, a series of holes  1750  are used where the holes are separated along the z-axis. Optionally, the series of holes are connected to form a groove similar to the cut  1720 . Similarly, groove  1720  is optionally a series of holes, similar to holes  1750 . 
     Referring now to  FIG. 19B , a vane  450  having a trailing vane wing  1630  with an optional aperture  1940  configuration is illustrated. In this example, the aperture  1942  expands from a first cross-sectional distance at the outer area of the wing  1920  to a larger second cross-sectional distance at the inner area of the wing  1930 . Preferably, the second cross-sectional distance is at least 1½ times that of the first cross-sectional distance and optionally about 2, 3, 4 times that of the first cross-sectional distance. the invented conical shape allows for expansion of the gas trapped between the trailing wing tip and the housing  430 , which aids in pressure relief and/or allows a greater surface area for the expanding gases in the reference expansion chamber  333  to push up along the y-axis, yielding a greater force pushing the vane  450  toward the housing  210 . 
     Booster 
     Referring now to  FIG. 20 , an example of a vane  450  having a booster  1300  is provided. The booster  1300  is applied in a vane booster  2010  configuration. The flow along the trailing pressure relief flow path  1755 , is optionally boosted or amplified using flow through the vane conduit  1025 . Flow from the vane conduit runs along a vane flow path  2040  to an acceleration chamber  2042  at least partially about the trailing flow path  1755 . Flow from the vane conduit  1025  exits the trailing vane wing  1630  through one or more exit ports  2044 . The flow from the vane conduit  1025  exiting through the exit ports  2044  provides a partial vacuum force that accelerates the flow along the trailing pressure relief flow path  1755 , which aids in pressure equalization above and below the trailing vane wing  1630 , which reduces vane  450  and rotary engine  110  chatter. Preferably, an insert  2012  contains one or more of and preferably all of: the inner area of the wing  1920 , the outer area of the wing  1930 , the acceleration chamber  2042 , and exit port  2044  along with a portion of the trailing pressure relief flow path  2030  and vane flow path  2020 . 
     Swing Vane 
     In another embodiment, a swing vane  2100  is used in combination with an offset rotor, such as a double offset rotor in the rotary engine  110 . More particularly, the rotary engine using a swing vane separating expansion chambers is provided for operation with a pressurized fuel or fuel expanding during a rotation of the engine. A swing vane pivots about a pivot point on the rotor yielding an expansion chamber separator ranging from the width of the swing vane to the length of the swing vane. The swing vane, optionally, slidingly extends to dynamically lengthen or shorten the length of the swing vane. The combination of the pivoting and the sliding of the vane allows for use of a double offset rotor in the rotary engine and the use of rotary engine housing wall cut-outs and/or buildups to expand rotary engine expansion chamber volumes with corresponding increases in rotary engine power and/or efficiency. 
     The swing vane  2100  is optionally used in place of the sliding vane  450 . The swing vane  2100  is optionally described as a separator between expansion chambers. For example, the swing vane  2100  separates expansion chamber  333  from leading chamber  334 . The swing vane  2100  is optionally used in combination with any of the elements described herein used with the sliding vane  450 . 
     Swing Vane Rotation 
     Referring now to  FIG. 21A  and  FIG. 21B , in one example, a swing vane  2100  includes a swing vane base  2110 , which is attached to the rotor  440  of a rotary engine  110  at a swing vane pivot  2115 . Preferably, a spring loaded pin provides a rotational force that rotates the swing vane base  2110  about the swing vane pivot  2115 . The spring-loaded pin additionally provides a damping force that prevents rapid collapse of the swing vane  2100  back to the rotor  440  after the power stroke in the exhaust phase. The swing vane  2100  pivots about the swing vane pivot  2115  attached to the rotor  440  during use. Since the swing vane pivots with rotation of the rotor in the rotary engine, the reach of the swing vane between the rotor and housing ranges from a narrow width of the swing vane to the length of the swing vane. For example, at about the 12 o&#39;clock position, the swing vane  2100  is laying on its side and the distance between the rotor  440  and inner housing  432  is the width of the swing vane  2100 . Further, at about the 3 o&#39;clock position the swing vane extends nearly perpendicularly outward from the rotor  440  and the distance between the rotor and the inner housing  432  is the length of the swing vane. Hence, the dynamic pivoting of the swing vane yields an expansion chamber separator ranging from the short width of the swing vane to the length of the swing vane, which allows use of an offset rotor in the rotary engine. 
     Swing Vane Extension 
     Preferably, the swing vane base  2110  includes an optional curved section, slideably or telescopically attached to a curved section of the vane base  2110 , referred to herein as a sliding swing vane  2120 . For example, the sliding swing vane  2120  slidingly extends along the curved section of the swing vane base  2110  during use to extend an extension length of the swing vane  2100 . The extension length extends the swing vane  2100  from the rotor  440  into proximate contact with the inner housing  432 . One or both of the curved sections on the swing vane base  2110  or sliding swing vane  2120  guides sliding movement of the sliding swing vane  2120  along the swing vane base  2110  to extend a length of the swing vane  2100 . For example, at about the 6 o&#39;clock position the swing vane extends nearly perpendicularly outward from the rotor  440  and the distance between the rotor and the inner housing  432  is the length of the swing vane plus the length of the extension between the sliding swing vane  2120  and swing vane base  2110 . In one case, an inner curved surface of the sliding swing vane  2120  slides along an outer curved surface of the swing vane base  2110 , which is illustrated in  FIG. 21A . In a second case, the sliding swing vane inserts into the swing vane base and an outer curved surface of the sliding swing vane slides along an inner curved surface of the swing vane base. 
     A vane actuator  2130  provides an outward force, where the outward force extends the sliding swing vane  2120  into proximate contact with the inner housing  432 . A first example of vane actuator is a spring attached to either the swing vane base  2110  or to the sliding swing vane  2120 . The spring provides a spring force resulting in sliding movement of the sliding swing vane  2120  relative to the swing vane base  2110 . A second example of vane actuator is a magnet and/or magnet pair where at least one magnet is attached or embedded in either the swing vane base  2110  or to the sliding swing vane  2120 . The magnet provides a repelling magnet force providing a partial internal separation between the swing vane base  2110  from the sliding swing vane  2120 . A third example of the vane actuator  2130  is air and/or fuel pressure directed through the swing vane base  2110  to the sliding swing vane  2120 . The fuel pressure provides an outward sliding force to the sliding swing vane  2120 , which extends the length of the swing vane  2100 . The spring, magnet, and fuel vane actuators are optionally used independently or in combination to extend the length of the swing vane  2100  and the vane actuator  2130  operates in combination with centrifugal force of the rotary engine  110 . 
     Referring now to  FIG. 21B , swing vanes  2100  are illustrated at various points in rotation and/or extension about the shaft  220 . The swing vanes  2100  pivot about the swing vane pivot  2115 . Additionally, from about the 12 o&#39;clock position to about the 6 o&#39;clock position, the swing vane  2100  extends to a greater length through sliding of the sliding swing vane  2120  along the swing vane base  2110  toward the inner housing  432 . The sliding of the swing vane  2100  is aided by centrifugal force and optionally with vane actuator  2130  force. From about the 6 o&#39;clock position to about the 12 o&#39;clock position, the swing vane  2100  length decreases as the sliding swing vane  2120  slides back along the swing vane base  2110  toward the rotor  440 . Hence, during use the swing vane  2100  both pivots and extends. The combination of swing vane  2100  pivoting and extension allows greater reach of the swing vane. The greater reach allows use of the double offset rotor, described supra. The combination of the swing vane  2100  and double offset rotor in a double offset rotary engine  400  yields increased volume in the expansion chamber from about the 12 o&#39;clock position to about the 6 o&#39;clock position, as described supra. Further, the combination of the pivoting and the sliding of the vane allows for use with a double offset rotary engine having housing wall cut-outs and/or buildups, described supra. The greater volume of the expansion chamber during the power stroke of the rotary engine results in the rotary engine  110  having increased power and/or efficiency. 
     Swing Vane Seals 
     Referring again to  FIG. 21A  and still to  FIG. 21B , the swing vane  2100  proximately contacts the inner housing  432  during use at one or more contact points or areas. A first example of a sliding vane seal is a rear sliding vane seal  2142  on an outer surface of the swing vane base  2110 . A second example of a sliding vane seal is a forward vane seal  2144  on an outer surface of the sliding swing vane  2120 . The rear seal  2142  and/or the forward seal  2142  is optionally a wiper seal or a double lip seal. A third example of a sliding vane seal is a tip seal  2146 , where a region of the end of the sliding swing vane  2120  proximately contacts the inner housing  432 . The tip seal is optionally a wiper seal, such as a smooth outer surface of the end of the sliding swing vane  2120 , and/or a secondary seal embedded into the wiper seal. At various times in rotation of the rotor  440  about the shaft  220 , one or more of the rear seal  2142 , forward seal  2144 , and tip seal  2146  contact the inner housing  432 . For example, from about the 12 o&#39;clock position to about the 8 o&#39;clock position, the tip seal  2146  of the sliding swing vane proximately contacts the inner housing  432 . From about the 9 o&#39;clock position to about the 12 o&#39;clock position, first the forward seal  2144  and then both the forward seal  2144  and the rear seal  2142  proximately contact the inner housing  432 . For example, when the vane  450  is in about the 11 o&#39;clock position both the forward seal  2144  and rear seal  2142  are in simultaneous/proximate contact the inner surface of the second cut-out  520  of the inner housing  432 . Generally, during one rotation of the rotor  440  and the reference swing vane  2100  about the shaft, first the tip seal  2146 , then the forward seal  2144 , then both the forward seal  2144  and rear seal  2142  contact the inner housing  432 . 
     Rotor-Vane Cut-Out 
     Optionally, the rotor  440  includes a rotor cut-out  2125 . The rotor cut-out allows the swing vane  2100  to fold into the rotor  440 . By folding the swing vane  2100  into the rotor  440 , the distance between the rotor  440  and inner housing  432  is reduced, since at least a portion of the width of the swing vane  2100  lays in the rotor  440 . By folding the swing vane  2100  into the rotor  440 , the double offset position of the rotor  440  is optionally increased to allow a larger expansion chamber, such as at the 4 o&#39;clock position and a smaller expansion/compression chamber at about the 11 o&#39;clock position, which enhances efficiency and power of the power stroke. Optionally, the swing vane  2100  includes a swing vane cap, described infra. 
     Scalability 
     The swing vane  2100  attaches to the rotor  440  via the swing vane pivot  2115 . Since, the swing vane movement is controlled by the swing vane pivot  2115 , the rotor-vane chamber  452  is not necessary. Hence, the rotor  440  does not necessitate the rotor-vane chamber  452 . When scaling down a rotor  440  guiding a sliding vane  450 , the rotor-vane chamber  452  limits the minimum size of the rotor. As the swing vane  2100  does not require the rotor-vane chamber  452 , the diameter of the rotor  440  is optionally about as small as ¼, ½, 1, or 2 inches or as large as about 1, 2, 3, or 5 feet. 
     Cap 
     Referring now to  FIG. 22 , in yet another embodiment, dynamic caps  2200  or seals seal boundaries between fuel containing regions and surrounding rotary engine  110  elements. For example, caps  2200  seal boundaries between the reference expansion chamber  333  and surrounding rotary engine elements, such as the rotor  440  and vane  450 . Types of caps  2200  include vane caps, rotor caps, and rotor-vane caps. Generally, dynamic caps float along an axis normal to the caps outer sealing surface. Herein, vane caps are first described in detail. Subsequently, rotor caps are described using the vane cap description and noting key differences. 
