Abstract:
A tether, and system using such a tether, adapted to provide mechanical and electrical coupling of an airborne flying platform to the ground. The tether may have a center structural core with electrical conductors on or near the outer diameter of the tether. The tether may utilize exterior configurations adapted to reduce drag.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Patent Application No. 61/365,655 to Vander Lind et al., filed Jul. 19, 2010. This application claims priority to U.S. Provisional Patent Application No. 61/409,894 to Vander Lind, filed Nov. 3, 2010. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     The present invention relates to high strength low drag tethers and systems using such tethers. 
     2. Description of Related Art 
     Some airborne wind energy systems, powered kites, tethered tidal power systems, moored platforms, tethered aerostats, and other tethered devices require high tether strength, significant tether power transmission, and are also sensitive to the effects of fluid-dynamic drag. 
     In the case of some airborne power generation systems, an aerial platform such as an airfoil may support an array of turbine driven generators. The platform may be linked to the ground with a tether which provides both the physical coupling as well as the electrical coupling of the tethered platform to the ground. In such a case, the electrical power generated by the turbine driven generators may travel along the tether from the aerial platform to the ground. In the case wherein the turbine driven generators also function as motor driven propellers, such as may be used when the platform is raised from the ground, the tether may provide electric power to the aerial platform. Also, the tether may be the conduit for telemetry related to control functions on the platform. 
     In addition, the tether provides the mechanical linkage of the platform to the ground. In the case of cross wind flying scenarios, such as when the aerial platform may be flying in patterns wherein the platform the apparent wind is much higher than the nominal actual wind speed, the drag of the tether may play a significant role in overall system function. Typically, the tether is wound on a reel of some sort either for storage of as part of the mechanical winching of the aerial platform. 
     What is called for is a tether, and system using a tether, that provides high strength for the support of an aerial platform from the ground. What is also called for is a tether that is low in drag such that it is suitable for support of airborne platforms. 
     SUMMARY OF THE INVENTION 
     A tether, and system using such a tether, adapted to provide mechanical and electrical coupling of an airborne flying platform to the ground. The tether may have a center structural core with electrical conductors on or near the outer diameter of the tether. The tether may utilize exterior configurations adapted to reduce drag. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating an embodiment of a high tensile strength electromechanical tether. 
         FIG. 2  is a diagram illustrating an embodiment of an electromechanical tether with bunched conductors, creating space for helical grooves. 
         FIG. 3  is a diagram illustrating an embodiment of an electromechanical tether incorporating secondary strain relief of conductive elements in the tether. 
         FIG. 4  is a diagram illustrating an embodiment of a specific example of an electromechanical tether incorporating two conductive elements and a jacket which serves as a low bulk modulus material. 
         FIG. 5  is a diagram illustrating an embodiment of an electromechanical tether incorporating strength members and conductors of alternate cross sectional configurations. 
         FIG. 6  is a graph of tether properties according to some embodiments of the present invention. 
         FIG. 7  is a cross-sectional view of a tether according to some embodiments of the present invention. 
         FIG. 8  illustrates various external configurations according to some embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     A detailed description of one or more embodiments of the invention is provided below along with accompanying figures that illustrate the principles of the invention. The invention is described in connection with such embodiments, but the invention is not limited to any embodiment. The scope of the invention is limited only by the claims and the invention encompasses numerous alternatives, modifications and equivalents. Numerous specific details are set forth in the following description in order to provide a thorough understanding of the invention. These details are provided for the purpose of example and the invention may be practiced according to the claims without some or all of these specific details. For the purpose of clarity, technical material that is known in the technical fields related to the invention has not been described in detail so that the invention is not unnecessarily obscured. 
     In some embodiments of the present invention, a high strength low drag electromechanical tether is adapted for use in a variety of applications, such as the coupling of an airborne power generation platform to the ground. In some embodiments, the tether comprises a high strength core made of individual composite rods wound in concentric layers of varying helical angle, a low bulk modulus material mounted concentrically about the high strength core, and individually or coaxially insulated electrical conductors helically wound or coaxially mounted about the low bulk modulus layer. The electrical conductors may be subject to heating while conducting electrical power, and the placement of the electrical conductors on or close to the outer diameter of the tether may enhance the cooling of the conductors in some aspects and reduce the temperature of the high strength core. 