     More particularly, a rotary engine method and apparatus configured with a dynamic cap seal is described. A dynamic cap  2200  or seal restricts fuel flow from a fuel compartment to a non-fuel compartment and/or fuel flow between fuel compartments, such as between a reference expansion chamber  333  and any of an engine: rotor, vane, housing, and/or a leading or the trailing expansion chamber. For a given type of cap, optional sub-cap types exist. In a first example, types of vane caps include: vane-housing caps, vane-rotor caps, and rotor-vane slot caps. As a second example, types of rotor caps include: rotor-slot caps, rotor/expansion chamber caps, and/or inner rotor/shaft caps. Generally, caps float along an axis normal to an outer seal forming surface of the cap. For example, a first vane cap  2210  includes an outer surface  2214 , which seals to the endplate element  212 ,  214 . Generally, the outer surface of the cap seals to a rotary engine element, such as a housing  210  or endplate element  212 ,  214 , providing a dynamic seal. Means for providing a cap sealing force to seal the cap against a rotary engine housing element comprise one or more of: a spring force, a magnetic force, a deformable seal force, and a fuel force. The dynamic caps ability to track a noncircular path while still providing a seal are particularly beneficial for use in a rotary engine having an offset rotor and with a non-circular inner rotary engine compartment having engine wall cut-outs and/or build-ups. For example, the dynamic caps ability to move to form a seal allows the seal to be maintained between a vane and a housing of the rotary engine even with a housing cut-out at about the 1 o&#39;clock position. Further, the dynamic sealing forces provide cap sealing forces over a range of temperatures and operating engine rotation speeds. 
     Still more particularly, caps  2200  dynamically move or float to seal a junction between a sealing surface of the cap and a rotary engine component. For example, a vane cap sealing to the inner housing  432  dynamically moves along the y-axis until an outer surface of the cap seals to the inner housing  432 . 
     In one example, caps  2200  function as seals between rotary chambers over a range of operating speeds and temperatures. For the case of operating speeds, the dynamic caps seal the rotary engine chambers at zero revolutions per minute (rpm) and continue to seal the rotary engine compartments as the engine accelerates to operating revolutions per minute, such as about 1000, 2000, 5000, or 10,000 rpm. For example, since the caps move along an axis normal to an outer surface and have dynamic means for forcing the movement to a sealed position, the caps seal the engine compartments when the engine is any of: off, in the process of starting, is just started, or is operating. In an exemplary case, the rotary engine vane  450  is sealed against the rotary engine housing  210  by a vane cap. For the case of operating temperatures, the same dynamic movement of the caps allows function over a range of temperatures. For example, the dynamic cap sealing forces function to apply cap sealing forces when an engine starts, such as at room temperature, and continues to apply appropriate sealing forces as the temperature of the rotary engine increases to operational temperature, such as at about 100, 250, 500, 1000, or 1500 degrees centigrade. The dynamic movement of the caps  2200  is described, infra. 
     Vane Caps 
     A vane  450  is optionally configured with one or more dynamic caps  2200 . A particular example of a cap  2200  is a vane/endplate cap, which provides a dynamic seal or wiper seal between the vane body  1610  and a housing endplate, such as the first endplate  212  and/or second endplate  214 . Vane/endplate caps cover one or both z-axis sides of the vane  450  or swing vane  2100 . Referring now to  FIG. 22 , an example of the first vane cap  2210  and the second vane cap  2220  covering an innermost and an outermost z-axis side of the vane  450 , respectively, is provided. The two vane endplate caps  2210 ,  2220  function as wiper seals, sealing the edges of the vane  450  or swing vane  2100  to the first endplate  212  and second endplate  214 , respectively. Preferably, a vane/endplate cap includes one or more z-axis vane cap bearings  2212 , which are affixed directly to the vane body  1610  and pass through the vane cap  2200  without interfering with the first vane cap  2210  movement and proximately contact the rotary engine endplates  212 ,  214 . For example,  FIG. 22  illustrates a first vane cap  2210  configured with five vane cap bearings  2212  that contact the first endplate  212  of the rotary engine  110  during use. Each of the vane/endplate cap elements are further described, infra. The vane and endplate cap elements described herein are exemplary of optional cap  2200  elements. 
     Herein, for a static position of a given vane, an x-axis runs through the vane body  1610  from the reference chamber  333  to the leading chamber  334 , a y-axis runs from the vane base  1612  to the vane-tip  1614 , and a z-axis is normal to the x,y-plane, such as defining the thickness of the vane between the first endplate  212  and second endplate  214 . Further, as the vane rotates, the axis system rotates and each vane has its own axis system at a given point in time. 
     Referring now to  FIG. 23A  and  FIG. 23B , an example of a cross-section of a dynamic vane/endplate cap  2300  is provided. The vane/endplate cap  2300  resides on the z-axis between the vane body  1610  and an endplate, such as the first endplate  212  and the second endplate  214 . In the illustrated example, the first vane cap  2210  resides on the z-axis between the vane body  1610  and the first endplate  212 . Further, the vane body  1610  and first vane cap  2210  combine to provide a separation, barrier, and seal between the reference expansion chamber  333  and leading expansion chamber  334 . Means for providing a z-axis force against the first vane cap  2210  forces the first vane cap  2210  into proximate contact with the first endplate  212  to form a seal between the first vane cap  2210  and first endplate  212 . Referring now to  FIG. 23A , it is observed that a cap/endplate gap  2310  could exist between an outer face  2214  of the first vane cap  2210  and the first endplate  212 . However, now referring to  FIG. 23B , the z-axis force positions the vane cap outer face  2214  of the first vane cap  2210  into proximate contact with the first endplate  212  reducing the cap/endplate gap  2310  to about a nominal zero distance, which provides a seal between the first vane cap  2210  and the first endplate  212 . While the vane/endplate cap  2210  moves into proximate contact with the housing endplate  212 , one or more inner seals  2320 ,  2330  prevent or minimize movement of fuel from the reference expansion chamber  333  to the leading chamber  334 , where the potential fuel leakage follows a path running between the vane body  1610  and first vane cap  2210 . 
     Vane Cap Movement 
     Still referring to  FIG. 23A  and  FIG. 23B , the means for providing a z-axis force against the first vane cap  2210 , which forces the first vane cap  2210  into proximate contact with the first endplate  212  to form a seal between the first vane cap  2210  and first endplate  212  is further described. The vane cap z-axis force moves the first vane cap  2210  along the z-axis relative to the vane  450 . 
     Examples of vane cap z-axis forces include one or more of:
         a spring force;   a magnetic force   a deformable seal force; and   a fuel flow or fuel force.       

     Examples are provided of a vane z-axis spring, magnet, deformable seal, and fuel force. 
     In a first example, a vane cap z-axis spring force is described. One or more vane cap springs  2340  are affixed to one or both of the vane body  1610  and the first vane cap  2210 . In  FIG. 23A , two vane cap springs  2340  are illustrated in a compressed configuration between the vane body  1610  and the first vane cap  2210 . As illustrated in  FIG. 23B  the springs extend or relax by pushing the first vane cap  2210  into proximate contact with the first endplate  212 , which seals the first vane cap  2210  to the first endplate  212  by reducing the cap/endplate gap  2310  to a distance of about zero, while increasing a second vane body/vane cap gap  2315  between the first vane cap  2210  and the vane body  1610 . 
     In a second example, a vane cap z-axis magnetic force is described. One or more vane cap magnets  2350  are: affixed to, partially embedded in, and/or are embedded within one or both of the vane body  1610  and first vane cap  2210 . In  FIG. 23A , two vane cap magnets  2350  are illustrated with like magnetic poles facing each other in a magnetic field resistant position. As illustrated in  FIG. 23B  the magnets  2350  repel each other to force the first vane cap  2210  into proximate contact with the first endplate  212 , thereby reducing the cap/endplate gap  2310  to a gap distance of about zero, which provides a seal between the first vane cap  2210  and first endplate  212 . 
     In a third example, a vane cap z-axis deformable seal force is described. One or more vane cap deformable seals  2330  are affixed to and/or are partially embedded in one or both of the vane body  1610  and first vane cap  2210 . In  FIG. 23A , a deformable seal  2330  in a high potential energy state is illustrated between the vane body  1610  and first vane cap  2210 . As illustrated in  FIG. 23B  the deformable seal  2330  expands toward a natural state to force the first vane cap  2210  into proximate contact with the first endplate  212 , thereby reducing the cap/endplate gap  2310  to a gap distance of about zero, which provides a seal between the first vane cap  2210  and first endplate  212 . An example of a deformable seal is a rope shaped flexible type material or a packing material type seal. The deformable seal is optionally positioned on an extension  2360  of the vane body  1610  or on an extension of the first vane cap  2210 , described infra. Notably, the deformable seal has duel functionality: (1) providing a z-axis force as described herein and (2) providing a seal between the vane body  1610  and first vane cap  2210 , described infra. 
     The spring force, magnetic force, and/or deformable seal force are optionally set to provide a sealing force that seals the vane cap outer face  2214  to the first endplate  212  with a force that is (1) great enough to provide a fuel leakage seal and (2) small enough to allow a wiper seal movement of the vane cap outer face  2214  against the first endplate  212  with rotation of the rotor  440  in the rotary engine  110 . The sealing force is further described, infra. 
     In a fourth example, a vane cap z-axis fuel force is described. As fuel penetrates into the vane body/cap gap  2315 , the fuel provides a z-axis fuel force pushing the first vane cap  2210  into proximate contact with the first endplate  212 . The cap/endplate gap  2310  and vane body/cap gap  2315  are exaggerated in the provided illustrations to clarify the subject matter. The potential fuel leak path between the first vane cap  2210  and vane body  1610  is blocked by one or more of a first seal  2320 , the deformable seal  2330 , and a flow-path reduction geometry. An example of a first seal  2320  is an O-ring positioned about either an extension  2360  of the vane body  1610  into the first vane cap  2210 , as illustrated, or an extension of the first vane cap  2210  into the vane body  1610 , not illustrated. In a first case, the first seal  2320  is affixed to the vane body  1610  and the first seal  2320  remains stationary relative to the vane body  1610  as the first vane cap  2210  moves along the z-axis. Similarly, in a second case the first seal  2320  is affixed to the first vane cap  2210  and the first seal  2320  remains stationary relative to the first vane cap  2210  as the first vane cap  2210  moves along the z-axis. The deformable seal  2330  was described, supra. The flow path reduction geometry reduces flow of the fuel between the vane body  1610  and first vane cap  2210  by forcing the fuel through a labyrinth type path having a series of at least 2, 4, 6, 8, 10, or more right angle turns about the above described extension. Fuel flowing through the labyrinth must turn multiple times breaking the flow velocity or momentum of the fuel from the reference expansion chamber  333  to the leading expansion chamber  334 . 
     Vane Cap Sealing Force 
     Referring now to  FIG. 24A  and  FIG. 24B , examples of applied sealing forces in a cap  2200  and controlled sealing forces are described using the vane/endplate cap  2300  as an example. Optionally, one or more vane cap bearings  2212  are incorporated into the vane  450  and/or vane cap  2210 . The vane cap bearing  2212  has a z-axis force applied via a vane body spring  2420  and intermediate vane/cap linkages  2430 , which transmits the force of the spring  2420  to the vane cap bearing  2212 . Optionally, a rigid support  2440 , such as a tube or bearing containment wall, extends from the vane cap outer face  2214  to and preferably into the vane body  1610 . The rigid support  2440  transmits the force of the vane  450  to the first endplate  212  via the vane cap bearing  2212 . Hence, the vane cap bearing  2212 , rigid support  2440 , and vane body spring  2420  support the majority of the force applied by the vane  450  to the first endplate  212 . The vane body spring  2420  preferably applies a greater outward z-axis force to the vane cap bearing  2212  compared to the lighter outward z-axis forces of one or more of the above described spring force, magnetic force, and/or deformable seal force. For example, the vane body spring  2420  results in a greater friction between the vane cap bearing  2212  and end plate  212  compared to the smaller friction resulting from the outward z-axis forces of one or more of spring force, magnetic force, and/or deformable seal force. Hence, there exists a first coefficient of friction resultant from the vane body spring  2420 , usable to set a load bearing force. Additionally, there exists a second coefficient of friction resultant from the spring force, magnetic force, and/or deformable seal force, usable to set a sealing force. Each of the load bearing force and spring force are independently controlled by their corresponding springs. Further, the reduced contact area of the bearing  2212  with the endplate  212 , compared to the potential contact area of all of outer surface  2214  with the endplate  212 , reduces friction between the vane  450  and the endplate  212 . Still further, since the greater outward force is supported by the vane cap bearing  2212 , rigid support  2440 , and vane body spring  2420 , the lighter spring force, magnetic force, and/or deformable seal force providing the sealing force to the cap  2200  are adjusted to provide a lesser wiper sealing force sufficient to maintain a seal between the first vane cap  2210  and first endplate  212 . Referring again to  FIG. 24B , the sealing force reduces the cap/endplate gap  2310  to a distance of about zero. 
     The rigid support  2440  additionally functions as a guide controlling x- and/or y-axis movement of the first vane cap  2210  while allowing z-axis sealing motion of the first vane cap  2210  against the first endplate  212 . 
     Positioning of Vane Caps 
       FIG. 22 ,  FIG. 23 , and  FIG. 24  illustrate a first vane cap  2210 . One or more of the elements of the first vane cap  2210  are applicable to a multitude of caps in various locations in the rotary engine  110 . Referring now to  FIG. 25 , additional vane caps  2300  or seals are illustrated and described. 
     The vane  450  in  FIG. 25  illustrates five optional vane caps: the first vane cap  2210 , the second vane cap  2220 , a reference chamber vane cap  2510 , a leading chamber vane cap  2520 , and vane tip cap  2530 . The reference chamber vane cap  2510  is a particular type of the lower trailing vane seal  1026 , where the reference chamber vane cap  2510  has functionality of sealing movement along the x-axis. Similarly, the leading chamber vane cap  2520  is a particular type of lower trailing seal  1028 . Though not illustrated, the upper trailing seal  1028  and upper leading seal  1029  each are optionally configured as dynamic x-axis vane caps. 
     The vane seals seal potential fuel leak paths. The first vane cap  2210 , second vane cap  2220  and the vane tip cap  2530  provide three x-axis seals between the expansion chamber  333  and the leading chamber  334 . As described, supra, the first vane cap  2210  provides a first x-axis seal between the expansion chamber  333  and the leading chamber  334 . The second vane cap  2220  is optionally and preferably a mirror image of the first vane cap  2210 . The second vane cap  2220  contains one or more elements that are as described for the first vane cap  2210 , with the second end cap  2220  positioned between the vane body  1610  and the second endplate  214 . Like the first end cap  2210 , the second end cap  2220  provides another x-axis seal between the reference expansion chamber  333  and the leading chamber  334 . Similarly, the vane tip cap  2530  preferably contains one or more elements as described for the first vane cap  2210 , only the vane tip cap is located between the vane body  1610  and inner wall  432  of the housing  210 . The vane tip cap  2530  provides yet another seal between the expansion chamber  333  and the leading chamber  334 . The vane tip cap  2530  optionally contains any of the elements of the vane head  1611 . For example, the vane tip cap  2530  preferably uses the roller bearings  1740  described in reference to the vane head  1611  in place of the bearings  2212 . The roller bearings  1740  aid in guiding rotational movement of the vane  450  about the shaft  220 . 
     The vane  450  optionally and preferably contains four additional seals between the expansion chamber  333  and rotor-vane chamber  452 . For example, the reference chamber vane cap  2510  provides a y-axis seal between the reference chamber  333  and the rotor-vane chamber  452 . Similarly, the leading chamber vane cap  2520  provides a y-axis seal between the leading chamber  334  and the rotor-vane chamber  452 . The reference chamber vane cap  2510  and/or leading chamber vane cap  2520  contain one or more elements that correspond with any of the sealing elements described herein. The reference and leading chamber vane caps  2510 ,  2520  preferably contain roller bearings  2522  in place of the bearings  2212 . The roller bearings  2522  aid in guiding movement of the vane  450  next to the rotor  440  along the y-axis as the roller bearings have unidirectional ability to rotate. The reference chamber vane cap  2510  and leading chamber vane cap  2520  each provide y-axis seals between an expansion chamber and the rotor-vane chamber  452 . The upper trailing seal  1028  and upper leading seal  1029  are optionally configured as dynamic x-axis floatable vane caps, which also function as y-axis seals, though the upper trailing seal  1028  and upper leading seal  1029  function as seals along the upper end of the rotor-vane chamber  452  next to the reference and leading expansion chambers  333 ,  334 , respectively. 
     Generally, the vane caps  2300  are species of the generic cap  2200 . Caps  2200  provide seals between the reference expansion chamber and any of: the leading expansion chamber  334 , the trailing expansion chamber  333 , the rotor-vane chamber  452 , the inner housing  432 , and a rotor face. Similarly, caps provide seals between the rotor-vane chamber  452  and any of: the leading expansion chamber  334 , the trailing expansion chamber  333 , and a rotor face. 
     Rotor Caps 
     Referring now to  FIG. 26 , examples of rotor caps  2600  between the first end plate  212  and a face of the rotor  446  are illustrated. Examples of rotor caps  2600  include: a rotor/vane slot cap  2610 , a rotor/expansion chamber cap  2620 , and an inner rotor cap  2630 . Any of the rotor caps  2600  exist on one or both z-axis faces of the rotor  446 , such as proximate the first end plate  212  and the second end plate  214 . The rotor/vane slot cap  2610  is a cap proximate the rotor-vane chamber  452  on the rotor endplate face  446  of the rotor  440 . The rotor/expansion cap  2620  is a cap proximate the reference expansion chamber  333  on an endplate face  446  of the rotor  440 . Herein, the reference expansion chamber  333  is also referred to as the trailing expansion chamber. The inner rotor cap  2630  is a cap proximate the shaft  220  on a rotor endplate face  446  of the rotor  440 . Generally, the rotor caps  2600  are caps  2200  that contain any of the elements described in terms of the vane caps  2300 . Generally, the rotor caps  2600  seal potential fuel leak paths, such as potential fuel leak paths originating in the reference chamber  333  or rotor-vane chamber  452 . The inner rotor cap  2630  optionally seals potential fuel leak paths originating in the rotor-vane chamber  452  and or in a fuel chamber proximate the shaft  220 . 
     Magnetic/Non-magnetic Rotary Engine Elements 
     Optionally, the bearing  2212 , roller bearing  1740 , and/or roller bearing  2522  are magnetic. Optionally, any of the remaining elements of rotary engine  110  are non-magnetic. Combined, the bearing  2212 , roller bearing  1740 , rigid support  2440 , intermediate vane/cap linkages  2430 , and/or vane body spring  2420  provide an electrically conductive pathway between the housing  210  and/or endplates  212 ,  214  to a conductor proximate the shaft  220 . Optionally, windings and/or coils are positioned in the housing  210  or radially outward from the housing  210  by the power stroke section of a the engine allowing a magnetic field/electrical current to be generated in the power stroke phase, where the electrical current is subsequently used for another purpose, such as opening or closing a valve and/or heating. 
     Lip Seals 
     Referring to  FIG. 21 , in still yet another embodiment, a lip seal  2710  is an optional rotary engine  110  seal sealing boundaries between fuel-containing regions and surrounding rotary engine  110  elements. A seal seals a gap between two surfaces with minimal force that allows movement of the seal relative to a rotary engine  110  component. For example, a lip seal  2710  seals boundaries between the reference expansion chamber  333  and surrounding rotary engine elements, such as the rotor  440 , vane  450 , housing  210 , and first and second end plates  212 ,  214 . Generally, one or more lip seals  2710  are inserted into any dynamic cap  2200  as a secondary seal, where the dynamic cap  2200  functions as a primary seal. However, a lip seal  2710  is optionally affixed or inserted into a rotary engine surface in place of the dynamic cap  2200 . For example, a lip seal  2710  is optionally placed in any location previously described for use of a cap seal  2200 . Herein, lips seals are first described in detail as affixed to a vane  450  or vane cap. Subsequently, lips seals are described for rotor  440  elements. When the lip seal  2710  moves in the rotary engine  110 , the lip seal  2710  functions as a wiper seal. 
     More particularly, a rotary engine method and apparatus configured with a lip seal  2710  is described. A lip seal  2710  restricts fuel flow from a fuel compartment to a non-fuel compartment and/or fuel flow between fuel compartments, such as between a reference expansion chamber and any of an engine: rotor  440 , vane  450 , housing  210 , a leading expansion chamber  334 , and/or the trailing expansion chamber also referred to as the reference chamber  333 . Generally, a lip seal  2710  is a semi-flexible insert, into a vane  450  or dynamic cap  2200 , that dynamically flexes in response to fuel flow to seal a boundary, such as sealing a vane  450  or rotor  440  to a rotary engine  110  housing  210  or endplate element  212 ,  214 . The lip seal  2710  provides a seal between a high pressure region, such as in the reference expansion chamber  333 , and a low pressure region, such as the leading chamber  334  past the 7 o&#39;clock position in the exhaust phase. Further, lip seals are inexpensive, and readily replaced. 
     Referring still to  FIG. 27 , a vane configured with lip seals  2700  is used as an example in a description of a lip seal  2710 . In  FIG. 27 , vane caps are illustrated with a plurality of optional lip seals  2710 , however, the lip seals  2710  are optionally affixed directly to the vane  450  without the use of a cap  2200 . As illustrated, lip seals  2710  are incorporated into each of the first vane cap  2210 , the second vane cap  2220 , the reference chamber vane cap  2510 , the leading chamber vane cap  2520 , and the vane tip cap  2530 . Each lip seal  2710  seals a potential fuel leak path. For example, the lip seals  2710  on the first vane cap  2210 , the second vane cap  2220 , and the vane tip cap  2530  provide three x-axis seals between the expansion reference chamber  333  and the leading chamber  334 . Lip seals  2710  are also illustrated on each of the reference chamber vane cap  2510  and the leading chamber vane cap  2520 , providing seals between an expansion chamber  333 ,  334  and the rotor-vane chamber  452 , respectively. Not illustrated are lip seals  2710  corresponding to the upper trailing seal  1028  and upper leading seal  1029 . For clarity of presentation, the lip seals  2710  are illustrated along most of a length of a supporting surface, so that individual lip seals are readily illustrated. In practice, each lip seal optionally and preferably extends along an entire longitudinal surface of the supporting element to which the lip seal is affixed and typically abut an adjoining lip seal. 
     Lip seals  2710  are compatible with one or more cap  2200  elements. For example, lip seals  2710  are optionally used in conjunction with any of bearings  2212 , roller bearings  2522 , and any of the means for dynamically moving the cap  2200 . 
     Referring now to  FIG. 28 , an example of a cap configured with seals  2800  is provided. Particularly, the leading chamber vane cap  2520  configured with two lip seals  2710  is figuratively illustrated. The leading chamber vane cap  2520  is configured with one, two, or more channels  2810 . The lip seal  2710  inserts into the channel  2810 . Preferably, the channel  2810  and lip seal  2710  are configured so that the outer surface of the lip seal  2712  is about flush and/or with the outer surface of the leading chamber vane cap  2822  or protrudes slightly therefrom. A ring-seal  2720 , such as an O-ring, restricts and/or prevents flow of fuel between the lip seal  2710  and the leading chamber vane cap  2520 . 
     Still referring to  FIG. 28 , as fuel flows between the outer surface of the leading chamber vane cap  2822  and housing  210 , the fuel hits the lip seal  2710 . The flexible lip seal  2710  deforms to form contact with the housing  210 . More particularly, the fuel provides a deforming force that pushes an outer edge of the flexible lip seal into the housing  210 . 