     In some embodiments, the helical winding of the core high tensile strength material allows relative slip between neighboring strands, and thus decreases the minimum winding radius of the tether about a sheave, drum, or pulley, which is a desirable property for storage of the tether. Successive layers within the high strength core may be wound at opposing helical angles to reduce or eliminate the torque about the tether axis resultant from tension along the tether. The electrical conductors may be susceptible to excessive strain, and failure, as they may be of lower strength than the high strength core. A variety of design considerations may address this concern. The conductors may be wound in helix of somewhat steeper angle such that the helix may expand as a spring, instead of staining the conductors themselves. Also, the low bulk modulus material between the conductors and the high strength core serves to strain relieve the wires, allowing some compression and concurrent narrowing of the helix diameter of the electrical conductors when the tether is under tension. The use of the low bulk modulus material between the electrical conductors and the high strength core may allow a minimal wire helical angle and thus minimize the free length of wire, reducing weight and heating loss. 
     The external location of the wires additionally serves to decrease the temperature increase due to resistive loss in the wire, and to allow convenient placement of helical grooves in the tether surface in order to reduce the critical Reynolds number at which the coefficient of drag of the tether decreases. In some embodiments, the radial spacing of the conductors along external diameter of the tether, allows both enhanced cooling and reduced drag via the same design feature. 
     According to some embodiments of the present invention, an electromechanical tether used in airborne wind power systems, tethered tidal power systems, powered kites, moored platforms or other applications where high strength, long life, and low fluid-dynamic drag are necessary can be designed to incorporate elements that passively reduce fluid-dynamic drag on the tether, and also incorporate elements that reduce strain in the conducting element. A tether used in these applications may additionally be required to wind on to a small diameter drum or over a small diameter sheave. This requirement may be facilitated by the helical winding of the strands within the tether such that the average radius of each strand is close to that of the neutral axis of the tether under bending, such that each strand sees alternating compressive and tensile loads which may equilibrate through slip between neighboring strands. Successive layers may then be wound in opposite directions to balance the possible resultant torque about the tether axis under loading. As many high strength materials elongate greater than 1% of their free length at yield or break, and many good conductors elongate less than 0.4% at yield or break, the conductive elements of a materially efficient electromechanical tether may be configured to undergo significantly less strain than the high strength elements during use tethering an airborne system, and during winding onto a drum. Conductive elements may be relieved of strain by winding at a helical angle which is steep or far from the tether axis. Conductive elements may additionally be relieved of strain by inclusion of a low bulk modulus layers at a station within the winding radius of the conductive elements, such that the low bulk modulus layer compresses under the tension of the conductive elements, allowing some inward radial travel of the conductive elements, and thus reduces the required free length of the conductive elements. To reduce the effect of tether diameter on fluid dynamic drag, the outer surface of the tether may be dimpled or grooved so as to reduce the Reynolds number at which the cylindrical profile of the tether sees a reduction in coefficient of drag. In some embodiments, the drag reducing grooves may be located between neighboring conductors in a manner which incurs a minimal increase in tether diameter. In some embodiments, the grouping of conductors operating at similar voltage levels may allow the amount of insulation needed between neighboring conductors to be reduced. 
     In some embodiments of the present invention, a low-drag lightweight electromechanical tether  101  comprises a high strength core  102 , a low bulk modulus material  103 , an insulation material  104 , conductors  105  and jacket  106 . In various embodiments, the high strength core  102  is comprised of numerous composite rods or pultrusion elements wound in layers of varying and alternating helical angle. The composite rods of the high strength core  102  may comprise fibrous elements such as aramid fibers, carbon fibers, or glass fibers, and a constraining matrix element such as an epoxy matrix or a vinyl ester matrix. The helical winding of the outer layers of the high strength core  102  allows the whole tether  101 , while in operation, to be wound onto a drum in a manner which induces finite slip or shear between neighboring rods. In various embodiments of the high strength core  102 , successive coaxial layers of composite rods are wound in opposite helical directions to partially or fully balance the torque created by the tether under tension, or are wound in the same helical direction. In various embodiments, the high strength core  102  is comprised of dry fibers, metal wire, or metal cable rather than composite rods. In various embodiments, the center layer  107  of the high strength core  102  is comprised of axial composite rods, a lower modulus material which still provides tensile strength, a low-load filler material, communications lines, or any other appropriate filler material. In various embodiments, the high strength core  102  is comprised of rods of round, square, or trapezoidal cross section, or of rods of any other appropriate cross-sectional shape, or of rods of differing cross-sectional shape. In some embodiments, the individual elements may be coated with a coating adapted to facilitate slippage between the elements. This coating may be a Teflon coating, a PEEK coating, or any other appropriate low friction coating. In some embodiments, the layers may be coated with a coating, or layer, adapted to facilitate slippage between the layers. These low friction coatings may reduce friction as elements and/or layers move relative to each other when the tether is wound on a drum, for example. In some embodiments, a radial wrap of a low friction material is placed between each successive helical layer of the high strength core. 