     Referring now to  FIG. 29A , an example of the lip seal  2710  is further illustrated. The flexible lip seal  2710  contains a trailing lip seal edge  2730  facing the reference expansion chamber  333 . The lip seal  2710  penetrates into the leading chamber vane cap to a depth  2732 , such as along an insert line. Referring now to  FIG. 29B , as fuel runs from the reference expansion chamber  333  between the leading chamber vane cap  2520  and the housing  210 , the trailing lip seal edge  2730  deforms to form tighter contact with the housing  210 . Similarly, as fuel runs from the leading expansion chamber  334  between the leading chamber vane cap  2520  and the housing  210 , the leading lip seal edge  2731  deforms to form tighter contact with the housing  210 . Optionally, both the trailing and leading lip seal edges  2730 ,  2731  are incorporated into a single inset within channel  2810 . 
     Referring now to  FIG. 30 , lip seals, such as the lip seal  2710  previously described, are optionally placed proximate the rotor face, such as next to the first end plate  212  and/or the second end plate  214 . Examples of lip seals on the rotor face include: a rotor/vane lip seal  2714 , a rotor/expansion chamber lip seal  2716 , and an inner rotor lip seal  2718 . The rotor/vane lip seal  2714  is located on the trailing edge of rotor-vane chamber  452  and/or on a leading edge of rotor/vane slot, which aids in sealing against fuel flow from the rotor-vane chamber  452  and/or reference expansion chamber  333  to the face of the rotor  440 . The rotor/expansion chamber lip seal  2716  aids in sealing against fuel flow from the reference expansion chamber  333  to the face of the rotor  440 . The inner rotor lip seal  2718  aids in sealing against fuel flow from the rotor-vane chamber  452  to the face of the rotor  440  toward the shaft  220 . For clarity of presentation, the rotor/vane lip seal  2714 , the rotor/expansion chamber lip seal  2716 , and the inner rotor lip seal  2718  form a continuously connected ring of seals on a rotor edge side of the reference chamber. A first end of the rotor/vane lip seal  2714  optionally terminates within about 1, 2, 3, or more millimeters from a termination of the rotor/expansion chamber lip seal  2716 . A second end of the rotor/vane lip seal  2714  optionally terminates within about 1, 2, 3, or more millimeters from the inner rotor lip seal  2718 . 
     Lip seals  2710  are optionally used alone or in pairs. Optionally a second lip seal lays parallel to the first lip seal. In a first case of a rotor face lip seal, the second seal provides an additional seal against fuel making it past the first lip seal. In a second case, referring again to  FIG. 29B , the two lip seals seal against fuel flow from two opposite directions, such as fuel from the reference expansion chamber  333  or leading expansion chamber  334  past seals  2730  and  2731  on the leading chamber vane cap  2520 , respectively. 
     Exhaust 
     Generally, a rotary engine method and apparatus is optionally configured with an exhaust system. The exhaust system includes an exhaust cut into one or more of a housing or an endplate of the rotary engine, which interrupts the seal surface of the expansion chamber housing. The exhaust cut directs spent fuel from the rotary engine fuel expansion/compression chamber out of the rotary engine either directly or via an optional exhaust port and/or an exhaust booster. The exhaust system vents fuel to atmosphere or into the condenser  120  for recirculation of fuel in a closed loop, circulating rotary engine system. Exhausting the engine reduces back pressure on the rotary engine thereby enhancing rotary engine efficiency and reducing negative work forces directed against the primary rotor rotation direction. 
     More specifically, fuel is exhausted from the rotary engine  110 . After the fuel has expanded in the rotary engine and the expansive forces have been used to turn the rotor  440  and shaft  220 , the fuel is still in the reference expansion chamber  333 . For example, the fuel is in the reference expansion chamber after about the 6 o&#39;clock position. As the reference expansion chamber decreases in volume from about the 6 o&#39;clock position to about the 12 o&#39;clock position, the fuel remaining in the reference expansion chamber resists rotation of the rotor. Hence, the fuel is preferentially exhausted from the rotary engine  110  after about the 6 o&#39;clock position. 
     For clarity, the reference expansion chamber  333  terminology is used herein in the exhaust phase or compression phase of the rotary engine, though the expansion chamber  333  is alternatively referred to as a compression chamber. Hence, the same terminology following the reference expansion chamber  333  through a rotary engine cycle is used in both the power phase and exhaust and/or compression phase of the rotary engine cycle. In the examples provided herein, the power phase of the engine is from about the 12 o&#39;clock to 6 o&#39;clock position and the exhaust phase or compression phase of the rotary engine is from about the 6 o&#39;clock position to about the 12 o&#39;clock position, assuming clockwise rotation of the rotary engine. 
     Exhaust Cut 
     Referring now to  FIG. 31 , an exhaust cut is illustrated. One method and apparatus for exhausting fuel  3100  from the rotary engine  110  is via the use of an exhaust cut channel or exhaust cut  3110 . The exhaust cut  3110  is one or more cuts venting fuel from the rotary engine. A first example of an exhaust cut  3110  is a cut in the housing  210  that directly or indirectly vents fuel from the reference expansion chamber  333  to a volume outside of the rotary engine  110 . 
     A second example of an exhaust cut  3110  is a cut in one or both of the first endplate  212  and second endplate  214  that directly or indirectly vents fuel from the reference expansion chamber  333  to a volume outside of the rotary engine  110 . Preferably the exhaust cuts vent the reference expansion  333  chamber from about the 6 o&#39;clock to 12 o&#39;clock position. More preferably, the exhaust cuts vent the reference expansion chamber  333  from about the 7 o&#39;clock to 9 o&#39;clock position. Specific embodiments of exhaust cuts  3110  are further described, infra. 
     Housing Exhaust Cut 
     Still referring to  FIG. 31 , a first example of an exhaust cut  3110  is illustrated. In the illustrated example, the exhaust cut  3110  forms an exhaust cut, exhaust hole, exhaust channel, or exhaust aperture  3105  into the reference expansion chamber  333  at about the 7 o&#39;clock position. The importance of the 7 o&#39;clock position is described, infra. The exhaust aperture  3105  is made into the housing  210 . The exhaust cut  3110  runs through the housing  210  from an inner wall  432  of the housing directly to an outer wall of the housing  433  or indirectly to an exhaust port  3120 . In the case of use of an exhaust port, the exhaust flows sequentially from the exhaust aperture  3105 , through the exhaust cut  3110 , into the exhaust port  3120 , and then either out through the outer wall  433  of the housing  210  or into an exhaust booster  3130 . The exhaust is then vented to atmosphere, to the condenser  120  as part of the circulation system  180 , to a pump or compressor, and/or to an inline pump or compressor. 
     Referring now to  FIG. 32A  and  FIG. 32B , an example of multiple housing exhaust ribs or housing exhaust ridges  3210  and multiple housing exhaust port channels or housing exhaust cuts  3220  is provided. Referring now to  FIG. 32A  and  FIG. 32B , the housing exhaust cuts  3220  are gaps or channels in the inner housing wall  432  into the housing  210 . Ridges formed between the housing exhaust cuts  3220  are the housing exhaust ridges  3210 . The multiple housing exhaust cuts  3220  are examples of the exhaust cut  3110  and are used to vent exhaust as described, supra, for the exhaust cut  3110 . Particularly, though not illustrated in  FIG. 32A  for clarity, the housing exhaust cuts  3110  vent through the outer wall  433  of the housing  210  or into the exhaust booster  3130  as described, supra. 
     Still referring to  FIG. 32A  and  FIG. 32B , the exhaust ridges are optionally and preferably positioned to support the load of the roller bearing  1740  of vane  450 . As illustrated, the three roller bearings  1740  on the vane-tip  1614  of vane  450  align with three exhaust ridges  3210 . The number of exhaust ridges is optionally 0, 1, 2, 3, 4, 5 or more in the rotary engine  110  and optionally preferably correlates to the number of roller bearings  1740  per vane  450 . 
     Referring again to  FIG. 31 , optional housing temperature control lines  3140  are illustrated. The housing temperature control lines are optionally embedded into the housing  210 , wrap the housing  210 , and/or carry a temperature controlled fluid used to maintain the housing  210  at about a set temperature. Optionally, the temperature control lines are used as a component of a vapor generator. 
     Referring now to  FIG. 33 , optional exhaust booster lines  3310 ,  3320  are illustrated. A first exhaust booster line  3310  runs substantially in the exhaust cut  3110  and originates proximate the exhaust aperture  3105 . A second exhaust booster line  3320  runs substantially outside of housing  210  and preferably originates in a clock position prior to the exhaust aperture  3105 . One or both of the first exhaust booster line  3310  and second exhaust booster line  3320  terminate at exhaust booster  3330  and function in the same manner as the booster line  1024 , described supra. Preferably, only the second exhaust booster line  3320  is used. Running the second exhaust booster line outside of the temperature controlled housing allows the spent fuel discharging via the second exhaust booster line to cool relative to the spent fuel discharging through the exhaust cuts  3110  or the housing exhaust cuts  3220 . The cooler spent fuel functions to accelerate or boost exhaust flowing through the exhaust cut  3110  in the booster  3130 . Further, the second housing exhaust booster line  3220  is preferably positioned in the clock cycle prior to the exhaust aperture  3105 , which allows a burst or period of high pressure exhaust vapor to flow from the reference expansion chamber  333  through the second housing exhausts booster line  3220  into the exhaust booster  3330  prior to any fuel being vented through the exhaust aperture  3105 . the burst of exhaust to form a partial vacuum outside of the exhaust booster  3330  to help pull exhaust out of the first compression chamber via the exhaust cut  3110 . 
     Referring now to  FIG. 31  and  FIG. 33 , the positioning of the exhaust cut  3110  is further described. In  FIG. 31 , the rotor  440  is positioned such that there exists a vane  450  at about the 6 o&#39;clock position. The power cycle is substantially over at about the 6 o&#39;clock position, so the exhaust aperture  3105  optionally is positioned anywhere after about the 6 o&#39;clock position. Referring now to  FIG. 33 , the rotor  440  is positioned such that there exists a vane  450  just before the 7 o&#39;clock position of the exhaust aperture  3105 . In  FIG. 33 , it is clear that if the exhaust aperture were to be positioned just after the 6 o&#39;clock position, then the reference chamber spanning about the 5 o&#39;clock to about the 7 o&#39;clock position would be both in the power phase and the exhaust phase at the same moment, which results in a loss of power as the reference chamber  333  begins to exhaust through the exhaust aperture  3105  before completion of the power phase of the trailing vane  450  reaching the about 6 o&#39;clock position. Hence, it is preferable to move the exhaust aperture clockwise. For a six vane  450  rotary engine  110 , the exhaust aperture is moved about one-sixth divided by two of a clock rotation past the 6 o&#39;clock position. When the vane  450  passes the exhaust aperture  3105 , the vane  450  changes function from that of a seal to a function of an open valve, exhausting the reference chamber  333  by opening the exhaust aperture  3105 . 
     Similarly, for a rotary engine having n vanes, the exhaust aperture is preferably rotated about ½n of a clock rotation past about the 6 o&#39;clock position and preferably a 1 to 15 extra degrees, depending on the thickness of the vane  450 . 
     In  FIG. 31 , the exhaust aperture  3105  is illustrated as a distinct opening. Preferably, the exhaust aperture begins at the beginning of a channel, such as the housing exhaust channels  3220  illustrated in  FIG. 32A  and  FIG. 32B . Preferably, each exhaust channels continues with an opening through the inner housing  432  to the reference chamber  333  from the point of the exhaust aperture  3105  until the exhaust port  3120 , which is figuratively illustrated as a dashed line in the inner wall  432  of the housing  210  in  FIG. 33 . 
     Endplate Exhaust Cut 
     As described supra, the exhaust cuts  3110  are made into the housing  210 . Optionally, the exhaust cuts  3110  are made into the first endplate  212  and second endplate  214  to directly or indirectly vent fuel from the reference expansion chamber  333 . Particularly, the exhaust cut  3110  optionally runs through the first and/or second endplate  212 ,  214  from an inner wall of the endplate directly to an outer wall of the endplate, to an exhaust port, or to a fuel input of a secondary or tertiary rotary engine. In the case of use of an exhaust port, the exhaust flows sequentially from and endplate exhaust aperture, through an endplate exhaust cut, into an endplate exhaust port, and then either out through the outer wall of the endplate or into an endplate exhaust booster. The exhaust is then vented to atmosphere, to the condenser  120  as part of the circulation system  180 , or to another engine as an input. 
     Optionally and preferably, the exhaust cuts  3110  exist on multiple planes about the reference expansion chamber, such as cut into two or more of the housing  210 , first endplate  212 , and second endplate  214 . 
     Exhaust Port 
     Preferably, the exhaust port  3120  is positioned at a point in the clock face that allows two vanes  450  to seal to the housing  210  before the initiation of a new power phase at about the 12 o&#39;clock position. Referring now to  FIG. 31 , the exhaust port  3120  is positioned at about the 10 o&#39;clock position, and is optionally positioned before the 10 o&#39;clock position, to allow two vanes  450  to seal to the inner wall  432  after the exhaust port  3120  and prior to the initiation of a new power phase at about the 12 o&#39;clock position. As with the exhaust aperture  3105 , the position of the exhaust port depends on the number of vanes  450  in the rotary engine  110 . For a six vane  450  rotary engine  110 , the exhaust port  3120  is moved about one-sixth divided by two of a clock rotation past the 6 o&#39;clock position. Similarly, for a rotary engine  110  having n vanes, the exhaust port  3120  is preferably rotated about ½n of a clock rotation past about the 6 o&#39;clock position and preferably a 1 to 15 fewer degrees, depending on the thickness of the vane  450 . 
     Twin Rotor/Multiple Rotor System 
     In yet another embodiment, the exhaust port  3120  vents into an inlet port of a second rotary engine. This process is optionally repeated to form a cascading rotary engine system. 
     Vane Insert 
     Historically, rotary engines using sliding vanes: (1) did not seal properly at start-up, such as at zero revolutions per minute, due to insufficient outward force applied by the vane to the stator and (2) had excessive outward centrifugal force at higher operational speeds. Herein, a stressed band system is described to overcome the historical problems. While, for clarity of presentation, the stressed band system is described in terms of sealing the vane  450  to the housing  210 , the stressed band system is optionally used to provide any seal, such as a seal to the rotor  440 , a seal to the first endplate  212 , and/or a seal to the second endplate  214 . 
     Generally, the stressed band system uses a stressed band wound around counterbalanced rollers in a controlled space, such as in two dynamically opposing C-shaped wraps and/or about an on force-axis S-shaped wrap of the stressed band wound around two rollers in a laterally fixed housing between two endplates or connection points. Still more generally, the stressed band is optionally of any elongated shape and three or more rollers are optionally used. The confined stressed/rotated bands provide a sealing force suitable at low rotary engine revolutions per minute and provide a controllable force reducing pressure at high rotary engine revolutions per minute. The stressed band is optionally a sheet of material, as opposed to a coil-like spring. The sheet of material is optionally a substantially rectangular sheet, such as a sheet of metal, bent or wound into a shape having a spring-like or potential energy. Generally, the sheet has an elongated length, a smaller width, and a still smaller thickness, where the length is greater than 50, 100, or 200 times the thickness and the width is greater than 10, 20, 30, 40, or 50 times the thickness. The stressed band system is further described, infra. 
     Referring now to  FIG. 34 , a vane insert  3400  used to provide a sealing force and/or used in control of a sealing force is described. Generally, the vane insert  3400  is integrated into, positioned, and/or inserted into the vane  450  between the rotor  440  and the housing  210 . The vane insert  3400  optionally includes a stressed band  3410 . Generally, the stressed band  3410  is in a compressed and/or higher potential energy state in a wound configuration and is in a relaxed and/or lower potential energy state in an extended configuration. As illustrated, the stressed band  3410  is in a wound configuration, where the stressed band  3410  applies at least a first force, F 1 , along a vector from the rotor  440  to the housing  210 . The stressed band  3410  is further described infra. 
     Still referring to  FIG. 34 , the stressed band  3410  in the vane insert  3400  is illustrated in a wound configuration between anchor points, such as a first anchor point  3422  and a second anchor point  3424 . The stressed band  3410  is additionally wrapped about and/or wound through a set of guide rollers  3430 , where the set of guide rollers  3430  comprises n guide rollers, where n is a positive integer. As illustrated, the stressed band  3410  is part-circumferentially wound around a first guide roller  3432 , about a second guide roller  3434 , and about a spooler  3436 , which is also referred to herein as a spooling roller. In this example, the first guide roller  3432  and second guide roller  3434  turn in opposite directions over a given time period. Further, in this example, the second guide roller  3434  and spooler  3436  rotate in the same direction over the given time period. The guide roller is optionally aligned along an axis ninety degrees off of the axis of the first guide roller  3432  and second guide roller  3434 . Generally, the stressed band is a low friction bearing that uses a stressed metal band and counter rotating rollers within an enclosure, such as in Rolamite technology. The metal band is optionally a metal band, a stressed plastic band, a laminated band in a high energy state attempting to straighten, a temperature sensitive band, and/or a material that deforms upon application of an electrical charge and/or current. 
     Still referring to  FIG. 34 , as illustrated, the stressed band  3410  in the vane insert  3400  releases potential energy by extending an outer band surface, such as toward the housing  210 , to yield the first force, F 1 , along the y-axis. In addition, the outer band surface naturally releases potential energy at other positions in the winding. Hence, any number of optional band guiding elements  3440  are used. As illustrated, a first band guiding element  3442  is a rotationally leading vane insert wall  3442 , which resists the potential energy release of the outer side of the stressed band along the x-axis toward the rotationally leading chamber. Further, as illustrated, a second band guiding element  3444  resists potential energy release of the stressed band  3410  away from the rotationally trailing chamber. 
     Herein, for clarity of presentation, a single stressed band is illustrated in the figures and examples. However, optionally and preferably more than one stressed band is used in place of the single illustrated stressed band. For example, 2, 3, or more stressed bands are optionally used in each vane  450 . 
     Still referring to  FIG. 34  and referring again to  FIG. 6 , motion of the vane insert  3400  is further described. In  FIG. 34 , the vane insert  3400  is illustrated in a retracted position at a first point in time t 1 , and in an extended position at a second point in time t 2 . The first anchor point  3422  is optionally attached to the rotor  440 , such as in a fixed position, whereas the second anchor point  3424  is attached to the spooler  3436 , which optionally freely rotates. Hence, referring now to  FIG. 6 , as illustrated, the inner wall  432  of the housing  210  forces the vane  450  inward toward the shaft at the 12 o&#39;clock position, which causes the stressed band  3410  to spool on the spooler  3436 , as illustrated at the first time, t 1 , in  FIG. 34 . As the rotor  440  rotates, such as to the 6 o&#39;clock position in  FIG. 6 , the distance between the rotor vane base  448  and the inner wall  432  of the housing  210  increases and the potential energy of the stressed band  3410  is released with the first force, F 1 , in the vane insert  3400  pushing the vane  450  outward, which provides a sealing force between the vane  450  and the housing  210 . Thus, as the rotor  440  rotates within the housing  210 , the stressed band  3410  dynamically unwinds and winds on the spooler  3436  providing a continuous, optionally varying, outer force on the vane  450  toward the housing  210  resisted by the first anchor point  3422 . It is observed that: (1) during the power stroke potential energy of the stressed band  3410  is released as the spooler  3436  unwinds and (2) during the exhaust phase the stressed band  3410  provides a continuous outer force on the vane  450  toward the housing  210  even with the sudden loss of pressure in the expansion chamber. The inventor notes that without the outer force during the exhaust phase, the vane  450  would chatter or rattle between inner and outer extension positions causing uncontrolled exhausting between expansion chambers and/or excessive wear on the vane element and the repeatedly struck inner wall  432  of the housing  210 . 
     Still referring to  FIG. 34 , the inventor notes that as illustrated the vane insert  3400  provides an outward sealing force or first force, F 1 , on the vane  450  toward the housing  210  even when the rotary engine  110  is not rotating. Thus, upon starting the rotary engine  110 , the rotary engine  110  does not need a starter to load the chambers, which eliminates an entire engine starting mechanism. Further, the seal at zero revolutions per minute allows energy to be provided by the engine immediately, such as during the first few revolutions of the rotary engine  110 . 
     Still referring to  FIG. 34 , the inventor further notes that as illustrated the vane insert  3400  provides the outward sealing force or first force, F 1 , on the vane  450  toward the housing  210  even when the rotary engine is operating a very low revolutions per minute, such as at less than 360, 180, 120, 60, 30, 20, 10, 5, or 2 revolutions per minute. Thus, the vane insert  3400  allows the rotary engine  110  to convert power from an energy source, such as a windmill or residual heat source, even when the energy source is minimal, such as at low wind speeds or when the residual heat is minimal, initially present, or fading. 
     Stressed Band 
     The stressed band  3410  is optionally a spring steel belt, contains an S-shape bend, comprises a tension band, and/or contains at least one laminated surface/material. Herein, spring steel is a low-alloy steel, a medium-carbon steel, and/or high-carbon steel with a very high yield strength that allows an object made from the spring steel to return to its original shape despite significant bending or twisting. Optionally and preferably, the stressed band  3410  operates in combination with counter rotating rollers in an enclosure to create a bearing device that loses very little energy to friction. The stressed band  3410  forms a C-shape around one roller and an S-shape around two rollers. The bearing device is optionally linear or non-linear, as further described infra. 
     In another embodiment, the stressed band  3410  comprises a shape memory alloy, which herein also refers to a memory metal, smart metal, and/or smart alloy. Generally, the shape memory alloy is formed in an extended shape, such as a shape that would push the vane  450  outward toward the housing  210 . The stressed band  3410 , containing the shape memory alloy, is then configured into a non-heated shape, such as wound about the band guiding elements  3440  between the first anchor point  3422  and second anchor point  3424  and/or guided by the band guiding elements  3440 . When heated, the shape memory alloy will attempt to revert to its original state, herein the original extended shape. Thus, when the engine runs and heats up, the stressed band  3410  will try to deform to the extended shape applying the first force, F 1 , on the vane  450  toward the housing  210 . An example of a shape memory metal is: tungsten coated with aluminum and/or a metal alloy of nickel and titanium, such as Nitinol, Nitinol  55 , and/or Nitinol  60 . Nitinol alloys exhibit two closely related properties: shape memory and super elasticity, which is also referred to as pseudo-elasticity. Shape memory is the ability of the shape metal to deform at one temperature, then recover its original, un-deformed shape upon heating above its transformation temperature. Optionally, a crystalline boron silicate mineral compounded with elements such as aluminum, iron, magnesium, sodium, lithium, or potassium, for example tourmaline, is added to, embedded into, and/or is affixed to the memory metal as a means for adding current, heat, and/or pressure to the memory metal. For example, a current/voltage is provided to the tourmaline to introduce heat to the memory metal inducing a shape change. Similarly, the memory metal, a coated memory metal, and/or tourmaline inserts are optionally positioned in vane vapor vortex generating side inlet ports, providing both piezoelectric and thermo-electric generation. In one case tourmaline in conjunction with the vane is used as part of an electromagneto-hydrodynamic device. 
     In yet another embodiment, an induced temperature change is applied to a memory shape alloy to move an element of the rotary engine  110 . For example, the main controller  110  injects into the rotary engine  110 , such as via a fuel inlet, a heated or cooled fuel, such as a liquefied nitrogen. The liquefied nitrogen expands in the expansion chamber functioning as an expansion fuel and changes the temperature of the memory shape alloy to perform a task, such as opening or closing a valve and/or extending or retracting the element of the rotary engine  110 . 