     In some embodiments, each helically wound layer of the high strength core  102  is wrapped with a hoop strength or hoop tension layer  108 . Although illustrated in  FIG. 1  only as a single hoop tension layer, there may be a plurality of hoop tension layers of different diameters, which may each be wound around an individual layer in some aspects. In various embodiments, a hoop strength or hoop tension layer  108  comprises a high strength rigid material, or a tensile loaded layer such as a polyester film or high strength fiber wrap utilized to prevent layers of the high strength core  102  from becoming out-of-round or unwrapping from the core. In some embodiments, the hoop tension layer  108  is further utilized to reduce friction between composite rods in successive concentric layers of the high strength core  102 . In some embodiments, the high strength core  102  is not made of concentric layers but instead is comprised of numerous elements in a radially symmetric pattern, which are each bound by, or compressed by, an element of hoop tension layer  108 , for example each rod within high strength core  102  of the tether is comprised of a bundle of smaller rods. In some embodiments, each element in the various layers of the core  102 , other than the center layer  107 , are of the same diameter and construction. In some embodiments, all of the layers of the core  102  are of the same diameter. In some embodiments, the helix winding angle of each successive layer is increased viewed from the center of the tether outwards. 
     In some embodiments, the high strength core  102  of the tether  101  is contained within a concentric low bulk modulus layer  103 , or is partially contained within the low bulk modulus layer  103 , with some concentric helically wound outer layers  110  of the high strength core  102  inside of the low bulk modulus layer  103  and some outer layers  110  of the high strength core  102  inside of the low bulk modulus layer  103 . In some embodiments, the low bulk modulus layer  103  serves to allow the conductors  105  to lie on a smaller radius shell within the tether  101  when the high strength core  102  stretches or when a stress is applied along the conductors  105 , so as to limit conductor strain to within acceptable limits when the maximum allowable conductor strain is significantly below the maximum allowable core material strain. In embodiments in which low bulk modulus material  103  is located concentrically within the outer layers  110  of the high strength core  102 , the outer layers  110  of the high strength core  102  aid in compressing the layer  103  at the expense of the outer layers  110  of the high strength core  102  carrying a lower proportion of the total tensile load on the tether  101 . In some embodiments, the conductors  105  are wound at a helical angle or a radius which varies along the length of the tether  101  as a mechanism of strain reduction. Thus, in addition to the helical angle of the conductors  105  allowing for some strain relief of the conductors (when the core  102  is strained under load), as in the linear extension of an axially coiled spring, the relative softness of the bulk modulus layer  103  allows for a decrease in the diameter of the helix of the conductors when under load, allowing for strain relief through a second mechanism. The strain in conductors, thus reduced, may be a result of the stretching of the tether when under load in support of an airborne flying platform, or when wound around a drum. In some embodiments, low bulk modulus layer  103  is not included in tether  101 . In some embodiments, other elements may reside within the tether  101 . For example, command signal lines, whether electrically conductive or fiber optic, may be reside within the tether  101 . 
     In some embodiments, an insulation material  104  insulates separate strands of conductors  105  electrically and mechanically. In some embodiments, separate elements of insulation material  104  insulate each strand or wire within conductors  105  such that each insulated conductor may slip relative to its neighbor when wound over a sheave or on a drum. In some embodiments, numerous elements of conductors  105  are embedded in a single element of insulation material  104 , and the insulation material  104  sustains a shear strain when the tether  101  is wound over a sheave. In various embodiments, the conductors  105  comprise numerous wires of aluminum, copper, or any other conductive material, each of which may comprise single or multiple strands. In various embodiments, the conductors  105  are comprised of any number of individual wires or are comprised two or more concentric or coaxial layers separated by insulation, wound about the high strength core  102 . In some embodiments, each element comprising the conductors  105  comprises a number of individual wires wound about either a hollow or low bulk modulus material to increase the strain along individual elements of the conductors  105  at which damage accumulates or material yielding occurs. In some embodiments, the insulation element  104  and low bulk modulus element  103  are the same element. 