     Vane Insert 
     Referring now to  FIG. 35A  and  FIG. 35B , the vane insert  3400 , which inserts into a vane  450 , is further described. Referring now to  FIG. 35A , the stressed band  3410  is illustrated in a perspective view, as an optional embodiment attached directly to the rotor  440  and with a band cutout  3412 . The band cutout  3412  is optionally of any geometric shape. 
     Referring now to  FIG. 35B , further optional elements of the stressed band  3410  are described. First, as illustrated, the band cutout  3412  is closer to the rotor  440  than any of the band guiding elements  3440  or rollers. Since the memory of the stressed band  3410  is dependent upon the cross-sectional area along the y/z-plane, the illustrated band cutout  3412  will weaken the partial force of the band where the band cutout  3412  is present, in this case making the rotor side of the stressed band  3412  weaker than the housing side of the stressed band. Second, as illustrated, an outer perimeter of the stressed band  3414  is optionally non-rectangular in the y/z-plane. As illustrated, the stressed band  3410  widens from a first band width  3414  at the rotor  440  to a second band width  3416 , proximate the vane cap  2210 , vane-tip  1614 , rotor side of the vane head  1611 , and/or inner portion of the vane body  1610  on the housing side of the stressed band  3410 . As illustrated, the band outer edge  3418 , rotationally trailing edge, and/or rotationally leading edge, defines the z-axis width of the stressed band  3410  as a function of y-axis position. The cut-out and perimeter shape of the stressed band  3410  alter the net force applied by the stressed band  3410  along the longitudinal axis of the stressed band  3410 . Through shape of the band outer edge  3418  and/or shape of the band cutout  3412 , the force, such as the first force F 1 , along the y-axis pushing the vane toward the housing  210  is optionally set to be proportional to the Fibonacci ration plus or minus ten percent as a function of rotation of the rotor in the power stroke. 
     Referring now to  FIG. 36 (A-D), additional shapes/features of the stressed band  3410  in a pre-installation flat orientation are described, to further clarify the invention. Referring now to  FIG. 36A  and  FIG. 36B , the stressed band  3410  is illustrated with a rectangular perimeter and a band cutout  3412  to a rotor side of a mid-line and to a housing side of the mid-line, respectively. Generally, moving a position of the band cutout  3412  changes the net force pushing in one direction or another. Here, in  FIG. 36A  the band cutout  3412  to the rotor side of the midline results in less stressed band potential energy to the rotor side of the mid-line and a net shift in applied force of the stressed band  3412  toward the rotor  440 . Similarly, in  FIG. 36B  the band cutout  3412  to the housing side of the midline results in less stressed band potential energy to the housing side of the mid-line and a net shift in applied force of the stressed band  3412  toward the housing  210 . Referring now to  FIG. 36C , the stressed band  3410  is illustrated with a sloping band outer edge  3418 , resultant in more force toward the housing  210  and additionally with an increasing x/z-plane band cutout  3412  with a sharp cutoff, resulting in a net peak force, such as through a power stroke of the rotary engine  110 , and a sharp drop-off in peak force, such as during an exhaust phase of the rotary engine  110 . Referring now to  FIG. 36D , the band outer edge  3418  is illustrated with a decreasing z-axis cross-sectional length as a function of y-axis position, where the decrease is non-linear. Optionally, the non-linear change in x/z-plane cross-sectional area changes at a calculated amount, such as at about the Fibonacci ratio and/or at about a multiple of the cross-sectional area of the expansion chamber  333  as a function of rotation of the rotor  440  through the power stroke, such as from a one o&#39;clock rotational position to a six o&#39;clock rotational position. 
     Dynamic Vane Force Actuation 
     Rotary engines traditionally have the problems of: (1) sealing the vane to the housing at low revolutions per minute, due to lack of centrifugal force, and (2) preventing excessive centrifugal force from applying undue resistance/binding pressure between the vane and the housing at high revolutions per minute. As described, supra, the stressed band  3410  allows for an appropriate contact force between the vane  450  and the housing  210  of the rotary engine  110 : (1) at zero revolutions per minute and (2) at higher revolutions per minute due to the balanced roller forces and/or changing y/z-plane cross-sectional area of the stressed band  3410  as a function of y-axis position in the vane  450 . 
     Referring now to  FIG. 37 , another vane force actuation embodiment is described. Generally, one end of the stressed band  3410 , such as the first anchor point  3422 , is optionally moved with time, need, fuel supply, engine performance, and/or rotation position. Several examples are provided to further illustrate the embodiment. 
     Example I 
     Referring still to  FIG. 37  and now referring to  FIG. 38 , in a first example, the first anchor point  3422  comprises use of a worm drive  3710 . The worm drive  3710  is used to alternately extend and retract a first end of the stressed band  3410 , where the stressed band  3410  is used to provide an outward force to the vane  450  toward the housing  210 . At a first point in time, such as when the rotary engine  110  is starting and/or operating at low revolutions per minute, the centrifugal force of the vane  450 , resultant from rotation of the vane  450 , toward the housing  210  is insufficient to form a seal. At the first point in time, the worm drive  3710  is optionally used to extend the stressed band  3410  into the vane  450 , which yields a larger first force, F 1 , from the stressed band  3410  on the vane  450  toward the housing  210 . At a second point in time, such as when the rotary engine  110  is operating at high revolutions per minute, the centrifugal force of the vane  450  toward the housing, due to high rotational speeds of the vane  450 , is greater. At the second point in time, the worm drive  3710  is optionally used to retract the stressed band  3410  away from the vane  450 , which yields a typically but optionally lower, zero, or negative first force, F 1 , from the stressed band  3410  on the vane  450  toward the housing  210 . Thus, (1) at low rotary engine  110  speeds, the stressed band  3410  is used to add the first force, F 1 , to the centrifugal force of the rotating vane and (2) at high speeds of the rotary engine  110 , the stressed band  3410  is optionally used to reduce the first force, F 1 , relative to a force applied when the stressed band  3410  is extended. The lower or negative first force, F 1 , thus reduces total force applied by the vane  450  to the housing  210  at the second point in time. 
     Example II 
     Referring still to  FIG. 37 , the worm drive  3422 , is optionally any mechanical/electromechanical element used to change the effective length of the stressed band  3410 , where the effective length is a distance from the first anchor point  3422  to the second anchor point  3424 , which moves on the spooler  3436 . For instance, a clamping mechanism  3712 , such as a clamp under control of the main controller  170 , optionally pins a section of the stressed band  3410  against an element, such as the vane  450 , thereby changing the effective length of the stressed band  3410 . Optional electromechanical elements used to control, extend, and/or retract a portion of the stress band include, but are not limited to, a gear, a lever, a sensor, a circuit, a controller, a switch, a solenoid, a relay, a valve, a clamp, a piston, and/or a computer, which is optionally linked to a look-up table containing pre-calculated values, such as a worm drive position to yield a radially outward force of a given amount, and/or computer code for controlling the stressed band. 
     Example III 
     Referring still to  FIG. 37 , movement of the first anchor point  3422  to alternately add and subtract from the first force, F 1 , is optionally controlled by the main controller  170  and/or a sub-control unit thereof. The main controller  170  optionally uses a sensor input, from the at least one sensor  190 , in the control of the first anchor point  3422 . In one case, the sensor input senses the outward force of the vane  450  against the housing  210 . In another case, the sensor  190  senses the revolutions per minute of the rotor  440  of the rotary engine  110 , which is related to centrifugal force of the vane  450  on the housing  210 . 
     Example IV 
     Referring still to  FIG. 37 , in place of the worm drive  3710 , optionally any electromagnetic element is used to: (1) dynamically move the first anchor point  3422  and/or (2) all or part of the vane insert  3400  relative to the housing along the y-axis. For example, a motor is used in place of the worm drive to retract the stressed band  3410  at high engine speeds and to extend the stressed band  3410  at low engine speeds. 
     Example V 
     In another example, a rotary engine having a housing, a rotor, and a set of vanes is used where the set of vanes divides a volume between the rotor and the housing into a set of chambers. A stressed sheet, such as the stressed band  3410 , in a first vane of the set of vanes, is used to apply a radially outward force on a section of the first vane toward said housing. Further, electromechanical means for controlling extension of the first vane toward said housing and/or away from the housing are used. Preferable, the electromechanical means: (1) extend the stressed sheet toward the housing when an operational speed, or rotation rate, of the engine decreases and/or (2) retract the stressed sheet away from the housing when the operational speed of the engine increases. Optionally, the stressed sheet yields: (1) a first force on the first vane toward the rotor at a first engine speed and (2) a second force on the first vane toward the rotor housing at a second engine speed, where the second engine speed is at least 2, 3, 5, 10, 25, 50, or 100 times said first engine speed and/or where the first force at least 1, 2, 5, 10, 20, or 50 percent greater than the second force. 
     Example VI 
     In another example, the stressed sheet, described supra, rolls into the spooler  3436 . For example, the spooler optionally contains two outer ends and a curved connecting surface, such as a spool of thread. The spooler optionally contains a slit, through which the stressed sheet passes and an interior surface about which the stress sheet spools. The outer curved connecting surface thus comprises a barrier against which the stressed sheet pushes, where the force is transferred by mechanical means to the vane, such as with the follower. 
     Vane Cam 
     In another embodiment, one or more sealing forces applied to the vane  450  toward the housing  210  are non-linear with rotation of the rotary engine  110 . An example of a non-linear force is provided, infra. 
     Referring now to  FIG. 39 , a non-linear cam roller  3920  used in actuation of the vane  450  is described. Generally, rotational motion of the cam roller  3920 , which is an example of the spooler  3436 , is transferred to linear motion of a cam follower  3926 , which in turns applies an outward force to an inside structure of the vane  450  toward the housing  210 . The cam roller  3920  is an example of the first guide roller  3432 , the second guide roller  3434 , or the spooler  3436 . 
     Example I 
     A non-limiting example is used to further describe a cam system  3900 . Referring again to  FIG. 3  and referring now to  FIG. 39 , this example describes vane actuation during the power stroke of the rotary engine  110  from about the one o&#39;clock to five o&#39;clock position plus or minus 2, 5, 10, 15, or 20 degrees. As the vane  450  rotates with the rotor  440  in the housing through the power stroke, the stressed band  3410  partially unwinds from the cam roller  3920 . Motion of the cam roller  3920  is transferred to the cam follower  3926 . For instance, a cam follower wheel  3927  rotates with the cam roller  3920  and the cam follower wheel  3927  forces a cam rod  3928  into a radially inward side of an element of the vane  450 , such as a cam guide slot, which pushes the vane  450  toward the housing  210 . Generally, the stressed band  450  extends releasing potential energy in the stressed band  3410 , which is transferred to an outward force on the vane  450 . In a first case, the stressed band  3410  exerts a linear force with motion, such as in the case of a rectangular stressed band and a circular spooling roller. In a second case, as the stressed band  450  extends, a non-linear force is applied as a function of time and/or a function of extension of the vane  450 , such as in the instances of: (1) a non-rectangular stressed band and/or (2) where the stressed band  3410  has an aperture therethrough. In a third case, the cam roller  3920  in the cam system  3900  is non-circular, such as oval or egg-shaped. In the third case, extension of the stressed band  3410  and translation of the cam follower  3926  yields a non-linear extension of the cam rod  3928  pushing the vane  450  in a non-linear fashion, such as that matching the distance between the rotor  450  and the housing  210  at the current rotational position of the vane  450  in the rotary engine  110 . For example, the non-linear force of the stressed band and/or the non-linear extension resultant from a curved outer shape of the cam roller  3920  tracks the expansion rate of the trailing expansion chambers as a function of rotational position. Stated again, for clarity, the cam shape optionally matches, within ten percent, a distance from the rotor face to the housing in the power stroke, which is non-linear with rotation positions, as illustrated in  FIG. 9 . Hence, the non-linear increase in cross-sectional distance with rotation position is optionally approximately correlated by the distance from the cam center to the cam edge as a function of rotation. 