     In various embodiments, the jacket  106  comprises a metal, a rubber, a plastic, a composite of fibers and a matrix, braided wires, or any other appropriate material or set of materials to contain and protect the other elements of the tether  101 . In some embodiments, the jacket  106  is the same element as the insulation material  104 . 
     In some embodiments, the jacket  106  has surface characteristics or shaping which reduce drag. In some embodiments, the jacket  106  has an aerodynamic profile such as that of an airfoil to reduce drag. In some embodiments, the jacket  106  has helical grooves  109  in concert with the gaps between the helically coiled groupings of conductors. The helical grooves  109  will reduce the drag of the tether, such as when used in support of an airborne flying platform. 
       FIG. 2  is a diagram illustrating an embodiment of an electromechanical tether with bunched conductors, creating space for helical grooves. In the example shown, a low drag lightweight electromechanical tether incorporates bunching of conductors  205  to allow space for boundary layer tripping elements  209  on the surface of the jacket  206  without significant diameter increase. In other embodiments, the tripping elements may comprise strakes, jagged edged grooves, or any other device which trips the boundary layer in the fluid flow about the tether to turbulence or introduces flow voracity prior to natural transition and thus increases the region of attached flow over the surface of the tether and thus reduces coefficient of drag. In some embodiments, elements  209  comprise individual strakes or divots in the surface of the jacket  206  such as the divots in a golf ball or flush surface vortex generators, such as triangular divots. In one embodiment, the elements  209  are not flush with the surface of the jacket  206 , but press flush with the surface of the jacket  206  under pressure to allow winding on a drum. In some embodiments, the elements  209  are selected in size and spacing according to the operating Reynolds number of the tether  201  to minimize drag, noise, unsteady dynamics, or some combination thereof at one or a range of operating conditions for the tether. In some embodiments, the boundary layer tripping elements  209  are placed on the outside of the tether  201  at a station with a known orientation relative to the external flow. In some embodiments the surface of tether  201  is smooth or has a uniform roughness. In some embodiments, each conductor within a grouping of conductors operates at the same voltage, to minimize the required insulation thickness. 
       FIG. 3  is a diagram illustrating an embodiment of a low drag lightweight electromechanical tether  301  incorporating secondary strain relief of conductive elements in the tether. In the example shown, the tether  301  comprises high strength composite rods  311  which are concentrically surrounded by low bulk modulus material  303 , conductors  305 , and insulation material  304 . In some embodiments, the rods  311  are electrically insulated from conductors  305 . In some embodiments, the rods  311  are not insulated from the conductors  305  but are insulated from other conductive elements within the tether termination. In some embodiments, the conductors  305  comprise a number of individually insulated wires wound about the high strength composite rods  311 . 
       FIG. 4  is a diagram illustrating an embodiment of a low drag lightweight electromechanical tether. In the example shown, the tether  401  has a length of 100 meters, comprising a high strength core  402 , which may be braided aramid fibers. This example further comprises conductors  405 , and a jacket  406 . The conductors  405  comprise two individually insulated braided  16  AWG copper wires. The jacket  406  comprises a compressively biased vinyl sheath, which serves to locate and compress the conductors  405 . When the tether  401  is not under tension, the combination of compressive loading in the conductors  405  and compliance in the jacket  406  serve as the equivalent of the low bulk modulus layers  102 ,  203 , and  303  seen in other embodiments, in reducing the change in lay length of the conductors  405  through the change in length of the high strength core  402  over a range of tensions. 
     In some embodiments of the present invention, as seen in  FIG. 5  a low drag lightweight electromechanical tether  501  is shown wherein the layers are of rectangular cross-section. In this embodiment, the tether  501 , which may have a length of 500 meters, comprises a multi-layered, high strength core  502 . Each layer of high strength core  502 , for example layer  510 , may comprise a number of individual carbon fiber pultrusions of square or rectangular cross section, which are designed to make the high strength core  502  have a smaller diameter than an equivalent high strength core built of cylindrical rods, as the packing factor is higher compared to layers of cylindrical elements. In some embodiments, each carbon fiber pultrusion in the high strength core  502  is pultruded along a helical path to eliminate latent stresses when assembled into the tether  501 . In one example, each pultrusion has a major cross sectional dimension of between 3 and 5 millimeters. 
     As the helical angle of layer  510  is small, the stresses in individual carbon fiber pultrusions due to the twist over length are low. In some embodiments, each carbon fiber pultrusion in high strength core  502  is pultruded along a helical path to further reduce latent stresses in tether  501 . In this example, each pultrusion has a major cross sectional dimension of between 3 and 5 millimeters. Tether  501  further comprises hoop tension layer  508 , which prevents dislocation of individual pultrusions within high strength core  502  in handling, bending, or under low tension. The tether  501  may have a hoop tension layer  508 , which may be an aramid weave impregnated in vinyl rubber. The hoop tension layer  508  is wrapped with a low bulk modulus layer  503 , which comprises a low firmness foam rubber rigidly bonded to both the hoop tension layer  508  and the insulation  504 . The conductors  505  may comprise a number of identical solid copper wires of square cross section each individually insulated with insulation material  504 . The insulation material  504  may comprise a die extruded layer of PVC about each conductive element of the conductors  505 . The conductors  505  may be grouped into two groups, one of which has an operating voltage of 5000 volts, and the other of which has an operating voltage of 0 volts. The conductors  505  are bound by the jacket  506 , which may comprise helical grooves  509 . The jacket  506  may comprise die-extruded vinyl rubber over an aramid weave. The helical grooves  509  are cut into the jacket  506  in some embodiments, and are of geometric dimensions suitable for the typical operating Reynolds numbers of the tether  501 . For example, the helical grooves  509  may be of a semicircular cross section of depth 1 millimeter and width 2 millimeters, spaced every 10 millimeters along the circumference of tether  501 . 
     In some embodiments, the tether is adapted to support an airborne power generation system of an airfoil with turbine driven generators. The drag of the tether may be minimized relative to the drag of the tethered airborne system, within the constraints of requirements for strength and electrical conductivity. The overall coefficient of drag of the tether, referenced to the wing area, can range from around 0.03 to 0.15. In such a case, the tether acts as if the wing has that much higher of a coefficient of drag. Referenced to its own cross section, the tether may have a coefficient of drag of around 1.2 for a smooth cylinder, whereas the grooves or dimples can bring that number down to approximately 0.6 for a large range of Reynolds numbers, or as low as 0.45 for narrow ranges of Reynolds numbers. In some aspects, larger grooves will cause a drag reduction at lower Reynolds number, but only a relatively smaller reduction. Smaller grooves may cause reduction of the coefficient of drag at higher Reynolds numbers, and may cause a more significant reduction. 
       FIG. 6  is a graph depicting the coefficient of drag of various embodiments of the tether, plotted on axis  601 , as a function of tether Reynolds number, which is plotted along axis  602 . The first curve  603  depicts the coefficient of drag of an embodiment of a tether with relatively larger surface grooves. The second curve  604  depicts the coefficient of drag of an embodiment of a tether with smaller surface grooves. The third curve  605  depicts the coefficient of drag of an embodiment of a tether with a smooth surface. When the invention is used to moor an airborne wind turbine, the speed of the airborne wind turbine must be kept below a maximum level in high wind situations. Surface shapes such as the helical grooves depicted on jacket  106  in  FIG. 1 , which result in coefficient of drag curves such as the first curve  603  and the second curve  604 , increase in coefficient of drag at high speeds and thus aid in maintaining the airborne wind turbine below a maximum velocity. As seen in the first and second curves  603 ,  604 , at higher Reynolds numbers (which in this example would indicate higher speeds) the low coefficient of drag begins to raise. Thus, a tether may be outfitted with a surface, such as helical grooves, which bring about a desired reduction in drag at preferred operational apparent wind speeds, but then also brings about a desired increase in drag at apparent wind speeds above preferred speeds. This effect serves the design by increasing drag at apparent wind speeds above desired speeds. 
     Many jacket surface treatments, again such as the helical grooves depicted in jacket  106 , also show increased in drag at low speeds, before the dip in drag at the middle speeds. In some embodiments of the preset invention, the helical grooves on jacket  106  are spaced and sized such that the increase in coefficient of drag at low speeds lies below the minimum preferred operational apparent flight speed of the airborne wind turbine. In the case of cross wind flying regimes, the apparent wind speed may be significantly higher than the ambient wind speed. In some embodiments, different surface shapes are utilized at different locations along the length of the tether, such as near the base and near the top of the tether, to match the apparent wind speeds at each location. In some embodiments, only the segment of the tether closest to the aerial platform is shaped to reduce drag. 
     In some embodiments, helical grooves are not cut into the surface of the tether and instead helical strakes, linear strakes, dimples, or some other boundary layer tripping mechanism is utilized to achieve low drag in the operating envelope. 