     Example II 
     A second non-limiting example is used to still further describe the cam system  3900 . As the cam roller  3920  rotates about a rotation axis, a radial cam distance  3924  between a circle  3922  about the rotation axis and an outer perimeter of the cam roller  3920  lengthens at the rate of expansion of the expansion chamber, such as within less than 1, 2, 4, 6, 8, 10, 15, or 20 percent of the Fibonacci ratio as a function of rotation of the rotor  450  through at least a portion of the power stroke. Hence, the cam shape as a function of rotation of the cam optionally matches the power stroke as a function of rotation of the rotor. Similarly, the opposite side of the cam has a shape that as a function of rotation matches the chamber between the rotor  440  and the housing  210  in the compression phase of the rotary engine  110 . Optionally, the vane  450  contains a cam cutout  3921  to accommodate steric cam rotation constraints. 
     Forces/Injection Ports 
     Referring now to  FIG. 2 ,  FIG. 3 ,  FIG. 38 , and  FIG. 39 , the rotary engine  110  optionally includes a set of injection ports  3910 . The set of injection ports  3910  includes: a first injection port  3912  in the first expansion chamber  335 ; a second injection port  3914  in the expansion chamber after a first rotation of the rotor  440 , such as in the second expansion chamber  345 ; a third injection port  3916  into the expansion chamber after a second rotation of the rotor  440 , such as the third expansion chamber  355 ; via a fuel path through the shaft  220  of the rotary engine  110 ; through the fourth injection port  3918  into a rotor-vane chamber  452  or rotor-vane slot between the rotor  440  and the vane  450 ; a fifth injection port, such as through flow tube  1510  and shaft valve  3811 ; and/or through the telescoping second rotor conduit insert  1512  and via the vane wing valve  3813 . Optionally, one or more of the injection ports  3910  are controlled through mechanical valving and/or through use of the main controller  170 . Optionally, the first, second, and/or third injection ports  3912 ,  3914 ,  3916  are through the first endplate  212  of the rotary engine  110  separating the rotor from a circumferential housing or housing  210 , through a second endplate  214  parallel to the first endplate  212 , through a centerplate between two conjoined rotary engines; and/or through the circumferential housing or housing  210 . The injection ports and radially outward sealing forces are further described, infra. 
     Referring now to  FIG. 38 , controllable forces acting radially outward from the vane  450  toward the housing  210  are further described. Generally, as the rotor  440  of the rotary engine  110  rotates, the vane  450  exhibits a centrifugal force on the housing  210 . Additional forces are optionally: (1) added to and/or (2) subtracted from the centrifugal force. The additional forces are optionally controlled through: (1) purely mechanical operation of valves, such as via the lower trailing vane seal  1026  valving the first rotor conduit  1022  described supra and/or (2) via electromechanically opening/closing valves under control of the main controller  170 . The inherent controlled forces are further described, infra. 
     Still referring to  FIG. 38 , the first force, F 1 , resultant from the stressed band  3410 /roller combination in a constrained space in the vane insert  3400  is described supra. 
     Still referring to  FIG. 38 , a second force, F 2 , and third force, F 3 , are resultant from expansion of the fuel in the trailing expansion chamber or reference  333  and leading expansion chamber  334 , respectively, exerting a force on the wing-tip bottom  1634 . The second force, F 2 , and third force, F 3 , are controllable by using the main controller  170  to control rate of fuel flow into the first inlet port  162 . Optionally, the main controller  170  uses input from a sensor  190 , such as a power load sensor and/or a fuel supply sensor in determination of a dynamically targeted fuel flow. 
     Still referring to  FIG. 38 , a fourth force, F 4 , and fifth force, F 5 , are resultant from expansion of the fuel in the rotor-vane chamber  452 , such as via the first rotor conduit  1022 . The fourth force, F 4 , acts on a rotor side of the base of the vane  450  from expansion of fuel in the rotor-vane chamber  452 . Similarly, the fifth force, F 5 , acts on a rotor side of a vane element, such as after passing through the vane conduit  1025 . Herein, the fifth force, F 5 , having a y-axis vector is illustrated as exiting the vane  450  on a trailing vane side into the trailing expansion chamber or reference chamber  333 . However, the fifth force, F 5 , is optionally routed through the wing-tip bottom  1634 , as illustrated for the sixth force, F 6 , described infra. 
     Still referring to  FIG. 38 , the sixth force, F 6 , optionally originates from fuel passing through the shaft  220 . More particularly, fuel sequentially flows through the shaft  220 , as described supra; through the flow tube  1510  passing through the rotor-vane chamber  452 ; into a shaft-vane conduit  1520 ; and out to the trailing expansion chamber  333  through the wing-tip bottom  1634 , where the expansion of the fuel and/or use of the vane flow booster  1340  provides a radial thrust or the sixth force, F 6 , toward the housing  210 . 
     Referring now to  FIG. 39 , a seventh force, F 7 , is resultant from expansion of a fuel through a port of the set of inlet ports  3910 , which are further described herein. The set of inlet ports  3910  are optionally fuel inlets through the housing  210 , first endplate  212 , second endplate  214 , and/or shaft  220 . Fuel is optionally simultaneously and/or nearly simultaneously injected into several compartments of the rotary engine  110 . 
     Several examples are used to illustrate the multi-injection port system. 
     Example I 
     Referring again to  FIG. 2  and  FIG. 3  and still referring to  FIG. 39 , in a first example, fuel is injected via multiple injection ports of the set of inlet ports  3910 , such as via: (1) a first injection port  3912  into the first expansion chamber  335 ; (2) a second injection port  3914  into the second expansion chamber  345 ; and/or (3) a third injection port into the third expansion chamber  355 . The injected fuel is optionally a cryogenic fuel and/or a liquid phase fuel that is a gas at room temperature, such as a liquid carbon dioxide or liquid nitrogen fuel, that rapidly expands in the warmer expansion chambers resulting in expansion forces. In addition to rotating the rotor  440  and vane  450 , the expansion forces provide an additional sealing force, F 7A . Optionally, the first injection port  3912 , the second injection port  3914 , and third injection port are of different diameters and/or deliver different amounts of fuel. For instance, the second injection port optionally delivers more fuel, such as through a larger diameter port or more compressed fuel source, into the second expansion chamber  345 , which is larger than the first expansion chamber  335  at the time of fuel injection. The larger fuel amount is optionally greater than 10, 20, 30, 40, 50 percent more fuel. In another case, rate of delivery of fuel through the first injection port  3912  is greater than via the second injection port  3914  to allow more time for fuel expansion in the power stroke of the rotary engine, such as from about the one o&#39;clock to six o&#39;clock position. In still another instance, fuel is initially injected via the first injection port  3912  into the first expansion chamber  335 ; subsequently injected into the second expansion chamber  345  upon rotation of the first expansion chamber  335  into the position of the second expansion chamber  345 ; and/or still later injected via the third injection port into the first expansion chamber  335  when rotated into the third expansion chamber  355  position, where subsequent fuel injections into the same rotating chamber boosts to the expansion force of the fuel by adding new non-expanded fuel to the rotating chamber. 
     Example II 
     Referring still to  FIG. 2 ,  FIG. 3 , and  FIG. 39 , in a second example, the first injection port  3912  is of a larger diameter, high fuel rate, and/or long open valve time delivers more fuel than the second injection port  3914 , which has a medium sized diameter, medium flow rate, and/or medium open valve time. Similarly, the second injection port  3914  of medium sized diameter, flow rate, or open valve time delivers more fuel than that delivered by the third injection port  3916  of small diameter, small flow rate, and/or short open valve time. In this example, the second injection port  3914  delivers a first boost of fuel and/or expander fuel to the expansion chamber passing the second injection port  3914  and the third injection port  3916  delivers a second boost of fuel and/or expander fuel to the expansion chamber passing the third injection port  3916 , yielding a stronger and optionally longer power stroke of the rotary engine  110 . 
     Example III 
     Referring now to  FIG. 2  and  FIG. 39 , in a third example the first injection port  3912  is the smallest, the second injection port  3914  is larger, and the third injection port  3916  is the largest of the three injection ports, which allow more fuel to be pumped into the increasing larger expansion chamber. 
     Example IV 
     Referring still to  FIG. 2 ,  FIG. 3 , and  FIG. 39 , in a fourth example fuel is injected into a fourth expansion or injection port  3918  of the set of inlet ports  3910 , where the fourth expansion port is into the rotor vane slot  452 , providing a sealing force, F 7b , to the base of the vane  450  toward the housing  210 . 
     Fuel Path/Timing Control 
     Referring again to  FIG. 38 , the main controller  170  optionally controls timing and/or direction of fuel flow based on sensor readings and/or operator provided input. Generally, the main controller  170  controls one or more of:
         one or more fuel valves, valves, gates, such as;
           a shaft valve  3811 , positioned in a fuel flow path prior to entering the vane through the flow tube  1510  from the shaft  220 ;   a vane path valve  3812 , positioned within the vane  450 ;   a vane wing valve  3813 , positioned within and/or on the perimeter of the wing of the vane  450 , such as the leading vane wing  1620  and/or the trailing vane wing  1630 ;   a rotor base valve  3814 , positioned at the base of the rotor-vane chamber  452 ;   a rotor conduit valve  3815 , positioned within and/or at an end of the first rotor conduit  1022 ; and/or   a trailing vane edge valve  3816 , positioned at a port on the trailing vane edge of the vane  450 ; and/or   
           a fuel supply, such as;
           fuel flow through the first inlet port  162 , such a through the housing  210 ;   fuel flow through the second inlet port  1014 , such as through the shaft  220 ; and   fuel flow through any element of the set of the inlet ports  3910 , such as through the inner wall of the first endplate  212  and/or an inner wall of the second endplate  214 .   
               

     Referring again to  FIG. 26  and  FIG. 38  and still referring to  FIG. 39 , optionally an exit port  3919  leads from any of the rotor-vane chambers  452  out of the rotary engine. The exit port is optionally: (1) an exhaust port, such as a valved exhaust port or (2) part of a pump, where a liquid is pumped into the rotor-vane chamber, such as via the fourth injection port  3918  and/or via a sixth injection port  3800 , which is optionally gated with a gate  3814 . In the pump, the sixth injection port passes a liquid through the shaft  220  and/or through the rotor  440  to the rotor-vane chamber  452  during the power stroke and the liquid is pumped out of the rotor-vane chamber  452  during the exhaust phase of the rotary engine  110 . 
     In yet still another embodiment, three rotary engines are linked via two centerplates, where the a first rotary engine is rotated one hundred twenty degrees counterclockwise and a second rotary engine is rotated one hundred twenty degrees clockwise from a rotational orientation of a third rotary engine, such as a centrally position rotary engine, which yields a continual power curve between the three rotary engines and a mechanically/dynamically balanced engine overcomes imbalance due to offset rotors. 
     In still yet another embodiment, the rotary engine is used as an element of a micro cooling, heating, and/or power system. 
     Paddle Board 
     Referring now to  FIGS. 40-44 , a human powered paddle board  4000  is described, such a manually powered paddle board. Without loss of generality and for clarity of presentation, the human powered paddle board  4000  is described as a child&#39;s water toy. The child/user cranks a paddle that propels the child through the water and/or blows bubbles about the child and is used as a partially submerged/diveable submarine ride experience. Again for clarity and without loss of generality, examples describe a child laying on the toy and hand cranking the propulsion unit to self-propel and blow bubbles for the enjoyment of the child. However, the elements of the human powered paddle board  4000  are optionally applicable to a range of devices beyond a toy, such as for adult use, water transport, or even military use, where the user optionally sits on the paddle board, floats/glides behind the paddle board, and/or cranks the toy with leg power. 
     Referring now to  FIG. 40 , the human powered paddle board  4000  is further described. The human powered paddle board  4000  includes a structure for supporting the human, such as kick board  4010  and/or a flotation board. Optionally and preferably, the user supports their upper body on the kick board  4010 . The kick board  4010  is attached to a propulsion unit  4020 , such as via a universal joint  4030 , where the universal joint  4030  allows for ready turning of the propulsion unit  4020  relative to the kick board  4010  and allows the user to apply force to the propulsion unit and/or change direction readily. However, the kick board  4010  is optionally rigidly attached to the propulsion unit  4020 . 
     Still referring to  FIG. 40 , the kick board  4010  is further described. Optionally and preferably, air from a snorkel  4040 , described infra, passes through a manifold  4050  in the kick board  4010  and exits the kick board  4010  through one or more exits. The exits are illustrated as optional jet ports  4060 . Generally, the user cranks a rotor to move air, such as via a hand pump, from the snorkel  4040  through the manifold  4050  to the jet ports  4060 , which emit the pumped air as bubbles for the enjoyment of the user. As the human powered paddle board  4000  is propelled through the water by the user, water is optionally and preferably mixed with the air in the jet port  4060  to further agitate the bubbles. For example, referring again to  FIG. 13 , water is moved through the jet port  4060  via a flow booster  1300 . In the flow booster  1300 , the water moves through the first cross-sectional distance  1310 , d 1 , through a region having the second cross-sectional distance  1320 , d 2 , where d 1 &gt;d 2 , which causes the water to accelerate to form a jet propulsion feeling for enjoyment of the user. At the same time, optionally and preferably, air from the snorkel  4040  passes through the manifold  4050  into the flow booster  1300  and mixes with the water, which forms a vortex with the now air-water mix and functions as a venturi to form fine bubbles exiting from the jet port  4060 , again for enjoyment of the user. The overall sensation to the child is an under water “jet engine” having a first sensation of propulsion and a second sensation of fine bubbles, where all sensations increase as the child cranks the propulsion unit  4020  harder. The propulsion unit  4020  is described herein. 
     Still referring to  FIG. 40 , referring now to  FIG. 43 , and referring again to  FIG. 6  and  FIG. 41 , an air pump system  4310 /air bubble formation system of the propulsion unit  4020  is further described. Generally, the child cranks a hand pump  4070  through turning a crank shaft  4074  via rotation of hand crank handles  4072  about a longitudinal axis of the crank shaft  4074 . The crank shaft is optionally the rotor  320 . As illustrated, the child lays on the kick board  4010  and cranks the hand pump  4070  via hand turning/peddling the hand crank handles  4072 . Referring now to  FIG. 41 , as the child cranks the hand pump  4070 , the inner wall  432  of the rotary engine  110  rotates, which pumps air from the snorkel  4040  into the manifold  4050  for distribution to the one or more jet ports  4060 ; the housing  210  is optionally and preferably connected to the crank shaft  4074  and/or the rotor  320  with a connector, such as a vane chamber separator. The manifold  4050  includes one or more air lines inside the propulsion unit  4020  and/or the kick board  4010 . Referring now to  FIG. 43 , as the child cranks the hand pump  4070 , air from the snorkel  4040  is pulled through the first inlet port  162  into the first and/or second expansion chamber  335 ,  345  and with a continuing rotation of the crank shaft  4074  is compressed before exiting the exit port of the rotary engine  110 , such as in the second or third compression chamber  375 ,  385 , as described supra. Generally, the child powers the rotary engine  110  to pump air/bubbles from the snorkel  4040  to the exits, such as the jet ports  4060 , where the hand pump  4070  uses any of the components of the rotary engine  110  described herein, such as the slideable vanes, expansion vanes, offset rotor, and/or the like. 
     Referring now to  FIG. 41 ,  FIG. 42 , and  FIG. 43 , the propulsion system of the propulsion unit  4020  is further described. Generally, as the child turns the hand crank, a set of paddle wheel blades  4120  attached to an outer surface of the housing  210  paddle water, which propels the human powered paddle board  4000  forward. Referring still to  FIG. 41 , water passes through an optional protective shroud  4160 , is pushed by paddle wheel blades of the set paddle wheel blades  4120  toward the rear of the propulsion unit  4020 , and exits through the protective shroud  4160 , which propels the human powered paddle board  4000  forward. 
     Referring now to  FIG. 42  and  FIG. 43 , a first paddle wheel blade  4211  of the set of paddle wheel blades  4120  is described as part of a paddle wheel blade unit  4210 . Generally, the set of paddle wheel blades rotate around the air pump system  4310 . As illustrated, the first paddle wheel blade  4211  is attached to the outer surface of the housing  210  using a hinge connector  4216 . Referring now to  FIG. 43 , the hinge connector  4216  allows the first paddle wheel blade to rotate outward to catch a first volume, V 1 , of water, such as at the leading edge of the housing  210 ; to rotate still further outward to catch a larger second volume, V 2 , of water, such as at the bottom edge of the housing  210 ; and to collapse/rotate/fold inward to catch progressively smaller third and fourth volumes, V 3 , V 4 , of water at the trailing and upper edges of the housing  210 , respectively. Hence, even if submerged, the first paddle wheel blade  4211  provides forward thrust by avoiding negative work of an extended paddle blade toward the rear and top of the housing  210 . Further, the first paddle wheel blade  4211  still functions if the set of paddle wheel blades  4120  is only partially submerged. Thus, forward propulsion of the human powered paddle board  4000  is maintained with a short/partial dive guided by the user pivoting the propulsion unit  4020  downward about the universal joint  4030 . 
     Referring still to  FIG. 43  and referring again to  FIG. 44 , a racetrack, which is also referred to as a guide  4130  is described, which controls the extent of outward/inward movement of the folding paddle wheel blade. For clarity of presentation and without loss of generality, four paddle wheel blades are illustrated, the first paddle wheel blade  4211 , a second paddle wheel blade  4212 , a third paddle wheel blade  4213 , and a fourth paddle wheel blade  4214 . 
     Generally, any integer number of paddle wheel blades are used, such as greater than 1, 2, 3, 4, 5, 6, 8, or 10 paddle wheel blades. With rotation of the crank shaft  4074 , the first paddle wheel blade  4211  successively moves to the illustrated positions of the second, third, and fourth paddle wheel blades. As the child rotates the crank shaft  4074 , the elliptical racetrack rotates with the less elliptical/round housing  210  between stationary endplates, such as the first endplate  212  and the second endplate  214 . As illustrated, an outer edge of the first paddle wheel blade  4211  is attached via a pin  4218  to a roller element  4219 , where the roller element  4219  travels in a groove along an elliptical path of the guide  4130 . For a fixed length of the first paddle wheel blade  4211 , where the first paddle wheel blade  4211  is hingedly attached to the rotating housing  210 , as the pin  4218  is limited to an elliptical path of the guide  4130 , the pin  4218  pulls the first paddle wheel blade  4211  outward, such as toward the illustrated position of a second paddle wheel blade  4212  before mechanically forcing, via the hinge connector  4216  and fixed length of the first paddle wheel blade  4211 , a folding/inward rotation of the first paddle wheel blade  4211  at the illustrated positions of the third and fourth paddle wheel blades. Each paddle wheel blade has a corresponding hinge connector, pin, and roller component. Optionally and preferably, each paddle wheel blade is pinned and guided by two pins and two roller components along two racetracks. 
     Referring now to  FIG. 44 , a dual air pump—paddle wheel system  4400  is illustrated in a semi-exploded view to yield a view of the central air pump system  4310  and the co-rotatable paddle wheel system, described supra. Again, as illustrated, the first and second endplates  212 ,  214  are stationary while the housing  210 , expansion chambers, vanes, and set of paddle wheel blades  4120  rotate with the hand powered crank shaft  4074 . 
     Referring again to  FIGS. 41-44 , the set of paddle wheel blades  4120  are further described. Each paddle wheel blade of the set of paddle wheel blades  4120  optionally and preferably alternatingly folds inward at a first point of rotation about the crank shaft  4074  and unfolds outward at second point of rotation about the crank shaft  4074 . For instance, a radially outer edge  4410  of the third paddle wheel blade  4213  is illustrated in  FIG. 44  as being radially extended relative to another radially outer edge of the first paddle wheel blade  4211 . As illustrated in  FIG. 42 , the extension of the radially outer edge  4410  from the center of the crank shaft crank shaft  4074  increases from a minimum distance, d 1 , to a maximum distance, d 2 , where the maximum distance is at least 5, 10, 15, 25, 50, 100, or 200 percent larger than the minimum distance. Stated another way, the racetrack/guide  4130  has a from a minimum distance, d 1 , from the center of the crank shaft  4074  and a maximum distance, d 2 , from the center of the crank shaft  4074 , where the maximum distance is at least 5, 10, 15, 25, 50, 100, or 200 percent larger than the minimum distance and where the pin  4218  pulls the radially outer edge  4410  of the third paddle wheel blade  4213  inward and outward to effectively fold and unfold the paddle wheel blade. Clearly, each pin of a set of pins folds and unfolds a respective paddle wheel blade as each pin and the associated roller element  4219  traverses along the guide  4130 . 
     Referring again to  FIG. 40  and  FIG. 41 , an optional viewing port  4150 , aligned with the child&#39;s forward vision during use includes: (1) a viewing port  4152 , such as a hollow rubber gasket; (2) a viewing tunnel  4154  passing through a sail of the submarine shaped front end, the propulsion unit  4020 ; and/or (3) a front window  4156 , such as a plastic window. 
     Still yet another embodiment includes any combination and/or permutation of any of the rotary engine elements described herein. 
     The particular implementations shown and described are illustrative of the invention and its best mode and are not intended to otherwise limit the scope of the present invention in any way. Indeed, for the sake of brevity, conventional manufacturing, connection, preparation, and other functional aspects of the system may not be described in detail. Furthermore, the connecting lines shown in the various figures are intended to represent exemplary functional relationships and/or physical couplings between the various elements. Many alternative or additional functional relationships or physical connections may be present in a practical system. 
     In the foregoing description, the invention has been described with reference to specific exemplary embodiments; however, it will be appreciated that various modifications and changes may be made without departing from the scope of the present invention as set forth herein. The description and figures are to be regarded in an illustrative manner, rather than a restrictive manner, and all such modifications are intended to be included within the scope of the present invention. Accordingly, the scope of the invention should be determined by the generic embodiments described herein and their legal equivalents rather than by merely the specific examples described above. For example, the steps recited in any method or process embodiment may be executed in any order and are not limited to the explicit order presented in the specific examples. Additionally, the components and/or elements recited in any apparatus embodiment may be assembled or otherwise operationally configured in a variety of permutations to produce substantially the same result as the present invention and are accordingly not limited to the specific configuration recited in the specific examples. 
     Benefits, other advantages and solutions to problems have been described above with regard to particular embodiments; however, any benefit, advantage, solution to problems or any element that may cause any particular benefit, advantage or solution to occur or to become more pronounced are not to be construed as critical, required or essential features or components. 
     As used herein, the terms “comprises”, “comprising”, or any variation thereof, are intended to reference a non-exclusive inclusion, such that a process, method, article, composition or apparatus that comprises a list of elements does not include only those elements recited, but may also include other elements not expressly listed or inherent to such process, method, article, composition or apparatus. Other combinations and/or modifications of the above-described structures, arrangements, applications, proportions, elements, materials or components used in the practice of the present invention, in addition to those not specifically recited, may be varied or otherwise particularly adapted to specific environments, manufacturing specifications, design parameters or other operating requirements without departing from the general principles of the same. 
     Although the invention has been described herein with reference to certain preferred embodiments, one skilled in the art will readily appreciate that other applications may be substituted for those set forth herein without departing from the spirit and scope of the present invention. Accordingly, the invention should only be limited by the Claims included below.