     In some embodiments of the present invention, as seen in  FIG. 7 , a tether may be used as the tether for a 400 kW airborne wind turbine. This tether  701  may be designed to withstand 300 kN of force at a safety factor of 2. The tether  701  may have 370 strands of carbon fiber 1 mm pultrusion  711 , in layers  702  of alternating helical angle. The inner strand (the 371st) core  707  is 2 mm in diameter. The helical angle on each successive layer increases starting at 1 degree at the first layer closest to the core  707  and increasing to 5 degrees on the outermost layer  710 . The pultrusions are of intermediate modulus carbon fiber. There are 10 layers  702  outside of the core. All layers are coated in teflon to reduce friction on winding. The innermost layer  711  has a helical angle of 1 degree, and the outermost layer  710  has a helical angle of 5 degrees. Intermediate layers have helical angles which increase roughly linearly from that of innermost later  711  to outermost layer  710 , but which are adjusted slightly to minimize torque about the tether base due to tension. The outermost layer  710  is wound at a helical angle approximately 1 degree larger than that of a zero-torque design to allow for free-spinning of the tether base about a bearing as the airborne wind turbine flies a circular flightpath. While the bearing drag at the base of the tether is not consistent over the life of the bearing, and has some nonlinear dependence on load on the tether, the added helical angle on the outermost layer  710  is set to match the average torque per tensile load from the bearing over its operating life. 
     Outside of these layers lie the conductors  705 , which are insulated with two layers of insulation: the inner insulation layer  704  of FEP, and the outer insulation layer  703  of medium durometer PVC. In each conductor portion are three wires, each individually insulated with FEP. In some embodiments, the conductor portions are helically wrapped with the opposite chirality of outermost layer  710 . The wires  705  may comprise strands of aluminum conductor and are rolled to the pictured cross-sectional shape and annealed prior to insulation with FEP insulation  704 . In some embodiments, the FEP insulation  704  is approximately 0.2 mm thick, and designed to provide the primary electrical barrier for wires  705  which convey DC current at approximately 5000 volts. 
     The silicone layers are extruded through a die which chamfers the edges  709  such that when all wires are bonded together about the outside of the core, there are helical grooves remaining in the surface. The helical grooves are roughly 2 mm deep and 16 in count about the perimeter. Although only a single insulated conductor is shown in  FIG. 7  for purposes of illustration, there would be a continuous layer of insulated conductors around the periphery of the tether. Because of the adjacent chamfered edges  709 , the edges combine to form a groove. The insulated conductors are wound in a helix about the carbon strands, thus resulting in a helical groove around the tether. In assembly, all 16 jackets are fused with heat to create a single uniform solid jacket. 
       FIG. 8  illustrates the cross-sectional shapes of various possible embodiments of a low drag lightweight electromechanical tether, such as tether  101  of  FIG. 1 , tether  201  of  FIG. 2 , or the tethers whose measured drag coefficient profiles are presented in  FIG. 6 . In various embodiments, the tether comprises a surface cross-sectional shape  801  with a number of hemispherical cuts along its circumference, a surface cross-sectional shape  802  of oscillating radius, a surface cross-sectional shape  803  with surface imperfections such as those introduced by sand blasting, or any other appropriate tether. In some embodiments, the tether is of some other shape that results in an increase in coefficient of drag above a cut-off Reynolds number or speed. In some embodiments, the tether deforms above a cut-off flight speed or above a cut-off tension such that the modified shape results in an increase in the tether drag coefficient. In higher wind speeds and at higher flight speeds, a larger segment of the tether of a crosswind kite system experiences apparent winds above any given cut-off speed. In some embodiments, the tether comprises a surface cross-sectional shape which exhibits a reduction in coefficient of drag above some speed or Reynolds number (e.g. shape  801  or shape  803 ). In some embodiments, the tether comprises such a cross-sectional shape only over a segment of the tether near the kite, such that the increased apparent wind on the tether near the ground attachment point does not contribute to a reduction in tether drag coefficient as the inertial wind speed or kite speed increase. 
     As evident from the above description, a wide variety of embodiments may be configured from the description given herein and additional advantages and modifications will readily occur to those skilled in the art. The invention in its broader aspects is, therefore, not limited to the specific details and illustrative examples shown and described. Accordingly, departures from such details may be made without departing from the spirit or scope of the applicant&#39;s general invention.